Finite Group Databasebeta

← C2×#21436102 #29465391

Subgroups — C2×#21436102 #29465391

Order 15104.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838098C211yesmaximal, characteristic, complemented
2#21436102C2116yesmaximal, direct product factor
3C2×#16837766C211yesmaximal, characteristic, complemented
4C2×#16837723C211yesmaximal, characteristic, complemented
5C2×#16837713C211yesmaximal, characteristic, complemented
6C2×#16837709C211yesmaximal, characteristic, complemented
7C2×#16837653C211yesmaximal, characteristic, complemented
8C2×#16837636C211yesmaximal, characteristic, complemented
9C2×#16837594C211yesmaximal, characteristic, complemented
10C2×#16837547C211yesmaximal, characteristic, complemented
11C2×#16837547C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837403C211yesmaximal, characteristic, complemented
15C2×#16837398C211yesmaximal, characteristic, complemented
16C2×C59×#550C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21C23×C59⋊C8C2211yescharacteristic
22#16838098—24no—
23#16838098C2218yescomplemented
24C2×#14273722—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273709—21no—
27C2×#14273701C2211yescharacteristic
28C2×#14273701C2211yescharacteristic
29C2×#14273699—21no—
30C2×C4×D236C2211yescharacteristic
31C2×(C22⋊D59)⋊C4—21no—
32C2×#14273686C2211yescharacteristic
33C22×C4⋊Dic59C2211yescharacteristic
34#16837766C2218yescomplemented
35#16837723C2218yescomplemented
36#16837713C2218yescomplemented
37#16837709C2218yescomplemented
38#16837653C2218yescomplemented
39#16837636C2218yescomplemented
40#16837594C2218yescomplemented
41#16837547C2218yescomplemented
42#16837547C2218yescomplemented
43#16837500C2218yescomplemented
44#16837474C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837403C2218yescomplemented
50#16837398C2218yescomplemented
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273648C2211yescharacteristic
55C2×#14273648C2211yescharacteristic
56C2×#14273648C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C22×#41×C59C2211yescharacteristic
65C22×#41×C59C2211yescharacteristic
66C59×#550—24no—
67C59×#550C2218yescomplemented
68C2×#127×C59—21no—
69C2×#127×C59C2211yescharacteristic
70C2×#121×C59—21no—
71C2×#121×C59—21no—
72C2×#121×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59—21no—
76C2×C4×D4×C59C2211yescharacteristic
77C22×D236C2311yescharacteristic
78C22×C22⋊D59—21no—
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81C22×C4×D59—21no—
82C2×#11745671—24no—
83C2×#11745671C2314yes—
84C2×#11745669—42no—
85C2×#11745669—42no—
86C2×#11745669C2314yes—
87C2×#11745669C2314yes—
88C2×#11745664—42no—
89C2×#11745664C2314yes—
90C22×C59⋊C8—42no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2314yes—
96#14273722—28no—
97#14273719—22no—
98#14273719C2314yes—
99#14273709—28no—
100#14273701—22no—
101#14273701—22no—
102#14273701C2314yes—
103#14273701C2314yes—
104#14273699—28no—
105C4×D236—22no—
106C4×D236C2314yes—
107(C22⋊D59)⋊C4—28no—
108#14273686—22no—
109#14273686C2314yes—
110C2×C4⋊Dic59—21no—
111C2×C4⋊Dic59—22no—
112C2×C4⋊Dic59C2311yescharacteristic
113C2×C4⋊Dic59C2311yescharacteristic
114C2×C4⋊Dic59C2311yescharacteristic
115C2×C4⋊Dic59C2314yes—
116C2×Dic59⋊C4—21no—
117C2×Dic59⋊C4—21no—
118C2×C22⋊Dic59—21no—
119C2×(C2×D59)⋊C4—21no—
120C2×(C2×D59)⋊C4—21no—
121C2×(C2×D59)⋊C4—21no—
122C2×C4×Dic59—21no—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273658C2314yes—
126C4⋊(C59⋊C8)C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273648C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273648C2314yes—
136#14273647C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C2×#41×C59—22no—
141C2×#41×C59—22no—
142C2×#41×C59—24no—
143C2×#41×C59—24no—
144C2×#41×C59—42no—
145C2×#41×C59—42no—
146C2×#41×C59C2314yes—
147C2×#41×C59C2314yes—
148C22×Q8×C59C2311yescharacteristic
149C22×D4×C59—21no—
150C22×D4×C59—21no—
151C22×D4×C59—21no—
152C22×D4×C59—21no—
153C22×D4×C59—21no—
154C22×D4×C59—21no—
155C22×D4×C59D411yescharacteristic
156C22×D4×C59C2311yescharacteristic
157C22×D4×C59C2311yescharacteristic
158C23×C4×C59—21no—
159C23×C4×C59—21no—
160C23×C4×C59C2311yescharacteristic
161C23×C4×C59C2311yescharacteristic
162#127×C59—28no—
163#127×C59—22no—
164#127×C59C2314yes—
165#121×C59—22no—
166#121×C59—22no—
167#121×C59—28no—
168#121×C59—28no—
169#121×C59C2314yes—
170#121×C59C2314yes—
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yes—
173C4×D4×C59—28no—
174C4×D4×C59D414yes—
175C4×D4×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C42×C59—21no—
184C2×C42×C59C2311yescharacteristic
185C24×C59—21no—
186C24×C59—21no—
187C24×C59C2×D411yescharacteristic
188C24×C59C2×D411yescharacteristic
189C23×D59—21no—
190#41×C59—28no—
191#41×C59—28no—
192#41×C59—44no—
193#41×C59—44no—
194#41×C59—48no—
195#41×C59—48no—
196C2×Q8×C59—21no—
197C2×Q8×C59—22no—
198C2×Q8×C59#4114yes—
199C2×Q8×C59C2412yes—
200C2×D4×C59—24no—
201C2×D4×C59—24no—
202C2×D4×C59—24no—
203C2×D4×C59—24no—
204C2×D4×C59—24no—
205C2×D4×C59—21no—
206C2×D4×C59—21no—
207C2×D4×C59—24no—
208C2×D4×C59—22no—
209C2×D4×C59—22no—
210C2×D4×C59—22no—
211C2×D4×C59—22no—
212C2×D4×C59—42no—
213C2×D4×C59—44no—
214C2×D4×C59—44no—
215C2×D4×C59—44no—
216C2×D4×C59—82no—
217C2×D4×C59—82no—
218C2×D4×C59—82no—
219C2×D4×C59C2×D414yes—
220C2×D4×C59C2412yes—
221C2×D4×C59C2412yes—
222C22×C4×C59—21no—
223C22×C4×C59—22no—
224C22×C4×C59—22no—
225C22×C4×C59—22no—
226C22×C4×C59—22no—
227C22×C4×C59—21no—
228C22×C4×C59—24no—
229C22×C4×C59—24no—
230C22×C4×C59—44no—
231C22×C4×C59—44no—
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59C2×D411yescharacteristic
234C22×C4×C59C2×D411yescharacteristic
235C22×C4×C59C2×D411yescharacteristic
236C22×C4×C59C2×D412yes—
237C22×C4×C59C2×D412yes—
238C22×C4×C59C2412yes—
239C22×C4×C59C2412yes—
240C22×C4×C59C2411yescharacteristic
241C2×C22⋊D59—24no—
242C2×C22⋊D59—24no—
243C2×C22⋊D59—44no—
244C2×C22⋊D59—82no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—24no—
249C22×Dic59—82no—
250C2×D236—22no—
251C2×D236—22no—
252C2×D236—21no—
253C2×D236C2412yes—
254C2×C4×D59—24no—
255C2×C4×D59—82no—
256C4⋊C4×C59—24no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C2×D414yes—
259C4⋊C4×C59C2412yes—
260C22⋊C4×C59—24no—
261C22⋊C4×C59—24no—
262C22⋊C4×C59C2×D414yes—
263C22⋊C4×C59C2×D414yes—
264C42×C59—24no—
265C42×C59C2×D412yes—
266C42×C59C2412yes—
267C22⋊Dic59—24no—
268#11745671—28no—
269#11745669—44no—
270#11745669—44no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274C4⋊Dic59—21no—
275C4⋊Dic59—21no—
276C4⋊Dic59—24no—
277C4⋊Dic59—21no—
278C4⋊Dic59C2412yes—
279C4⋊Dic59C2412yes—
280C4⋊Dic59C2412yes—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283C4×Dic59—24no—
284#11745664—44no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8—44no—
290C2×C59⋊C8C2412yes—
291C2×C59⋊C8C2412yes—
292C2×C59⋊C8C2412yes—
293C2×C59⋊C8C2412yes—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
301C23×C59—22no—
302C23×C59—42no—
303C23×C59—42no—
304C23×C59—42no—
305C23×C59—42no—
306C23×C59—42no—
307C23×C59—42no—
308C23×C59C22×D412yes—
309C23×C59C22×D412yes—
310C23×C59C22×D411yescharacteristic
311C22×D59—22no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315Q8×C59—24no—
316Q8×C59—22no—
317Q8×C59C2×#4114yes—
318D4×C59—22no—
319D4×C59—22no—
320D4×C59—22no—
321D4×C59—22no—
322D4×C59—44no—
323D4×C59—48no—
324D4×C59—48no—
325D4×C59—48no—
326D4×C59—42no—
327D4×C59—42no—
328D4×C59—84no—
329D4×C59—84no—
330D4×C59—84no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—24no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—24no—
338C2×C4×C59—24no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—48no—
345C2×C4×C59—48no—
346C2×C4×C59—42no—
347C2×C4×C59C22×D412yes—
348C2×C4×C59C22×D412yes—
349C2×C4×C59C22×D412yes—
350C2×C4×C59C22×D412yes—
351C2×C4×C59C22×D411yescharacteristic
352C2×C4×C59C2×#4112yes—
353C2×C4×C59H(5,𝔽2)12yes—
354C2×C4×C59C2511yescharacteristic
355C22⋊D59—48no—
356C22⋊D59—84no—
357C2×Dic59—22no—
358C2×Dic59—22no—
359C2×Dic59—22no—
360C2×Dic59—42no—
361C2×Dic59—42no—
362C2×Dic59—42no—
363C2×Dic59—84no—
364D236—22no—
365D236—22no—
366D236—42no—
367C4×D59—84no—
368C59⋊C8—22no—
369C59⋊C8—22no—
370C59⋊C8—22no—
371C59⋊C8—22no—
372C2×#3309—591nomaximal, Sylow
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—44no—
380C22×C59—44no—
381C22×C59—42no—
382C22×C59—42no—
383C22×C59—42no—
384C22×C59—42no—
385C22×C59—42no—
386C22×C59—42no—
387C22×C59—84no—
388C22×C59—84no—
389C22×C59#54612yes—
390C22×C59#57512yes—
391C22×C59#57612yes—
392C22×C59C23×D411yescharacteristic
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—84no—
397C4×C59—22no—
398C4×C59—22no—
399C4×C59—24no—
400C4×C59—22no—
401C4×C59—22no—
402C4×C59—42no—
403C4×C59#54612yes—
404C4×C59C22×#4111yescharacteristic
405C4×C59C2×H(5,𝔽2)11yescharacteristic
406Dic59—42no—
407Dic59—42no—
408Dic59—42no—
409C2×#553—591no—
410C2×#550D5911yescharacteristic, complemented
411#3309—5916no—
412C2×#490—591no—
413C2×#482—591no—
414C2×#480—591no—
415C2×#479—591no—
416C2×#469—591no—
417C2×#466—591no—
418C2×#459—591no—
419C2×#449—591no—
420C2×#449—591no—
421C2×#440—591no—
422C2×#435—591no—
423C2×#417—591no—
424C2×#416—591no—
425C2×C59—42no—
426C2×C59—42no—
427C2×C59—82no—
428C2×C59—82no—
429C2×C59#330914yescomplemented
430C2×C59C2×#54611yescharacteristic
431C2×C59C2×#57511yescharacteristic
432C2×C59C2×#57611yescharacteristic
433D59—82no—
434C22×#41C2×D5911yescharacteristic
435C22×#41C2×D5911yescharacteristic
436C22×SD16—591no—
437C22×D8—591no—
438C22×D8—591no—
439C22×M16—591no—
440C23×C8—591no—
441#553—598no—
442#553—1184no—
443#550—24no—
444#550C2×D5918yescomplemented
445C2×#127—21no—
446C2×#127C2×D5911yescharacteristic
447C2×#126—1181no—
448C2×#125—591no—
449C2×#123—1181no—
450C2×#121—21no—
451C2×#121—21no—
452C2×#121—591no—
453C2×#121—591no—
454C2×#121—1181no—
455C2×#121C2×D5911yescharacteristic
456C2×#121C2×D5911yescharacteristic
457C2×C4×Q8C2×D5911yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4—591no—
460C2×C4×D4—1181no—
461C2×C4×D4C2×D5911yescharacteristic
462C2×#117—591no—
463C22×C4⋊C4—591no—
464#490—598no—
465#482—598no—
466#480—598no—
467#479—598no—
468#469—598no—
469#466—598no—
470#459—598no—
471#449—598no—
472#449—598no—
473#440—598no—
474#435—598no—
475C2×#107—591no—
476C2×#107—591no—
477C2×#106—591no—
478C2×C4⋊C8—591no—
479#417—598no—
480#416—598no—
481C2×#103—591no—
482C2×#103—591no—
483C2×#103—591no—
484C2×#102—591no—
485C2×#102—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×C22⋊C8—591no—
492C2×C22⋊C8—591no—
493C2×#97—591no—
494C59C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—24no—
498C2×#41—24no—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41C22×D5914yes—
502C2×#41C22×D5914yes—
503C22×Q8C22×D5911yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—591no—
511C22×D4—1181no—
512C22×D4—1181no—
513C22×D4C22⋊D5911yescharacteristic
514C22×D4C22×D5911yescharacteristic
515C22×D4C22×D5911yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—1181no—
519C23×C4—1181no—
520C23×C4C22×D5911yescharacteristic
521C23×C4C22×D5911yescharacteristic
522C2×SD16—594no—
523C2×SD16—1184no—
524C2×D8—594no—
525C2×D8—594no—
526C2×D8—2362no—
527C2×D8—2362no—
528C2×M16—594no—
529C2×M16—2362no—
530C22×C8—591no—
531C22×C8—591no—
532C22×C8—591no—
533C22×C8—591no—
534C22×C8—594no—
535C22×C8—2362no—
536#127—28no—
537#127—22no—
538#127C22×D5914yes—
539#126—1188no—
540#125—594no—
541#125—1182no—
542#123—1188no—
543#121—22no—
544#121—22no—
545#121—28no—
546#121—28no—
547#121—594no—
548#121—594no—
549#121—1188no—
550#121—1182no—
551#121—1182no—
552#121C22×D5914yes—
553#121C22×D5914yes—
554C4×Q8—22no—
555C4×Q8C22×D5914yes—
556C4×D4—28no—
557C4×D4—594no—
558C4×D4—1188no—
559C4×D4—1182no—
560C4×D4C22⋊D5914yes—
561C4×D4C22×D5914yes—
562#117—594no—
563#117—1182no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—591no—
566C2×C4⋊C4—591no—
567C2×C4⋊C4—594no—
568C2×C4⋊C4—591no—
569C2×C4⋊C4—1181no—
570C2×C4⋊C4—1182no—
571C2×C4⋊C4—1181no—
572C2×C4⋊C4—1181no—
573C2×C4⋊C4C22⋊D5911yescharacteristic
574C2×C4⋊C4C22×D5911yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—1181no—
578C2×C22⋊C4—1181no—
579C2×C22⋊C4—1181no—
580C2×C22⋊C4—1181no—
581C2×C22⋊C4C22⋊D5911yescharacteristic
582C2×C22⋊C4C22⋊D5911yescharacteristic
583C2×C42—21no—
584C2×C42—1181no—
585C2×C42C22×D5911yescharacteristic
586#107—594no—
587#107—594no—
588#106—594no—
589C4⋊C8—594no—
590#103—594no—
591#103—594no—
592#103—594no—
593#102—594no—
594#102—594no—
595#102—594no—
596#102—594no—
597#102—594no—
598#102—594no—
599#102—594no—
600C22⋊C8—594no—
601C22⋊C8—594no—
602#97—594no—
603C24—21no—
604C24—21no—
605C24—1181no—
606C24C2×C22⋊D5911yescharacteristic
607C24C2×C22⋊D5911yescharacteristic
608#41—28no—
609#41—28no—
610#41—44no—
611#41—44no—
612#41—48no—
613#41—48no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1174568714yes—
617C2×Q8C23×D5912yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—24no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—82no—
635C2×D4—82no—
636C2×D4—82no—
637C2×D4—592no—
638C2×D4—1184no—
639C2×D4—1184no—
640C2×D4—1181no—
641C2×D4—1182no—
642C2×D4—1182no—
643C2×D4—4722no—
644C2×D4—2364no—
645C2×D4C2×C22⋊D5914yes—
646C2×D4C23×D5912yes—
647C2×D4C23×D5912yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—1184no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4—1184no—
663C22×C4—4722no—
664C22×C4—4722no—
665C22×C4C2×C22⋊D5912yes—
666C22×C4C2×C22⋊D5912yes—
667C22×C4C2×C22⋊D5911yescharacteristic
668C22×C4C2×C22⋊D5911yescharacteristic
669C22×C4C2×C22⋊D5911yescharacteristic
670C22×C4C2×C22⋊D5911yescharacteristic
671C22×C4C23×D5912yes—
672C22×C4C23×D5912yes—
673C22×C4C23×D5911yescharacteristic
674SD16—1188no—
675D8—2364no—
676D8—2364no—
677M16—2364no—
678C2×C8—592no—
679C2×C8—592no—
680C2×C8—592no—
681C2×C8—592no—
682C2×C8—1182no—
683C2×C8—1182no—
684C2×C8—1182no—
685C2×C8—1182no—
686C2×C8—2364no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—592no—
690C4⋊C4—592no—
691C4⋊C4—592no—
692C4⋊C4—1181no—
693C4⋊C4—1181no—
694C4⋊C4—1184no—
695C4⋊C4—1181no—
696C4⋊C4—1184no—
697C4⋊C4—1184no—
698C4⋊C4C2×C22⋊D5914yes—
699C4⋊C4C23×D5912yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—1184no—
703C22⋊C4—1184no—
704C22⋊C4—1184no—
705C22⋊C4—1184no—
706C22⋊C4C2×C22⋊D5914yes—
707C22⋊C4C2×C22⋊D5914yes—
708C42—24no—
709C42—1184no—
710C42C2×C22⋊D5912yes—
711C42C23×D5912yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—1182no—
727C23—2362no—
728C23—2362no—
729C23—2362no—
730C23C22×C22⋊D5912yes—
731C23C22×C22⋊D5912yes—
732C23C22×C22⋊D5911yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1174568714yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—44no—
741D4—48no—
742D4—48no—
743D4—48no—
744D4—42no—
745D4—42no—
746D4—84no—
747D4—84no—
748D4—84no—
749D4—1182no—
750D4—1182no—
751D4—4724no—
752D4—2368no—
753D4—2362no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—4724no—
774C2×C4—4724no—
775C2×C4—2362no—
776C2×C4—2362no—
777C2×C4—2362no—
778C2×C4C22×C22⋊D5912yes—
779C2×C4C22×C22⋊D5912yes—
780C2×C4C22×C22⋊D5912yes—
781C2×C4C22×C22⋊D5912yes—
782C2×C4C22×C22⋊D5911yescharacteristic
783C2×C4C2×#1174568712yes—
784C2×C4#1427377212yes—
785C2×C4C24×D5911yescharacteristic
786C8—1182no—
787C8—1182no—
788C8—1182no—
789C8—1182no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—84no—
806C22—4724no—
807C22—2362no—
808C22—2362no—
809C22—2362no—
810C22#1683804612yes—
811C22#1683820012yes—
812C22#1683820512yes—
813C22C23×C22⋊D5911yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—2362no—
821C4—2362no—
822C4—2362no—
823C4#1683804612yes—
824C4C22×#1174568711yescharacteristic
825C4C2×#1427377211yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—82no—
830C2—4722no—
831C2#2143610214yesdirect product factor
832C2C2×#1683804611yescharacteristic
833C2C2×#1683820011yescharacteristic
834C2C2×#1683820511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#550C2
socleC23×C59C22×D4
hypercenterC2×#550D59
hypocenterC59C2×#3309
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16838098C2semidirect
2. #21436102C2direct (N × H)
3. C2×#16837766C2semidirect
4. C2×#16837723C2semidirect
5. C2×#16837713C2semidirect
6. C2×#16837709C2semidirect
7. C2×#16837653C2semidirect
8. C2×#16837636C2semidirect
9. C2×#16837594C2semidirect
10. C2×#16837547C2semidirect
11. C2×#16837547C2semidirect
12. C2×#16837500C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837403C2semidirect
15. C2×#16837398C2semidirect
16. C2×C59×#550C2semidirect
23. #16838098C22semidirect
34. #16837766C22semidirect
35. #16837723C22semidirect
36. #16837713C22semidirect
37. #16837709C22semidirect
38. #16837653C22semidirect
39. #16837636C22semidirect
40. #16837594C22semidirect
41. #16837547C22semidirect
42. #16837547C22semidirect
43. #16837500C22semidirect
44. #16837474C22semidirect
49. #16837403C22semidirect
50. #16837398C22semidirect
67. C59×#550C22semidirect
410. C2×#550D59semidirect
429. C2×C59#3309semidirect
444. #550C2×D59semidirect
494. C59C2×#3309semidirect
831. C2#21436102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380982
#214361022
C2×#168377662
C2×#168377232
C2×#168377132
C2×#168377092
C2×#168376532
C2×#168376362
C2×#168375942
C2×#168375472
C2×#168375002
C2×#168374742
C2×#168374032
C2×#168373982
C2×C59×#5502
C2×#330959