Finite Group Databasebeta

← C2×#21437713 #29495781

Subgroups — C2×#21437713 #29495781

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#21437713C2132yesmaximal, direct product factor
2C2×#16838128C211yesmaximal, characteristic, complemented
3C2×#16838124C213yesmaximal, complemented
4C2×#16838093C213yesmaximal, complemented
5C2×#16838087C213yesmaximal, complemented
6C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
7C2×#16838064C211yesmaximal, characteristic, complemented
8C2×#16838063C211yesmaximal, characteristic, complemented
9C2×#16838053C213yesmaximal, complemented
10C2×#16837956C213yesmaximal, complemented
11C2×#16837939C213yesmaximal, complemented
12C2×#16837936C213yesmaximal, complemented
13C2×C4×#11745689C211yesmaximal, characteristic, complemented
14C2×C4×#11745685C213yesmaximal, complemented
15C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C59C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745685C2213yes—
19C22×Q8×D59C2211yescharacteristic
20#16838128C22116yescomplemented
21#16838124C22148yescomplemented
22#16838093C22148yescomplemented
23#16838087C22148yescomplemented
24Q8×C22⋊D59C22116yescomplemented
25#16838064C22116yescomplemented
26#16838063C22116yescomplemented
27#16838053C22148yescomplemented
28#16837956C22148yescomplemented
29C2×#14273726C2213yes—
30C2×#14273725C2213yes—
31#16837939C22148yescomplemented
32#16837936C22148yescomplemented
33C2×#14273722C2216yes—
34C2×#14273721C2216yes—
35C2×#14273719C2213yes—
36C2×#14273718C2213yes—
37C2×#14273717C2216yes—
38C2×#14273716C2213yes—
39C2×#14273715C2213yes—
40C2×#14273712C2216yes—
41C2×#14273710C2216yes—
42C2×#14273707C2213yes—
43C2×#14273706C2213yes—
44C2×#14273705C2216yes—
45C2×#14273703C2213yes—
46C2×#14273703C2213yes—
47C2×#14273702C2213yes—
48C2×#14273701C2213yes—
49C4×#11745689C22116yescomplemented
50C4×#11745685C22148yescomplemented
51C2×Q8×Dic59C2211yescharacteristic
52C2×Q8×Dic59C2211yescharacteristic
53C2×C4×Dic118C2213yes—
54C2×C4×Dic118C2213yes—
55C2×C4×Dic118C2213yes—
56C2×#14273692C2213yes—
57C4×Q8×D59C22116yescomplemented
58C2×C4×D236C2213yes—
59C2×C4×D236C2213yes—
60C2×C4×D236C2213yes—
61C2×#14273689C2213yes—
62C2×C4×C22⋊D59C2211yescharacteristic
63C2×C4×C22⋊D59C2213yes—
64C2×C4×C22⋊D59C2213yes—
65C2×C4×C22⋊D59C2213yes—
66C2×#14273686C2213yes—
67C2×#14273685C2213yes—
68C2×#14273684C2213yes—
69C2×#14273684C2213yes—
70C2×#14273684C2216yes—
71C2×C4⋊C4×D59C2213yes—
72C2×C42×D59C2213yes—
73C2×C42×D59C2213yes—
74C23×Q8×C59C2211yescharacteristic
75C2×C4×Q8×C59C2211yescharacteristic
76C2×C4×Q8×C59C2211yescharacteristic
77C2×C4×Q8×C59C2213yes—
78C2×C4×Q8×C59C2213yes—
79C2×C4×Q8×C59C22116yescomplemented
80C22×C4⋊C4×C59C2213yes—
81C22×C42×C59C2213yes—
82C2×#11745689—28no—
83C2×#11745689C2318yes—
84C2×#11745685—224no—
85C2×#11745685C23124yes—
86C22×Dic118C2313yes—
87C22×Dic118C2313yes—
88C2×Q8×D59—28no—
89C2×Q8×D59C2318yes—
90C22×D236C2313yes—
91C22×D236C2313yes—
92C22×C22⋊D59C2313yes—
93C22×C22⋊D59C2311yescharacteristic
94C22×C4×D59C2313yes—
95C22×C4×D59C2313yes—
96C22×C4×D59C2313yes—
97C22×C4×D59C2313yes—
98C22×C4×D59C2311yescharacteristic
99C22×C4×D59C2313yes—
100#14273726C23124yes—
101#14273725C23124yes—
102#14273722C23148yes—
103#14273721C23148yes—
104#14273719C23124yes—
105#14273718C23124yes—
106#14273717C23148yes—
107#14273716C23124yes—
108#14273715C23124yes—
109#14273712C23148yes—
110#14273710C23148yes—
111#14273707C23124yes—
112#14273706C23124yes—
113#14273705C23148yes—
114#14273703C23124yes—
115#14273703C23124yes—
116#14273702C23124yes—
117#14273701C23124yes—
118Q8×Dic59C2318yes—
119Q8×Dic59C2318yes—
120C4×Dic118C23124yes—
121C4×Dic118C23124yes—
122C4×Dic118C23124yes—
123#14273692C23124yes—
124C4×D236C23124yes—
125C4×D236C23124yes—
126C4×D236C23124yes—
127#14273689C23124yes—
128C4×C22⋊D59C23124yes—
129C4×C22⋊D59C23124yes—
130C4×C22⋊D59C23124yes—
131C4×C22⋊D59C2318yes—
132#14273686C23124yes—
133#14273685C23124yes—
134#14273684C23148yes—
135#14273684C23124yes—
136#14273684C23124yes—
137C2×C4⋊Dic59C2313yes—
138C2×C4⋊Dic59C2313yes—
139C2×C4⋊Dic59C2313yes—
140C2×C4⋊Dic59C2313yes—
141C2×Dic59⋊C4C2313yes—
142C2×Dic59⋊C4C2316yes—
143C2×Dic59⋊C4C2313yes—
144C2×Dic59⋊C4C2316yes—
145C2×Dic59⋊C4C2316yes—
146C2×Dic59⋊C4C2313yes—
147C2×Dic59⋊C4C2311yescharacteristic
148C4⋊C4×D59C23124yes—
149C2×C22⋊Dic59C2313yes—
150C2×C22⋊Dic59C2311yescharacteristic
151C2×(C2×D59)⋊C4C2316yes—
152C2×(C2×D59)⋊C4C2316yes—
153C2×(C2×D59)⋊C4C2313yes—
154C2×(C2×D59)⋊C4C2316yes—
155C2×(C2×D59)⋊C4C2313yes—
156C2×(C2×D59)⋊C4C2313yes—
157C2×(C2×D59)⋊C4C2311yescharacteristic
158C2×C4×Dic59C2313yes—
159C2×C4×Dic59C2313yes—
160C2×C4×Dic59C2313yes—
161C2×C4×Dic59C2313yes—
162C2×C4×Dic59C2311yescharacteristic
163C2×C4×Dic59C2313yes—
164C42×D59C23124yes—
165C42×D59C23124yes—
166C22×Q8×C59—28no—
167C22×Q8×C59C2313yes—
168C22×Q8×C59C2318yes—
169C22×Q8×C59C2311yescharacteristic
170C23×C4×C59C2313yes—
171C23×C4×C59C2313yes—
172C23×C4×C59C2311yescharacteristic
173C4×Q8×C59C23124yes—
174C4×Q8×C59C2318yes—
175C4×Q8×C59C23124yes—
176C4×Q8×C59C2318yes—
177C2×C4⋊C4×C59C2313yes—
178C2×C4⋊C4×C59C2316yes—
179C2×C4⋊C4×C59C23124yes—
180C2×C4⋊C4×C59C2313yes—
181C2×C42×C59C2313yes—
182C2×C42×C59C2313yes—
183C2×C42×C59C23124yes—
184C2×C42×C59C2313yes—
185C2×C42×C59C2313yes—
186C24×C59C2411yescharacteristic
187C23×D59C2413yes—
188C23×D59C2411yescharacteristic
189C2×Q8×C59—232no—
190C2×Q8×C59—212no—
191C2×Q8×C59#4118yescomplemented
192C2×Q8×C59C24112yes—
193C2×Q8×C59C2414yes—
194C22×C4×C59—212no—
195C22×C4×C59—212no—
196C22×C4×C59—24no—
197C22×C4×C59C2411yescharacteristic
198C22×C4×C59C2414yes—
199C22×C4×C59C2413yes—
200C22×C4×C59C2413yes—
201C22×C4×C59C24112yes—
202C22×C4×C59C2413yes—
203C22×C4×C59C24112yes—
204C22×C4×C59C2413yes—
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—212no—
207C2×C22⋊D59#4118yescomplemented
208C2×C22⋊D59C24112yes—
209C2×C22⋊D59C2414yes—
210C22×Dic59C2411yescharacteristic
211C22×Dic59C2411yescharacteristic
212C22×Dic59C2413yes—
213C22×Dic59C2413yes—
214C22×Dic59C2413yes—
215C22×Dic59C2411yescharacteristic
216#11745689—232no—
217Q8×D59—232no—
218#11745685—296no—
219C2×D236—212no—
220C2×D236—212no—
221C2×D236C24112yes—
222C2×D236C24112yes—
223C2×C4×D59—212no—
224C2×C4×D59—212no—
225C2×C4×D59—212no—
226C2×C4×D59—24no—
227C2×C4×D59—212no—
228C2×C4×D59—212no—
229C2×C4×D59C2414yes—
230C2×C4×D59C24112yes—
231C2×C4×D59C24112yes—
232C2×C4×D59C24112yes—
233C2×C4×D59C24112yes—
234C2×C4×D59C24112yes—
235C2×Dic118—212no—
236C2×Dic118—212no—
237C2×Dic118C24112yes—
238C2×Dic118C24112yes—
239C4⋊C4×C59C24112yes—
240C4⋊C4×C59C24112yes—
241C4⋊C4×C59C24124yes—
242C42×C59C24112yes—
243C42×C59C24112yes—
244C42×C59C24112yes—
245C42×C59C24112yes—
246C22⋊Dic59C2414yes—
247C22⋊Dic59C24112yes—
248(C2×D59)⋊C4C2414yes—
249(C2×D59)⋊C4C24112yes—
250(C2×D59)⋊C4C24112yes—
251(C2×D59)⋊C4C24112yes—
252(C2×D59)⋊C4C24124yes—
253(C2×D59)⋊C4C24124yes—
254(C2×D59)⋊C4C24124yes—
255C4⋊Dic59C24112yes—
256C4⋊Dic59C24112yes—
257C4⋊Dic59C24112yes—
258C4⋊Dic59C24112yes—
259Dic59⋊C4C24124yes—
260Dic59⋊C4C2414yes—
261Dic59⋊C4C24112yes—
262Dic59⋊C4C24112yes—
263Dic59⋊C4C24112yes—
264Dic59⋊C4C24124yes—
265Dic59⋊C4C24124yes—
266C4×Dic59C2414yes—
267C4×Dic59C24112yes—
268C4×Dic59C24112yes—
269C4×Dic59C24112yes—
270C4×Dic59C24112yes—
271C4×Dic59C24112yes—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59C2×#4114yes—
275C23×C59C2512yes—
276C23×C59C2511yescharacteristic
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—26no—
280C22×D59—26no—
281C22×D59—26no—
282C22×D59C2×#4114yes—
283C22×D59C2516yes—
284C22×D59C2512yes—
285Q8×C59—224no—
286Q8×C59C2×#41116yescomplemented
287C2×C4×C59—26no—
288C2×C4×C59—26no—
289C2×C4×C59—224no—
290C2×C4×C59—26no—
291C2×C4×C59—22no—
292C2×C4×C59—224no—
293C2×C4×C59—28no—
294C2×C4×C59C2×#41112yes—
295C2×C4×C592−1+414yes—
296C2×C4×C59C2516yes—
297C2×C4×C59C2512yes—
298C2×C4×C59C2516yes—
299C2×C4×C59C2516yes—
300C2×C4×C59C2516yes—
301C2×C4×C59C2512yes—
302C22⋊D59—224no—
303C22⋊D59C2×#41116yescomplemented
304C2×Dic59—26no—
305C2×Dic59—26no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—26no—
309C2×Dic59C2×#4114yes—
310C2×Dic59C2512yes—
311C2×Dic59C2512yes—
312C2×Dic59C2516yes—
313C2×Dic59C2516yes—
314C2×Dic59C2516yes—
315C2×Dic59C2512yes—
316D236—224no—
317D236—224no—
318C4×D59—224no—
319C4×D59—224no—
320C4×D59—224no—
321C4×D59—28no—
322C4×D59—224no—
323C4×D59—224no—
324Dic118—224no—
325Dic118—224no—
326C2×#3482—591nomaximal, Sylow
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—28no—
330C22×C59C22×#4114yes—
331C22×C59C22×#4112yes—
332C22×C59C22×#4112yes—
333C22×C59C2×2−1+412yes—
334C22×C59C2611yescharacteristic
335C2×D59—22no—
336C2×D59—22no—
337C2×D59—28no—
338C2×D59—26no—
339C2×D59—26no—
340C2×D59—26no—
341C2×D59—412no—
342C2×D59C22×#4114yes—
343C4×C59—26no—
344C4×C59—26no—
345C4×C59—26no—
346C4×C59—22no—
347C4×C59C22×#41112yes—
348C4×C59C2×2−1+414yes—
349Dic59—26no—
350Dic59—26no—
351Dic59—22no—
352Dic59—22no—
353Dic59—26no—
354Dic59C22×#4114yes—
355#3482—5932no—
356C2×#557—591no—
357C2×#556—593no—
358C2×#552—593no—
359C2×#552—593no—
360C2×D4×Q8—591no—
361C2×#548—591no—
362C2×#548—591no—
363C2×#547—593no—
364C2×#533—593no—
365C2×#529—593no—
366C2×#529—593no—
367C2×C4×#41—593no—
368C2×C4×#41—591no—
369C22×C4×Q8—591no—
370C22×C4×Q8D5911yescharacteristic, complemented
371C2×C59—24no—
372C2×C59#348214yescomplemented
373C2×C59C23×#4111yescharacteristic
374C2×C59C23×#4111yescharacteristic
375C2×C59C22×2−1+411yescharacteristic
376D59—24no—
377D59—46no—
378C22×#41—591no—
379C22×#41—593no—
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#548—5916no—
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×#124—593no—
402C2×#123—596no—
403C2×#123—596no—
404C2×C22⋊Q8—593no—
405C2×C22⋊Q8—593no—
406C2×C22⋊Q8—593no—
407C2×C22⋊Q8—596no—
408C2×C22⋊Q8—593no—
409C2×#121—593no—
410C2×#121—593no—
411C4×#41—5916no—
412C4×#41—5948no—
413C2×C4×Q8—591no—
414C2×C4×Q8—591no—
415C2×C4×Q8—5916no—
416C2×C4×Q8—593no—
417C2×C4×Q8—593no—
418C2×C4×Q8—593no—
419C2×C4×Q8—593no—
420C2×C4×Q8C2×D5911yescharacteristic
421C2×C4×Q8C2×D5913yes—
422C2×C4×Q8C2×D5911yescharacteristic
423C2×C4×Q8C2×D5913yes—
424C2×C4×Q8C2×D59116yescomplemented
425C2×C4×D4—591no—
426C2×C4×D4—593no—
427C2×C4×D4—593no—
428C2×C4×D4—593no—
429C2×C4×D4—593no—
430C2×C4×D4—593no—
431C2×C4×D4—593no—
432C2×C4×D4—593no—
433C2×#117—593no—
434C2×#117—593no—
435C2×#117—593no—
436C2×#117—593no—
437C2×#117—596no—
438C22×C4⋊C4—593no—
439C22×C4⋊C4C2×D5913yes—
440C22×C42—593no—
441C22×C42—593no—
442C22×C42C2×D5913yes—
443C59C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—598no—
445C2×#41—5924no—
446C2×#41—11824no—
447C2×#41—1188no—
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×D4—593no—
459C22×D4—593no—
460C23×C4—593no—
461C23×C4—593no—
462C23×C4—593no—
463C23×C4—593no—
464C23×C4—593no—
465C23×C4—591no—
466C23×C4C22×D5913yes—
467C23×C4C22×D5913yes—
468C23×C4C22×D5911yescharacteristic
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#124—5924no—
478#123—5948no—
479#123—5948no—
480C22⋊Q8—5924no—
481C22⋊Q8—5924no—
482C22⋊Q8—5924no—
483C22⋊Q8—5948no—
484C22⋊Q8—5924no—
485#121—5924no—
486#121—5924no—
487C4×Q8—598no—
488C4×Q8—598no—
489C4×Q8—5924no—
490C4×Q8—5924no—
491C4×Q8—5924no—
492C4×Q8—5924no—
493C4×Q8C22×D5918yes—
494C4×Q8C22×D59124yes—
495C4×Q8C22×D5918yes—
496C4×Q8C22×D59124yes—
497C4×D4—598no—
498C4×D4—5924no—
499C4×D4—5924no—
500C4×D4—5924no—
501C4×D4—5924no—
502C4×D4—5924no—
503C4×D4—5924no—
504C4×D4—5924no—
505#117—5924no—
506#117—5924no—
507#117—5924no—
508#117—5924no—
509#117—5948no—
510C2×C4⋊C4—593no—
511C2×C4⋊C4—596no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—593no—
514C2×C4⋊C4—593no—
515C2×C4⋊C4—593no—
516C2×C4⋊C4—593no—
517C2×C4⋊C4—593no—
518C2×C4⋊C4—593no—
519C2×C4⋊C4—596no—
520C2×C4⋊C4—596no—
521C2×C4⋊C4—5924no—
522C2×C4⋊C4C22×D5913yes—
523C2×C4⋊C4C22×D5913yes—
524C2×C4⋊C4C22×D5916yes—
525C2×C4⋊C4C22×D59124yes—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—593no—
528C2×C22⋊C4—591no—
529C2×C22⋊C4—593no—
530C2×C22⋊C4—596no—
531C2×C22⋊C4—593no—
532C2×C22⋊C4—593no—
533C2×C22⋊C4—596no—
534C2×C22⋊C4—596no—
535C2×C42—593no—
536C2×C42—593no—
537C2×C42—593no—
538C2×C42—593no—
539C2×C42—593no—
540C2×C42—591no—
541C2×C42—5924no—
542C2×C42—5924no—
543C2×C42C22×D5913yes—
544C2×C42C22×D5913yes—
545C2×C42C22×D59124yes—
546C2×C42C22×D5913yes—
547C2×C42C22×D5913yes—
548C24—591no—
549C24—593no—
550C24C23×D5911yescharacteristic
551#41—11896no—
552#41—11832no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—5912no—
556C2×Q8—5912no—
557C2×Q8—11812no—
558C2×Q8—11832no—
559C2×Q8—11812no—
560C2×Q8#1174568518yescomplemented
561C2×Q8C23×D59112yes—
562C2×Q8C23×D5914yes—
563C2×D4—598no—
564C2×D4—594no—
565C2×D4—5912no—
566C2×D4—5912no—
567C2×D4—5912no—
568C2×D4—11812no—
569C2×D4—11812no—
570C2×D4—11812no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—593no—
578C22×C4—593no—
579C22×C4—593no—
580C22×C4—594no—
581C22×C4—5912no—
582C22×C4—5912no—
583C22×C4—5912no—
584C22×C4—5912no—
585C22×C4—5912no—
586C22×C4—11812no—
587C22×C4—11812no—
588C22×C4—11812no—
589C22×C4—11812no—
590C22×C4—1184no—
591C22×C4—11812no—
592C22×C4C23×D5913yes—
593C22×C4C23×D5911yescharacteristic
594C22×C4C23×D5914yes—
595C22×C4C23×D5913yes—
596C22×C4C23×D5913yes—
597C22×C4C23×D59112yes—
598C22×C4C23×D59112yes—
599C22×C4C23×D5913yes—
600C22×C4C23×D5911yescharacteristic
601C4⋊C4—5912no—
602C4⋊C4—5924no—
603C4⋊C4—594no—
604C4⋊C4—5912no—
605C4⋊C4—5912no—
606C4⋊C4—5912no—
607C4⋊C4—5912no—
608C4⋊C4—5912no—
609C4⋊C4—5912no—
610C4⋊C4—5924no—
611C4⋊C4—5924no—
612C4⋊C4C23×D59112yes—
613C4⋊C4C23×D59112yes—
614C4⋊C4C23×D59124yes—
615C22⋊C4—594no—
616C22⋊C4—5912no—
617C22⋊C4—594no—
618C22⋊C4—5912no—
619C22⋊C4—5924no—
620C22⋊C4—5912no—
621C22⋊C4—5912no—
622C22⋊C4—5924no—
623C22⋊C4—5924no—
624C42—594no—
625C42—5912no—
626C42—5912no—
627C42—5912no—
628C42—5912no—
629C42—5912no—
630C42C23×D59112yes—
631C42C23×D59112yes—
632C42C23×D59112yes—
633C42C23×D59112yes—
634C23—22no—
635C23—22no—
636C23—594no—
637C23—592no—
638C23—596no—
639C23—1182no—
640C23—1182no—
641C23—1186no—
642C23—1186no—
643C23—1186no—
644C23#41×D5914yes—
645C23C24×D5912yes—
646C23C24×D5911yescharacteristic
647Q8—224no—
648Q8—11824no—
649Q8—11824no—
650Q8C2×#11745685116yescomplemented
651D4—5916no—
652D4—11824no—
653D4—11824no—
654D4—11824no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—594no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—592no—
666C2×C4—596no—
667C2×C4—596no—
668C2×C4—596no—
669C2×C4—11824no—
670C2×C4—11824no—
671C2×C4—1186no—
672C2×C4—1182no—
673C2×C4—1186no—
674C2×C4—1182no—
675C2×C4—1186no—
676C2×C4—11824no—
677C2×C4—11824no—
678C2×C4—1188no—
679C2×C4—11824no—
680C2×C4C2×#11745685112yes—
681C2×C4#1427377514yes—
682C2×C4C24×D5916yes—
683C2×C4C24×D5912yes—
684C2×C4C24×D5916yes—
685C2×C4C24×D5916yes—
686C2×C4C24×D5916yes—
687C2×C4C24×D5912yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—594no—
692C22—1188no—
693C22—1182no—
694C22—1182no—
695C22—1186no—
696C22—1186no—
697C22—1186no—
698C22—23612no—
699C22C2×#41×D5914yes—
700C22C2×#41×D5912yes—
701C22C22×#1174568512yes—
702C22C2×#1427377512yes—
703C22C25×D5911yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—594no—
709C4—1186no—
710C4—1182no—
711C4—1186no—
712C4—1182no—
713C4—1186no—
714C4C22×#11745685112yes—
715C4C2×#1427377514yes—
716C2—24no—
717C2—1184no—
718C2—2366no—
719C2#2143771314yesdirect product factor
720C2C22×#41×D5911yescharacteristic
721C2C23×#1174568511yescharacteristic
722C2C22×#1427377511yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×C4×Q8×C59C2
socleC23×C59C25
hypercenterC22×C4×Q8D59
hypocenterC59C2×#3482
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21437713C2direct (N × H)
2. C2×#16838128C2semidirect
3. C2×#16838124C2semidirect
4. C2×#16838093C2semidirect
5. C2×#16838087C2semidirect
6. C2×Q8×C22⋊D59C2semidirect
7. C2×#16838064C2semidirect
8. C2×#16838063C2semidirect
9. C2×#16838053C2semidirect
10. C2×#16837956C2semidirect
11. C2×#16837939C2semidirect
12. C2×#16837936C2semidirect
13. C2×C4×#11745689C2semidirect
14. C2×C4×#11745685C2semidirect
15. C2×C4×Q8×D59C2semidirect
16. C22×C4×Q8×C59C2semidirect
20. #16838128C22semidirect
21. #16838124C22semidirect
22. #16838093C22semidirect
23. #16838087C22semidirect
24. Q8×C22⋊D59C22semidirect
25. #16838064C22semidirect
26. #16838063C22semidirect
27. #16838053C22semidirect
28. #16837956C22semidirect
31. #16837939C22semidirect
32. #16837936C22semidirect
49. C4×#11745689C22semidirect
50. C4×#11745685C22semidirect
57. C4×Q8×D59C22semidirect
79. C2×C4×Q8×C59C22semidirect
191. C2×Q8×C59#41semidirect
207. C2×C22⋊D59#41semidirect
286. Q8×C59C2×#41semidirect
303. C22⋊D59C2×#41semidirect
370. C22×C4×Q8D59semidirect
372. C2×C59#3482semidirect
424. C2×C4×Q8C2×D59semidirect
443. C59C2×#3482semidirect
560. C2×Q8#11745685semidirect
650. Q8C2×#11745685semidirect
719. C2#21437713direct (N × H)

Maximal subgroups

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

subgroupindex
#214377132
C2×#168381282
C2×#168381242
C2×#168380932
C2×#168380872
C2×Q8×C22⋊D592
C2×#168380642
C2×#168380632
C2×#168380532
C2×#168379562
C2×#168379392
C2×#168379362
C2×C4×#117456892
C2×C4×#117456852
C2×C4×Q8×D592
C22×C4×Q8×C592
C2×#348259