Finite Group Databasebeta

← C2×#21427178 #28748321

Subgroups — C2×#21427178 #28748321

Order 15104.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273707C211yesmaximal, characteristic
2#21427178C2116yesmaximal, direct product factor
3C2×#16837306C211yesmaximal, characteristic, complemented
4C2×#16837306C211yesmaximal, characteristic, complemented
5C2×#16837288C211yesmaximal, characteristic, complemented
6C2×#16837287C211yesmaximal, characteristic, complemented
7C2×#16837285C211yesmaximal, characteristic, complemented
8C2×#16837276C211yesmaximal, characteristic
9C2×#16837273C211yesmaximal, characteristic
10C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic59C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
13C2×#16837249C211yesmaximal, characteristic
14C2×#16837249C211yesmaximal, characteristic
15C2×#95×D59C211yesmaximal, characteristic
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21C2×#14273707C4116yescomplemented
22C2×#14273707C2218yes—
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37#16837306C2218yescomplemented
38#16837306C2218yescomplemented
39#16837288C2218yescomplemented
40#16837287C2218yescomplemented
41#16837285C2218yescomplemented
42#16837276C2218yes—
43#16837273C2218yes—
44C4⋊C4×Dic59C2218yescomplemented
45C4×C4⋊Dic59C2218yescomplemented
46C4×(C2×D59)⋊C4C2218yes—
47#16837249C2218yes—
48#16837249C2218yes—
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59#95×D59C2218yes—
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C42×C59C2211yescharacteristic
63C59×#387C2218yescomplemented
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C24×D59C2311yescharacteristic
69C22×Dic118—42no—
70C22×Dic118—42no—
71C22×Dic118C2×C418yescomplemented
72C22×Dic118C2314yes—
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C22×C4×D59—24no—
81C22×C4×D59—24no—
82C22×C4×D59—24no—
83C22×C4×D59—24no—
84C22×C4×D59—42no—
85C22×C4×D59—42no—
86C22×C4×D59—42no—
87C22×C4×D59—42no—
88C22×C4×D59C2×C418yes—
89C22×C4×D59C2314yes—
90C22×C4×D59C2314yes—
91C22×C4×D59C2314yes—
92#14273707C2×C4164yescomplemented
93C2×C4⋊Dic59—24no—
94C2×C4⋊Dic59C2×C418yescomplemented
95C2×C4⋊Dic59C2×C418yescomplemented
96C2×C4⋊Dic59C2314yes—
97C2×C4⋊Dic59C2314yes—
98C2×C4⋊Dic59C2314yes—
99C2×Dic59⋊C4—42no—
100C2×Dic59⋊C4—42no—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×(C2×D59)⋊C4—24no—
104C2×(C2×D59)⋊C4C2×C418yes—
105C2×(C2×D59)⋊C4C2×C418yes—
106C2×(C2×D59)⋊C4Q818yescomplemented
107C2×(C2×D59)⋊C4C2314yes—
108C2×(C2×D59)⋊C4C2314yes—
109C2×(C2×D59)⋊C4C2314yes—
110C2×(C2×D59)⋊C4C2314yes—
111C2×C4×Dic59—24no—
112C2×C4×Dic59—42no—
113C2×C4×Dic59—42no—
114C2×C4×Dic59—42no—
115C2×C4×Dic59—42no—
116C2×C4×Dic59C2314yes—
117C2×C4×Dic59C2314yes—
118C2×C4×Dic59C2314yes—
119C2×C4×Dic59C2314yes—
120C2×C4×Dic59C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59—24no—
139C2×C4⋊C4×C59C2×C418yescomplemented
140C2×C4⋊C4×C59C2314yes—
141C2×C4⋊C4×C59C2314yes—
142C2×C42×C59—24no—
143C2×C42×C59C2314yes—
144#95×C59C2314yes—
145#95×C59C2314yes—
146#95×C59C2314yes—
147#95×C59C2314yes—
148C24×C59C2411yescharacteristic
149C23×D59—22no—
150C23×D59—22no—
151C23×D59—22no—
152C23×D59—22no—
153C23×D59C22×C414yes—
154C23×D59C2×Q814yes—
155C23×D59#4114yes—
156C23×D59C2412yes—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59C22×C414yes—
174C22×C4×C59C22×C414yes—
175C22×C4×C59C22×C414yes—
176C22×C4×C59C2×Q814yes—
177C22×C4×C59#4114yes—
178C22×C4×C59C2412yes—
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59C22×C414yes—
202C22×Dic59C22×C414yes—
203C22×Dic59C22×C414yes—
204C22×Dic59C2×Q814yes—
205C22×Dic59#4114yes—
206C22×Dic59C2412yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C2×C4×D59—28no—
214C2×C4×D59—28no—
215C2×C4×D59—28no—
216C2×C4×D59—28no—
217C2×C4×D59—416no—
218C2×C4×D59—44no—
219C2×C4×D59—44no—
220C2×C4×D59—44no—
221C2×C4×D59—44no—
222C2×C4×D59—416no—
223C2×C4×D59—416no—
224C2×C4×D59C22×C4116yes—
225C2×Dic118—416no—
226C2×Dic118—44no—
227C2×Dic118—44no—
228C2×Dic118C22×C4116yescomplemented
229C4⋊C4×C59—28no—
230C4⋊C4×C59C22×C4116yescomplemented
231C42×C59—28no—
232(C2×D59)⋊C4—28no—
233(C2×D59)⋊C4C22×C4116yes—
234(C2×D59)⋊C4C22×C4116yes—
235(C2×D59)⋊C4C2×Q8116yescomplemented
236C4⋊Dic59—28no—
237C4⋊Dic59C22×C4116yescomplemented
238C4⋊Dic59C22×C4116yescomplemented
239Dic59⋊C4—44no—
240Dic59⋊C4—44no—
241C4×Dic59—28no—
242C4×Dic59—44no—
243C4×Dic59—44no—
244C4×Dic59—44no—
245C4×Dic59—44no—
246C23×C59C23×C412yes—
247C23×C59C22×Q812yes—
248C23×C59C2×#4112yes—
249C23×C59C2×#4112yes—
250C23×C59C2×#4112yes—
251C23×C59H(5,𝔽2)12yes—
252C23×C59H(5,𝔽2)12yes—
253C23×C59C2511yescharacteristic
254C22×D59—28no—
255C22×D59—28no—
256C22×D59—28no—
257C22×D59—28no—
258C22×D59—28no—
259C22×D59—28no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59C4×Q8116yes—
265C22×D59C23×C414yes—
266C22×D59C22×Q814yes—
267C22×D59C2×#4114yes—
268C2×C4×C59—28no—
269C2×C4×C59—28no—
270C2×C4×C59—28no—
271C2×C4×C59—28no—
272C2×C4×C59—28no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—44no—
290C2×C4×C59—44no—
291C2×C4×C59C23×C414yes—
292C2×C4×C59C23×C414yes—
293C2×C4×C59C23×C414yes—
294C2×C4×C59C22×Q814yes—
295C2×C4×C59C2×#4114yes—
296C2×Dic59—28no—
297C2×Dic59—28no—
298C2×Dic59—28no—
299C2×Dic59—28no—
300C2×Dic59—28no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—44no—
318C2×Dic59—44no—
319C2×Dic59C23×C414yes—
320C2×Dic59C23×C414yes—
321C2×Dic59C23×C414yes—
322C2×Dic59C22×Q814yes—
323C2×Dic59C2×#4114yes—
324C4×D59—416no—
325C4×D59—416no—
326C4×D59—416no—
327Dic118—416no—
328C2×#2368—591nomaximal, Sylow
329C22×C59C2×C4×Q814yes—
330C22×C59C4×#4114yes—
331C22×C59#51814yes—
332C22×C59#55114yes—
333C22×C59#55114yes—
334C22×C59#55414yes—
335C22×C59#55414yes—
336C22×C59C24×C411yescharacteristic
337C22×C59C23×Q811yescharacteristic
338C22×C59C22×#4111yescharacteristic
339C22×C59C22×#4111yescharacteristic
340C22×C59C22×#4111yescharacteristic
341C22×C59C2×H(5,𝔽2)11yescharacteristic
342C22×C59C2×H(5,𝔽2)11yescharacteristic
343C2×D59—232no—
344C2×D59—24no—
345C2×D59—24no—
346C2×D59—24no—
347C2×D59—24no—
348C2×D59—24no—
349C2×D59—24no—
350C2×D59C2×C4×Q818yes—
351C4×C59—24no—
352C4×C59—24no—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—24no—
356C4×C59—42no—
357C4×C59—42no—
358Dic59—24no—
359Dic59—24no—
360Dic59—24no—
361Dic59—24no—
362Dic59—24no—
363Dic59—42no—
364Dic59—42no—
365C22×C22⋊Q8—591no—
366#2368—5916no—
367C2×#391—591no—
368C2×#391—591no—
369C2×#387—591no—
370C2×#387—591no—
371C2×#387—591no—
372C2×#387D5911yescharacteristic, complemented
373C2×#385—591no—
374C2×#385—591no—
375C2×C4×C4⋊C4—591no—
376C2×C4×C4⋊C4—591no—
377C2×C4×C22⋊C4—591no—
378C2×C4×C22⋊C4—591no—
379C2×C4×C22⋊C4—591no—
380C22×#95—591no—
381C2×C59#236818yescomplemented
382C2×C59C22×C4×Q811yescharacteristic
383C2×C59C2×C4×#4111yescharacteristic
384C2×C59C2×#51811yescharacteristic
385C2×C59C2×#55111yescharacteristic
386C2×C59C2×#55111yescharacteristic
387C2×C59C2×#55411yescharacteristic
388C2×C59C2×#55411yescharacteristic
389D59—28no—
390C23×Q8—591no—
391C24×C4—591no—
392C24×C4—591no—
393C24×C4—591no—
394C2×C22⋊Q8—5916no—
395C2×C22⋊Q8—598no—
396C22×C4⋊C4—591no—
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—591no—
400C22×C4⋊C4—591no—
401C22×C4⋊C4C2×D5911yescharacteristic
402C22×C4⋊C4C2×D5911yescharacteristic
403C22×C22⋊C4—591no—
404C22×C22⋊C4—591no—
405C22×C22⋊C4—591no—
406C22×C22⋊C4—591no—
407C22×C42—591no—
408C22×C42—591no—
409C22×C42—591no—
410C22×C42—591no—
411C22×C42—591no—
412C22×C42C2×D5911yescharacteristic
413#391—598no—
414#391—598no—
415#387—598no—
416#387—598no—
417#387—598no—
418#387C2×D5918yescomplemented
419#385—598no—
420#385—598no—
421C4×C4⋊C4—598no—
422C4×C4⋊C4—598no—
423C4×C22⋊C4—598no—
424C4×C22⋊C4—598no—
425C4×C22⋊C4—598no—
426C2×#95—591no—
427C2×#95—591no—
428C2×#95—591no—
429C2×#95—591no—
430C2×#95—591no—
431C2×#95—591no—
432C2×#95—591no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—598no—
437C2×#95C2×D5911yescharacteristic
438C2×#95C2×D5911yescharacteristic
439C2×#95C2×D5911yescharacteristic
440C2×#95C2×D5911yescharacteristic
441C59C2×#236811yescharacteristic, complemented, Sylow
442C25—591no—
443C22×Q8—598no—
444C22×Q8—594no—
445C22×Q8—2362no—
446C22×Q8—2362no—
447C23×C4—591no—
448C23×C4—591no—
449C23×C4—591no—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—598no—
453C23×C4—594no—
454C23×C4—591no—
455C23×C4—591no—
456C23×C4—594no—
457C23×C4—594no—
458C23×C4—1184no—
459C23×C4—1184no—
460C23×C4—1184no—
461C23×C4—1184no—
462C23×C4—2362no—
463C23×C4—2362no—
464C23×C4—2362no—
465C23×C4—2362no—
466C23×C4C22×D5911yescharacteristic
467C23×C4C22×D5911yescharacteristic
468C23×C4C22×D5911yescharacteristic
469C23×C4C22×D5911yescharacteristic
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C22⋊Q8—5964no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—598no—
476C2×C4⋊C4—598no—
477C2×C4⋊C4—594no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—594no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—1184no—
483C2×C4⋊C4—2362no—
484C2×C4⋊C4—2362no—
485C2×C4⋊C4C4×D5918yescomplemented
486C2×C4⋊C4C22×D5914yes—
487C2×C4⋊C4C22×D5914yes—
488C2×C22⋊C4—598no—
489C2×C22⋊C4—598no—
490C2×C22⋊C4—598no—
491C2×C22⋊C4—594no—
492C2×C22⋊C4—594no—
493C2×C22⋊C4—594no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—1184no—
496C2×C42—24no—
497C2×C42—594no—
498C2×C42—594no—
499C2×C42—594no—
500C2×C42—594no—
501C2×C42—594no—
502C2×C42—1184no—
503C2×C42—2362no—
504C2×C42—2362no—
505C2×C42—2362no—
506C2×C42—2362no—
507C2×C42C22×D5914yes—
508#95—594no—
509#95—594no—
510#95—594no—
511#95—594no—
512#95—594no—
513#95—594no—
514#95—594no—
515#95—594no—
516#95—594no—
517#95—594no—
518#95C22×D5914yes—
519#95C22×D5914yes—
520#95C22×D5914yes—
521#95C22×D5914yes—
522C24—594no—
523C24—594no—
524C24—594no—
525C24—592no—
526C24—1182no—
527C24—1182no—
528C24—1182no—
529C24—1182no—
530C24C23×D5911yescharacteristic
531C2×Q8—5916no—
532C2×Q8—2364no—
533C2×Q8—2364no—
534C2×Q8—23616no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—594no—
552C22×C4—594no—
553C22×C4—594no—
554C22×C4—594no—
555C22×C4—594no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—592no—
560C22×C4—592no—
561C22×C4—5916no—
562C22×C4—592no—
563C22×C4—592no—
564C22×C4—1188no—
565C22×C4—1188no—
566C22×C4—1188no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—1182no—
572C22×C4—1182no—
573C22×C4—1182no—
574C22×C4—1182no—
575C22×C4—1182no—
576C22×C4—1182no—
577C22×C4—1182no—
578C22×C4—1182no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1188no—
584C22×C4—2364no—
585C22×C4—2364no—
586C22×C4—2364no—
587C22×C4—23616no—
588C22×C4—2364no—
589C22×C4—23616no—
590C22×C4—23616no—
591C22×C4C2×C4×D5914yes—
592C22×C4C2×C4×D5914yes—
593C22×C4C2×C4×D5914yes—
594C22×C4#1174568714yes—
595C22×C4Q8×D5914yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5912yes—
598C22×C4C23×D5912yes—
599C22×C4C23×D5912yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5912yes—
602C22×C4C23×D5912yes—
603C4⋊C4—28no—
604C4⋊C4—5916no—
605C4⋊C4—5916no—
606C4⋊C4—1188no—
607C4⋊C4—2364no—
608C4⋊C4—2364no—
609C4⋊C4C2×C4×D59116yescomplemented
610C22⋊C4—5916no—
611C22⋊C4—5916no—
612C22⋊C4—5916no—
613C22⋊C4—1188no—
614C42—28no—
615C42—1188no—
616C42—2364no—
617C42—2364no—
618C42—2364no—
619C42—2364no—
620C23—594no—
621C23—594no—
622C23—594no—
623C23—5916no—
624C23—1182no—
625C23—1182no—
626C23—1182no—
627C23—1182no—
628C23—1188no—
629C23—1188no—
630C23—1188no—
631C23—1188no—
632C23—1188no—
633C23—1188no—
634C23C22×C4×D5912yes—
635C23C2×Q8×D5912yes—
636C23#41×D5912yes—
637C23#41×D5912yes—
638C23C2×#1174568712yes—
639C23#1427377312yes—
640C23#1427377312yes—
641C23C24×D5911yescharacteristic
642Q8—23616no—
643C2×C4—22no—
644C2×C4—22no—
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—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—594no—
667C2×C4—594no—
668C2×C4—594no—
669C2×C4—594no—
670C2×C4—594no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1188no—
682C2×C4—1188no—
683C2×C4—1188no—
684C2×C4—1188no—
685C2×C4—1188no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—23616no—
693C2×C4—23616no—
694C2×C4—23616no—
695C2×C4—2364no—
696C2×C4—2364no—
697C2×C4C22×C4×D5914yes—
698C2×C4C22×C4×D5914yes—
699C2×C4C22×C4×D5914yes—
700C2×C4C2×Q8×D5914yes—
701C2×C4C2×#1174568714yes—
702C22—598no—
703C22—1184no—
704C22—1184no—
705C22—1184no—
706C22—1184no—
707C22—1184no—
708C22—1184no—
709C22—11832no—
710C22C4×Q8×D5914yes—
711C22C4×#1174568714yes—
712C22#1683787614yes—
713C22#1683807514yes—
714C22#1683807714yes—
715C22#1683810814yes—
716C22#1683811014yes—
717C22C23×C4×D5911yescharacteristic
718C22C22×Q8×D5911yescharacteristic
719C22C2×#41×D5911yescharacteristic
720C22C2×#41×D5911yescharacteristic
721C22C22×#1174568711yescharacteristic
722C22C2×#1427377311yescharacteristic
723C22C2×#1427377311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—42no—
731C4—1184no—
732C4—1184no—
733C4—1184no—
734C4—1184no—
735C4—1184no—
736C4—2362no—
737C4—2362no—
738C2—1188no—
739C2#2142717818yesdirect product factor
740C2C2×C4×Q8×D5911yescharacteristic
741C2C2×C4×#1174568711yescharacteristic
742C2C2×#1683787611yescharacteristic
743C2C2×#1683807511yescharacteristic
744C2C2×#1683807711yescharacteristic
745C2C2×#1683810811yescharacteristic
746C2C2×#1683811011yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC24×D59C23
cosocleC23×C59C25
hypercenterC2×#387D59
hypocenterC59C2×#2368
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #21427178C2direct (N × H)
3. C2×#16837306C2semidirect
4. C2×#16837306C2semidirect
5. C2×#16837288C2semidirect
6. C2×#16837287C2semidirect
7. C2×#16837285C2semidirect
10. C2×C4⋊C4×Dic59C2semidirect
11. C2×C4×C4⋊Dic59C2semidirect
16. C2×C59×#387C2semidirect
21. C2×#14273707C4semidirect
37. #16837306C22semidirect
38. #16837306C22semidirect
39. #16837288C22semidirect
40. #16837287C22semidirect
41. #16837285C22semidirect
44. C4⋊C4×Dic59C22semidirect
45. C4×C4⋊Dic59C22semidirect
63. C59×#387C22semidirect
71. C22×Dic118C2×C4semidirect
92. #14273707C2×C4semidirect
94. C2×C4⋊Dic59C2×C4semidirect
95. C2×C4⋊Dic59C2×C4semidirect
106. C2×(C2×D59)⋊C4Q8semidirect
139. C2×C4⋊C4×C59C2×C4semidirect
228. C2×Dic118C22×C4semidirect
230. C4⋊C4×C59C22×C4semidirect
235. (C2×D59)⋊C4C2×Q8semidirect
237. C4⋊Dic59C22×C4semidirect
238. C4⋊Dic59C22×C4semidirect
372. C2×#387D59semidirect
381. C2×C59#2368semidirect
418. #387C2×D59semidirect
441. C59C2×#2368semidirect
485. C2×C4⋊C4C4×D59semidirect
609. C4⋊C4C2×C4×D59semidirect
739. C2#21427178direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737072
#214271782
C2×#168373062
C2×#168372882
C2×#168372872
C2×#168372852
C2×#168372762
C2×#168372732
C2×C4⋊C4×Dic592
C2×C4×C4⋊Dic592
C2×C4×(C2×D59)⋊C42
C2×#168372492
C2×#95×D592
C2×C59×#3872
C2×#236859