Finite Group Databasebeta

← C2×#21427769 #28757329

Subgroups — C2×#21427769 #28757329

Order 15104.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273703C211yesmaximal, characteristic
2C22×#14273684C211yesmaximal, characteristic
3#21427769C2116yesmaximal, direct product factor
4C2×#16837343C211yesmaximal, characteristic, complemented
5C2×#16837336C211yesmaximal, characteristic, complemented
6C2×#16837332C211yesmaximal, characteristic, complemented
7C2×#16837321C211yesmaximal, characteristic, complemented
8C2×#16837299C211yesmaximal, characteristic, complemented
9C2×#16837289C211yesmaximal, characteristic, complemented
10C2×#16837286C211yesmaximal, characteristic, complemented
11C2×#16837276C211yesmaximal, characteristic
12C2×#16837273C211yesmaximal, characteristic
13C2×#16837264C211yesmaximal, characteristic
14C2×#16837261C211yesmaximal, characteristic
15C2×#95×D59C211yesmaximal, characteristic
16C2×C59×#391C211yesmaximal, characteristic, complemented
17C23×C4×D59C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273703—28no—
21C2×#14273703C2218yes—
22C2×#14273684—28no—
23C2×#14273684C2218yes—
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
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×C4×Dic59C2211yescharacteristic
39#16837343C2218yescomplemented
40#16837336C2218yescomplemented
41#16837332C2218yescomplemented
42#16837321C2218yescomplemented
43#16837299C2218yescomplemented
44#16837289C2218yescomplemented
45#16837286C2218yescomplemented
46#16837276C2218yes—
47#16837273C2218yes—
48#16837264C2218yes—
49#16837261C2218yes—
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
59C2×C59⋊#95C2211yescharacteristic
60#95×D59C2218yes—
61C23×Q8×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C59×#391C2218yescomplemented
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C22×C4×D59—24no—
78C22×C4×D59—24no—
79C22×C4×D59—24no—
80C22×C4×D59—24no—
81C22×C4×D59—24no—
82C22×C4×D59—24no—
83C22×C4×D59—42no—
84C22×C4×D59—42no—
85C22×C4×D59Q818yescomplemented
86C22×C4×D59C2314yes—
87C22×C4×D59C2314yes—
88C22×C4×D59C2314yes—
89#14273703—232no—
90#14273684—232no—
91C2×C4⋊Dic59—24no—
92C2×C4⋊Dic59—42no—
93C2×C4⋊Dic59C2314yes—
94C2×C4⋊Dic59C2314yes—
95C2×Dic59⋊C4—24no—
96C2×Dic59⋊C4—24no—
97C2×Dic59⋊C4—24no—
98C2×Dic59⋊C4—24no—
99C2×Dic59⋊C4—24no—
100C2×Dic59⋊C4—24no—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4—42no—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×Dic59⋊C4C2314yes—
110C2×Dic59⋊C4C2314yes—
111C2×(C2×D59)⋊C4—24no—
112C2×(C2×D59)⋊C4—24no—
113C2×(C2×D59)⋊C4—24no—
114C2×(C2×D59)⋊C4D418yes—
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
119C2×C4×Dic59—24no—
120C2×C4×Dic59C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C22×Q8×C59—24no—
132C22×Q8×C59—24no—
133C22×Q8×C59—42no—
134C22×Q8×C59C2314yes—
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59—42no—
143C2×C4⋊C4×C59C2314yes—
144C2×C42×C59—24no—
145C2×C42×C59C2314yes—
146#95×C59C2314yes—
147#95×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150C24×C59C2411yescharacteristic
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—22no—
155C23×D59C2×D414yes—
156C23×D59C2×Q814yes—
157C23×D59#4114yes—
158C23×D59C2412yes—
159C2×Q8×C59—28no—
160C2×Q8×C59—28no—
161C2×Q8×C59—44no—
162C2×Q8×C59—416no—
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×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59C2×D414yes—
182C22×C4×C59C2×Q814yes—
183C22×C4×C59#4114yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
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×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59C2×D414yes—
210C22×Dic59C2×Q814yes—
211C22×Dic59#4114yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C2×C4×D59—232no—
220C2×C4×D59—28no—
221C2×C4×D59—28no—
222C2×C4×D59—28no—
223C2×C4×D59—28no—
224C2×C4×D59—28no—
225C2×C4×D59—28no—
226C2×C4×D59—44no—
227C2×C4×D59—44no—
228C2×C4×D59—416no—
229C2×C4×D59—416no—
230C2×C4×D59C2×Q8116yescomplemented
231C4⋊C4×C59—44no—
232C42×C59—28no—
233(C2×D59)⋊C4—28no—
234(C2×D59)⋊C4—28no—
235(C2×D59)⋊C4—28no—
236(C2×D59)⋊C4C2×D4116yes—
237C4⋊Dic59—28no—
238C4⋊Dic59—44no—
239Dic59⋊C4—28no—
240Dic59⋊C4—28no—
241Dic59⋊C4—28no—
242Dic59⋊C4—28no—
243Dic59⋊C4—28no—
244Dic59⋊C4—28no—
245Dic59⋊C4—28no—
246Dic59⋊C4—44no—
247C4×Dic59—28no—
248C23×C59C22×D412yes—
249C23×C59C22×Q812yes—
250C23×C59C2×#4112yes—
251C23×C59C2×#4112yes—
252C23×C59C2×#4112yes—
253C23×C59H(5,𝔽2)12yes—
254C23×C592−1+412yes—
255C23×C59C2511yescharacteristic
256C22×D59—28no—
257C22×D59—28no—
258C22×D59—28no—
259C22×D59—28no—
260C22×D59—28no—
261C22×D59—28no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59—22no—
265C22×D59—22no—
266C22×D59C22⋊Q8116yes—
267C22×D59C22×D414yes—
268C22×D59C22×Q814yes—
269C22×D59C2×#4114yes—
270Q8×C59—416no—
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—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—44no—
293C2×C4×C59—44no—
294C2×C4×C59—44no—
295C2×C4×C59—44no—
296C2×C4×C59C22×D414yes—
297C2×C4×C59C22×Q814yes—
298C2×C4×C59C2×#4114yes—
299C2×Dic59—28no—
300C2×Dic59—28no—
301C2×Dic59—28no—
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—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—44no—
321C2×Dic59—44no—
322C2×Dic59—44no—
323C2×Dic59—44no—
324C2×Dic59C22×D414yes—
325C2×Dic59C22×Q814yes—
326C2×Dic59C2×#4114yes—
327C4×D59—232no—
328C4×D59—416no—
329C4×D59—416no—
330C2×#2438—591nomaximal, Sylow
331C22×C59C2×C22⋊Q814yes—
332C22×C59#53314yes—
333C22×C59#54414yes—
334C22×C59#54614yes—
335C22×C59#54714yes—
336C22×C59#55114yes—
337C22×C59#55214yes—
338C22×C59C23×D411yescharacteristic
339C22×C59C23×Q811yescharacteristic
340C22×C59C22×#4111yescharacteristic
341C22×C59C22×#4111yescharacteristic
342C22×C59C22×#4111yescharacteristic
343C22×C59C2×H(5,𝔽2)11yescharacteristic
344C22×C59C2×2−1+411yescharacteristic
345C2×D59—24no—
346C2×D59—24no—
347C2×D59—232no—
348C2×D59—24no—
349C2×D59—24no—
350C2×D59—24no—
351C2×D59—24no—
352C2×D59C2×C22⋊Q818yes—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—24no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360Dic59—24no—
361Dic59—24no—
362Dic59—24no—
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C22×C22⋊Q8—591no—
368C22×#117—591no—
369#2438—5916no—
370C2×#400—591no—
371C2×#398—591no—
372C2×#398—591no—
373C2×#395—591no—
374C2×#391D5911yescharacteristic, complemented
375C2×#389—591no—
376C2×#387—591no—
377C2×#387—591no—
378C2×#385—591no—
379C2×#385—591no—
380C2×#381—591no—
381C2×#380—591no—
382C22×#95—591no—
383C2×C59#243818yescomplemented
384C2×C59C22×C22⋊Q811yescharacteristic
385C2×C59C2×#53311yescharacteristic
386C2×C59C2×#54411yescharacteristic
387C2×C59C2×#54611yescharacteristic
388C2×C59C2×#54711yescharacteristic
389C2×C59C2×#55111yescharacteristic
390C2×C59C2×#55211yescharacteristic
391D59—28no—
392C23×Q8C2×D5911yescharacteristic
393C24×C4—591no—
394C24×C4—591no—
395C24×C4—591no—
396C2×C22⋊Q8—598no—
397C2×C22⋊Q8—1188no—
398C2×#117—598no—
399C2×#117—1188no—
400C22×C4⋊C4—591no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4—591no—
408C22×C4⋊C4—591no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4C2×D5911yescharacteristic
411C22×C22⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C22⋊C4—591no—
414C22×C22⋊C4—591no—
415C22×C42—591no—
416C22×C42C2×D5911yescharacteristic
417#400—598no—
418#398—598no—
419#398—598no—
420#395—598no—
421#391C2×D5918yescomplemented
422#389—598no—
423#387—598no—
424#387—598no—
425#385—598no—
426#385—598no—
427#381—598no—
428#380—598no—
429C2×#95—591no—
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×#95—591no—
439C2×#95—598no—
440C2×#95C2×D5911yescharacteristic
441C2×#95C2×D5911yescharacteristic
442C2×#95C2×D5911yescharacteristic
443C2×#95C2×D5911yescharacteristic
444C59C2×#243811yescharacteristic, complemented, Sylow
445C25—591no—
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D5914yes—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—591no—
453C23×C4—598no—
454C23×C4—594no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—591no—
459C23×C4—594no—
460C23×C4—594no—
461C23×C4—1184no—
462C23×C4—1184no—
463C23×C4—1184no—
464C23×C4—1184no—
465C23×C4—1184no—
466C23×C4—1184no—
467C23×C4—2362no—
468C23×C4—2362no—
469C23×C4C22×D5911yescharacteristic
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C23×C4C22×D5911yescharacteristic
476C22⋊Q8—11832no—
477#117—11832no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—594no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—594no—
483C2×C4⋊C4—594no—
484C2×C4⋊C4—594no—
485C2×C4⋊C4—594no—
486C2×C4⋊C4—594no—
487C2×C4⋊C4—594no—
488C2×C4⋊C4—594no—
489C2×C4⋊C4—1184no—
490C2×C4⋊C4—1184no—
491C2×C4⋊C4—1184no—
492C2×C4⋊C4—1184no—
493C2×C4⋊C4—1184no—
494C2×C4⋊C4—1184no—
495C2×C4⋊C4—1184no—
496C2×C4⋊C4—1184no—
497C2×C4⋊C4—2362no—
498C2×C4⋊C4—2362no—
499C2×C4⋊C4C22×D5914yes—
500C2×C22⋊C4—598no—
501C2×C22⋊C4—594no—
502C2×C22⋊C4—594no—
503C2×C22⋊C4—594no—
504C2×C22⋊C4—594no—
505C2×C22⋊C4—1184no—
506C2×C22⋊C4—1184no—
507C2×C22⋊C4—1184no—
508C2×C42—24no—
509C2×C42—594no—
510C2×C42—1184no—
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#95—594no—
521#95—594no—
522#95C22×D5914yes—
523#95C22×D5914yes—
524#95C22×D5914yes—
525#95C22×D5914yes—
526C24—594no—
527C24—594no—
528C24—594no—
529C24—592no—
530C24—1182no—
531C24—1182no—
532C24—1182no—
533C24—1182no—
534C24C23×D5911yescharacteristic
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—44no—
538C2×Q8—416no—
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—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—594no—
558C22×C4—594no—
559C22×C4—594no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—5916no—
564C22×C4—592no—
565C22×C4—592no—
566C22×C4—592no—
567C22×C4—592no—
568C22×C4—1188no—
569C22×C4—1188no—
570C22×C4—11832no—
571C22×C4—1188no—
572C22×C4—1188no—
573C22×C4—1188no—
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—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1188no—
593C22×C4—2364no—
594C22×C4—2364no—
595C22×C4—23616no—
596C22×C4—23616no—
597C22×C4#1174568514yes—
598C22×C4D4×D5914yes—
599C22×C4Q8×D5914yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5912yes—
602C22×C4C23×D5912yes—
603C22×C4C23×D5912yes—
604C22×C4C23×D5912yes—
605C22×C4C23×D5912yes—
606C22×C4C23×D5912yes—
607C4⋊C4—44no—
608C4⋊C4—1188no—
609C4⋊C4—1188no—
610C4⋊C4—1188no—
611C4⋊C4—1188no—
612C4⋊C4—1188no—
613C4⋊C4—1188no—
614C4⋊C4—1188no—
615C4⋊C4—1188no—
616C4⋊C4—2364no—
617C4⋊C4—2364no—
618C22⋊C4—5916no—
619C22⋊C4—1188no—
620C22⋊C4—1188no—
621C22⋊C4—1188no—
622C42—28no—
623C42—1188no—
624C23—5916no—
625C23—594no—
626C23—594no—
627C23—594no—
628C23—1188no—
629C23—1182no—
630C23—1182no—
631C23—1182no—
632C23—1182no—
633C23—1188no—
634C23—1188no—
635C23—1188no—
636C23—1188no—
637C23—1188no—
638C23C2×D4×D5912yes—
639C23C2×Q8×D5912yes—
640C23#41×D5912yes—
641C23#41×D5912yes—
642C23C2×#1174568512yes—
643C23#1427377212yes—
644C23#1427377512yes—
645C23C24×D5911yescharacteristic
646Q8—416no—
647C2×C4—28no—
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—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—594no—
673C2×C4—594no—
674C2×C4—594no—
675C2×C4—11832no—
676C2×C4—1188no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1188no—
684C2×C4—1188no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—23616no—
698C2×C4—23616no—
699C2×C4—2364no—
700C2×C4—2364no—
701C2×C4—2364no—
702C2×C4—2364no—
703C2×C4C2×D4×D5914yes—
704C2×C4C2×Q8×D5914yes—
705C2×C4C2×#1174568514yes—
706C22—598no—
707C22—1184no—
708C22—11832no—
709C22—1184no—
710C22—1184no—
711C22—1184no—
712C22—1184no—
713C22—1184no—
714C22C22⋊Q8×D5914yes—
715C22#1683795614yes—
716C22#1683802914yes—
717C22#1683804214yes—
718C22#1683805414yes—
719C22#1683808214yes—
720C22#1683809314yes—
721C22C22×D4×D5911yescharacteristic
722C22C22×Q8×D5911yescharacteristic
723C22C2×#41×D5911yescharacteristic
724C22C2×#41×D5911yescharacteristic
725C22C22×#1174568511yescharacteristic
726C22C2×#1427377211yescharacteristic
727C22C2×#1427377511yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—1184no—
736C4—1184no—
737C4—1184no—
738C4—2362no—
739C4—2362no—
740C4—2362no—
741C4—2362no—
742C2—1188no—
743C2#2142776918yesdirect product factor
744C2C2×C22⋊Q8×D5911yescharacteristic
745C2C2×#1683795611yescharacteristic
746C2C2×#1683802911yescharacteristic
747C2C2×#1683804211yescharacteristic
748C2C2×#1683805411yescharacteristic
749C2C2×#1683808211yescharacteristic
750C2C2×#1683809311yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#391C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#391D59
hypocenterC59C2×#2438
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #21427769C2direct (N × H)
4. C2×#16837343C2semidirect
5. C2×#16837336C2semidirect
6. C2×#16837332C2semidirect
7. C2×#16837321C2semidirect
8. C2×#16837299C2semidirect
9. C2×#16837289C2semidirect
10. C2×#16837286C2semidirect
16. C2×C59×#391C2semidirect
39. #16837343C22semidirect
40. #16837336C22semidirect
41. #16837332C22semidirect
42. #16837321C22semidirect
43. #16837299C22semidirect
44. #16837289C22semidirect
45. #16837286C22semidirect
64. C59×#391C22semidirect
85. C22×C4×D59Q8semidirect
230. C2×C4×D59C2×Q8semidirect
374. C2×#391D59semidirect
383. C2×C59#2438semidirect
421. #391C2×D59semidirect
444. C59C2×#2438semidirect
743. C2#21427769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737032
C22×#142736842
#214277692
C2×#168373432
C2×#168373362
C2×#168373322
C2×#168373212
C2×#168372992
C2×#168372892
C2×#168372862
C2×#168372762
C2×#168372732
C2×#168372642
C2×#168372612
C2×#95×D592
C2×C59×#3912
C2×#243859