Finite Group Databasebeta

← C2×#21437712 #29495782

Subgroups — C2×#21437712 #29495782

Order 15104.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437712C2132yesmaximal, direct product factor
2C2×#16838128C211yesmaximal, characteristic, complemented
3C2×#16838121C213yesmaximal, complemented
4C2×#16838092C213yesmaximal, complemented
5C2×#16838086C213yesmaximal, complemented
6C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
7C2×#16838059C211yesmaximal, characteristic, complemented
8C2×#16838052C213yesmaximal, complemented
9C2×#16837954C213yesmaximal, complemented
10C2×#16837933C213yesmaximal, complemented
11C2×#16837931C213yesmaximal, complemented
12C2×#41×Dic59C211yesmaximal, characteristic, complemented
13C2×C4×#11745687C213yesmaximal, complemented
14C22×Q8×Dic59C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
16C2×C59×#548C211yesmaximal, characteristic, complemented
17C22×#11745687C2213yes—
18C22×Q8×D59C2211yescharacteristic
19#16838128C22116yescomplemented
20#16838121C22148yescomplemented
21#16838092C22148yescomplemented
22#16838086C22148yescomplemented
23Q8×C22⋊D59C22116yescomplemented
24#16838059C22116yescomplemented
25#16838052C22148yescomplemented
26#16837954C22148yescomplemented
27C2×#14273726C2213yes—
28C2×#14273725C2213yes—
29#16837933C22148yescomplemented
30#16837931C22148yescomplemented
31C2×#14273720C2216yes—
32C2×#14273720C2216yes—
33C2×#14273719C2213yes—
34C2×#14273718C2213yes—
35C2×#14273717C2216yes—
36C2×#14273714C2213yes—
37C2×#14273709C2216yes—
38C2×#14273708C2216yes—
39C2×#14273706C2213yes—
40C2×#14273706C2213yes—
41C2×#14273704C2216yes—
42C2×#14273703C2213yes—
43C2×#14273698C2213yes—
44#41×Dic59C22116yescomplemented
45C4×#11745687C22148yescomplemented
46C2×Q8×Dic59C2211yescharacteristic
47C2×Q8×Dic59C2211yescharacteristic
48C2×Q8×Dic59C2213yes—
49C2×Q8×Dic59C2213yes—
50C2×Q8×Dic59C2211yescharacteristic
51C2×Q8×Dic59C22116yescomplemented
52C2×C4×Dic118C2213yes—
53C2×C4×Dic118C2213yes—
54C2×#14273692C2213yes—
55C2×#14273692C2213yes—
56C4×Q8×D59C22116yescomplemented
57C2×D4×Dic59C2213yes—
58C2×D4×Dic59C2213yes—
59C2×D4×Dic59C2213yes—
60C2×C4×C22⋊D59C2213yes—
61C2×C4×C22⋊D59C2213yes—
62C2×(C22⋊D59)⋊C4C2211yescharacteristic
63C2×(C22⋊D59)⋊C4C2213yes—
64C2×#14273686C2213yes—
65C2×#14273685C2213yes—
66C2×#14273683C2213yes—
67C2×#14273683C2213yes—
68C2×#14273683C2216yes—
69C22×C4⋊Dic59C2213yes—
70C2×C4⋊C4×D59C2213yes—
71C22×C4×Dic59C2213yes—
72C22×C4×Dic59C2213yes—
73C2×C42×D59C2213yes—
74C22×#41×C59C2211yescharacteristic
75C23×Q8×C59C2211yescharacteristic
76C59×#548C22116yescomplemented
77C2×#124×C59C2213yes—
78C2×C22⋊Q8×C59C2213yes—
79C2×#121×C59C2213yes—
80C2×C4×Q8×C59C2211yescharacteristic
81C2×C4×D4×C59C2213yes—
82C2×#11745687—224no—
83C2×#11745687C23124yes—
84C22×Dic118C2313yes—
85C22×Dic118C2313yes—
86C2×Q8×D59—28no—
87C2×Q8×D59C2318yes—
88C22×C22⋊D59C2313yes—
89C22×C22⋊D59C2311yescharacteristic
90C23×Dic59C2313yes—
91C23×Dic59C2313yes—
92C23×Dic59C2311yescharacteristic
93C23×Dic59C2313yes—
94C22×C4×D59C2313yes—
95C22×C4×D59C2313yes—
96C22×C4×D59C2311yescharacteristic
97#14273726C23124yes—
98#14273725C23124yes—
99#14273720C23148yes—
100#14273720C23148yes—
101#14273719C23124yes—
102#14273718C23124yes—
103#14273717C23148yes—
104#14273714C23124yes—
105#14273709C23148yes—
106#14273708C23148yes—
107#14273706C23124yes—
108#14273706C23124yes—
109#14273704C23148yes—
110#14273703C23124yes—
111#14273698C23124yes—
112Q8×Dic59C23124yes—
113Q8×Dic59C2318yes—
114Q8×Dic59C2318yes—
115Q8×Dic59C23124yes—
116Q8×Dic59C2318yes—
117C4×Dic118C23124yes—
118C4×Dic118C23124yes—
119#14273692C23124yes—
120#14273692C23124yes—
121D4×Dic59C23124yes—
122D4×Dic59C23124yes—
123D4×Dic59C23124yes—
124C4×C22⋊D59C23124yes—
125C4×C22⋊D59C23124yes—
126(C22⋊D59)⋊C4C23124yes—
127(C22⋊D59)⋊C4C2318yes—
128#14273686C23124yes—
129#14273685C23124yes—
130#14273683C23148yes—
131#14273683C23124yes—
132#14273683C23124yes—
133C2×C4⋊Dic59C2313yes—
134C2×C4⋊Dic59C2313yes—
135C2×C4⋊Dic59C2316yes—
136C2×C4⋊Dic59C2313yes—
137C2×C4⋊Dic59C23124yes—
138C2×C4⋊Dic59C2313yes—
139C2×Dic59⋊C4C2316yes—
140C2×Dic59⋊C4C2313yes—
141C2×Dic59⋊C4C2316yes—
142C2×Dic59⋊C4C2313yes—
143C2×Dic59⋊C4C2316yes—
144C2×Dic59⋊C4C2313yes—
145C2×Dic59⋊C4C2311yescharacteristic
146C4⋊C4×D59C23124yes—
147C2×C22⋊Dic59C2316yes—
148C2×C22⋊Dic59C2313yes—
149C2×C22⋊Dic59C2316yes—
150C2×C22⋊Dic59C2313yes—
151C2×(C2×D59)⋊C4C2313yes—
152C2×(C2×D59)⋊C4C2311yescharacteristic
153C2×C4×Dic59C2313yes—
154C2×C4×Dic59C2313yes—
155C2×C4×Dic59C2313yes—
156C2×C4×Dic59C2313yes—
157C2×C4×Dic59C23124yes—
158C2×C4×Dic59C2313yes—
159C2×C4×Dic59C23124yes—
160C2×C4×Dic59C2313yes—
161C2×C4×Dic59C2313yes—
162C2×C4×Dic59C2311yescharacteristic
163C2×C4×Dic59C2313yes—
164C42×D59C23124yes—
165C2×#41×C59—28no—
166C2×#41×C59C2318yes—
167C22×Q8×C59—28no—
168C22×Q8×C59C2313yes—
169C22×Q8×C59C2318yes—
170C22×Q8×C59C2311yescharacteristic
171C22×D4×C59C2313yes—
172C22×D4×C59C2313yes—
173C23×C4×C59C2313yes—
174C23×C4×C59C2313yes—
175#124×C59C23124yes—
176C22⋊Q8×C59C23124yes—
177#121×C59C23124yes—
178C4×Q8×C59C2318yes—
179C4×D4×C59C23124yes—
180C2×C4⋊C4×C59C2313yes—
181C2×C4⋊C4×C59C2313yes—
182C2×C22⋊C4×C59C2316yes—
183C2×C22⋊C4×C59C2313yes—
184C2×C22⋊C4×C59C2311yescharacteristic
185C2×C42×C59C2313yes—
186C24×C59C2413yes—
187C24×C59C2411yescharacteristic
188C23×D59C2411yescharacteristic
189#41×C59—232no—
190C2×Q8×C59—232no—
191C2×Q8×C59—212no—
192C2×Q8×C59#4118yescomplemented
193C2×Q8×C59C24112yes—
194C2×Q8×C59C2414yes—
195C2×D4×C59—212no—
196C2×D4×C59—212no—
197C2×D4×C59C24112yes—
198C2×D4×C59C24112yes—
199C22×C4×C59—212no—
200C22×C4×C59—212no—
201C22×C4×C59C2411yescharacteristic
202C22×C4×C59C2413yes—
203C22×C4×C59C2413yes—
204C22×C4×C59C2411yescharacteristic
205C22×C4×C59C24112yes—
206C22×C4×C59C24112yes—
207C22×C4×C59C2413yes—
208C2×C22⋊D59—212no—
209C2×C22⋊D59#4118yescomplemented
210C2×C22⋊D59C24112yes—
211C2×C22⋊D59C2414yes—
212C22×Dic59—212no—
213C22×Dic59—212no—
214C22×Dic59—24no—
215C22×Dic59—212no—
216C22×Dic59C2411yescharacteristic
217C22×Dic59C2414yes—
218C22×Dic59C2413yes—
219C22×Dic59C2413yes—
220C22×Dic59C2413yes—
221C22×Dic59C2413yes—
222C22×Dic59C24112yes—
223C22×Dic59C24112yes—
224C22×Dic59C24112yes—
225C22×Dic59C2411yescharacteristic
226C22×Dic59C2411yescharacteristic
227Q8×D59—232no—
228#11745687—296no—
229C2×C4×D59—212no—
230C2×C4×D59—212no—
231C2×C4×D59—24no—
232C2×C4×D59C2414yes—
233C2×C4×D59C24112yes—
234C2×C4×D59C24112yes—
235C2×Dic118—212no—
236C2×Dic118—212no—
237C2×Dic118C24112yes—
238C2×Dic118C24112yes—
239C4⋊C4×C59C24112yes—
240C4⋊C4×C59C24112yes—
241C22⋊C4×C59C2414yes—
242C22⋊C4×C59C24112yes—
243C22⋊C4×C59C24124yes—
244C42×C59C24112yes—
245C22⋊Dic59C24112yes—
246C22⋊Dic59C24112yes—
247C22⋊Dic59C24124yes—
248C22⋊Dic59C24124yes—
249(C2×D59)⋊C4C2414yes—
250(C2×D59)⋊C4C24112yes—
251C4⋊Dic59C24112yes—
252C4⋊Dic59C24112yes—
253C4⋊Dic59C24124yes—
254C4⋊Dic59C24112yes—
255C4⋊Dic59C24112yes—
256Dic59⋊C4C24124yes—
257Dic59⋊C4C2414yes—
258Dic59⋊C4C24112yes—
259Dic59⋊C4C24112yes—
260Dic59⋊C4C24112yes—
261Dic59⋊C4C24124yes—
262Dic59⋊C4C24124yes—
263C4×Dic59C24112yes—
264C4×Dic59C24112yes—
265C4×Dic59C24112yes—
266C4×Dic59C2414yes—
267C4×Dic59C24112yes—
268C4×Dic59C24112yes—
269C4×Dic59C24112yes—
270C4×Dic59C24112yes—
271C4×Dic59C24112yes—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—26no—
275C23×C59—26no—
276C23×C59—26no—
277C23×C59C2×#4114yes—
278C23×C59C2516yes—
279C23×C59C2512yes—
280C23×C59C2511yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59C2×#4114yes—
284C22×D59C2512yes—
285Q8×C59—224no—
286Q8×C59C2×#41116yescomplemented
287D4×C59—224no—
288D4×C59—224no—
289C2×C4×C59—26no—
290C2×C4×C59—22no—
291C2×C4×C59—26no—
292C2×C4×C59—22no—
293C2×C4×C59—224no—
294C2×C4×C59—224no—
295C2×C4×C59C2×#41112yes—
296C2×C4×C59C2512yes—
297C2×C4×C59C2512yes—
298C2×C4×C59C2516yes—
299C2×C4×C59C2516yes—
300C2×C4×C59C2516yes—
301C22⋊D59—224no—
302C22⋊D59C2×#41116yescomplemented
303C2×Dic59—26no—
304C2×Dic59—26no—
305C2×Dic59—26no—
306C2×Dic59—224no—
307C2×Dic59—22no—
308C2×Dic59—26no—
309C2×Dic59—224no—
310C2×Dic59—28no—
311C2×Dic59—224no—
312C2×Dic59C2×#4114yes—
313C2×Dic592−1+414yes—
314C2×Dic59C2512yes—
315C2×Dic59C2516yes—
316C2×Dic59C2516yes—
317C2×Dic59C2516yes—
318C2×Dic59C2516yes—
319C2×Dic59C2512yes—
320C2×Dic59C2512yes—
321C4×D59—224no—
322C4×D59—224no—
323C4×D59—28no—
324Dic118—224no—
325Dic118—224no—
326C2×#3482—591nomaximal, Sylow
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—28no—
330C22×C59—26no—
331C22×C59—26no—
332C22×C59—26no—
333C22×C59—412no—
334C22×C59C22×#4114yes—
335C22×C59C22×#4112yes—
336C22×C59C22×#4112yes—
337C22×C59C2×2−1+412yes—
338C22×C59C2611yescharacteristic
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—28no—
342C2×D59C22×#4114yes—
343C4×C59—26no—
344C4×C59—22no—
345C4×C59—26no—
346C4×C59—22no—
347C4×C59C22×#41112yes—
348Dic59—26no—
349Dic59—26no—
350Dic59—26no—
351Dic59—22no—
352Dic59—26no—
353Dic59C22×#4114yes—
354Dic59C2×2−1+414yes—
355#3482—5932no—
356C2×#557—591no—
357C2×#556—593no—
358C2×#552—593no—
359C2×#552—593no—
360C2×D4×Q8—591no—
361C2×#548—591no—
362C2×#548D5911yescharacteristic, complemented
363C2×#547—593no—
364C2×#533—593no—
365C2×#529—593no—
366C2×#529—593no—
367C2×C4×#41—591no—
368C2×C4×#41—593no—
369C22×C4×Q8—591no—
370C22×C4×Q8—591no—
371C2×C59—24no—
372C2×C59—46no—
373C2×C59#348214yescomplemented
374C2×C59C23×#4111yescharacteristic
375C2×C59C23×#4111yescharacteristic
376C2×C59C22×2−1+411yescharacteristic
377D59—24no—
378C22×#41—593no—
379C22×#41C2×D5911yescharacteristic
380C23×Q8—591no—
381C23×Q8C2×D5911yescharacteristic
382#557—5916no—
383#556—5948no—
384#552—5948no—
385#552—5948no—
386D4×Q8—5916no—
387#548—5916no—
388#548C2×D59116yescomplemented
389#547—5948no—
390#533—5948no—
391C2×C4⋊Q8—593no—
392C2×C4⋊Q8—593no—
393#529—5948no—
394#529—5948no—
395C2×#126—596no—
396C2×#126—596no—
397C2×#125—596no—
398C2×#125—593no—
399C2×#125—593no—
400C2×#124—593no—
401C2×#124C2×D5913yes—
402C2×#123—596no—
403C2×#123—596no—
404C2×C22⋊Q8—593no—
405C2×C22⋊Q8—593no—
406C2×C22⋊Q8—593no—
407C2×C22⋊Q8—596no—
408C2×C22⋊Q8C2×D5913yes—
409C2×#121—593no—
410C2×#121C2×D5913yes—
411C4×#41—5916no—
412C4×#41—5948no—
413C2×C4×Q8—591no—
414C2×C4×Q8—593no—
415C2×C4×Q8—591no—
416C2×C4×Q8—593no—
417C2×C4×Q8—5916no—
418C2×C4×Q8—591no—
419C2×C4×Q8—5916no—
420C2×C4×Q8—593no—
421C2×C4×Q8—593no—
422C2×C4×Q8—593no—
423C2×C4×Q8—593no—
424C2×C4×Q8C2×D5911yescharacteristic
425C2×C4×D4—593no—
426C2×C4×D4—593no—
427C2×C4×D4—593no—
428C2×C4×D4—593no—
429C2×C4×D4—593no—
430C2×C4×D4—591no—
431C2×C4×D4—593no—
432C2×C4×D4C2×D5913yes—
433C2×#117—593no—
434C2×#117—593no—
435C2×#117—593no—
436C2×#117—593no—
437C2×#117—596no—
438C22×C4⋊C4—593no—
439C22×C4⋊C4—593no—
440C22×C42—593no—
441C22×C42—593no—
442C22×C42—593no—
443C59C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—28no—
445C2×#41—5924no—
446C2×#41—11824no—
447C2×#41C22×D5918yes—
448C22×Q8—28no—
449C22×Q8—598no—
450C22×Q8—593no—
451C22×Q8—593no—
452C22×Q8—1188no—
453C22×Q8C22×D5913yes—
454C22×Q8C22×D5918yes—
455C22×Q8C22×D5911yescharacteristic
456C22×D4—591no—
457C22×D4—593no—
458C22×D4C22×D5913yes—
459C22×D4C22×D5913yes—
460C23×C4—593no—
461C23×C4—593no—
462C23×C4—593no—
463C23×C4—591no—
464C23×C4—593no—
465C23×C4—593no—
466C23×C4—591no—
467C23×C4C22×D5913yes—
468C23×C4C22×D5913yes—
469C4⋊Q8—5924no—
470C4⋊Q8—5924no—
471#126—5948no—
472#126—5948no—
473#125—5924no—
474#125—5948no—
475#125—5924no—
476#124—5924no—
477#124C22×D59124yes—
478#123—5948no—
479#123—5948no—
480C22⋊Q8—5924no—
481C22⋊Q8—5924no—
482C22⋊Q8—5924no—
483C22⋊Q8—5948no—
484C22⋊Q8C22×D59124yes—
485#121—5924no—
486#121C22×D59124yes—
487C4×Q8—598no—
488C4×Q8—5924no—
489C4×Q8—598no—
490C4×Q8—5924no—
491C4×Q8—598no—
492C4×Q8—5924no—
493C4×Q8—5924no—
494C4×Q8—5924no—
495C4×Q8—5924no—
496C4×Q8C22×D5918yes—
497C4×D4—5924no—
498C4×D4—5924no—
499C4×D4—5924no—
500C4×D4—5924no—
501C4×D4—5924no—
502C4×D4—598no—
503C4×D4—5924no—
504C4×D4C22×D59124yes—
505#117—5924no—
506#117—5924no—
507#117—5924no—
508#117—5924no—
509#117—5948no—
510C2×C4⋊C4—593no—
511C2×C4⋊C4—593no—
512C2×C4⋊C4—596no—
513C2×C4⋊C4—596no—
514C2×C4⋊C4—5924no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—593no—
517C2×C4⋊C4—593no—
518C2×C4⋊C4—593no—
519C2×C4⋊C4—593no—
520C2×C4⋊C4—593no—
521C2×C4⋊C4—596no—
522C2×C4⋊C4—596no—
523C2×C4⋊C4—5924no—
524C2×C4⋊C4C22×D5913yes—
525C2×C4⋊C4C22×D5913yes—
526C2×C22⋊C4—593no—
527C2×C22⋊C4—596no—
528C2×C22⋊C4—593no—
529C2×C22⋊C4—596no—
530C2×C22⋊C4—591no—
531C2×C22⋊C4—593no—
532C2×C22⋊C4C22×D5911yescharacteristic
533C2×C22⋊C4C22×D5913yes—
534C2×C22⋊C4C22×D5916yes—
535C2×C42—593no—
536C2×C42—593no—
537C2×C42—593no—
538C2×C42—593no—
539C2×C42—593no—
540C2×C42—593no—
541C2×C42—593no—
542C2×C42—591no—
543C2×C42—593no—
544C2×C42—5924no—
545C2×C42—5924no—
546C2×C42—5924no—
547C2×C42C22×D5913yes—
548C24—591no—
549C24C23×D5913yes—
550C24C23×D5911yescharacteristic
551#41—232no—
552#41—11896no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—5912no—
556C2×Q8—5912no—
557C2×Q8—11812no—
558C2×Q8—11832no—
559C2×Q8—11812no—
560C2×Q8#1174568718yescomplemented
561C2×Q8C23×D59112yes—
562C2×Q8C23×D5914yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—598no—
566C2×D4—594no—
567C2×D4—5912no—
568C2×D4—11812no—
569C2×D4C23×D59112yes—
570C2×D4C23×D59112yes—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—591no—
574C22×C4—591no—
575C22×C4—594no—
576C22×C4—5912no—
577C22×C4—5912no—
578C22×C4—5912no—
579C22×C4—591no—
580C22×C4—593no—
581C22×C4—593no—
582C22×C4—593no—
583C22×C4—593no—
584C22×C4—594no—
585C22×C4—5912no—
586C22×C4—5912no—
587C22×C4—1184no—
588C22×C4—11812no—
589C22×C4—11812no—
590C22×C4—1184no—
591C22×C4—11812no—
592C22×C4—11812no—
593C22×C4—11812no—
594C22×C4C23×D59112yes—
595C22×C4C23×D59112yes—
596C22×C4C23×D5911yescharacteristic
597C22×C4C23×D5911yescharacteristic
598C22×C4C23×D5913yes—
599C22×C4C23×D5913yes—
600C22×C4C23×D5913yes—
601C4⋊C4—5912no—
602C4⋊C4—5912no—
603C4⋊C4—5924no—
604C4⋊C4—5924no—
605C4⋊C4—594no—
606C4⋊C4—5912no—
607C4⋊C4—5912no—
608C4⋊C4—5912no—
609C4⋊C4—5912no—
610C4⋊C4—5912no—
611C4⋊C4—5924no—
612C4⋊C4—5924no—
613C4⋊C4C23×D59112yes—
614C4⋊C4C23×D59112yes—
615C22⋊C4—5912no—
616C22⋊C4—5924no—
617C22⋊C4—5912no—
618C22⋊C4—5924no—
619C22⋊C4—594no—
620C22⋊C4—5912no—
621C22⋊C4C23×D5914yes—
622C22⋊C4C23×D59112yes—
623C22⋊C4C23×D59124yes—
624C42—594no—
625C42—5912no—
626C42—5912no—
627C42—5912no—
628C42—5912no—
629C42—5912no—
630C42—5912no—
631C42—5912no—
632C42—5912no—
633C42C23×D59112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—594no—
640C23—592no—
641C23—1182no—
642C23—1182no—
643C23#41×D5914yes—
644C23C24×D5916yes—
645C23C24×D5912yes—
646C23C24×D5911yescharacteristic
647Q8—224no—
648Q8—11824no—
649Q8—11824no—
650Q8C2×#11745687116yescomplemented
651D4—224no—
652D4—224no—
653D4—5916no—
654D4—11824no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—26no—
658C2×C4—22no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—594no—
662C2×C4—594no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—596no—
667C2×C4—596no—
668C2×C4—596no—
669C2×C4—596no—
670C2×C4—1188no—
671C2×C4—11824no—
672C2×C4—1188no—
673C2×C4—11824no—
674C2×C4—11824no—
675C2×C4—1186no—
676C2×C4—1186no—
677C2×C4—11824no—
678C2×C4—1186no—
679C2×C4—1182no—
680C2×C4—1186no—
681C2×C4—11824no—
682C2×C4C2×#11745687112yes—
683C2×C4C24×D5912yes—
684C2×C4C24×D5912yes—
685C2×C4C24×D5916yes—
686C2×C4C24×D5916yes—
687C2×C4C24×D5916yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—594no—
696C22—1188no—
697C22—1182no—
698C22—1182no—
699C22C2×#41×D5914yes—
700C22C2×#41×D5912yes—
701C22C22×#1174568712yes—
702C222−1+4×D5912yes—
703C22C25×D5911yescharacteristic
704C4—26no—
705C4—22no—
706C4—26no—
707C4—22no—
708C4—594no—
709C4—594no—
710C4—1186no—
711C4—1186no—
712C4—1186no—
713C4—1182no—
714C4—1186no—
715C4C22×#11745687112yes—
716C2—24no—
717C2—46no—
718C2—1184no—
719C2#2143771214yesdirect product factor
720C2C22×#41×D5911yescharacteristic
721C2C23×#1174568711yescharacteristic
722C2C2×2−1+4×D5911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#548C2
socleC23×C59C25
hypercenterC2×#548D59
hypocenterC59C2×#3482
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #21437712C2direct (N × H)
2. C2×#16838128C2semidirect
3. C2×#16838121C2semidirect
4. C2×#16838092C2semidirect
5. C2×#16838086C2semidirect
6. C2×Q8×C22⋊D59C2semidirect
7. C2×#16838059C2semidirect
8. C2×#16838052C2semidirect
9. C2×#16837954C2semidirect
10. C2×#16837933C2semidirect
11. C2×#16837931C2semidirect
12. C2×#41×Dic59C2semidirect
13. C2×C4×#11745687C2semidirect
14. C22×Q8×Dic59C2semidirect
15. C2×C4×Q8×D59C2semidirect
16. C2×C59×#548C2semidirect
19. #16838128C22semidirect
20. #16838121C22semidirect
21. #16838092C22semidirect
22. #16838086C22semidirect
23. Q8×C22⋊D59C22semidirect
24. #16838059C22semidirect
25. #16838052C22semidirect
26. #16837954C22semidirect
29. #16837933C22semidirect
30. #16837931C22semidirect
44. #41×Dic59C22semidirect
45. C4×#11745687C22semidirect
51. C2×Q8×Dic59C22semidirect
56. C4×Q8×D59C22semidirect
76. C59×#548C22semidirect
192. C2×Q8×C59#41semidirect
209. C2×C22⋊D59#41semidirect
286. Q8×C59C2×#41semidirect
302. C22⋊D59C2×#41semidirect
362. C2×#548D59semidirect
373. C2×C59#3482semidirect
388. #548C2×D59semidirect
443. C59C2×#3482semidirect
560. C2×Q8#11745687semidirect
650. Q8C2×#11745687semidirect
719. C2#21437712direct (N × H)

Maximal subgroups

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

subgroupindex
#214377122
C2×#168381282
C2×#168381212
C2×#168380922
C2×#168380862
C2×Q8×C22⋊D592
C2×#168380592
C2×#168380522
C2×#168379542
C2×#168379332
C2×#168379312
C2×#41×Dic592
C2×C4×#117456872
C22×Q8×Dic592
C2×C4×Q8×D592
C2×C59×#5482
C2×#348259