Finite Group Databasebeta

← C2×#21437694 #29495747

Subgroups — C2×#21437694 #29495747

Order 15104.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437694C2132yesmaximal, direct product factor
2C2×#16838135C213yesmaximal, complemented
3C2×#16838128C211yesmaximal, characteristic, complemented
4C2×#16838120C213yesmaximal, complemented
5C2×#16838102C213yesmaximal, complemented
6C2×#16838096C213yesmaximal, complemented
7C2×#16838071C211yesmaximal, characteristic, complemented
8C2×#16838064C211yesmaximal, characteristic, complemented
9C2×#16838059C211yesmaximal, characteristic, complemented
10C2×#16837949C213yesmaximal, complemented
11C2×#16837936C213yesmaximal, complemented
12C2×#16837934C213yesmaximal, complemented
13C2×C4×#11745689C211yesmaximal, characteristic, complemented
14C2×C4×#11745685C213yesmaximal, complemented
15C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
16C2×C4×#41×C59C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745685C2213yes—
19C22×Q8×D59C2211yescharacteristic
20#16838135C22148yescomplemented
21#16838128C22116yescomplemented
22#16838120C22148yescomplemented
23#16838102C22148yescomplemented
24#16838096C22148yescomplemented
25#16838071C22116yescomplemented
26#16838064C22116yescomplemented
27#16838059C22116yescomplemented
28#16837949C22148yescomplemented
29C2×#14273726C2213yes—
30C2×#14273723C2213yes—
31#16837936C22148yescomplemented
32#16837934C22148yescomplemented
33C2×#14273721C2216yes—
34C2×#14273720C2216yes—
35C2×#14273719C2213yes—
36C2×#14273718C2213yes—
37C2×#14273715C2213yes—
38C2×#14273714C2213yes—
39C2×#14273713C2216yes—
40C2×#14273710C2216yes—
41C2×#14273709C2216yes—
42C2×#14273707C2213yes—
43C2×#14273706C2213yes—
44C2×#14273702C2213yes—
45C2×#14273701C2213yes—
46C2×#14273700C2216yes—
47C2×#14273698C2213yes—
48C2×#14273698C2213yes—
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⋊D59C2213yes—
63C2×C4×C22⋊D59C2213yes—
64C2×C4×C22⋊D59C2213yes—
65C2×C4×C22⋊D59C2213yes—
66C2×C4×C22⋊D59C2216yes—
67C2×#14273686C2213yes—
68C2×#14273685C2213yes—
69C2×#14273684C2211yescharacteristic
70C2×#14273684C2213yes—
71C2×C4⋊C4×D59C2213yes—
72C2×C42×D59C2213yes—
73C2×C42×D59C2213yes—
74C22×#41×C59C2211yescharacteristic
75C4×#41×C59C22116yescomplemented
76C2×C4×Q8×C59C2211yescharacteristic
77C2×C4×Q8×C59C2211yescharacteristic
78C2×C4×D4×C59C2213yes—
79C2×C4×D4×C59C2213yes—
80C2×#117×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⋊D59C2313yes—
94C22×C22⋊D59C2316yes—
95C22×C4×D59C2313yes—
96C22×C4×D59C2313yes—
97C22×C4×D59C2313yes—
98C22×C4×D59C2313yes—
99C22×C4×D59C2313yes—
100C22×C4×D59C2311yescharacteristic
101#14273726C23124yes—
102#14273723C23124yes—
103#14273721C23148yes—
104#14273720C23148yes—
105#14273719C23124yes—
106#14273718C23124yes—
107#14273715C23124yes—
108#14273714C23124yes—
109#14273713C23148yes—
110#14273710C23148yes—
111#14273709C23148yes—
112#14273707C23124yes—
113#14273706C23124yes—
114#14273702C23124yes—
115#14273701C23124yes—
116#14273700C23148yes—
117#14273698C23124yes—
118#14273698C23124yes—
119Q8×Dic59C2318yes—
120Q8×Dic59C2318yes—
121C4×Dic118C23124yes—
122C4×Dic118C23124yes—
123C4×Dic118C23124yes—
124#14273692C23124yes—
125C4×D236C23124yes—
126C4×D236C23124yes—
127C4×D236C23124yes—
128#14273689C23124yes—
129C4×C22⋊D59C23148yes—
130C4×C22⋊D59C23124yes—
131C4×C22⋊D59C23124yes—
132C4×C22⋊D59C23124yes—
133C4×C22⋊D59C23124yes—
134#14273686C23124yes—
135#14273685C23124yes—
136#14273684C23124yes—
137#14273684C2318yes—
138C2×C4⋊Dic59C2313yes—
139C2×C4⋊Dic59C2313yes—
140C2×C4⋊Dic59C2313yes—
141C2×C4⋊Dic59C2313yes—
142C2×Dic59⋊C4C2316yes—
143C2×Dic59⋊C4C2313yes—
144C2×Dic59⋊C4C2316yes—
145C2×Dic59⋊C4C2313yes—
146C2×Dic59⋊C4C2311yescharacteristic
147C2×Dic59⋊C4C2311yescharacteristic
148C4⋊C4×D59C23124yes—
149C2×C22⋊Dic59C2313yes—
150C2×C22⋊Dic59C2316yes—
151C2×C22⋊Dic59C2313yes—
152C2×(C2×D59)⋊C4C2316yes—
153C2×(C2×D59)⋊C4C2313yes—
154C2×(C2×D59)⋊C4C2316yes—
155C2×(C2×D59)⋊C4C2313yes—
156C2×(C2×D59)⋊C4C2311yescharacteristic
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—
166C2×#41×C59—28no—
167C2×#41×C59C2318yes—
168C22×Q8×C59C2311yescharacteristic
169C22×D4×C59C2313yes—
170C23×C4×C59C2313yes—
171C23×C4×C59C2313yes—
172C23×C4×C59C2313yes—
173C4×Q8×C59C2318yes—
174C4×Q8×C59C2318yes—
175C4×D4×C59C23124yes—
176C4×D4×C59C23124yes—
177#117×C59C23124yes—
178C2×C4⋊C4×C59C2313yes—
179C2×C4⋊C4×C59C2313yes—
180C2×C22⋊C4×C59C2316yes—
181C2×C42×C59C2313yes—
182C2×C42×C59C2313yes—
183C2×C42×C59C23124yes—
184C2×C42×C59C2311yescharacteristic
185C2×C42×C59C2313yes—
186C24×C59C2413yes—
187C23×D59C2413yes—
188C23×D59C2411yescharacteristic
189#41×C59—232no—
190C2×Q8×C59#4118yescomplemented
191C2×Q8×C59C2414yes—
192C2×D4×C59—212no—
193C2×D4×C59C24112yes—
194C22×C4×C59—212no—
195C22×C4×C59—212no—
196C22×C4×C59—46no—
197C22×C4×C59C2411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×C4×C59C2413yes—
200C22×C4×C59C2413yes—
201C22×C4×C59C24112yes—
202C22×C4×C59C24112yes—
203C22×C4×C59C24112yes—
204C22×C4×C59C2413yes—
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—212no—
207C2×C22⋊D59—212no—
208C2×C22⋊D59—412no—
209C2×C22⋊D59C24112yes—
210C2×C22⋊D59C24112yes—
211C2×C22⋊D59C24124yes—
212C22×Dic59C2411yescharacteristic
213C22×Dic59C2411yescharacteristic
214C22×Dic59C2413yes—
215C22×Dic59C2413yes—
216C22×Dic59C2413yes—
217C22×Dic59C2411yescharacteristic
218#11745689—232no—
219Q8×D59—232no—
220#11745685—296no—
221C2×D236—212no—
222C2×D236—212no—
223C2×D236C24112yes—
224C2×D236C24112yes—
225C2×C4×D59—212no—
226C2×C4×D59—212no—
227C2×C4×D59—212no—
228C2×C4×D59—46no—
229C2×C4×D59—46no—
230C2×C4×D59#4118yescomplemented
231C2×C4×D59C24112yes—
232C2×C4×D59C24112yes—
233C2×C4×D59C24112yes—
234C2×C4×D59C24112yes—
235C2×C4×D59C24112yes—
236C2×C4×D59C2414yes—
237C2×Dic118—212no—
238C2×Dic118—212no—
239C2×Dic118C24112yes—
240C2×Dic118C24112yes—
241C4⋊C4×C59C24112yes—
242C4⋊C4×C59C24112yes—
243C22⋊C4×C59C24124yes—
244C42×C59C2414yes—
245C42×C59C24112yes—
246C42×C59C24112yes—
247C42×C59C24112yes—
248C22⋊Dic59C24112yes—
249C22⋊Dic59C24112yes—
250C22⋊Dic59C24124yes—
251(C2×D59)⋊C4C2414yes—
252(C2×D59)⋊C4C2414yes—
253(C2×D59)⋊C4C24112yes—
254(C2×D59)⋊C4C24112yes—
255(C2×D59)⋊C4C24124yes—
256(C2×D59)⋊C4C24124yes—
257C4⋊Dic59C24112yes—
258C4⋊Dic59C24112yes—
259C4⋊Dic59C24112yes—
260C4⋊Dic59C24112yes—
261Dic59⋊C4C24124yes—
262Dic59⋊C4C2414yes—
263Dic59⋊C4C2414yes—
264Dic59⋊C4C24112yes—
265Dic59⋊C4C24112yes—
266Dic59⋊C4C24124yes—
267C4×Dic59C2414yes—
268C4×Dic59C24112yes—
269C4×Dic59C24112yes—
270C4×Dic59C24112yes—
271C4×Dic59C24112yes—
272C4×Dic59C24112yes—
273C23×C59—26no—
274C23×C59—26no—
275C23×C59—26no—
276C23×C59C2516yes—
277C23×C59C2511yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—26no—
281C22×D59—26no—
282C22×D59—26no—
283C22×D59C2×#4114yes—
284C22×D59C2516yes—
285C22×D59C2512yes—
286Q8×C59C2×#41116yescomplemented
287D4×C59—224no—
288C2×C4×C59—26no—
289C2×C4×C59—22no—
290C2×C4×C59—26no—
291C2×C4×C59—22no—
292C2×C4×C59—224no—
293C2×C4×C59—224no—
294C2×C4×C59—412no—
295C2×C4×C59C2×#4114yes—
296C2×C4×C59C2×#41112yes—
297C2×C4×C59C2516yes—
298C2×C4×C59C2512yes—
299C2×C4×C59C2512yes—
300C2×C4×C59C2516yes—
301C2×C4×C59C2512yes—
302C2×C4×C59C2516yes—
303C22⋊D59—224no—
304C22⋊D59—224no—
305C22⋊D59—424no—
306C2×Dic59—26no—
307C2×Dic59—26no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—26no—
311C2×Dic59C2×#4114yes—
312C2×Dic59C2512yes—
313C2×Dic59C2512yes—
314C2×Dic59C2516yes—
315C2×Dic59C2516yes—
316C2×Dic59C2516yes—
317C2×Dic59C2512yes—
318D236—224no—
319D236—224no—
320C4×D59—224no—
321C4×D59—224no—
322C4×D59—224no—
323C4×D59—412no—
324C4×D59—412no—
325C4×D59C2×#41116yescomplemented
326Dic118—224no—
327Dic118—224no—
328C2×#3480—591nomaximal, Sylow
329C22×C59—26no—
330C22×C59—26no—
331C22×C59—26no—
332C22×C59—412no—
333C22×C59C22×#4112yes—
334C22×C59C22×#4112yes—
335C22×C59#58512yes—
336C22×C59C2611yescharacteristic
337C2×D59—22no—
338C2×D59—22no—
339C2×D59—28no—
340C2×D59—26no—
341C2×D59—26no—
342C2×D59—26no—
343C2×D59—412no—
344C2×D59C22×#4114yes—
345C4×C59—26no—
346C4×C59—22no—
347C4×C59—26no—
348C4×C59—22no—
349C4×C59C22×#4114yes—
350C4×C59C22×#41112yes—
351Dic59—26no—
352Dic59—26no—
353Dic59—22no—
354Dic59—22no—
355Dic59—26no—
356Dic59C22×#4114yes—
357#3480—5932no—
358C2×#559—593no—
359C2×#557—591no—
360C2×#556—593no—
361C2×#553—593no—
362C2×#553—593no—
363C2×#550—591no—
364C2×#548—591no—
365C2×#548—591no—
366C2×#532—593no—
367C2×#529—593no—
368C2×#529—593no—
369C2×C4×#41—593no—
370C2×C4×#41—591no—
371C2×C4×#41D5911yescharacteristic, complemented
372C22×C4×Q8—591no—
373C2×C59—46no—
374C2×C59#348014yescomplemented
375C2×C59C23×#4111yescharacteristic
376C2×C59C23×#4111yescharacteristic
377C2×C59C2×#58511yescharacteristic
378D59—24no—
379D59—46no—
380C22×#41—591no—
381C22×#41—593no—
382C22×#41C2×D5911yescharacteristic
383C23×Q8—591no—
384#559—5948no—
385#557—5916no—
386#556—5948no—
387#553—5948no—
388#553—5948no—
389#550—5916no—
390#548—5916no—
391#548—5916no—
392#532—5948no—
393C2×C4⋊Q8—593no—
394C2×#127—593no—
395#529—5948no—
396#529—5948no—
397C2×#126—596no—
398C2×#126—596no—
399C2×#125—593no—
400C2×#125—593no—
401C2×#124—593no—
402C2×#124—596no—
403C2×#124—593no—
404C2×#123—596no—
405C2×#123—596no—
406C2×C22⋊Q8—593no—
407C2×C22⋊Q8—593no—
408C2×#121—593no—
409C2×#121—593no—
410C2×#121—593no—
411C2×#121—593no—
412C2×#121—596no—
413C4×#41—5916no—
414C4×#41—5948no—
415C4×#41C2×D59116yescomplemented
416C2×C4×Q8—591no—
417C2×C4×Q8—591no—
418C2×C4×Q8—5916no—
419C2×C4×Q8—593no—
420C2×C4×Q8—593no—
421C2×C4×Q8—593no—
422C2×C4×Q8—593no—
423C2×C4×Q8C2×D5911yescharacteristic
424C2×C4×Q8C2×D5911yescharacteristic
425C2×C4×D4—593no—
426C2×C4×D4—593no—
427C2×C4×D4—593no—
428C2×C4×D4—593no—
429C2×C4×D4—596no—
430C2×C4×D4—593no—
431C2×C4×D4—593no—
432C2×C4×D4—593no—
433C2×C4×D4—593no—
434C2×C4×D4C2×D5913yes—
435C2×C4×D4C2×D5913yes—
436C2×#117—593no—
437C2×#117—593no—
438C2×#117—591no—
439C2×#117—593no—
440C2×#117C2×D5913yes—
441C22×C4⋊C4—593no—
442C22×C42—593no—
443C22×C42—593no—
444C22×C42C2×D5913yes—
445C59C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—598no—
448C2×#41—5924no—
449C2×#41—11824no—
450C2×#41—1188no—
451C2×#41C22×D5918yes—
452C22×Q8—598no—
453C22×Q8—593no—
454C22×Q8—593no—
455C22×Q8—1188no—
456C22×Q8C22×D5911yescharacteristic
457C22×D4—593no—
458C22×D4—593no—
459C22×D4—596no—
460C22×D4—593no—
461C22×D4—593no—
462C22×D4C22×D5913yes—
463C23×C4—591no—
464C23×C4—593no—
465C23×C4—593no—
466C23×C4—593no—
467C23×C4—593no—
468C23×C4—593no—
469C23×C4C22×D5913yes—
470C23×C4C22×D5913yes—
471C23×C4C22×D5913yes—
472C4⋊Q8—5924no—
473#127—5924no—
474#126—5948no—
475#126—5948no—
476#125—5924no—
477#125—5924no—
478#124—5924no—
479#124—5948no—
480#124—5924no—
481#123—5948no—
482#123—5948no—
483C22⋊Q8—5924no—
484C22⋊Q8—5924no—
485#121—5924no—
486#121—5924no—
487#121—5924no—
488#121—5924no—
489#121—5948no—
490C4×Q8—598no—
491C4×Q8—598no—
492C4×Q8—5924no—
493C4×Q8—5924no—
494C4×Q8—5924no—
495C4×Q8—5924no—
496C4×Q8C22×D5918yes—
497C4×Q8C22×D5918yes—
498C4×D4—5924no—
499C4×D4—5924no—
500C4×D4—5924no—
501C4×D4—5924no—
502C4×D4—5948no—
503C4×D4—5924no—
504C4×D4—5924no—
505C4×D4—5924no—
506C4×D4—5924no—
507C4×D4C22×D59124yes—
508C4×D4C22×D59124yes—
509#117—5924no—
510#117—5924no—
511#117—598no—
512#117—5924no—
513#117C22×D59124yes—
514C2×C4⋊C4—593no—
515C2×C4⋊C4—596no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—593no—
519C2×C4⋊C4—593no—
520C2×C4⋊C4—593no—
521C2×C4⋊C4—593no—
522C2×C4⋊C4—593no—
523C2×C4⋊C4—596no—
524C2×C4⋊C4—5924no—
525C2×C4⋊C4C22×D5913yes—
526C2×C4⋊C4C22×D5913yes—
527C2×C22⋊C4—593no—
528C2×C22⋊C4—593no—
529C2×C22⋊C4—596no—
530C2×C22⋊C4—591no—
531C2×C22⋊C4—591no—
532C2×C22⋊C4—593no—
533C2×C22⋊C4—596no—
534C2×C22⋊C4—593no—
535C2×C22⋊C4—596no—
536C2×C22⋊C4C22×D5916yes—
537C2×C42—593no—
538C2×C42—593no—
539C2×C42—593no—
540C2×C42—593no—
541C2×C42—591no—
542C2×C42—593no—
543C2×C42—5924no—
544C2×C42—5924no—
545C2×C42C22×D5913yes—
546C2×C42C22×D5913yes—
547C2×C42C22×D59124yes—
548C2×C42C22×D5911yescharacteristic
549C2×C42C22×D5913yes—
550C24—591no—
551C24—593no—
552C24C23×D5913yes—
553#41—232no—
554#41—11896no—
555#41—11832no—
556C2×Q8—5912no—
557C2×Q8—5912no—
558C2×Q8—11812no—
559C2×Q8—11832no—
560C2×Q8—11812no—
561C2×Q8#1174568518yescomplemented
562C2×Q8C23×D5914yes—
563C2×D4—212no—
564C2×D4—5912no—
565C2×D4—5912no—
566C2×D4—5924no—
567C2×D4—5912no—
568C2×D4—5912no—
569C2×D4—11812no—
570C2×D4—11812no—
571C2×D4—11812no—
572C2×D4—11812no—
573C2×D4—23612no—
574C2×D4C23×D59112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—591no—
579C22×C4—598no—
580C22×C4—594no—
581C22×C4—591no—
582C22×C4—591no—
583C22×C4—593no—
584C22×C4—593no—
585C22×C4—593no—
586C22×C4—5912no—
587C22×C4—5912no—
588C22×C4—5912no—
589C22×C4—5912no—
590C22×C4—5912no—
591C22×C4—11812no—
592C22×C4—11812no—
593C22×C4—11812no—
594C22×C4—2366no—
595C22×C4—2366no—
596C22×C4C23×D5913yes—
597C22×C4C23×D5911yescharacteristic
598C22×C4C23×D5911yescharacteristic
599C22×C4C23×D5913yes—
600C22×C4C23×D59112yes—
601C22×C4C23×D59112yes—
602C22×C4C23×D59112yes—
603C22×C4C23×D5913yes—
604C22×C4C23×D5911yescharacteristic
605C4⋊C4—5912no—
606C4⋊C4—5924no—
607C4⋊C4—594no—
608C4⋊C4—594no—
609C4⋊C4—5912no—
610C4⋊C4—5912no—
611C4⋊C4—5912no—
612C4⋊C4—5912no—
613C4⋊C4—5912no—
614C4⋊C4—5924no—
615C4⋊C4C23×D59112yes—
616C4⋊C4C23×D59112yes—
617C22⋊C4—5912no—
618C22⋊C4—5912no—
619C22⋊C4—5924no—
620C22⋊C4—594no—
621C22⋊C4—594no—
622C22⋊C4—5912no—
623C22⋊C4—5924no—
624C22⋊C4—5912no—
625C22⋊C4—5924no—
626C22⋊C4C23×D59124yes—
627C42—594no—
628C42—5912no—
629C42—5912no—
630C42—5912no—
631C42—5912no—
632C42—5912no—
633C42C23×D59112yes—
634C42C23×D5914yes—
635C42C23×D59112yes—
636C42C23×D59112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—594no—
641C23—592no—
642C23—596no—
643C23—1182no—
644C23—1182no—
645C23—1186no—
646C23—1186no—
647C23—1186no—
648C23C24×D5916yes—
649C23C24×D5911yescharacteristic
650Q8—11824no—
651Q8—11824no—
652Q8C2×#11745685116yescomplemented
653D4—224no—
654D4—11824no—
655D4—11824no—
656D4—11824no—
657D4—11824no—
658D4—23624no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—594no—
667C2×C4—592no—
668C2×C4—5916no—
669C2×C4—592no—
670C2×C4—592no—
671C2×C4—596no—
672C2×C4—596no—
673C2×C4—596no—
674C2×C4—1186no—
675C2×C4—1182no—
676C2×C4—1186no—
677C2×C4—1182no—
678C2×C4—1186no—
679C2×C4—11824no—
680C2×C4—11824no—
681C2×C4—11824no—
682C2×C4—23612no—
683C2×C4—23612no—
684C2×C4#41×D5914yes—
685C2×C4C2×#11745685112yes—
686C2×C4C24×D5916yes—
687C2×C4C24×D5912yes—
688C2×C4C24×D5912yes—
689C2×C4C24×D5916yes—
690C2×C4C24×D5912yes—
691C2×C4C24×D5916yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—594no—
697C22—1182no—
698C22—1182no—
699C22—1188no—
700C22—1186no—
701C22—1186no—
702C22—1186no—
703C22—23612no—
704C22C2×#41×D5912yes—
705C22C22×#1174568512yes—
706C22#1683823812yes—
707C22C25×D5911yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—594no—
713C4—1186no—
714C4—1182no—
715C4—1186no—
716C4—1182no—
717C4—1186no—
718C4C2×#41×D5914yes—
719C4C22×#11745685112yes—
720C2—46no—
721C2—1184no—
722C2—2366no—
723C2#2143769414yesdirect product factor
724C2C22×#41×D5911yescharacteristic
725C2C23×#1174568511yescharacteristic
726C2C2×#1683823811yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C4×#41×C59C2
socleC23×C59C25
hypercenterC2×C4×#41D59
hypocenterC59C2×#3480
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #21437694C2direct (N × H)
2. C2×#16838135C2semidirect
3. C2×#16838128C2semidirect
4. C2×#16838120C2semidirect
5. C2×#16838102C2semidirect
6. C2×#16838096C2semidirect
7. C2×#16838071C2semidirect
8. C2×#16838064C2semidirect
9. C2×#16838059C2semidirect
10. C2×#16837949C2semidirect
11. C2×#16837936C2semidirect
12. C2×#16837934C2semidirect
13. C2×C4×#11745689C2semidirect
14. C2×C4×#11745685C2semidirect
15. C2×C4×Q8×D59C2semidirect
16. C2×C4×#41×C59C2semidirect
20. #16838135C22semidirect
21. #16838128C22semidirect
22. #16838120C22semidirect
23. #16838102C22semidirect
24. #16838096C22semidirect
25. #16838071C22semidirect
26. #16838064C22semidirect
27. #16838059C22semidirect
28. #16837949C22semidirect
31. #16837936C22semidirect
32. #16837934C22semidirect
49. C4×#11745689C22semidirect
50. C4×#11745685C22semidirect
57. C4×Q8×D59C22semidirect
75. C4×#41×C59C22semidirect
190. C2×Q8×C59#41semidirect
230. C2×C4×D59#41semidirect
286. Q8×C59C2×#41semidirect
325. C4×D59C2×#41semidirect
371. C2×C4×#41D59semidirect
374. C2×C59#3480semidirect
415. C4×#41C2×D59semidirect
445. C59C2×#3480semidirect
561. C2×Q8#11745685semidirect
652. Q8C2×#11745685semidirect
723. C2#21437694direct (N × H)

Maximal subgroups

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

subgroupindex
#214376942
C2×#168381352
C2×#168381282
C2×#168381202
C2×#168381022
C2×#168380962
C2×#168380712
C2×#168380642
C2×#168380592
C2×#168379492
C2×#168379362
C2×#168379342
C2×C4×#117456892
C2×C4×#117456852
C2×C4×Q8×D592
C2×C4×#41×C592
C2×#348059