Finite Group Databasebeta

← C2×#21436545 #29467230

Subgroups — C2×#21436545 #29467230

Order 15104.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic
2#21436545C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837737C211yesmaximal, characteristic, complemented
5C2×#16837740C211yesmaximal, characteristic, complemented
6C2×#16837732C211yesmaximal, characteristic, complemented
7C2×#16837730C211yesmaximal, characteristic, complemented
8C2×#16837709C211yesmaximal, characteristic, complemented
9C2×#16837684C211yesmaximal, characteristic, complemented
10C2×#16837658C211yesmaximal, characteristic, complemented
11C2×#16837641C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic
14C2×#16837442C211yesmaximal, characteristic, complemented
15C22×#14273658C211yesmaximal, characteristic, complemented
16C2×C59×#554C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20#16838092—24no—
21#16838092C2218yes—
22C2×#14273720—21no—
23C2×#14273719C2211yescharacteristic
24C2×#14273717—21no—
25C2×#14273708—21no—
26C2×#14273706C2211yescharacteristic
27C2×#14273706C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×#14273686C2211yescharacteristic
30C2×#14273683—21no—
31C22×C4⋊Dic59C2211yescharacteristic
32#16837808C2218yescomplemented
33#16837740C2218yescomplemented
34#16837737C2218yescomplemented
35#16837732C2218yescomplemented
36#16837730C2218yescomplemented
37#16837709C2218yescomplemented
38#16837684C2218yescomplemented
39#16837658C2218yescomplemented
40#16837641C2218yescomplemented
41#16837507C2218yescomplemented
42#16837474C2218yes—
43#16837442C2218yescomplemented
44C2×#14273660C2211yescharacteristic
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×#14273658C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×#14273658C2211yescharacteristic
51C2×#14273658C2211yescharacteristic
52C2×#14273658C2211yescharacteristic
53C2×#14273658C2218yescomplemented
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273651C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273650C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#554—24no—
65C59×#554C2218yes—
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×Dic118C2311yescharacteristic
78C23×Dic59—21no—
79C2×#11745672—24no—
80C2×#11745672C2314yes—
81C2×#11745664—24no—
82C2×#11745664C2314yes—
83C22×C59⋊C8—24no—
84C22×C59⋊C8C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89#14273720—28no—
90#14273719—22no—
91#14273719C2314yes—
92#14273717—28no—
93#14273708—28no—
94#14273706—22no—
95#14273706—22no—
96#14273706C2314yes—
97#14273706C2314yes—
98C4×Dic118—22no—
99C4×Dic118C2314yes—
100#14273686—22no—
101#14273686C2314yes—
102#14273683—28no—
103C2×C4⋊Dic59—21no—
104C2×C4⋊Dic59—22no—
105C2×C4⋊Dic59C2311yescharacteristic
106C2×C4⋊Dic59C2311yescharacteristic
107C2×C4⋊Dic59C2311yescharacteristic
108C2×C4⋊Dic59C2314yes—
109C2×Dic59⋊C4—21no—
110C2×Dic59⋊C4—21no—
111C2×Dic59⋊C4—21no—
112C2×Dic59⋊C4—21no—
113C2×Dic59⋊C4—21no—
114C2×C22⋊Dic59—21no—
115C2×C22⋊Dic59—21no—
116C2×C22⋊Dic59—21no—
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119#14273660C2314yes—
120#14273660C2314yes—
121#14273660C2314yes—
122#14273658C2314yes—
123#14273658C2314yes—
124#14273658C2314yes—
125#14273658C2314yes—
126#14273658C2314yes—
127#14273658C2314yes—
128C4⋊(C59⋊C8)C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273650C2314yes—
133#14273650C2314yes—
134#14273650C2314yes—
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
181C2×Q8×C59—21no—
182C2×Q8×C59—24no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—82no—
186C2×Q8×C59C2412yes—
187C2×D4×C59—24no—
188C2×D4×C59C2×D414yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—24no—
198C22×C4×C59—24no—
199C22×C4×C59—82no—
200C22×C4×C59—82no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2×D412yes—
207C22×C4×C59C2412yes—
208C22×C4×C59C2412yes—
209C22×C4×C59C2411yescharacteristic
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—44no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—21no—
219C2×Dic118C2412yes—
220C4⋊C4×C59—21no—
221C4⋊C4×C59—24no—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—24no—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—24no—
229C4⋊C4×C59C2×D414yes—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C4⋊C4×C59C2412yes—
233C22⋊C4×C59—24no—
234C22⋊C4×C59—24no—
235C22⋊C4×C59C2×D414yes—
236C22⋊C4×C59C2×D414yes—
237C42×C59—24no—
238C42×C59C2×D412yes—
239C42×C59C2412yes—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243#11745672—28no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258#11745664—28no—
259C2×C59⋊C8—22no—
260C2×C59⋊C8—22no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—28no—
263C2×C59⋊C8#4114yes—
264C2×C59⋊C8C2412yes—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59#13714yes—
274C23×C59C22×D412yes—
275C23×C59C22×D412yes—
276C23×C59C22×D411yescharacteristic
277Q8×C59—22no—
278Q8×C59—22no—
279Q8×C59—42no—
280Q8×C59—84no—
281D4×C59—28no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—24no—
287C2×C4×C59—24no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—84no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D411yescharacteristic
307C2×C4×C59C2×#4112yes—
308C2×C4×C592−1+412yes—
309C2×C4×C59C2511yescharacteristic
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—42no—
315C2×Dic59—48no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319Dic118—22no—
320Dic118—22no—
321Dic118—42no—
322C59⋊C8—22no—
323C59⋊C8—22no—
324C59⋊C8—22no—
325C59⋊C8C2×#4114yes—
326C2×#3344—591nomaximal, Sylow
327C22×C59—28no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—44no—
334C22×C59#54712yes—
335C22×C59C2×#13714yes—
336C22×C59C2×#13712yes—
337C22×C59#57712yes—
338C22×C59C23×D411yescharacteristic
339C4×C59—22no—
340C4×C59—22no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59—42no—
346C4×C59—42no—
347C4×C59#54712yes—
348C4×C59C22×#4111yescharacteristic
349C4×C59C2×2−1+411yescharacteristic
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
353Dic59—42no—
354C2×#554D5911yescharacteristic
355C2×#552—591no—
356#3344—5916no—
357C2×#501—591no—
358C2×#484—591no—
359C2×#485—591no—
360C2×#483—591no—
361C2×#483—591no—
362C2×#479—591no—
363C2×#475—591no—
364C2×#470—591no—
365C2×#467—591no—
366C2×#441—591no—
367C2×#435—591no—
368C2×#428—591no—
369C22×#106—591no—
370C2×C59—24no—
371C2×C59—42no—
372C2×C59#334414yescomplemented
373C2×C59C2×#54711yescharacteristic
374C2×C59C22×#13711yescharacteristic
375C2×C59C2×#57711yescharacteristic
376C22×Q16—591no—
377C22×M16—591no—
378C23×C8—591no—
379#554—24no—
380#554C2×D5918yes—
381#552—598no—
382#552—1184no—
383C2×C4⋊Q8C2×D5911yescharacteristic
384C2×#126—1181no—
385C2×#125—21no—
386C2×#125—591no—
387C2×#125—1181no—
388C2×#123—1181no—
389C2×C22⋊Q8—21no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—591no—
392C2×C22⋊Q8—591no—
393C2×C22⋊Q8C2×D5911yescharacteristic
394C2×C22⋊Q8C2×D5911yescharacteristic
395C2×C4×Q8—591no—
396C2×C4×Q8C2×D5911yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4C2×D5911yescharacteristic
399C2×#117—591no—
400C2×#117—1181no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4C2×D5911yescharacteristic
403C22×C4⋊C4C2×D5911yescharacteristic
404#501—598no—
405#485—598no—
406#484—598no—
407#483—598no—
408#483—598no—
409#479—598no—
410#475—598no—
411#470—598no—
412#467—598no—
413#441—598no—
414#435—598no—
415#428—598no—
416C2×#107—591no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—598no—
424C2×#106—591no—
425C2×#106—591no—
426C2×C4⋊C8—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×C22⋊C8—591no—
434C2×C22⋊C8—591no—
435C2×#97—591no—
436C59C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—591no—
439C22×Q8C22×D5911yescharacteristic
440C22×D4C22⋊D5911yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1181no—
444C23×C4C22×D5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C2×Q16—594no—
447C2×Q16—1184no—
448C2×M16—594no—
449C2×M16—1184no—
450C22×C8—591no—
451C22×C8—591no—
452C22×C8—594no—
453C22×C8—591no—
454C22×C8—591no—
455C22×C8—1184no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D5914yes—
458#126—1188no—
459#125—28no—
460#125—594no—
461#125—1188no—
462#125—1182no—
463#123—1188no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—594no—
469C22⋊Q8—594no—
470C22⋊Q8—1182no—
471C22⋊Q8—1182no—
472C22⋊Q8C22×D5914yes—
473C22⋊Q8C22×D5914yes—
474C4×Q8—22no—
475C4×Q8—594no—
476C4×Q8—1182no—
477C4×Q8C22×D5914yes—
478C4×D4—28no—
479C4×D4C22⋊D5914yes—
480C4×D4C22×D5914yes—
481#117—594no—
482#117—1182no—
483#117—1188no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1182no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4C22⋊D5911yescharacteristic
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C4⋊C4C22×D5914yes—
508C2×C4⋊C4C22×D5914yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4C22⋊D5911yescharacteristic
515C2×C22⋊C4C22⋊D5911yescharacteristic
516C2×C42—21no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42C22×D5911yescharacteristic
520#107—594no—
521#107—594no—
522#107—594no—
523#106—594no—
524#106—594no—
525#106—594no—
526#106—594no—
527#106—594no—
528#106—594no—
529C4⋊C8—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103—594no—
535#103—594no—
536C22⋊C8—594no—
537C22⋊C8—594no—
538#97—594no—
539C24C2×C22⋊D5911yescharacteristic
540C24C2×C22⋊D5911yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—592no—
547C2×Q8—1181no—
548C2×Q8—1182no—
549C2×Q8—1182no—
550C2×Q8C23×D5912yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D5914yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—1184no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—2364no—
571C22×C4C2×C22⋊D5912yes—
572C22×C4C2×C22⋊D5912yes—
573C22×C4C2×C22⋊D5911yescharacteristic
574C22×C4C2×C22⋊D5911yescharacteristic
575C22×C4C2×C22⋊D5911yescharacteristic
576C22×C4C2×C22⋊D5911yescharacteristic
577C22×C4C23×D5912yes—
578C22×C4C23×D5912yes—
579C22×C4C23×D5911yescharacteristic
580Q16—1188no—
581M16—1188no—
582C2×C8—594no—
583C2×C8—592no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—592no—
587C2×C8—1188no—
588C2×C8—1182no—
589C2×C8—1182no—
590C2×C8—1182no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—592no—
601C4⋊C4—592no—
602C4⋊C4—592no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1184no—
606C4⋊C4—1181no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4C2×C22⋊D5914yes—
613C4⋊C4C23×D5912yes—
614C4⋊C4C23×D5912yes—
615C4⋊C4C23×D5912yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4C2×C22⋊D5914yes—
622C22⋊C4C2×C22⋊D5914yes—
623C42—24no—
624C42—1184no—
625C42—1184no—
626C42C2×C22⋊D5912yes—
627C42C23×D5912yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1427375814yes—
634C23C22×C22⋊D5912yes—
635C23C22×C22⋊D5912yes—
636C23C22×C22⋊D5911yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—1182no—
642Q8—1182no—
643Q8—2362no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—2368no—
670C2×C4—2362no—
671C2×C4—2362no—
672C2×C4—2362no—
673C2×C4—2362no—
674C2×C4C22×C22⋊D5912yes—
675C2×C4C22×C22⋊D5912yes—
676C2×C4C22×C22⋊D5912yes—
677C2×C4C22×C22⋊D5912yes—
678C2×C4C22×C22⋊D5911yescharacteristic
679C2×C4#41×D5912yes—
680C2×C4#1427377412yes—
681C2×C4C24×D5911yescharacteristic
682C8—594no—
683C8—1182no—
684C8—1182no—
685C8—1182no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1683805112yes—
694C22C2×#1427375814yes—
695C22C2×#1427375812yes—
696C22#1683821312yes—
697C22C23×C22⋊D5911yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2362no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C4#1683805112yes—
711C4C2×#41×D5911yescharacteristic
712C4C2×#1427377411yescharacteristic
713C2—24no—
714C2—42no—
715C2#2143654514yesdirect product factor
716C2C2×#1683805111yescharacteristic
717C2C22×#1427375811yescharacteristic
718C2C2×#1683821311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#554C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×#554D59
hypocenterC59C2×#3344
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. #21436545C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837737C2semidirect
5. C2×#16837740C2semidirect
6. C2×#16837732C2semidirect
7. C2×#16837730C2semidirect
8. C2×#16837709C2semidirect
9. C2×#16837684C2semidirect
10. C2×#16837658C2semidirect
11. C2×#16837641C2semidirect
12. C2×#16837507C2semidirect
14. C2×#16837442C2semidirect
15. C22×#14273658C2semidirect
32. #16837808C22semidirect
33. #16837740C22semidirect
34. #16837737C22semidirect
35. #16837732C22semidirect
36. #16837730C22semidirect
37. #16837709C22semidirect
38. #16837684C22semidirect
39. #16837658C22semidirect
40. #16837641C22semidirect
41. #16837507C22semidirect
43. #16837442C22semidirect
53. C2×#14273658C22semidirect
372. C2×C59#3344semidirect
436. C59C2×#3344semidirect
715. C2#21436545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380922
#214365452
C2×#168378082
C2×#168377372
C2×#168377402
C2×#168377322
C2×#168377302
C2×#168377092
C2×#168376842
C2×#168376582
C2×#168376412
C2×#168375072
C2×#168374742
C2×#168374422
C22×#142736582
C2×C59×#5542
C2×#334459