Finite Group Databasebeta

← C2×#21429174 #28758786

Subgroups — C2×#21429174 #28758786

Order 15104.

2726 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
1C22×#14273717C211yesmaximal, characteristic, complemented
2C22×#14273705C211yesmaximal, characteristic
3#21429174C2116yesmaximal, direct product factor
4C2×#16837339C211yesmaximal, characteristic
5C2×#16837332C211yesmaximal, characteristic, complemented
6C2×#16837324C211yesmaximal, characteristic
7C2×#16837323C211yesmaximal, characteristic, complemented
8C2×#16837308C211yesmaximal, characteristic, complemented
9C2×#16837300C211yesmaximal, characteristic, complemented
10C2×#16837300C211yesmaximal, characteristic, complemented
11C2×#16837293C211yesmaximal, characteristic
12C2×#16837293C211yesmaximal, characteristic
13C2×#16837287C211yesmaximal, characteristic, complemented
14C2×#16837276C211yesmaximal, characteristic
15C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C2×#14273717—28no—
20C2×#14273717C2218yescomplemented
21C2×#14273705—28no—
22C2×#14273705C2218yes—
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C4⋊Dic59C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×(C2×D59)⋊C4C2211yescharacteristic
36C22×(C2×D59)⋊C4C2211yescharacteristic
37C22×(C2×D59)⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41#16837339C2218yes—
42#16837332C2218yescomplemented
43#16837324C2218yes—
44#16837323C2218yescomplemented
45#16837308C2218yescomplemented
46#16837300C2218yescomplemented
47#16837300C2218yescomplemented
48#16837293C2218yes—
49#16837293C2218yes—
50#16837287C2218yescomplemented
51#16837276C2218yes—
52C4×(C2×D59)⋊C4C2218yes—
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C22×C42×C59C2211yescharacteristic
65C22×C42×C59C2211yescharacteristic
66C4×C4⋊C4×C59C2218yescomplemented
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C22×Dic118—24no—
71C22×Dic118—24no—
72C22×Dic118—42no—
73C22×Dic118C2314yes—
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C22×C4×D59—24no—
82C22×C4×D59—24no—
83C22×C4×D59—42no—
84C22×C4×D59C2314yes—
85#14273717—232no—
86#14273705—232no—
87C2×C4⋊Dic59—24no—
88C2×C4⋊Dic59—24no—
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59—24no—
91C2×C4⋊Dic59—42no—
92C2×C4⋊Dic59C2314yes—
93C2×C4⋊Dic59C2314yes—
94C2×C4⋊Dic59C2314yes—
95C2×C4⋊Dic59C2314yes—
96C2×C4⋊Dic59C2314yes—
97C2×Dic59⋊C4—24no—
98C2×Dic59⋊C4—24no—
99C2×Dic59⋊C4—24no—
100C2×Dic59⋊C4—24no—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4—24no—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×(C2×D59)⋊C4—24no—
110C2×(C2×D59)⋊C4—24no—
111C2×(C2×D59)⋊C4—24no—
112C2×(C2×D59)⋊C4—24no—
113C2×(C2×D59)⋊C4—42no—
114C2×(C2×D59)⋊C4Q818yescomplemented
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
119C2×(C2×D59)⋊C4C2314yes—
120C2×(C2×D59)⋊C4C2314yes—
121C2×C4×Dic59—24no—
122C2×C4×Dic59C2314yes—
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×C59D418yes—
140C2×C4⋊C4×C59C2314yes—
141C2×C4⋊C4×C59C2314yes—
142C2×C42×C59—24no—
143C2×C42×C59—42no—
144C2×C42×C59—42no—
145C2×C42×C59C2314yes—
146C2×C42×C59C2314yes—
147C2×C42×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150C24×C59C2411yescharacteristic
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59C2×Q814yes—
158C23×D59C2412yes—
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×C59—22no—
174C22×C4×C59C2×D414yes—
175C22×C4×C59C2×D414yes—
176C22×C4×C59C2×D414yes—
177C22×C4×C59C2×Q814yes—
178C22×C4×C59#4114yes—
179C22×C4×C59#4114yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
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×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—22no—
204C22×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59C2×Q814yes—
207C22×Dic59#4114yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C2×C4×D59—28no—
216C2×C4×D59—28no—
217C2×C4×D59—44no—
218C2×C4×D59—416no—
219C2×Dic118—28no—
220C2×Dic118—28no—
221C2×Dic118—44no—
222C2×Dic118—416no—
223C4⋊C4×C59—28no—
224C4⋊C4×C59C2×D4116yes—
225C42×C59—28no—
226C42×C59—44no—
227C42×C59—44no—
228(C2×D59)⋊C4—28no—
229(C2×D59)⋊C4—28no—
230(C2×D59)⋊C4—28no—
231(C2×D59)⋊C4—28no—
232(C2×D59)⋊C4—44no—
233(C2×D59)⋊C4C2×Q8116yescomplemented
234C4⋊Dic59—28no—
235C4⋊Dic59—28no—
236C4⋊Dic59—28no—
237C4⋊Dic59—28no—
238C4⋊Dic59—44no—
239Dic59⋊C4—28no—
240Dic59⋊C4—28no—
241Dic59⋊C4—28no—
242Dic59⋊C4—28no—
243Dic59⋊C4—28no—
244Dic59⋊C4—28no—
245C4×Dic59—28no—
246C23×C59C22×D412yes—
247C23×C59C22×Q812yes—
248C23×C59C2×#4112yes—
249C23×C59C2×#4112yes—
250C23×C59C2×#4112yes—
251C23×C59H(5,𝔽2)12yes—
252C23×C592−1+412yes—
253C23×C59C2511yescharacteristic
254C22×D59—28no—
255C22×D59—28no—
256C22×D59—28no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—44no—
264C22×D59—44no—
265C22×D59—44no—
266C22×D59—44no—
267C22×D59C22×Q814yes—
268C2×C4×C59—28no—
269C2×C4×C59—28no—
270C2×C4×C59—28no—
271C2×C4×C59—28no—
272C2×C4×C59—28no—
273C2×C4×C59—28no—
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×C59C22×D414yes—
291C2×C4×C59C22×D414yes—
292C2×C4×C59C22×D414yes—
293C2×C4×C59C22×Q814yes—
294C2×C4×C59C2×#4114yes—
295C2×C4×C59C2×#4114yes—
296C2×Dic59—28no—
297C2×Dic59—28no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
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×Dic59—44no—
320C2×Dic59—44no—
321C2×Dic59—44no—
322C2×Dic59C22×Q814yes—
323C2×Dic59C2×#4114yes—
324C4×D59—416no—
325Dic118—416no—
326C2×#2556—591nomaximal, Sylow
327C22×C59#53214yes—
328C22×C59#53314yes—
329C22×C59#53914yes—
330C22×C59#54614yes—
331C22×C59D4×Q814yes—
332C22×C59#55214yes—
333C22×C59#55414yes—
334C22×C59C23×D411yescharacteristic
335C22×C59C23×Q811yescharacteristic
336C22×C59C22×#4111yescharacteristic
337C22×C59C22×#4111yescharacteristic
338C22×C59C22×#4111yescharacteristic
339C22×C59C2×H(5,𝔽2)11yescharacteristic
340C22×C59C2×2−1+411yescharacteristic
341C2×D59—24no—
342C2×D59—24no—
343C2×D59—24no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C2×D59—42no—
348C2×D59—416no—
349C4×C59—24no—
350C4×C59—24no—
351C4×C59—24no—
352C4×C59—24no—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—42no—
356Dic59—24no—
357Dic59—24no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363C22×#125—591no—
364C22×C22⋊Q8—591no—
365#2556—5916no—
366C2×#399—591no—
367C2×#398—591no—
368C2×#396—591no—
369C2×#395—591no—
370C2×#391—591no—
371C2×#389—591no—
372C2×#389—591no—
373C2×#388—591no—
374C2×#388—591no—
375C2×#387—591no—
376C2×#385—591no—
377C2×C4×C4⋊C4D5911yescharacteristic, complemented
378C2×C4×C22⋊C4—591no—
379C2×C59#255618yescomplemented
380C2×C59C2×#53211yescharacteristic
381C2×C59C2×#53311yescharacteristic
382C2×C59C2×#53911yescharacteristic
383C2×C59C2×#54611yescharacteristic
384C2×C59C2×D4×Q811yescharacteristic
385C2×C59C2×#55211yescharacteristic
386C2×C59C2×#55411yescharacteristic
387D59—44no—
388C23×Q8—591no—
389C24×C4—591no—
390C2×#125—598no—
391C2×#125—1188no—
392C2×C22⋊Q8—598no—
393C2×C22⋊Q8—1188no—
394C22×C4⋊C4—591no—
395C22×C4⋊C4—591no—
396C22×C4⋊C4—591no—
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—591no—
400C22×C4⋊C4—591no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4C2×D5911yescharacteristic
406C22×C4⋊C4C2×D5911yescharacteristic
407C22×C22⋊C4—591no—
408C22×C22⋊C4—591no—
409C22×C22⋊C4—591no—
410C22×C22⋊C4—591no—
411C22×C22⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C42—591no—
414C22×C42C2×D5911yescharacteristic
415C22×C42C2×D5911yescharacteristic
416C22×C42C2×D5911yescharacteristic
417#399—598no—
418#398—598no—
419#396—598no—
420#395—598no—
421#391—598no—
422#389—598no—
423#389—598no—
424#388—598no—
425#388—598no—
426#387—598no—
427#385—598no—
428C4×C4⋊C4C2×D5918yescomplemented
429C4×C22⋊C4—598no—
430C2×#95—591no—
431C2×#95—591no—
432C2×#95—591no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—591no—
437C2×#95—591no—
438C2×#95C2×D5911yescharacteristic
439C2×#95C2×D5911yescharacteristic
440C59C2×#255611yescharacteristic, complemented, Sylow
441C25—591no—
442C22×Q8—594no—
443C22×Q8—1184no—
444C22×Q8—1184no—
445C22×Q8—2362no—
446C23×C4—591no—
447C23×C4—591no—
448C23×C4—591no—
449C23×C4—591no—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—591no—
453C23×C4—594no—
454C23×C4—1184no—
455C23×C4—1184no—
456C23×C4—2362no—
457C23×C4C22×D5911yescharacteristic
458C23×C4C22×D5911yescharacteristic
459C23×C4C22×D5911yescharacteristic
460C23×C4C22×D5911yescharacteristic
461C23×C4C22×D5911yescharacteristic
462C23×C4C22×D5911yescharacteristic
463C23×C4C22×D5911yescharacteristic
464#125—11832no—
465C22⋊Q8—11832no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—594no—
468C2×C4⋊C4—594no—
469C2×C4⋊C4—594no—
470C2×C4⋊C4—594no—
471C2×C4⋊C4—594no—
472C2×C4⋊C4—594no—
473C2×C4⋊C4—594no—
474C2×C4⋊C4—594no—
475C2×C4⋊C4—594no—
476C2×C4⋊C4—594no—
477C2×C4⋊C4—594no—
478C2×C4⋊C4—1184no—
479C2×C4⋊C4—1184no—
480C2×C4⋊C4—1184no—
481C2×C4⋊C4—1184no—
482C2×C4⋊C4—1184no—
483C2×C4⋊C4—1184no—
484C2×C4⋊C4—1184no—
485C2×C4⋊C4—1184no—
486C2×C4⋊C4—1184no—
487C2×C4⋊C4—1184no—
488C2×C4⋊C4—2362no—
489C2×C4⋊C4D23618yes—
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—598no—
493C2×C22⋊C4—594no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—1184no—
500C2×C22⋊C4—1184no—
501C2×C22⋊C4—1184no—
502C2×C22⋊C4—1184no—
503C2×C22⋊C4—2362no—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42—42no—
507C2×C42—594no—
508C2×C42—1184no—
509C2×C42C22×D5914yes—
510C2×C42C22×D5914yes—
511C2×C42C22×D5914yes—
512#95—594no—
513#95—594no—
514#95—594no—
515#95—594no—
516#95—594no—
517#95—594no—
518#95—594no—
519#95—594no—
520#95C22×D5914yes—
521#95C22×D5914yes—
522C24—594no—
523C24—592no—
524C24—1182no—
525C24—1182no—
526C24—1182no—
527C24—1182no—
528C24—1182no—
529C24—1182no—
530C24C23×D5911yescharacteristic
531C2×Q8—1188no—
532C2×Q8—1188no—
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—594no—
551C22×C4—594no—
552C22×C4—592no—
553C22×C4—592no—
554C22×C4—592no—
555C22×C4—592no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—1188no—
560C22×C4—1182no—
561C22×C4—1182no—
562C22×C4—1182no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1182no—
566C22×C4—1182no—
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—1188no—
580C22×C4—2364no—
581C22×C4—23616no—
582C22×C4C2×D23614yes—
583C22×C4C2×D23614yes—
584C22×C4C2×D23614yes—
585C22×C4#1174568514yes—
586C22×C4#1174568514yes—
587C22×C4Q8×D5914yes—
588C22×C4C23×D5912yes—
589C22×C4C23×D5912yes—
590C22×C4C23×D5912yes—
591C22×C4C23×D5912yes—
592C22×C4C23×D5912yes—
593C22×C4C23×D5912yes—
594C22×C4C23×D5912yes—
595C4⋊C4—28no—
596C4⋊C4—1188no—
597C4⋊C4—1188no—
598C4⋊C4—1188no—
599C4⋊C4—1188no—
600C4⋊C4—1188no—
601C4⋊C4—1188no—
602C4⋊C4—1188no—
603C4⋊C4—1188no—
604C4⋊C4—1188no—
605C4⋊C4—1188no—
606C4⋊C4—2364no—
607C4⋊C4C2×D236116yes—
608C22⋊C4—5916no—
609C22⋊C4—1188no—
610C22⋊C4—1188no—
611C22⋊C4—1188no—
612C22⋊C4—1188no—
613C22⋊C4—2364no—
614C42—28no—
615C42—44no—
616C42—44no—
617C42—1188no—
618C23—594no—
619C23—1188no—
620C23—1182no—
621C23—1182no—
622C23—1182no—
623C23—1182no—
624C23—1182no—
625C23—1182no—
626C23—1188no—
627C23—1188no—
628C23—2364no—
629C23—2364no—
630C23—2364no—
631C23—2364no—
632C23C22×D23612yes—
633C23C2×Q8×D5912yes—
634C23#41×D5912yes—
635C23C2×#1174568512yes—
636C23C2×#1174568512yes—
637C23#1427377212yes—
638C23#1427377412yes—
639C23C24×D5911yescharacteristic
640Q8—23616no—
641C2×C4—28no—
642C2×C4—22no—
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—22no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—594no—
664C2×C4—594no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1188no—
670C2×C4—1188no—
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—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—23616no—
687C2×C4—2364no—
688C2×C4—2364no—
689C2×C4—2364no—
690C2×C4—2364no—
691C2×C4—2364no—
692C2×C4C22×D23614yes—
693C2×C4C22×D23614yes—
694C2×C4C22×D23614yes—
695C2×C4C2×Q8×D5914yes—
696C2×C4C2×#1174568514yes—
697C2×C4C2×#1174568514yes—
698C22—1184no—
699C22—1184no—
700C22—1184no—
701C22—2362no—
702C22—2362no—
703C22—2362no—
704C22—23616no—
705C22—2362no—
706C22#1683795214yes—
707C22#1683795614yes—
708C22#1683799414yes—
709C22#1683804714yes—
710C22Q8×D23614yes—
711C22#1683808514yes—
712C22#1683810714yes—
713C22C23×D23611yescharacteristic
714C22C22×Q8×D5911yescharacteristic
715C22C2×#41×D5911yescharacteristic
716C22C22×#1174568511yescharacteristic
717C22C22×#1174568511yescharacteristic
718C22C2×#1427377211yescharacteristic
719C22C2×#1427377411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—24no—
726C4—42no—
727C4—1184no—
728C4—1184no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4—2362no—
734C2—2364no—
735C2#2142917418yesdirect product factor
736C2C2×#1683795211yescharacteristic
737C2C2×#1683795611yescharacteristic
738C2C2×#1683799411yescharacteristic
739C2C2×#1683804711yescharacteristic
740C2C2×Q8×D23611yescharacteristic
741C2C2×#1683808511yescharacteristic
742C2C2×#1683810711yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C4×C4⋊C4×C59C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×C4×C4⋊C4D59
hypocenterC59C2×#2556
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14273717C2semidirect
3. #21429174C2direct (N × H)
5. C2×#16837332C2semidirect
7. C2×#16837323C2semidirect
8. C2×#16837308C2semidirect
9. C2×#16837300C2semidirect
10. C2×#16837300C2semidirect
13. C2×#16837287C2semidirect
16. C2×C4×C4⋊C4×C59C2semidirect
20. C2×#14273717C22semidirect
42. #16837332C22semidirect
44. #16837323C22semidirect
45. #16837308C22semidirect
46. #16837300C22semidirect
47. #16837300C22semidirect
50. #16837287C22semidirect
66. C4×C4⋊C4×C59C22semidirect
114. C2×(C2×D59)⋊C4Q8semidirect
233. (C2×D59)⋊C4C2×Q8semidirect
377. C2×C4×C4⋊C4D59semidirect
379. C2×C59#2556semidirect
428. C4×C4⋊C4C2×D59semidirect
440. C59C2×#2556semidirect
735. C2#21429174direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737172
C22×#142737052
#214291742
C2×#168373392
C2×#168373322
C2×#168373242
C2×#168373232
C2×#168373082
C2×#168373002
C2×#168372932
C2×#168372872
C2×#168372762
C2×C4×(C2×D59)⋊C42
C2×C4×C4⋊C4×C592
C2×#255659