Finite Group Databasebeta

← D59×#3538 #29495929

Subgroups — D59×#3538 #29495929

Order 15104.

7162 conjugacy classes of subgroups.

The subgroup lattice has 1490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438345C211yesmaximal, characteristic, complemented
2#21438344C212yesmaximal, complemented
3#21438343C214yesmaximal, complemented
4#21438342C214yesmaximal, complemented
5#21438341C212yesmaximal, complemented
6#21438340C214yesmaximal, complemented
7#21438339C212yesmaximal, complemented
8#21438338C214yesmaximal, complemented
9#21438337C214yesmaximal, complemented
10#21438336C214yesmaximal, complemented
11#563×D59C214yesmaximal, complemented
12#552×D59C214yesmaximal, complemented
13#551×D59C214yesmaximal, complemented
14D4×Q8×D59C214yesmaximal, complemented
15#544×D59C214yesmaximal, complemented
16#541×D59C212yesmaximal, complemented
17#539×D59C214yesmaximal, complemented
18#536×D59C212yesmaximal, complemented
19#525×D59C211yesmaximal, characteristic
20C2×C22⋊Q8×D59C212yesmaximal, complemented
21C59×#3538C211yesmaximal, characteristic, complemented
22C2×#41×D59C2211yescharacteristic
23C22×Q8×D59C2212yes—
24C22×Q8×D59C2212yescomplemented
25C23×C4×D59C2211yescharacteristic
26#16838156C2218yescomplemented
27#16838155C2214yescomplemented
28#16838155C2214yescomplemented
29#16838154C2218yescomplemented
30#16838154C2218yescomplemented
31#16838153C2218yescomplemented
32#16838153C2218yescomplemented
33#16838152C2214yescomplemented
34#16838151C2218yescomplemented
35#16838094C2214yescomplemented
36#16838093C2214yescomplemented
37#16838092C2214yescomplemented
38#16838091C2214yescomplemented
39#16838090C2214yescomplemented
40#16838089C2218yescomplemented
41#16838088C2218yescomplemented
42#16838087C2214yescomplemented
43#16838086C2214yescomplemented
44#16838085C2218yescomplemented
45#16838084C2218yescomplemented
46#16838083C2214yescomplemented
47#16838082C2214yescomplemented
48#16838081C2218yescomplemented
49#16838080C2214yescomplemented
50#16838079C2218yescomplemented
51#16838078C2218yescomplemented
52#16838077C2218yescomplemented
53#16838076C2218yescomplemented
54#16838075C2218yescomplemented
55Q8×D236C2214yescomplemented
56D4×Dic118C2218yescomplemented
57D4×Dic118C2214yescomplemented
58#16838067C2214yescomplemented
59#16838067C2218yescomplemented
60Q8×C22⋊D59C2214yescomplemented
61Q8×C22⋊D59C2214yescomplemented
62#16838065C2218yescomplemented
63#16838065C2214yescomplemented
64#16838065C2214yescomplemented
65#16838065C2218yescomplemented
66#16838033C2214yescomplemented
67#16838032C2218yescomplemented
68#16838032C2218yescomplemented
69#16838031C2218yescomplemented
70#16838031C2214yescomplemented
71#16838031C2214yescomplemented
72#16838030C2218yescomplemented
73#16838029C2218yescomplemented
74#16838029C2218yescomplemented
75#16838015C2212yescomplemented
76#16838014C2212yescomplemented
77#16838013C2212yescomplemented
78#16838012C2214yescomplemented
79#16838011C2218yescomplemented
80#16838010C2214yescomplemented
81#16838009C2218yescomplemented
82#16838001C2214yescomplemented
83#16838000C2218yescomplemented
84#16837999C2214yescomplemented
85#16837998C2218yescomplemented
86#16837997C2214yescomplemented
87#16837996C2218yescomplemented
88#16837995C2218yescomplemented
89#16837994C2218yescomplemented
90#16837993C2218yescomplemented
91#16837978C2212yescomplemented
92#16837977C2214yescomplemented
93#16837976C2212yescomplemented
94#16837975C2214yescomplemented
95#16837975C2214yescomplemented
96#16837974C2214yescomplemented
97#16837974C2214yescomplemented
98#16837973C2212yescomplemented
99#16837972C2214yescomplemented
100C4⋊Q8×D59C2218yescomplemented
101C4⋊Q8×D59C2212yescomplemented
102C4⋊Q8×D59C2214yescomplemented
103#126×D59C2218yes—
104#126×D59C2218yescomplemented
105#125×D59C2218yescomplemented
106#125×D59C2218yescomplemented
107#125×D59C2212yescomplemented
108#124×D59C2214yes—
109#16837915C2212yes—
110#16837914C2211yescharacteristic
111#16837913C2211yescharacteristic
112#16837912C2212yes—
113#16837911C2214yes—
114#16837910C2212yes—
115#16837909C2211yescharacteristic
116#16837908C2212yes—
117#123×D59C2218yes—
118#123×D59C2212yes—
119#123×D59C2214yes—
120#123×D59C2214yescomplemented
121C2×#14273707C2212yescomplemented
122C2×#14273706C2212yescomplemented
123C2×#14273705C2214yescomplemented
124C2×#14273704C2214yescomplemented
125C2×#14273703C2212yescomplemented
126C22⋊Q8×D59C2214yes—
127C22⋊Q8×D59C2214yes—
128C22⋊Q8×D59C2214yes—
129C22⋊Q8×D59C2212yes—
130C22⋊Q8×D59C2218yes—
131C22⋊Q8×D59C2214yes—
132C22⋊Q8×D59C2214yescomplemented
133C22⋊Q8×D59C2214yescomplemented
134C22⋊Q8×D59C2214yescomplemented
135C22⋊Q8×D59C2214yescomplemented
136C22⋊Q8×D59C2218yescomplemented
137C22⋊Q8×D59C2214yescomplemented
138#121×D59C2212yes—
139#120×D59C2212yes—
140C4×Q8×D59C2214yescomplemented
141C4×D4×D59C2218yes—
142C4×D4×D59C2214yes—
143#117×D59C2211yescharacteristic
144#117×D59C2218yes—
145#117×D59C2212yescomplemented
146C2×C4⋊C4×D59C2214yes—
147C2×C4⋊C4×D59C2212yes—
148C2×C22⋊C4×D59C2214yes—
149C59×#563C2214yescomplemented
150C59×#552C2214yescomplemented
151C59×#551C2214yescomplemented
152D4×Q8×C59C2214yescomplemented
153C59×#544C2214yescomplemented
154C59×#541C2212yescomplemented
155C59×#539C2214yescomplemented
156C59×#536C2212yescomplemented
157C59×#525C2211yescharacteristic
158C2×C22⋊Q8×C59C2212yescomplemented
159C24×D59C2311yescharacteristic
160C2×#11745689C2311yescharacteristic
161C2×#11745685C2312yes—
162C2×#11745685C2311yescharacteristic
163C2×#11745687C2312yes—
164C2×#11745687C2311yescharacteristic
165#41×D59—44no—
166C22×Dic118C2314yes—
167C22×Dic118C2312yes—
168C22×Dic118C2312yescomplemented
169C22×Dic118C2314yescomplemented
170C2×Q8×D59—48no—
171C2×Q8×D59—48no—
172C2×Q8×D59C2314yes—
173C2×Q8×D59C2314yes—
174C2×Q8×D59C2314yes—
175C2×Q8×D59C2311yescharacteristic
176C2×Q8×D59C2314yes—
177C2×Q8×D59C2314yes—
178C2×Q8×D59C2314yescomplemented
179C2×Q8×D59C2314yescomplemented
180C2×D4×D59C2314yes—
181C2×D4×D59C2311yescharacteristic
182C2×D4×D59C2312yes—
183C23×Dic59C2311yescharacteristic
184C22×C4×D59—44no—
185C22×C4×D59C2311yescharacteristic
186C22×C4×D59C2312yes—
187C22×C4×D59C2312yes—
188C22×C4×D59C2314yes—
189C22×C4×D59C2312yes—
190C22×C4×D59C2311yescharacteristic
191C22×C4×D59C2314yes—
192C22×C4×D59C2311yescharacteristic
193C22×C4×D59C2311yescharacteristic
194C22×C4×D59C2312yes—
195C22×C4×D59C2312yes—
196C22×C4×D59C2314yes—
197#14273727C2318yescomplemented
198#14273727C2314yescomplemented
199#14273727C2312yescomplemented
200#14273726C2318yescomplemented
201#14273726C2318yescomplemented
202#14273726C2318yescomplemented
203#14273726C2318yescomplemented
204#14273726C2318yescomplemented
205#14273726C2318yescomplemented
206#14273726C2318yescomplemented
207#14273725C2318yescomplemented
208#14273725C2318yescomplemented
209#14273725C2314yescomplemented
210#14273725C2314yescomplemented
211#14273725C2314yescomplemented
212#14273722C2318yes—
213#14273722C2318yes—
214#14273722C2318yes—
215#14273722C2318yescomplemented
216#14273722C2318yescomplemented
217#14273722C2318yescomplemented
218#14273721C2318yes—
219#14273721C2318yescomplemented
220#14273720C2318yes—
221#14273720C2318yes—
222#14273720C2318yes—
223#14273720C2318yescomplemented
224#14273720C2318yescomplemented
225#14273720C2318yescomplemented
226#14273719C2318yescomplemented
227#14273719C2318yescomplemented
228#14273719C2312yescomplemented
229#14273718C2318yescomplemented
230#14273718C2318yescomplemented
231#14273718C2318yescomplemented
232#14273718C2318yescomplemented
233#14273718C2314yescomplemented
234#14273717C2318yescomplemented
235#14273717C2318yescomplemented
236#14273717C2318yescomplemented
237#14273717C2318yescomplemented
238#14273717C2318yescomplemented
239#14273717C2318yescomplemented
240#14273717C2318yescomplemented
241#14273717C2318yescomplemented
242#14273717C2318yescomplemented
243#14273716C2314yes—
244#14273715C2314yes—
245#14273714C2314yes—
246#14273713C2318yes—
247#14273713C2318yes—
248#14273712C2314yes—
249#14273712C2318yes—
250#14273712C2318yes—
251#14273712C2318yes—
252#14273712C2318yescomplemented
253#14273711C2312yes—
254#14273711C2314yes—
255#14273711C2318yes—
256#14273711C2314yescomplemented
257#14273710C2312yes—
258#14273710C2314yes—
259#14273710C2318yes—
260#14273710C2314yescomplemented
261#14273709C2314yes—
262#14273709C2318yes—
263#14273709C2318yes—
264#14273709C2318yes—
265#14273709C2318yescomplemented
266#14273708C2312yes—
267#14273708C2314yes—
268#14273708C2318yes—
269#14273708C2314yescomplemented
270#14273707C2314yes—
271#14273707C2314yes—
272#14273707C2314yes—
273#14273707C2314yes—
274#14273707C2312yes—
275#14273707C2318yes—
276#14273707C2318yescomplemented
277#14273707C2314yescomplemented
278#14273706C2314yes—
279#14273706C2314yes—
280#14273706C2314yes—
281#14273706C2314yes—
282#14273706C2312yes—
283#14273706C2318yes—
284#14273706C2318yescomplemented
285#14273706C2314yescomplemented
286#14273705C2318yes—
287#14273705C2318yes—
288#14273705C2318yes—
289#14273705C2318yes—
290#14273705C2314yes—
291#14273705C2318yes—
292#14273705C2318yes—
293#14273705C2318yescomplemented
294#14273705C2318yescomplemented
295#14273705C2318yescomplemented
296#14273704C2318yes—
297#14273704C2318yes—
298#14273704C2318yes—
299#14273704C2318yes—
300#14273704C2314yes—
301#14273704C2318yes—
302#14273704C2318yes—
303#14273704C2318yescomplemented
304#14273704C2318yescomplemented
305#14273704C2318yescomplemented
306#14273703C2314yes—
307#14273703C2314yes—
308#14273703C2314yes—
309#14273703C2314yes—
310#14273703C2312yes—
311#14273703C2318yes—
312#14273703C2318yescomplemented
313#14273703C2314yescomplemented
314#14273702C2312yes—
315#14273701C2312yes—
316#14273700C2314yes—
317#14273699C2314yes—
318#14273698C2312yes—
319#14273697C2312yes—
320#14273697C2314yes—
321#14273696C2312yes—
322#14273695C2312yes—
323#14273695C2314yes—
324Q8×Dic59C2314yescomplemented
325C4×Dic118C2318yescomplemented
326C4×Dic118C2314yescomplemented
327#14273692C2318yescomplemented
328#14273692C2314yescomplemented
329C4×D236C2314yes—
330C4×D236C2318yes—
331D4×Dic59C2314yes—
332D4×Dic59C2318yes—
333#14273689C2314yes—
334#14273689C2318yes—
335C4×C22⋊D59C2314yes—
336C4×C22⋊D59C2314yes—
337C4×C22⋊D59C2318yes—
338C4×C22⋊D59C2318yes—
339(C22⋊D59)⋊C4C2314yes—
340(C22⋊D59)⋊C4C2314yes—
341(C22⋊D59)⋊C4C2318yes—
342(C22⋊D59)⋊C4C2318yes—
343#14273686C2311yescharacteristic
344#14273686C2318yes—
345#14273686C2312yescomplemented
346#14273685C2312yes—
347#14273685C2318yes—
348#14273685C2318yes—
349#14273685C2314yescomplemented
350#14273684C2312yes—
351#14273684C2318yes—
352#14273684C2318yes—
353#14273684C2314yescomplemented
354#14273683C2312yes—
355#14273683C2318yes—
356#14273683C2318yes—
357#14273683C2314yescomplemented
358C2×C4⋊Dic59C2312yes—
359C2×C4⋊Dic59C2314yes—
360C2×Dic59⋊C4C2314yes—
361C2×Dic59⋊C4C2314yes—
362C2×Dic59⋊C4C2314yes—
363C4⋊C4×D59C2312yes—
364C4⋊C4×D59C2318yes—
365C4⋊C4×D59C2314yes—
366C4⋊C4×D59C2318yes—
367C4⋊C4×D59C2314yes—
368C4⋊C4×D59C2318yes—
369C4⋊C4×D59C2318yes—
370C4⋊C4×D59C2318yes—
371C4⋊C4×D59C2314yes—
372C4⋊C4×D59C2318yes—
373C4⋊C4×D59C2318yes—
374C4⋊C4×D59C2314yes—
375C4⋊C4×D59C2314yes—
376C4⋊C4×D59C2318yes—
377C2×C22⋊Dic59C2314yes—
378C2×(C2×D59)⋊C4C2314yes—
379C2×(C2×D59)⋊C4C2314yes—
380C22⋊C4×D59C2314yes—
381C22⋊C4×D59C2318yes—
382C22⋊C4×D59C2314yes—
383C22⋊C4×D59C2318yes—
384C22⋊C4×D59C2318yes—
385C22⋊C4×D59C2318yes—
386C22⋊C4×D59C2318yes—
387C22⋊C4×D59C2314yes—
388C22⋊C4×D59C2312yes—
389C42×D59C2314yes—
390C42×D59C2318yes—
391C42×D59C2312yes—
392C2×#41×C59C2311yescharacteristic
393C22×Q8×C59C2312yes—
394C22×Q8×C59C2312yescomplemented
395C23×C4×C59C2311yescharacteristic
396C4⋊Q8×C59C2318yescomplemented
397C4⋊Q8×C59C2314yescomplemented
398C4⋊Q8×C59C2312yescomplemented
399#126×C59C2318yes—
400#126×C59C2318yescomplemented
401#125×C59C2318yescomplemented
402#125×C59C2318yescomplemented
403#125×C59C2312yescomplemented
404#124×C59C2314yes—
405#123×C59C2312yes—
406#123×C59C2314yes—
407#123×C59C2318yes—
408#123×C59C2314yescomplemented
409C22⋊Q8×C59C2314yes—
410C22⋊Q8×C59C2314yes—
411C22⋊Q8×C59C2314yes—
412C22⋊Q8×C59C2314yes—
413C22⋊Q8×C59C2312yes—
414C22⋊Q8×C59C2318yes—
415C22⋊Q8×C59C2318yescomplemented
416C22⋊Q8×C59C2314yescomplemented
417#121×C59C2312yes—
418#120×C59C2312yes—
419C4×Q8×C59C2314yescomplemented
420C4×D4×C59C2314yes—
421C4×D4×C59C2318yes—
422#117×C59C2311yescharacteristic
423#117×C59C2318yes—
424#117×C59C2312yescomplemented
425C2×C4⋊C4×C59C2314yes—
426C2×C4⋊C4×C59C2312yes—
427C2×C22⋊C4×C59C2314yes—
428C24×C59C2411yescharacteristic
429C23×D59—28no—
430C23×D59—42no—
431C23×D59C2411yescharacteristic
432C23×D59C2412yes—
433C23×D59C2411yescharacteristic
434C23×D59C2412yes—
435C23×D59C2412yes—
436#41×C59—42no—
437C2×Q8×C59—44no—
438C2×Q8×C59—44no—
439C2×Q8×C59C2414yes—
440C2×Q8×C59C2414yes—
441C2×Q8×C59C2414yes—
442C2×Q8×C59C2411yescharacteristic
443C2×D4×C59C2414yes—
444C2×D4×C59C2412yes—
445C2×D4×C59C2411yescharacteristic
446C22×C4×C59—42no—
447C22×C4×C59C2414yes—
448C22×C4×C59C2412yes—
449C22×C4×C59C2411yescharacteristic
450C22×C4×C59C2412yes—
451C22×C4×C59C2414yes—
452C22×C4×C59C2412yes—
453C22×C4×C59C2414yes—
454C22×C4×C59C2411yescharacteristic
455C2×C22⋊D59C2414yes—
456C2×C22⋊D59C2414yes—
457C2×C22⋊D59C2412yes—
458C2×C22⋊D59C2412yes—
459C2×C22⋊D59C2412yes—
460C22×Dic59—42no—
461C22×Dic59C2414yes—
462C22×Dic59C2412yes—
463C22×Dic59C2411yescharacteristic
464C22×Dic59C2412yes—
465C22×Dic59C2414yes—
466C22×Dic59C2412yes—
467C22×Dic59C2414yes—
468C22×Dic59C2411yescharacteristic
469#11745689—42no—
470Q8×D59—216no—
471Q8×D59—48no—
472Q8×D59—48no—
473Q8×D59—48no—
474Q8×D59—48no—
475Q8×D59—48no—
476Q8×D59—48no—
477Q8×D59—42no—
478#11745687—42no—
479#11745687—44no—
480D4×D59—216no—
481D4×D59—42no—
482D4×D59—44no—
483#11745685—44no—
484#11745685—42no—
485C2×D236C2414yes—
486C2×D236C2412yes—
487C2×D236C2411yescharacteristic
488C2×C4×D59—216no—
489C2×C4×D59—28no—
490C2×C4×D59—24no—
491C2×C4×D59—28no—
492C2×C4×D59—44no—
493C2×C4×D59—42no—
494C2×C4×D59—44no—
495C2×C4×D59—42no—
496C2×C4×D59—44no—
497C2×C4×D59—42no—
498C2×C4×D59—48no—
499C2×C4×D59—48no—
500C2×C4×D59C2414yes—
501C2×C4×D59C2418yes—
502C2×C4×D59C2412yes—
503C2×C4×D59C2418yes—
504C2×C4×D59C2412yes—
505C2×C4×D59C2418yes—
506C2×C4×D59C2411yescharacteristic
507C2×C4×D59C2412yes—
508C2×C4×D59C2412yes—
509C2×C4×D59C2411yescharacteristic
510C2×C4×D59C2412yes—
511C2×C4×D59C2411yescharacteristic
512C2×C4×D59C2412yes—
513C2×C4×D59C2418yes—
514C2×C4×D59C2412yes—
515C2×C4×D59C2412yes—
516C2×C4×D59C2418yes—
517C2×C4×D59C2412yes—
518C2×C4×D59C2411yescharacteristic
519C2×Dic118—48no—
520C2×Dic118—48no—
521C2×Dic118—44no—
522C2×Dic118—44no—
523C2×Dic118C2418yes—
524C2×Dic118C2414yes—
525C2×Dic118C2418yes—
526C2×Dic118C2414yes—
527C2×Dic118C2412yes—
528C2×Dic118C2418yes—
529C2×Dic118C2414yes—
530C2×Dic118C2411yescharacteristic
531C4⋊C4×C59C2414yes—
532C4⋊C4×C59C2418yes—
533C4⋊C4×C59C2418yes—
534C4⋊C4×C59C2414yes—
535C4⋊C4×C59C2412yes—
536C4⋊C4×C59C2418yes—
537C4⋊C4×C59C2418yes—
538C4⋊C4×C59C2418yes—
539C4⋊C4×C59C2414yes—
540C4⋊C4×C59C2418yes—
541C22⋊C4×C59C2418yes—
542C22⋊C4×C59C2418yes—
543C22⋊C4×C59C2414yes—
544C22⋊C4×C59C2412yes—
545C22⋊C4×C59C2414yes—
546C22⋊C4×C59C2414yes—
547C22⋊C4×C59C2418yes—
548C42×C59C2414yes—
549C42×C59C2412yes—
550C42×C59C2418yes—
551C22⋊Dic59C2418yes—
552C22⋊Dic59C2418yes—
553C22⋊Dic59C2414yes—
554C22⋊Dic59C2412yes—
555C22⋊Dic59C2414yes—
556C22⋊Dic59C2414yes—
557C22⋊Dic59C2418yes—
558(C2×D59)⋊C4C2418yes—
559(C2×D59)⋊C4C2418yes—
560(C2×D59)⋊C4C2418yes—
561(C2×D59)⋊C4C2418yes—
562(C2×D59)⋊C4C2414yes—
563(C2×D59)⋊C4C2414yes—
564(C2×D59)⋊C4C2414yes—
565(C2×D59)⋊C4C2418yes—
566(C2×D59)⋊C4C2414yes—
567(C2×D59)⋊C4C2418yes—
568(C2×D59)⋊C4C2414yes—
569(C2×D59)⋊C4C2418yes—
570C4⋊Dic59C2414yes—
571C4⋊Dic59C2414yes—
572C4⋊Dic59C2418yes—
573C4⋊Dic59C2418yes—
574C4⋊Dic59C2412yes—
575C4⋊Dic59C2418yes—
576C4⋊Dic59C2418yes—
577C4⋊Dic59C2418yes—
578C4⋊Dic59C2414yes—
579C4⋊Dic59C2418yes—
580Dic59⋊C4C2418yes—
581Dic59⋊C4C2418yes—
582Dic59⋊C4C2418yes—
583Dic59⋊C4C2418yes—
584Dic59⋊C4C2418yes—
585Dic59⋊C4C2418yes—
586Dic59⋊C4C2414yes—
587Dic59⋊C4C2418yes—
588Dic59⋊C4C2418yes—
589Dic59⋊C4C2418yes—
590Dic59⋊C4C2418yes—
591Dic59⋊C4C2418yes—
592Dic59⋊C4C2414yes—
593Dic59⋊C4C2418yes—
594Dic59⋊C4C2414yes—
595Dic59⋊C4C2418yes—
596Dic59⋊C4C2418yes—
597C4×Dic59C2414yes—
598C4×Dic59C2418yes—
599C4×Dic59C2414yes—
600C4×Dic59C2418yes—
601C4×Dic59C2418yes—
602C4×Dic59C2418yes—
603C4×Dic59C2412yes—
604C23×C59—24no—
605C23×C59—41no—
606C23×C59C2511yescharacteristic
607C23×C59C2512yes—
608C23×C59C2512yes—
609C22×D59—24no—
610C22×D59—24no—
611C22×D59—24no—
612C22×D59—24no—
613C22×D59—22no—
614C22×D59—28no—
615C22×D59—24no—
616C22×D59—24no—
617C22×D59—24no—
618C22×D59—41no—
619C22×D59—42no—
620C22×D59—416no—
621C22×D592−1+418yes—
622C22×D59C2511yescharacteristic
623C22×D59C2512yes—
624C22×D59C2512yes—
625C22×D59C2511yescharacteristic
626Q8×C59—28no—
627Q8×C59—44no—
628Q8×C59—44no—
629Q8×C59—41no—
630D4×C59—28no—
631D4×C59—42no—
632D4×C59—41no—
633C2×C4×C59—28no—
634C2×C4×C59—24no—
635C2×C4×C59—24no—
636C2×C4×C59—22no—
637C2×C4×C59—44no—
638C2×C4×C59—44no—
639C2×C4×C59—41no—
640C2×C4×C59—42no—
641C2×C4×C59C2514yes—
642C2×C4×C59C2512yes—
643C2×C4×C59C2518yes—
644C2×C4×C59C2518yes—
645C2×C4×C59C2511yescharacteristic
646C2×C4×C59C2512yes—
647C2×C4×C59C2511yescharacteristic
648C22⋊D59—28no—
649C22⋊D59—28no—
650C22⋊D59—42no—
651C22⋊D59—42no—
652C22⋊D59—42no—
653C2×Dic59—28no—
654C2×Dic59—24no—
655C2×Dic59—24no—
656C2×Dic59—22no—
657C2×Dic59—44no—
658C2×Dic59—44no—
659C2×Dic59—41no—
660C2×Dic59—42no—
661C2×Dic59C2514yes—
662C2×Dic59C2518yes—
663C2×Dic59C2512yes—
664C2×Dic59C2518yes—
665C2×Dic59C2511yescharacteristic
666C2×Dic59C2512yes—
667C2×Dic59C2511yescharacteristic
668D236—28no—
669D236—42no—
670D236—41no—
671C4×D59—22no—
672C4×D59—24no—
673C4×D59—24no—
674C4×D59—216no—
675C4×D59—216no—
676C4×D59—216no—
677C4×D59—28no—
678C4×D59—22no—
679C4×D59—24no—
680C4×D59—24no—
681C4×D59—22no—
682C4×D59—24no—
683C4×D59—24no—
684C4×D59—42no—
685C4×D59—42no—
686C4×D59—42no—
687C4×D59—48no—
688C4×D59—48no—
689C4×D59H(5,𝔽2)14yes—
690Dic118—28no—
691Dic118—216no—
692Dic118—44no—
693Dic118—44no—
694Dic118—48no—
695Dic118—48no—
696Dic118—41no—
697Dic118—42no—
698C2×#3538—591nomaximal, Sylow
699C22×C59—22no—
700C22×C59—22no—
701C22×C59—22no—
702C22×C59—21no—
703C22×C59—24no—
704C22×C59—22no—
705C22×C59—44no—
706C22×C59C2×2−1+414yes—
707C22×C59C2611yescharacteristic
708C2×D59—22no—
709C2×D59—22no—
710C2×D59—216no—
711C2×D59—22no—
712C2×D59—21no—
713C2×D59—24no—
714C2×D59—22no—
715C2×D59—44no—
716C2×D59—48no—
717C2×D59—48no—
718C2×D59—44no—
719C2×D59C2×H(5,𝔽2)12yes—
720C2×D59C2×2−1+414yes—
721C2×D59C2×2−1+414yes—
722C4×C59—28no—
723C4×C59—22no—
724C4×C59—22no—
725C4×C59—21no—
726C4×C59—28no—
727C4×C59—24no—
728C4×C59C2×H(5,𝔽2)12yes—
729Dic59—28no—
730Dic59—22no—
731Dic59—22no—
732Dic59—21no—
733Dic59—28no—
734Dic59—24no—
735Dic59C2×H(5,𝔽2)12yes—
736#3538—594no—
737#3538—594no—
738#3538—594no—
739#3538—594no—
740#3538—594no—
741#3538—592no—
742#3538—594no—
743#3538—592no—
744#3538—591no—
745#3538—592no—
746#3538D5911yescharacteristic, direct product factor
747C2×#563—594no—
748C2×#552—594no—
749C2×#551—594no—
750C2×D4×Q8—594no—
751C2×#544—594no—
752C2×#541—592no—
753C2×#539—594no—
754C2×#536—592no—
755C2×#525—591no—
756C22×C22⋊Q8—592no—
757C2×C59—24no—
758C2×C59—41no—
759C2×C59—42no—
760C2×C59C22×H(5,𝔽2)11yescharacteristic
761C2×C59C22×2−1+412yes—
762D59—24no—
763D59—42no—
764D59—41no—
765D59#353814yesdirect product factor
766C22×#41—591no—
767C23×Q8—592no—
768C23×Q8—592no—
769C24×C4—591no—
770#563—598no—
771#563—598no—
772#563—598no—
773#563—598no—
774#563—594no—
775#563—594no—
776#563—594no—
777#563—598no—
778#563—598no—
779#563C2×D5914yescomplemented
780#552—598no—
781#552—598no—
782#552—594no—
783#552—598no—
784#552—594no—
785#552—594no—
786#552—594no—
787#552—594no—
788#552—598no—
789#552—594no—
790#552—594no—
791#552C2×D5914yescomplemented
792#551—598no—
793#551—594no—
794#551—598no—
795#551—594no—
796#551—598no—
797#551—594no—
798#551—598no—
799#551—598no—
800#551—598no—
801#551C2×D5914yescomplemented
802D4×Q8—594no—
803D4×Q8—594no—
804D4×Q8—598no—
805D4×Q8—594no—
806D4×Q8—594no—
807D4×Q8—598no—
808D4×Q8—594no—
809D4×Q8—598no—
810D4×Q8—594no—
811D4×Q8—598no—
812D4×Q8—594no—
813D4×Q8C2×D5914yescomplemented
814#544—598no—
815#544—598no—
816#544—598no—
817#544—598no—
818#544—594no—
819#544—594no—
820#544—598no—
821#544—598no—
822#544—594no—
823#544C2×D5914yescomplemented
824#541—592no—
825#541—598no—
826#541—598no—
827#541—592no—
828#541—594no—
829#541—594no—
830#541—592no—
831#541C2×D5912yescomplemented
832#539—598no—
833#539—598no—
834#539—598no—
835#539—598no—
836#539—594no—
837#539—598no—
838#539—594no—
839#539—598no—
840#539—594no—
841#539C2×D5914yescomplemented
842#536—592no—
843#536—592no—
844#536—594no—
845#536—594no—
846#536—594no—
847#536—594no—
848#536—594no—
849#536—594no—
850#536—592no—
851#536C2×D5912yescomplemented
852C2×C4⋊Q8—594no—
853C2×C4⋊Q8—592no—
854C2×C4⋊Q8—598no—
855C2×#126—598no—
856C2×#126—598no—
857C2×#125—598no—
858C2×#125—592no—
859C2×#125—598no—
860C2×#124—594no—
861#525—591no—
862#525—591no—
863#525—592no—
864#525—592no—
865#525—592no—
866#525—592no—
867#525—594no—
868#525—591no—
869#525C2×D5911yescharacteristic
870C2×#123—592no—
871C2×#123—594no—
872C2×#123—598no—
873C2×#123—594no—
874C2×C22⋊Q8—592no—
875C2×C22⋊Q8—592no—
876C2×C22⋊Q8—594no—
877C2×C22⋊Q8—594no—
878C2×C22⋊Q8—594no—
879C2×C22⋊Q8—594no—
880C2×C22⋊Q8—592no—
881C2×C22⋊Q8—598no—
882C2×C22⋊Q8—594no—
883C2×C22⋊Q8—594no—
884C2×C22⋊Q8—594no—
885C2×C22⋊Q8—594no—
886C2×C22⋊Q8—594no—
887C2×C22⋊Q8—598no—
888C2×C22⋊Q8—594no—
889C2×C22⋊Q8—592no—
890C2×C22⋊Q8—594no—
891C2×C22⋊Q8C2×D5912yescomplemented
892C2×#121—592no—
893C2×#120—592no—
894C2×C4×Q8—594no—
895C2×C4×D4—594no—
896C2×C4×D4—598no—
897C2×#117—591no—
898C2×#117—598no—
899C2×#117—592no—
900C22×C4⋊C4—594no—
901C22×C4⋊C4—592no—
902C22×C22⋊C4—594no—
903C59C2×#353811yescharacteristic, complemented, Sylow
904C25—591no—
905C2×#41—591no—
906C2×#41—591no—
907C2×#41—592no—
908C2×#41—591no—
909C2×#41—592no—
910C2×#41—2364no—
911C2×#41C22×D5911yescharacteristic
912C22×Q8—594no—
913C22×Q8—594no—
914C22×Q8—594no—
915C22×Q8—591no—
916C22×Q8—594no—
917C22×Q8—594no—
918C22×Q8—594no—
919C22×Q8—594no—
920C22×Q8—594no—
921C22×Q8—592no—
922C22×Q8—594no—
923C22×Q8—592no—
924C22×Q8—2368no—
925C22×Q8—2368no—
926C22×Q8C22×D5912yes—
927C22×Q8C22×D5912yescomplemented
928C22×D4—594no—
929C22×D4—592no—
930C22×D4—591no—
931C23×C4—591no—
932C23×C4—594no—
933C23×C4—592no—
934C23×C4—592no—
935C23×C4—591no—
936C23×C4—594no—
937C23×C4—592no—
938C23×C4—594no—
939C23×C4—591no—
940C23×C4—592no—
941C23×C4—591no—
942C23×C4—592no—
943C23×C4—591no—
944C23×C4—2364no—
945C23×C4C22×D5911yescharacteristic
946C4⋊Q8—594no—
947C4⋊Q8—594no—
948C4⋊Q8—594no—
949C4⋊Q8—598no—
950C4⋊Q8—598no—
951C4⋊Q8—598no—
952C4⋊Q8—598no—
953C4⋊Q8—598no—
954C4⋊Q8—598no—
955C4⋊Q8—598no—
956C4⋊Q8—598no—
957C4⋊Q8—598no—
958C4⋊Q8—594no—
959C4⋊Q8—592no—
960C4⋊Q8—598no—
961C4⋊Q8C22×D5914yescomplemented
962C4⋊Q8C22×D5912yescomplemented
963C4⋊Q8C22×D5918yescomplemented
964#126—598no—
965#126—598no—
966#126—598no—
967#126—598no—
968#126—598no—
969#126—598no—
970#126—598no—
971#126—598no—
972#126—598no—
973#126—598no—
974#126—598no—
975#126—598no—
976#126—598no—
977#126—598no—
978#126C22×D5918yes—
979#126C22×D5918yescomplemented
980#125—598no—
981#125—598no—
982#125—598no—
983#125—598no—
984#125—598no—
985#125—598no—
986#125—598no—
987#125—594no—
988#125—598no—
989#125—598no—
990#125—598no—
991#125—598no—
992#125—598no—
993#125—598no—
994#125—598no—
995#125—592no—
996#125—598no—
997#125C22×D5918yescomplemented
998#125C22×D5912yescomplemented
999#125C22×D5918yescomplemented
1000#124—594no—
1001#124—594no—
1002#124—598no—
1003#124—598no—
1004#124—594no—
1005#124C22×D5914yes—
1006#123—592no—
1007#123—594no—
1008#123—594no—
1009#123—598no—
1010#123—592no—
1011#123—594no—
1012#123—594no—
1013#123—598no—
1014#123—594no—
1015#123—598no—
1016#123—598no—
1017#123—598no—
1018#123—598no—
1019#123—594no—
1020#123—592no—
1021#123—598no—
1022#123—594no—
1023#123—598no—
1024#123—594no—
1025#123—598no—
1026#123—598no—
1027#123—598no—
1028#123C22×D5912yes—
1029#123C22×D5914yes—
1030#123C22×D5918yes—
1031#123C22×D5914yescomplemented
1032C22⋊Q8—594no—
1033C22⋊Q8—594no—
1034C22⋊Q8—594no—
1035C22⋊Q8—594no—
1036C22⋊Q8—592no—
1037C22⋊Q8—594no—
1038C22⋊Q8—598no—
1039C22⋊Q8—598no—
1040C22⋊Q8—594no—
1041C22⋊Q8—594no—
1042C22⋊Q8—594no—
1043C22⋊Q8—594no—
1044C22⋊Q8—592no—
1045C22⋊Q8—594no—
1046C22⋊Q8—598no—
1047C22⋊Q8—598no—
1048C22⋊Q8—598no—
1049C22⋊Q8—594no—
1050C22⋊Q8—598no—
1051C22⋊Q8—594no—
1052C22⋊Q8—598no—
1053C22⋊Q8—594no—
1054C22⋊Q8—598no—
1055C22⋊Q8—594no—
1056C22⋊Q8—594no—
1057C22⋊Q8—592no—
1058C22⋊Q8—598no—
1059C22⋊Q8—594no—
1060C22⋊Q8—598no—
1061C22⋊Q8—598no—
1062C22⋊Q8—598no—
1063C22⋊Q8—598no—
1064C22⋊Q8—598no—
1065C22⋊Q8—598no—
1066C22⋊Q8—598no—
1067C22⋊Q8—598no—
1068C22⋊Q8—598no—
1069C22⋊Q8—598no—
1070C22⋊Q8—594no—
1071C22⋊Q8—598no—
1072C22⋊Q8—598no—
1073C22⋊Q8—598no—
1074C22⋊Q8—598no—
1075C22⋊Q8—598no—
1076C22⋊Q8C22×D5914yes—
1077C22⋊Q8C22×D5914yes—
1078C22⋊Q8C22×D5914yes—
1079C22⋊Q8C22×D5914yes—
1080C22⋊Q8C22×D5912yes—
1081C22⋊Q8C22×D5918yes—
1082C22⋊Q8C22×D5914yescomplemented
1083C22⋊Q8C22×D5918yescomplemented
1084#121—592no—
1085#121—594no—
1086#121—592no—
1087#121—592no—
1088#121—594no—
1089#121C22×D5912yes—
1090#120—592no—
1091#120—594no—
1092#120—592no—
1093#120—592no—
1094#120—594no—
1095#120C22×D5912yes—
1096C4×Q8—594no—
1097C4×Q8—598no—
1098C4×Q8—594no—
1099C4×Q8—598no—
1100C4×Q8—594no—
1101C4×Q8C22×D5914yescomplemented
1102C4×D4—594no—
1103C4×D4—598no—
1104C4×D4—594no—
1105C4×D4—594no—
1106C4×D4—598no—
1107C4×D4—598no—
1108C4×D4—594no—
1109C4×D4—598no—
1110C4×D4—594no—
1111C4×D4—594no—
1112C4×D4—598no—
1113C4×D4—598no—
1114C4×D4—594no—
1115C4×D4—598no—
1116C4×D4C22×D5914yes—
1117C4×D4C22×D5918yes—
1118#117—591no—
1119#117—592no—
1120#117—598no—
1121#117—592no—
1122#117—594no—
1123#117—598no—
1124#117—598no—
1125#117—592no—
1126#117—594no—
1127#117—598no—
1128#117—598no—
1129#117—592no—
1130#117—594no—
1131#117—598no—
1132#117—598no—
1133#117C22×D5911yescharacteristic
1134#117C22×D5918yes—
1135#117C22×D5912yescomplemented
1136C2×C4⋊C4—594no—
1137C2×C4⋊C4—594no—
1138C2×C4⋊C4—594no—
1139C2×C4⋊C4—594no—
1140C2×C4⋊C4—592no—
1141C2×C4⋊C4—594no—
1142C2×C4⋊C4—598no—
1143C2×C4⋊C4—598no—
1144C2×C4⋊C4—594no—
1145C2×C4⋊C4—598no—
1146C2×C4⋊C4—598no—
1147C2×C4⋊C4—594no—
1148C2×C4⋊C4—594no—
1149C2×C4⋊C4—592no—
1150C2×C4⋊C4—598no—
1151C2×C4⋊C4—598no—
1152C2×C4⋊C4—598no—
1153C2×C4⋊C4—594no—
1154C2×C4⋊C4—598no—
1155C2×C4⋊C4C22×D5914yes—
1156C2×C4⋊C4C22×D5912yes—
1157C2×C22⋊C4—594no—
1158C2×C22⋊C4—594no—
1159C2×C22⋊C4—594no—
1160C2×C22⋊C4—598no—
1161C2×C22⋊C4—598no—
1162C2×C22⋊C4—598no—
1163C2×C22⋊C4—598no—
1164C2×C22⋊C4—594no—
1165C2×C22⋊C4—592no—
1166C2×C22⋊C4—594no—
1167C2×C22⋊C4—594no—
1168C2×C22⋊C4—598no—
1169C2×C22⋊C4C22×D5914yes—
1170C2×C42—594no—
1171C2×C42—592no—
1172C2×C42—598no—
1173C24—592no—
1174C24—591no—
1175C24—592no—
1176C24—591no—
1177C24—592no—
1178C24—1188no—
1179C24—2362no—
1180C24C23×D5911yescharacteristic
1181#41—42no—
1182#41—2362no—
1183#41—2364no—
1184#41—2362no—
1185#41—2364no—
1186#41—2362no—
1187C2×Q8—44no—
1188C2×Q8—44no—
1189C2×Q8—598no—
1190C2×Q8—594no—
1191C2×Q8—594no—
1192C2×Q8—598no—
1193C2×Q8—598no—
1194C2×Q8—594no—
1195C2×Q8—591no—
1196C2×Q8—592no—
1197C2×Q8—11816no—
1198C2×Q8—2364no—
1199C2×Q8—2364no—
1200C2×Q8—2368no—
1201C2×Q8—2368no—
1202C2×Q8—2368no—
1203C2×Q8—2368no—
1204C2×Q8—2362no—
1205C2×Q8—2368no—
1206C2×Q8—2368no—
1207C2×Q8—2368no—
1208C2×Q8—2368no—
1209C2×Q8C23×D5914yes—
1210C2×Q8C23×D5914yes—
1211C2×Q8C23×D5914yes—
1212C2×Q8C23×D5911yescharacteristic
1213C2×D4—594no—
1214C2×D4—594no—
1215C2×D4—592no—
1216C2×D4—592no—
1217C2×D4—592no—
1218C2×D4—594no—
1219C2×D4—592no—
1220C2×D4—591no—
1221C2×D4—11816no—
1222C2×D4—2362no—
1223C2×D4—2364no—
1224C2×D4C23×D5914yes—
1225C2×D4C23×D5912yes—
1226C2×D4C23×D5911yescharacteristic
1227C22×C4—42no—
1228C22×C4—591no—
1229C22×C4—594no—
1230C22×C4—592no—
1231C22×C4—592no—
1232C22×C4—591no—
1233C22×C4—594no—
1234C22×C4—592no—
1235C22×C4—594no—
1236C22×C4—591no—
1237C22×C4—594no—
1238C22×C4—598no—
1239C22×C4—592no—
1240C22×C4—598no—
1241C22×C4—592no—
1242C22×C4—598no—
1243C22×C4—591no—
1244C22×C4—592no—
1245C22×C4—592no—
1246C22×C4—592no—
1247C22×C4—592no—
1248C22×C4—591no—
1249C22×C4—591no—
1250C22×C4—598no—
1251C22×C4—592no—
1252C22×C4—592no—
1253C22×C4—598no—
1254C22×C4—592no—
1255C22×C4—1188no—
1256C22×C4—1184no—
1257C22×C4—1188no—
1258C22×C4—11816no—
1259C22×C4—2364no—
1260C22×C4—2362no—
1261C22×C4—2362no—
1262C22×C4—2364no—
1263C22×C4—2364no—
1264C22×C4—2362no—
1265C22×C4—2368no—
1266C22×C4—2368no—
1267C22×C4—2362no—
1268C22×C4C23×D5914yes—
1269C22×C4C23×D5912yes—
1270C22×C4C23×D5911yescharacteristic
1271C22×C4C23×D5912yes—
1272C22×C4C23×D5914yes—
1273C22×C4C23×D5912yes—
1274C22×C4C23×D5914yes—
1275C22×C4C23×D5911yescharacteristic
1276C4⋊C4—598no—
1277C4⋊C4—594no—
1278C4⋊C4—598no—
1279C4⋊C4—598no—
1280C4⋊C4—598no—
1281C4⋊C4—598no—
1282C4⋊C4—598no—
1283C4⋊C4—598no—
1284C4⋊C4—598no—
1285C4⋊C4—594no—
1286C4⋊C4—594no—
1287C4⋊C4—592no—
1288C4⋊C4—598no—
1289C4⋊C4—598no—
1290C4⋊C4—598no—
1291C4⋊C4—598no—
1292C4⋊C4—598no—
1293C4⋊C4—598no—
1294C4⋊C4—598no—
1295C4⋊C4—598no—
1296C4⋊C4—598no—
1297C4⋊C4—594no—
1298C4⋊C4—594no—
1299C4⋊C4—594no—
1300C4⋊C4—598no—
1301C4⋊C4—598no—
1302C4⋊C4—598no—
1303C4⋊C4C23×D5914yes—
1304C4⋊C4C23×D5918yes—
1305C4⋊C4C23×D5918yes—
1306C4⋊C4C23×D5914yes—
1307C4⋊C4C23×D5912yes—
1308C4⋊C4C23×D5918yes—
1309C4⋊C4C23×D5918yes—
1310C4⋊C4C23×D5918yes—
1311C4⋊C4C23×D5914yes—
1312C4⋊C4C23×D5918yes—
1313C22⋊C4—598no—
1314C22⋊C4—598no—
1315C22⋊C4—594no—
1316C22⋊C4—592no—
1317C22⋊C4—594no—
1318C22⋊C4—594no—
1319C22⋊C4—598no—
1320C22⋊C4—598no—
1321C22⋊C4—598no—
1322C22⋊C4—598no—
1323C22⋊C4—598no—
1324C22⋊C4—594no—
1325C22⋊C4—594no—
1326C22⋊C4—594no—
1327C22⋊C4—598no—
1328C22⋊C4—594no—
1329C22⋊C4—594no—
1330C22⋊C4—598no—
1331C22⋊C4—598no—
1332C22⋊C4C23×D5918yes—
1333C22⋊C4C23×D5918yes—
1334C22⋊C4C23×D5914yes—
1335C22⋊C4C23×D5912yes—
1336C22⋊C4C23×D5914yes—
1337C22⋊C4C23×D5914yes—
1338C22⋊C4C23×D5918yes—
1339C42—594no—
1340C42—598no—
1341C42—594no—
1342C42—592no—
1343C42—598no—
1344C42—598no—
1345C42—598no—
1346C42C23×D5914yes—
1347C42C23×D5912yes—
1348C42C23×D5918yes—
1349C23—24no—
1350C23—41no—
1351C23—591no—
1352C23—598no—
1353C23—592no—
1354C23—591no—
1355C23—592no—
1356C23—1184no—
1357C23—1184no—
1358C23—1184no—
1359C23—1182no—
1360C23—1188no—
1361C23—1184no—
1362C23—1184no—
1363C23—1184no—
1364C23—1184no—
1365C23—2362no—
1366C23—2361no—
1367C23—23616no—
1368C23C24×D5911yescharacteristic
1369C23C24×D5912yes—
1370C23C24×D5912yes—
1371Q8—28no—
1372Q8—44no—
1373Q8—44no—
1374Q8—41no—
1375Q8—11816no—
1376Q8—1188no—
1377Q8—2364no—
1378Q8—2364no—
1379Q8—2368no—
1380Q8—2368no—
1381Q8—2361no—
1382Q8—2362no—
1383D4—28no—
1384D4—41no—
1385D4—42no—
1386D4—1188no—
1387D4—1188no—
1388D4—1188no—
1389D4—2361no—
1390D4—2362no—
1391D4—2362no—
1392D4—2362no—
1393D4—2362no—
1394C2×C4—28no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—42no—
1399C2×C4—41no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—591no—
1403C2×C4—594no—
1404C2×C4—594no—
1405C2×C4—598no—
1406C2×C4—592no—
1407C2×C4—598no—
1408C2×C4—592no—
1409C2×C4—591no—
1410C2×C4—1184no—
1411C2×C4—1182no—
1412C2×C4—1184no—
1413C2×C4—11816no—
1414C2×C4—11816no—
1415C2×C4—1182no—
1416C2×C4—1184no—
1417C2×C4—1184no—
1418C2×C4—11816no—
1419C2×C4—1188no—
1420C2×C4—1184no—
1421C2×C4—1182no—
1422C2×C4—1184no—
1423C2×C4—1188no—
1424C2×C4—1184no—
1425C2×C4—1182no—
1426C2×C4—1184no—
1427C2×C4—2362no—
1428C2×C4—2362no—
1429C2×C4—2362no—
1430C2×C4—2368no—
1431C2×C4—2368no—
1432C2×C4—2362no—
1433C2×C4—2361no—
1434C2×C4—2364no—
1435C2×C4—2364no—
1436C2×C4C24×D5914yes—
1437C2×C4C24×D5918yes—
1438C2×C4C24×D5912yes—
1439C2×C4C24×D5918yes—
1440C2×C4C24×D5912yes—
1441C2×C4C24×D5911yescharacteristic
1442C2×C4C24×D5911yescharacteristic
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—21no—
1447C22—24no—
1448C22—22no—
1449C22—44no—
1450C22—592no—
1451C22—594no—
1452C22—594no—
1453C22—11816no—
1454C22—1182no—
1455C22—1182no—
1456C22—1182no—
1457C22—1181no—
1458C22—1184no—
1459C22—1182no—
1460C22—2368no—
1461C22—2364no—
1462C22—2368no—
1463C22—2364no—
1464C222−1+4×D5914yes—
1465C22C25×D5911yescharacteristic
1466C4—21no—
1467C4—22no—
1468C4—22no—
1469C4—28no—
1470C4—28no—
1471C4—24no—
1472C4—592no—
1473C4—1181no—
1474C4—1182no—
1475C4—1182no—
1476C4—1188no—
1477C4—1188no—
1478C4—1184no—
1479C4H(5,𝔽2)×D5912yes—
1480C2—24no—
1481C2—41no—
1482C2—42no—
1483C2—594no—
1484C2—1184no—
1485C2—2361no—
1486C2—2362no—
1487C2C2×H(5,𝔽2)×D5911yescharacteristic
1488C2C2×2−1+4×D5912yes—
subgroupG/H
center, FrattiniC22C25×D59
commutator, socle, cosocleC22×C59C26
FittingC59×#3538C2
prime radical#525×D59C2
hypercenter#3538D59
hypocenterC59C2×#3538
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #3538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21438345C2semidirect
2. #21438344C2semidirect
3. #21438343C2semidirect
4. #21438342C2semidirect
5. #21438341C2semidirect
6. #21438340C2semidirect
7. #21438339C2semidirect
8. #21438338C2semidirect
9. #21438337C2semidirect
10. #21438336C2semidirect
11. #563×D59C2semidirect
12. #552×D59C2semidirect
13. #551×D59C2semidirect
14. D4×Q8×D59C2semidirect
15. #544×D59C2semidirect
16. #541×D59C2semidirect
17. #539×D59C2semidirect
18. #536×D59C2semidirect
20. C2×C22⋊Q8×D59C2semidirect
21. C59×#3538C2semidirect
24. C22×Q8×D59C22semidirect
26. #16838156C22semidirect
27. #16838155C22semidirect
28. #16838155C22semidirect
29. #16838154C22semidirect
30. #16838154C22semidirect
31. #16838153C22semidirect
32. #16838153C22semidirect
33. #16838152C22semidirect
34. #16838151C22semidirect
35. #16838094C22semidirect
36. #16838093C22semidirect
37. #16838092C22semidirect
38. #16838091C22semidirect
39. #16838090C22semidirect
40. #16838089C22semidirect
41. #16838088C22semidirect
42. #16838087C22semidirect
43. #16838086C22semidirect
44. #16838085C22semidirect
45. #16838084C22semidirect
46. #16838083C22semidirect
47. #16838082C22semidirect
48. #16838081C22semidirect
49. #16838080C22semidirect
50. #16838079C22semidirect
51. #16838078C22semidirect
52. #16838077C22semidirect
53. #16838076C22semidirect
54. #16838075C22semidirect
55. Q8×D236C22semidirect
56. D4×Dic118C22semidirect
57. D4×Dic118C22semidirect
58. #16838067C22semidirect
59. #16838067C22semidirect
60. Q8×C22⋊D59C22semidirect
61. Q8×C22⋊D59C22semidirect
62. #16838065C22semidirect
63. #16838065C22semidirect
64. #16838065C22semidirect
65. #16838065C22semidirect
66. #16838033C22semidirect
67. #16838032C22semidirect
68. #16838032C22semidirect
69. #16838031C22semidirect
70. #16838031C22semidirect
71. #16838031C22semidirect
72. #16838030C22semidirect
73. #16838029C22semidirect
74. #16838029C22semidirect
75. #16838015C22semidirect
76. #16838014C22semidirect
77. #16838013C22semidirect
78. #16838012C22semidirect
79. #16838011C22semidirect
80. #16838010C22semidirect
81. #16838009C22semidirect
82. #16838001C22semidirect
83. #16838000C22semidirect
84. #16837999C22semidirect
85. #16837998C22semidirect
86. #16837997C22semidirect
87. #16837996C22semidirect
88. #16837995C22semidirect
89. #16837994C22semidirect
90. #16837993C22semidirect
91. #16837978C22semidirect
92. #16837977C22semidirect
93. #16837976C22semidirect
94. #16837975C22semidirect
95. #16837975C22semidirect
96. #16837974C22semidirect
97. #16837974C22semidirect
98. #16837973C22semidirect
99. #16837972C22semidirect
100. C4⋊Q8×D59C22semidirect
101. C4⋊Q8×D59C22semidirect
102. C4⋊Q8×D59C22semidirect
104. #126×D59C22semidirect
105. #125×D59C22semidirect
106. #125×D59C22semidirect
107. #125×D59C22semidirect
120. #123×D59C22semidirect
121. C2×#14273707C22semidirect
122. C2×#14273706C22semidirect
123. C2×#14273705C22semidirect
124. C2×#14273704C22semidirect
125. C2×#14273703C22semidirect
132. C22⋊Q8×D59C22semidirect
133. C22⋊Q8×D59C22semidirect
134. C22⋊Q8×D59C22semidirect
135. C22⋊Q8×D59C22semidirect
136. C22⋊Q8×D59C22semidirect
137. C22⋊Q8×D59C22semidirect
140. C4×Q8×D59C22semidirect
145. #117×D59C22semidirect
149. C59×#563C22semidirect
150. C59×#552C22semidirect
151. C59×#551C22semidirect
152. D4×Q8×C59C22semidirect
153. C59×#544C22semidirect
154. C59×#541C22semidirect
155. C59×#539C22semidirect
156. C59×#536C22semidirect
158. C2×C22⋊Q8×C59C22semidirect
168. C22×Dic118C23semidirect
169. C22×Dic118C23semidirect
178. C2×Q8×D59C23semidirect
179. C2×Q8×D59C23semidirect
197. #14273727C23semidirect
198. #14273727C23semidirect
199. #14273727C23semidirect
200. #14273726C23semidirect
201. #14273726C23semidirect
202. #14273726C23semidirect
203. #14273726C23semidirect
204. #14273726C23semidirect
205. #14273726C23semidirect
206. #14273726C23semidirect
207. #14273725C23semidirect
208. #14273725C23semidirect
209. #14273725C23semidirect
210. #14273725C23semidirect
211. #14273725C23semidirect
215. #14273722C23semidirect
216. #14273722C23semidirect
217. #14273722C23semidirect
219. #14273721C23semidirect
223. #14273720C23semidirect
224. #14273720C23semidirect
225. #14273720C23semidirect
226. #14273719C23semidirect
227. #14273719C23semidirect
228. #14273719C23semidirect
229. #14273718C23semidirect
230. #14273718C23semidirect
231. #14273718C23semidirect
232. #14273718C23semidirect
233. #14273718C23semidirect
234. #14273717C23semidirect
235. #14273717C23semidirect
236. #14273717C23semidirect
237. #14273717C23semidirect
238. #14273717C23semidirect
239. #14273717C23semidirect
240. #14273717C23semidirect
241. #14273717C23semidirect
242. #14273717C23semidirect
252. #14273712C23semidirect
256. #14273711C23semidirect
260. #14273710C23semidirect
265. #14273709C23semidirect
269. #14273708C23semidirect
276. #14273707C23semidirect
277. #14273707C23semidirect
284. #14273706C23semidirect
285. #14273706C23semidirect
293. #14273705C23semidirect
294. #14273705C23semidirect
295. #14273705C23semidirect
303. #14273704C23semidirect
304. #14273704C23semidirect
305. #14273704C23semidirect
312. #14273703C23semidirect
313. #14273703C23semidirect
324. Q8×Dic59C23semidirect
325. C4×Dic118C23semidirect
326. C4×Dic118C23semidirect
327. #14273692C23semidirect
328. #14273692C23semidirect
345. #14273686C23semidirect
349. #14273685C23semidirect
353. #14273684C23semidirect
357. #14273683C23semidirect
394. C22×Q8×C59C23semidirect
396. C4⋊Q8×C59C23semidirect
397. C4⋊Q8×C59C23semidirect
398. C4⋊Q8×C59C23semidirect
400. #126×C59C23semidirect
401. #125×C59C23semidirect
402. #125×C59C23semidirect
403. #125×C59C23semidirect
408. #123×C59C23semidirect
415. C22⋊Q8×C59C23semidirect
416. C22⋊Q8×C59C23semidirect
419. C4×Q8×C59C23semidirect
424. #117×C59C23semidirect
746. #3538D59direct (N × H)
765. D59#3538direct (N × H)
779. #563C2×D59semidirect
791. #552C2×D59semidirect
801. #551C2×D59semidirect
813. D4×Q8C2×D59semidirect
823. #544C2×D59semidirect
831. #541C2×D59semidirect
841. #539C2×D59semidirect
851. #536C2×D59semidirect
891. C2×C22⋊Q8C2×D59semidirect
903. C59C2×#3538semidirect
927. C22×Q8C22×D59semidirect
961. C4⋊Q8C22×D59semidirect
962. C4⋊Q8C22×D59semidirect
963. C4⋊Q8C22×D59semidirect
979. #126C22×D59semidirect
997. #125C22×D59semidirect
998. #125C22×D59semidirect
999. #125C22×D59semidirect
1031. #123C22×D59semidirect
1082. C22⋊Q8C22×D59semidirect
1083. C22⋊Q8C22×D59semidirect
1101. C4×Q8C22×D59semidirect
1135. #117C22×D59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214383452
#214383442
#214383432
#214383422
#214383412
#214383402
#214383392
#214383382
#214383372
#214383362
#563×D592
#552×D592
#551×D592
D4×Q8×D592
#544×D592
#541×D592
#539×D592
#536×D592
#525×D592
C2×C22⋊Q8×D592
C59×#35382
C2×#353859