Finite Group Databasebeta

← C2×#21429181 #28758787

Subgroups — C2×#21429181 #28758787

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×#14273704C211yesmaximal, characteristic
3#21429181C2116yesmaximal, direct product factor
4C2×#16837333C211yesmaximal, characteristic, complemented
5C2×#16837325C211yesmaximal, characteristic
6C2×#16837323C211yesmaximal, characteristic, complemented
7C2×#16837307C211yesmaximal, characteristic, complemented
8C2×#16837301C211yesmaximal, characteristic, complemented
9C2×#16837298C211yesmaximal, characteristic, complemented
10C2×#16837296C211yesmaximal, characteristic
11C2×#16837290C211yesmaximal, characteristic
12C2×#16837288C211yesmaximal, characteristic, complemented
13C2×#16837277C211yesmaximal, characteristic
14C2×#16837253C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic59C211yesmaximal, characteristic
16C2×C59×#399C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×#14273717—28no—
20C2×#14273717C2218yescomplemented
21C2×#14273704—28no—
22C2×#14273704C2218yes—
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×C22⋊Dic59C2211yescharacteristic
34C22×C22⋊Dic59C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40#16837333C2218yescomplemented
41#16837325C2218yes—
42#16837323C2218yescomplemented
43#16837307C2218yescomplemented
44#16837301C2218yescomplemented
45#16837298C2218yescomplemented
46#16837296C2218yes—
47#16837290C2218yes—
48#16837288C2218yescomplemented
49#16837277C2218yes—
50#16837253C2218yescomplemented
51C22⋊C4×Dic59C2218yes—
52C2×C59⋊#95C2211yescharacteristic
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×C4⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C22×C22⋊C4×C59C2211yescharacteristic
66C22×C22⋊C4×C59C2211yescharacteristic
67C59×#399C2218yes—
68C2×#95×C59C2211yescharacteristic
69C22×Dic118—24no—
70C22×Dic118—24no—
71C22×Dic118—42no—
72C22×Dic118C2314yes—
73C23×Dic59—24no—
74C23×Dic59—24no—
75C23×Dic59—42no—
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2314yes—
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85#14273717—232no—
86#14273704—232no—
87C2×C4⋊Dic59—24no—
88C2×C4⋊Dic59—24no—
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59—42no—
91C2×C4⋊Dic59C2314yes—
92C2×C4⋊Dic59C2314yes—
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⋊C4D418yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×C22⋊Dic59—24no—
108C2×C22⋊Dic59—42no—
109C2×C22⋊Dic59Q818yescomplemented
110C2×C22⋊Dic59C2314yes—
111C2×C22⋊Dic59C2314yes—
112C2×C22⋊Dic59C2314yes—
113C2×C4×Dic59—24no—
114C2×C4×Dic59—24no—
115C2×C4×Dic59—42no—
116C2×C4×Dic59—42no—
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—
130C25×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59—24no—
138C2×C4⋊C4×C59—24no—
139C2×C4⋊C4×C59—24no—
140C2×C4⋊C4×C59C2314yes—
141C2×C4⋊C4×C59C2314yes—
142C2×C4⋊C4×C59C2314yes—
143C2×C22⋊C4×C59—24no—
144C2×C22⋊C4×C59—24no—
145C2×C22⋊C4×C59—24no—
146C2×C22⋊C4×C59C2314yes—
147C2×C22⋊C4×C59C2314yes—
148C2×C22⋊C4×C59C2314yes—
149#95×C59C2314yes—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59C2×Q814yes—
157C24×C59C2412yes—
158C24×C59C2411yescharacteristic
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×C59#4114yes—
176C22×C4×C59#4114yes—
177C22×C4×C59C2412yes—
178C22×C4×C59C2412yes—
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×Dic59—22no—
184C22×Dic59—22no—
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×Dic59—22no—
202C22×Dic59—28no—
203C22×Dic59—28no—
204C22×Dic59—44no—
205C22×Dic59—416no—
206C22×Dic59C2×D414yes—
207C22×Dic59C2×D414yes—
208C22×Dic59C2×Q814yes—
209C22×Dic59C2×Q814yes—
210C22×Dic59#4114yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C2×Dic118—28no—
220C2×Dic118—28no—
221C2×Dic118—44no—
222C2×Dic118—416no—
223C4⋊C4×C59—28no—
224C4⋊C4×C59—28no—
225C4⋊C4×C59—28no—
226C22⋊C4×C59—28no—
227C22⋊C4×C59—28no—
228C22⋊C4×C59—28no—
229C22⋊Dic59—28no—
230C22⋊Dic59—44no—
231C22⋊Dic59C2×Q8116yescomplemented
232C4⋊Dic59—28no—
233C4⋊Dic59—28no—
234C4⋊Dic59—28no—
235C4⋊Dic59—44no—
236Dic59⋊C4—28no—
237Dic59⋊C4—28no—
238Dic59⋊C4—28no—
239Dic59⋊C4—28no—
240Dic59⋊C4—28no—
241Dic59⋊C4C2×D4116yes—
242C4×Dic59—28no—
243C4×Dic59—28no—
244C4×Dic59—44no—
245C4×Dic59—44no—
246C23×C59—28no—
247C23×C59—28no—
248C23×C59—28no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—44no—
256C23×C59—44no—
257C23×C59—44no—
258C23×C59—44no—
259C23×C59C22×D412yes—
260C23×C59C22×Q814yes—
261C23×C59C22×Q812yes—
262C23×C59C2×#4112yes—
263C23×C59C2×#4112yes—
264C23×C59C2×#4112yes—
265C23×C59H(5,𝔽2)12yes—
266C23×C592−1+412yes—
267C23×C59C2511yescharacteristic
268C2×C4×C59—28no—
269C2×C4×C59—28no—
270C2×C4×C59—28no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
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—44no—
287C2×C4×C59—44no—
288C2×C4×C59—44no—
289C2×C4×C59C22×D414yes—
290C2×C4×C59C2×#4114yes—
291C2×C4×C59C2×#4114yes—
292C2×Dic59—28no—
293C2×Dic59—28no—
294C2×Dic59—28no—
295C2×Dic59—28no—
296C2×Dic59—28no—
297C2×Dic59—22no—
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—416no—
317C2×Dic59—44no—
318C2×Dic59—44no—
319C2×Dic59—44no—
320C2×Dic59C22×D414yes—
321C2×Dic59C22×D414yes—
322C2×Dic59C22×Q814yes—
323C2×Dic59C22×Q814yes—
324C2×Dic59C2×#4114yes—
325Dic118—416no—
326C2×#2556—591nomaximal, Sylow
327C22×C59—24no—
328C22×C59—24no—
329C22×C59—24no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—416no—
335C22×C59#53214yes—
336C22×C59#53314yes—
337C22×C59#53914yes—
338C22×C59#54614yes—
339C22×C59D4×Q814yes—
340C22×C59#55214yes—
341C22×C59#55414yes—
342C22×C59C23×D411yescharacteristic
343C22×C59C23×Q811yescharacteristic
344C22×C59C22×#4111yescharacteristic
345C22×C59C22×#4111yescharacteristic
346C22×C59C22×#4111yescharacteristic
347C22×C59C2×H(5,𝔽2)11yescharacteristic
348C22×C59C2×2−1+411yescharacteristic
349C4×C59—24no—
350C4×C59—24no—
351C4×C59—24no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355Dic59—24no—
356Dic59—24no—
357Dic59—24no—
358Dic59—24no—
359Dic59—24no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363C22×#125—591no—
364C22×C22⋊Q8—591no—
365#2556—5916no—
366C2×#399D5911yescharacteristic
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⋊C4—591no—
378C2×C4×C22⋊C4—591no—
379C2×C59—44no—
380C2×C59#255618yescomplemented
381C2×C59C2×#53211yescharacteristic
382C2×C59C2×#53311yescharacteristic
383C2×C59C2×#53911yescharacteristic
384C2×C59C2×#54611yescharacteristic
385C2×C59C2×D4×Q811yescharacteristic
386C2×C59C2×#55211yescharacteristic
387C2×C59C2×#55411yescharacteristic
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⋊C4C2×D5911yescharacteristic
405C22×C4⋊C4C2×D5911yescharacteristic
406C22×C4⋊C4C2×D5911yescharacteristic
407C22×C22⋊C4—591no—
408C22×C22⋊C4—591no—
409C22×C22⋊C4—591no—
410C22×C22⋊C4C2×D5911yescharacteristic
411C22×C22⋊C4C2×D5911yescharacteristic
412C22×C22⋊C4C2×D5911yescharacteristic
413C22×C42—591no—
414C22×C42—591no—
415C22×C42—591no—
416C22×C42—591no—
417#399C2×D5918yes—
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⋊C4—598no—
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×#95—591no—
439C2×#95C2×D5911yescharacteristic
440C59C2×#255611yescharacteristic, complemented, Sylow
441C25C22×D5911yescharacteristic
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—591no—
454C23×C4—594no—
455C23×C4—1184no—
456C23×C4—1184no—
457C23×C4—2362no—
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—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—598no—
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—594no—
479C2×C4⋊C4—594no—
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⋊C4C22×D5914yes—
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—598no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—1184no—
500C2×C22⋊C4—2362no—
501C2×C22⋊C4C22×D5914yes—
502C2×C22⋊C4C22×D5914yes—
503C2×C22⋊C4C22×D5914yes—
504C2×C42—594no—
505C2×C42—594no—
506C2×C42—594no—
507C2×C42—594no—
508C2×C42—1184no—
509C2×C42—1184no—
510C2×C42—2362no—
511C2×C42—2362no—
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#95C22×D5914yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24Q8×D5914yes—
529C24C23×D5912yes—
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—594no—
553C22×C4—594no—
554C22×C4—594no—
555C22×C4—592no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—592no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—1188no—
564C22×C4—1188no—
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—1182no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—2364no—
585C22×C4—23616no—
586C22×C4D4×D5914yes—
587C22×C4#1174568714yes—
588C22×C4#1174568714yes—
589C22×C4C23×D5912yes—
590C22×C4C23×D5912yes—
591C22×C4C23×D5912yes—
592C22×C4C23×D5912yes—
593C22×C4C23×D5912yes—
594C22×C4C23×D5912yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—5916no—
599C4⋊C4—1188no—
600C4⋊C4—1188no—
601C4⋊C4—1188no—
602C4⋊C4—1188no—
603C4⋊C4—1188no—
604C4⋊C4—1188no—
605C4⋊C4—1188no—
606C4⋊C4—1188no—
607C4⋊C4—2364no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—5916no—
612C22⋊C4—1188no—
613C22⋊C4—2364no—
614C42—1188no—
615C42—1188no—
616C42—2364no—
617C42—2364no—
618C23—28no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—28no—
626C23—28no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D5912yes—
632C23C2×Q8×D5914yes—
633C23C2×Q8×D5912yes—
634C23#41×D5912yes—
635C23C2×#1174568712yes—
636C23C2×#1174568712yes—
637C23#1427377312yes—
638C23#1427377412yes—
639C23C24×D5911yescharacteristic
640Q8—23616no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—594no—
663C2×C4—594no—
664C2×C4—594no—
665C2×C4—594no—
666C2×C4—594no—
667C2×C4—1188no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1188no—
679C2×C4—1188no—
680C2×C4—1188no—
681C2×C4—1188no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—23616no—
692C2×C4—2364no—
693C2×C4—2364no—
694C2×C4—2364no—
695C2×C4C2×D4×D5914yes—
696C2×C4C2×#1174568714yes—
697C2×C4C2×#1174568714yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—416no—
705C22—42no—
706C22#1683795014yes—
707C22#1683795414yes—
708C22#1683799614yes—
709C22#1683804414yes—
710C22#1683806514yes—
711C22#1683808914yes—
712C22#1683811014yes—
713C22C22×D4×D5911yescharacteristic
714C22C22×Q8×D5911yescharacteristic
715C22C2×#41×D5911yescharacteristic
716C22C22×#1174568711yescharacteristic
717C22C22×#1174568711yescharacteristic
718C22C2×#1427377311yescharacteristic
719C22C2×#1427377411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1184no—
727C4—1184no—
728C4—1184no—
729C4—1184no—
730C4—1184no—
731C4—2362no—
732C4—2362no—
733C4—2362no—
734C2—44no—
735C2#2142918118yesdirect product factor
736C2C2×#1683795011yescharacteristic
737C2C2×#1683795411yescharacteristic
738C2C2×#1683799611yescharacteristic
739C2C2×#1683804411yescharacteristic
740C2C2×#1683806511yescharacteristic
741C2C2×#1683808911yescharacteristic
742C2C2×#1683811011yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#399C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#399D59
hypocenterC59C2×#2556
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#14273717C2semidirect
3. #21429181C2direct (N × H)
4. C2×#16837333C2semidirect
6. C2×#16837323C2semidirect
7. C2×#16837307C2semidirect
8. C2×#16837301C2semidirect
9. C2×#16837298C2semidirect
12. C2×#16837288C2semidirect
14. C2×#16837253C2semidirect
20. C2×#14273717C22semidirect
40. #16837333C22semidirect
42. #16837323C22semidirect
43. #16837307C22semidirect
44. #16837301C22semidirect
45. #16837298C22semidirect
48. #16837288C22semidirect
50. #16837253C22semidirect
109. C2×C22⋊Dic59Q8semidirect
231. C22⋊Dic59C2×Q8semidirect
380. C2×C59#2556semidirect
440. C59C2×#2556semidirect
735. C2#21429181direct (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×#142737042
#214291812
C2×#168373332
C2×#168373252
C2×#168373232
C2×#168373072
C2×#168373012
C2×#168372982
C2×#168372962
C2×#168372902
C2×#168372882
C2×#168372772
C2×#168372532
C2×C22⋊C4×Dic592
C2×C59×#3992
C2×#255659