Finite Group Databasebeta

← C2×#21436575 #29467262

Subgroups — C2×#21436575 #29467262

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838098C211yesmaximal, characteristic
2#21436575C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837735C211yesmaximal, characteristic, complemented
5C2×#16837720C211yesmaximal, characteristic, complemented
6C2×#16837740C211yesmaximal, characteristic, complemented
7C2×#16837715C211yesmaximal, characteristic, complemented
8C2×#16837709C211yesmaximal, characteristic, complemented
9C2×#16837679C211yesmaximal, characteristic, complemented
10C2×#16837650C211yesmaximal, characteristic, complemented
11C2×#16837633C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837442C211yesmaximal, characteristic, complemented
15C22×#14273660C211yesmaximal, characteristic, complemented
16C2×C59×#554C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16838098—24no—
21#16838098C2218yes—
22C2×#14273722—21no—
23C2×#14273719C2211yescharacteristic
24C2×#14273709—21no—
25C2×#14273701C2211yescharacteristic
26C2×#14273701C2211yescharacteristic
27C2×#14273699—21no—
28C2×C4×D236C2211yescharacteristic
29C2×(C22⋊D59)⋊C4—21no—
30C2×#14273686C2211yescharacteristic
31C22×C4⋊Dic59C2211yescharacteristic
32#16837808C2218yescomplemented
33#16837740C2218yescomplemented
34#16837735C2218yescomplemented
35#16837720C2218yescomplemented
36#16837715C2218yescomplemented
37#16837709C2218yescomplemented
38#16837679C2218yescomplemented
39#16837650C2218yescomplemented
40#16837633C2218yescomplemented
41#16837500C2218yescomplemented
42#16837474C2218yescomplemented
43#16837442C2218yescomplemented
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273660C2211yescharacteristic
48C2×#14273660C2211yescharacteristic
49C2×#14273660C2211yescharacteristic
50C2×#14273660C2218yescomplemented
51C2×#14273658C2211yescharacteristic
52C2×#14273658C2211yescharacteristic
53C2×#14273658C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#554—24no—
65C59×#554C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#125×C59—21no—
68C2×C22⋊Q8×C59—21no—
69C2×C22⋊Q8×C59—21no—
70C2×C22⋊Q8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×D4×C59—21no—
74C2×C4×D4×C59C2211yescharacteristic
75C22×C4⋊C4×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×D236C2311yescharacteristic
78C22×C22⋊D59—21no—
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81C22×C4×D59—21no—
82C2×#11745671—24no—
83C2×#11745671C2314yes—
84C2×#11745664—24no—
85C2×#11745664C2314yes—
86C22×C59⋊C8—24no—
87C22×C59⋊C8C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92#14273722—28no—
93#14273719—22no—
94#14273719C2314yes—
95#14273709—28no—
96#14273701—22no—
97#14273701—22no—
98#14273701C2314yes—
99#14273701C2314yes—
100#14273699—28no—
101C4×D236—22no—
102C4×D236C2314yes—
103(C22⋊D59)⋊C4—28no—
104#14273686—22no—
105#14273686C2314yes—
106C2×C4⋊Dic59—21no—
107C2×C4⋊Dic59—22no—
108C2×C4⋊Dic59C2311yescharacteristic
109C2×C4⋊Dic59C2311yescharacteristic
110C2×C4⋊Dic59C2311yescharacteristic
111C2×C4⋊Dic59C2314yes—
112C2×Dic59⋊C4—21no—
113C2×Dic59⋊C4—21no—
114C2×C22⋊Dic59—21no—
115C2×(C2×D59)⋊C4—21no—
116C2×(C2×D59)⋊C4—21no—
117C2×(C2×D59)⋊C4—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273660C2314yes—
121#14273660C2314yes—
122#14273660C2314yes—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273647C2314yes—
133#14273647C2314yes—
134#14273647C2314yes—
135C22⋊(C59⋊C8)C2314yes—
136C22⋊(C59⋊C8)C2314yes—
137#14273638C2314yes—
138C22×Q8×C59—21no—
139C22×Q8×C59C2311yescharacteristic
140C22×D4×C59D411yescharacteristic
141C23×C4×C59—21no—
142C23×C4×C59—21no—
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C4⋊Q8×C59—22no—
146C4⋊Q8×C59C2314yes—
147#125×C59—28no—
148C22⋊Q8×C59—22no—
149C22⋊Q8×C59—22no—
150C22⋊Q8×C59—28no—
151C22⋊Q8×C59—28no—
152C22⋊Q8×C59C2314yes—
153C22⋊Q8×C59C2314yes—
154C4×Q8×C59—22no—
155C4×Q8×C59C2314yes—
156C4×D4×C59—28no—
157C4×D4×C59D414yes—
158C4×D4×C59C2314yes—
159C2×C4⋊C4×C59—21no—
160C2×C4⋊C4×C59—21no—
161C2×C4⋊C4×C59—22no—
162C2×C4⋊C4×C59—22no—
163C2×C4⋊C4×C59—21no—
164C2×C4⋊C4×C59—21no—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2314yes—
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59D411yescharacteristic
176C2×C22⋊C4×C59D411yescharacteristic
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C24×C59C2×D411yescharacteristic
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—24no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59—82no—
187C2×Q8×C59C2412yes—
188C2×D4×C59—24no—
189C2×D4×C59C2×D414yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—24no—
199C22×C4×C59—24no—
200C22×C4×C59—82no—
201C22×C4×C59—82no—
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D412yes—
207C22×C4×C59C2×D412yes—
208C22×C4×C59C2412yes—
209C22×C4×C59C2412yes—
210C22×C4×C59C2411yescharacteristic
211C2×C22⋊D59—24no—
212C2×C22⋊D59—24no—
213C2×C22⋊D59—44no—
214C2×C22⋊D59—82no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—24no—
219C22×Dic59—82no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—21no—
223C2×D236C2412yes—
224C2×C4×D59—24no—
225C2×C4×D59—82no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—24no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—24no—
235C4⋊C4×C59C2×D414yes—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊C4×C59C2×D414yes—
242C22⋊C4×C59C2×D414yes—
243C42×C59—24no—
244C42×C59C2×D412yes—
245C42×C59C2412yes—
246C22⋊Dic59—24no—
247#11745671—28no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—21no—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260C4×Dic59—24no—
261#11745664—28no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—28no—
266C2×C59⋊C8#4114yes—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59#13714yes—
277C23×C59C22×D412yes—
278C23×C59C22×D412yes—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—42no—
282C22×D59—42no—
283C22×D59—42no—
284Q8×C59—22no—
285Q8×C59—22no—
286Q8×C59—42no—
287Q8×C59—84no—
288D4×C59—28no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—24no—
294C2×C4×C59—24no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—84no—
308C2×C4×C59—84no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D412yes—
311C2×C4×C59C22×D412yes—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C592−1+412yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—48no—
318C22⋊D59—84no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—84no—
326D236—22no—
327D236—22no—
328D236—42no—
329C4×D59—84no—
330C59⋊C8—22no—
331C59⋊C8—22no—
332C59⋊C8—22no—
333C59⋊C8C2×#4114yes—
334C2×#3346—591nomaximal, Sylow
335C22×C59—28no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—44no—
342C22×C59#54712yes—
343C22×C59C2×#13714yes—
344C22×C59C2×#13712yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—84no—
351C4×C59—22no—
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59#54712yes—
360C4×C59C22×#4111yescharacteristic
361C4×C59C2×2−1+411yescharacteristic
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#554D5911yescharacteristic, complemented
366C2×#553—591no—
367#3346—5916no—
368C2×#501—591no—
369C2×#484—591no—
370C2×#481—591no—
371C2×#485—591no—
372C2×#480—591no—
373C2×#479—591no—
374C2×#474—591no—
375C2×#468—591no—
376C2×#465—591no—
377C2×#440—591no—
378C2×#435—591no—
379C2×#428—591no—
380C22×#107—591no—
381C2×C59—24no—
382C2×C59—42no—
383C2×C59#334614yescomplemented
384C2×C59C2×#54711yescharacteristic
385C2×C59C22×#13711yescharacteristic
386C2×C59C2×#57611yescharacteristic
387D59—82no—
388C22×SD16—591no—
389C22×M16—591no—
390C23×C8—591no—
391#554—24no—
392#554C2×D5918yescomplemented
393#553—598no—
394#553—1184no—
395C2×C4⋊Q8C2×D5911yescharacteristic
396C2×#126—1181no—
397C2×#125—21no—
398C2×#125—591no—
399C2×#123—1181no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8C2×D5911yescharacteristic
403C2×C22⋊Q8C2×D5911yescharacteristic
404C2×#121—591no—
405C2×#121—591no—
406C2×#121—1181no—
407C2×C4×Q8C2×D5911yescharacteristic
408C2×C4×D4—21no—
409C2×C4×D4—591no—
410C2×C4×D4—1181no—
411C2×C4×D4C2×D5911yescharacteristic
412C2×#117—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4C2×D5911yescharacteristic
415C22×C4⋊C4C2×D5911yescharacteristic
416#501—598no—
417#485—598no—
418#484—598no—
419#481—598no—
420#480—598no—
421#479—598no—
422#474—598no—
423#468—598no—
424#465—598no—
425#440—598no—
426#435—598no—
427#428—598no—
428C2×#107—591no—
429C2×#107—591no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—598no—
433C2×#107—591no—
434C2×#107—591no—
435C2×#106—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×#102—591no—
445C2×C22⋊C8—591no—
446C2×C22⋊C8—591no—
447C2×#97—591no—
448C59C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8C22×D5911yescharacteristic
451C22×D4—591no—
452C22×D4—1181no—
453C22×D4—1181no—
454C22×D4C22⋊D5911yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1181no—
458C23×C4—1181no—
459C23×C4C22×D5911yescharacteristic
460C23×C4C22×D5911yescharacteristic
461C2×SD16—594no—
462C2×SD16—1184no—
463C2×M16—594no—
464C2×M16—1184no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—594no—
468C22×C8—591no—
469C22×C8—591no—
470C22×C8—1184no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D5914yes—
473#126—1188no—
474#125—28no—
475#125—594no—
476#125—1182no—
477#123—1188no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D5914yes—
483C22⋊Q8C22×D5914yes—
484#121—594no—
485#121—594no—
486#121—1188no—
487#121—1182no—
488#121—1182no—
489C4×Q8—22no—
490C4×Q8C22×D5914yes—
491C4×D4—28no—
492C4×D4—594no—
493C4×D4—1188no—
494C4×D4—1182no—
495C4×D4C22⋊D5914yes—
496C4×D4C22×D5914yes—
497#117—594no—
498#117—1182no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4C22⋊D5911yescharacteristic
516C2×C4⋊C4C22×D5911yescharacteristic
517C2×C4⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5914yes—
520C2×C4⋊C4C22×D5914yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4C22⋊D5911yescharacteristic
528C2×C22⋊C4C22⋊D5911yescharacteristic
529C2×C42—21no—
530C2×C42—1181no—
531C2×C42C22×D5911yescharacteristic
532#107—594no—
533#107—594no—
534#107—594no—
535#107—594no—
536#107—594no—
537#107—594no—
538#106—594no—
539#106—594no—
540#106—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#102—594no—
546#102—594no—
547#102—594no—
548C22⋊C8—594no—
549C22⋊C8—594no—
550#97—594no—
551C24—1181no—
552C24C2×C22⋊D5911yescharacteristic
553C24C2×C22⋊D5911yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D5912yes—
560C2×D4—24no—
561C2×D4—592no—
562C2×D4—1184no—
563C2×D4—1184no—
564C2×D4—1181no—
565C2×D4—1182no—
566C2×D4—1182no—
567C2×D4—4722no—
568C2×D4—2364no—
569C2×D4C2×C22⋊D5914yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—1184no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1184no—
587C22×C4—4722no—
588C22×C4—4722no—
589C22×C4C2×C22⋊D5912yes—
590C22×C4C2×C22⋊D5912yes—
591C22×C4C2×C22⋊D5911yescharacteristic
592C22×C4C2×C22⋊D5911yescharacteristic
593C22×C4C2×C22⋊D5911yescharacteristic
594C22×C4C2×C22⋊D5911yescharacteristic
595C22×C4C23×D5912yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598SD16—1188no—
599M16—1188no—
600C2×C8—594no—
601C2×C8—592no—
602C2×C8—592no—
603C2×C8—592no—
604C2×C8—592no—
605C2×C8—1188no—
606C2×C8—1182no—
607C2×C8—1182no—
608C2×C8—1182no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—592no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1184no—
624C4⋊C4—1181no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4C2×C22⋊D5914yes—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4C2×C22⋊D5914yes—
638C22⋊C4C2×C22⋊D5914yes—
639C42—24no—
640C42—1184no—
641C42C2×C22⋊D5912yes—
642C42C23×D5912yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—1182no—
649C23—2362no—
650C23—2362no—
651C23—2362no—
652C23#1427375814yes—
653C23C22×C22⋊D5912yes—
654C23C22×C22⋊D5912yes—
655C23C22×C22⋊D5911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—1182no—
662D4—1182no—
663D4—4724no—
664D4—2368no—
665D4—2362no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—4724no—
690C2×C4—4724no—
691C2×C4—2362no—
692C2×C4—2362no—
693C2×C4—2362no—
694C2×C4C22×C22⋊D5912yes—
695C2×C4C22×C22⋊D5912yes—
696C2×C4C22×C22⋊D5912yes—
697C2×C4C22×C22⋊D5912yes—
698C2×C4C22×C22⋊D5911yescharacteristic
699C2×C4#41×D5912yes—
700C2×C4#1427377412yes—
701C2×C4C24×D5911yescharacteristic
702C8—594no—
703C8—1182no—
704C8—1182no—
705C8—1182no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—4724no—
714C22—2362no—
715C22—2362no—
716C22—2362no—
717C22#1683805112yes—
718C22C2×#1427375814yes—
719C22C2×#1427375812yes—
720C22#1683820512yes—
721C22C23×C22⋊D5911yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4#1683805112yes—
734C4C2×#41×D5911yescharacteristic
735C4C2×#1427377411yescharacteristic
736C2—24no—
737C2—42no—
738C2—4722no—
739C2#2143657514yesdirect product factor
740C2C2×#1683805111yescharacteristic
741C2C22×#1427375811yescharacteristic
742C2C2×#1683820511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#554C2
socleC23×C59C22×D4
prime radicalC2×#16838098C2
hypercenterC2×#554D59
hypocenterC59C2×#3346
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #21436575C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837735C2semidirect
5. C2×#16837720C2semidirect
6. C2×#16837740C2semidirect
7. C2×#16837715C2semidirect
8. C2×#16837709C2semidirect
9. C2×#16837679C2semidirect
10. C2×#16837650C2semidirect
11. C2×#16837633C2semidirect
12. C2×#16837500C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837442C2semidirect
15. C22×#14273660C2semidirect
16. C2×C59×#554C2semidirect
32. #16837808C22semidirect
33. #16837740C22semidirect
34. #16837735C22semidirect
35. #16837720C22semidirect
36. #16837715C22semidirect
37. #16837709C22semidirect
38. #16837679C22semidirect
39. #16837650C22semidirect
40. #16837633C22semidirect
41. #16837500C22semidirect
42. #16837474C22semidirect
43. #16837442C22semidirect
50. C2×#14273660C22semidirect
65. C59×#554C22semidirect
365. C2×#554D59semidirect
383. C2×C59#3346semidirect
392. #554C2×D59semidirect
448. C59C2×#3346semidirect
739. C2#21436575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380982
#214365752
C2×#168378082
C2×#168377352
C2×#168377202
C2×#168377402
C2×#168377152
C2×#168377092
C2×#168376792
C2×#168376502
C2×#168376332
C2×#168375002
C2×#168374742
C2×#168374422
C22×#142736602
C2×C59×#5542
C2×#334659