Finite Group Databasebeta

← C2×#22573807 #31762889

Subgroups — C2×#22573807 #31762889

Order 17152.

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#22573807C2132yesmaximal, direct product factor
2C2×#16864129C213yesmaximal, complemented
3C2×#16864122C211yesmaximal, characteristic, complemented
4C2×#16864114C213yesmaximal, complemented
5C2×#16864096C213yesmaximal, complemented
6C2×#16864090C213yesmaximal, complemented
7C2×#16864065C211yesmaximal, characteristic, complemented
8C2×#16864058C211yesmaximal, characteristic, complemented
9C2×#16864053C211yesmaximal, characteristic, complemented
10C2×#16863943C213yesmaximal, complemented
11C2×#16863930C213yesmaximal, complemented
12C2×#16863928C213yesmaximal, complemented
13C2×C4×#11761629C211yesmaximal, characteristic, complemented
14C2×C4×#11761628C213yesmaximal, complemented
15C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
16C2×C4×#41×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761628C2213yes—
19C22×Q8×D67C2211yescharacteristic
20#16864129C22148yescomplemented
21#16864122C22116yescomplemented
22#16864114C22148yescomplemented
23#16864096C22148yescomplemented
24#16864090C22148yescomplemented
25#16864065C22116yescomplemented
26#16864058C22116yescomplemented
27#16864053C22116yescomplemented
28#16863943C22148yescomplemented
29C2×#14524042C2213yes—
30C2×#14524039C2213yes—
31#16863930C22148yescomplemented
32#16863928C22148yescomplemented
33C2×#14524037C2216yes—
34C2×#14524036C2216yes—
35C2×#14524035C2213yes—
36C2×#14524034C2213yes—
37C2×#14524031C2213yes—
38C2×#14524030C2213yes—
39C2×#14524029C2216yes—
40C2×#14524026C2216yes—
41C2×#14524025C2216yes—
42C2×#14524023C2213yes—
43C2×#14524022C2213yes—
44C2×#14524018C2213yes—
45C2×#14524017C2213yes—
46C2×#14524016C2216yes—
47C2×#14524014C2213yes—
48C2×#14524014C2213yes—
49C4×#11761629C22116yescomplemented
50C4×#11761628C22148yescomplemented
51C2×Q8×Dic67C2211yescharacteristic
52C2×Q8×Dic67C2211yescharacteristic
53C2×C4×Dic134C2213yes—
54C2×C4×Dic134C2213yes—
55C2×C4×Dic134C2213yes—
56C2×#14524008C2213yes—
57C4×Q8×D67C22116yescomplemented
58C2×C4×D268C2213yes—
59C2×C4×D268C2213yes—
60C2×C4×D268C2213yes—
61C2×#14524005C2213yes—
62C2×C4×C22⋊D67C2213yes—
63C2×C4×C22⋊D67C2213yes—
64C2×C4×C22⋊D67C2213yes—
65C2×C4×C22⋊D67C2213yes—
66C2×C4×C22⋊D67C2216yes—
67C2×#14524002C2213yes—
68C2×#14524001C2213yes—
69C2×#14524000C2211yescharacteristic
70C2×#14524000C2213yes—
71C2×C4⋊C4×D67C2213yes—
72C2×C42×D67C2213yes—
73C2×C42×D67C2213yes—
74C22×#41×C67C2211yescharacteristic
75C4×#41×C67C22116yescomplemented
76C2×C4×Q8×C67C2211yescharacteristic
77C2×C4×Q8×C67C2211yescharacteristic
78C2×C4×D4×C67C2213yes—
79C2×C4×D4×C67C2213yes—
80C2×#117×C67C2213yes—
81C22×C42×C67C2213yes—
82C2×#11761629—28no—
83C2×#11761629C2318yes—
84C2×#11761628—224no—
85C2×#11761628C23124yes—
86C22×Dic134C2313yes—
87C22×Dic134C2313yes—
88C2×Q8×D67—28no—
89C2×Q8×D67C2318yes—
90C22×D268C2313yes—
91C22×D268C2313yes—
92C22×C22⋊D67C2313yes—
93C22×C22⋊D67C2313yes—
94C22×C22⋊D67C2316yes—
95C22×C4×D67C2313yes—
96C22×C4×D67C2313yes—
97C22×C4×D67C2313yes—
98C22×C4×D67C2313yes—
99C22×C4×D67C2313yes—
100C22×C4×D67C2311yescharacteristic
101#14524042C23124yes—
102#14524039C23124yes—
103#14524037C23148yes—
104#14524036C23148yes—
105#14524035C23124yes—
106#14524034C23124yes—
107#14524031C23124yes—
108#14524030C23124yes—
109#14524029C23148yes—
110#14524026C23148yes—
111#14524025C23148yes—
112#14524023C23124yes—
113#14524022C23124yes—
114#14524018C23124yes—
115#14524017C23124yes—
116#14524016C23148yes—
117#14524014C23124yes—
118#14524014C23124yes—
119Q8×Dic67C2318yes—
120Q8×Dic67C2318yes—
121C4×Dic134C23124yes—
122C4×Dic134C23124yes—
123C4×Dic134C23124yes—
124#14524008C23124yes—
125C4×D268C23124yes—
126C4×D268C23124yes—
127C4×D268C23124yes—
128#14524005C23124yes—
129C4×C22⋊D67C23124yes—
130C4×C22⋊D67C23124yes—
131C4×C22⋊D67C23124yes—
132C4×C22⋊D67C23124yes—
133C4×C22⋊D67C23148yes—
134#14524002C23124yes—
135#14524001C23124yes—
136#14524000C2318yes—
137#14524000C23124yes—
138C2×C4⋊Dic67C2313yes—
139C2×C4⋊Dic67C2313yes—
140C2×C4⋊Dic67C2313yes—
141C2×C4⋊Dic67C2313yes—
142C2×Dic67⋊C4C2316yes—
143C2×Dic67⋊C4C2311yescharacteristic
144C2×Dic67⋊C4C2311yescharacteristic
145C2×Dic67⋊C4C2313yes—
146C2×Dic67⋊C4C2313yes—
147C2×Dic67⋊C4C2316yes—
148C4⋊C4×D67C23124yes—
149C2×C22⋊Dic67C2313yes—
150C2×C22⋊Dic67C2313yes—
151C2×C22⋊Dic67C2316yes—
152C2×(C2×D67)⋊C4C2311yescharacteristic
153C2×(C2×D67)⋊C4C2311yescharacteristic
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2313yes—
156C2×(C2×D67)⋊C4C2316yes—
157C2×(C2×D67)⋊C4C2316yes—
158C2×C4×Dic67C2311yescharacteristic
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C2313yes—
162C2×C4×Dic67C2313yes—
163C2×C4×Dic67C2313yes—
164C42×D67C23124yes—
165C42×D67C23124yes—
166C2×#41×C67—28no—
167C2×#41×C67C2318yes—
168C22×Q8×C67C2311yescharacteristic
169C22×D4×C67C2313yes—
170C23×C4×C67C2313yes—
171C23×C4×C67C2313yes—
172C23×C4×C67C2313yes—
173C4×Q8×C67C2318yes—
174C4×Q8×C67C2318yes—
175C4×D4×C67C23124yes—
176C4×D4×C67C23124yes—
177#117×C67C23124yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C4⋊C4×C67C2313yes—
180C2×C22⋊C4×C67C2316yes—
181C2×C42×C67C2311yescharacteristic
182C2×C42×C67C2313yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C2313yes—
185C2×C42×C67C23124yes—
186C23×D67C2413yes—
187C23×D67C2411yescharacteristic
188#11761629—232no—
189#11761628—296no—
190C2×Dic134—212no—
191C2×Dic134—212no—
192C2×Dic134C24112yes—
193C2×Dic134C24112yes—
194Q8×D67—232no—
195C2×D268—212no—
196C2×D268—212no—
197C2×D268C24112yes—
198C2×D268C24112yes—
199C2×C22⋊D67—212no—
200C2×C22⋊D67—212no—
201C2×C22⋊D67—412no—
202C2×C22⋊D67C24112yes—
203C2×C22⋊D67C24112yes—
204C2×C22⋊D67C24124yes—
205C22×Dic67C2411yescharacteristic
206C22×Dic67C2411yescharacteristic
207C22×Dic67C2413yes—
208C22×Dic67C2413yes—
209C22×Dic67C2413yes—
210C22×Dic67C2411yescharacteristic
211C2×C4×D67—212no—
212C2×C4×D67—212no—
213C2×C4×D67—212no—
214C2×C4×D67—46no—
215C2×C4×D67—46no—
216C2×C4×D67#4118yescomplemented
217C2×C4×D67C24112yes—
218C2×C4×D67C24112yes—
219C2×C4×D67C24112yes—
220C2×C4×D67C24112yes—
221C2×C4×D67C24112yes—
222C2×C4×D67C2414yes—
223C4⋊Dic67C24112yes—
224C4⋊Dic67C24112yes—
225C4⋊Dic67C24112yes—
226C4⋊Dic67C24112yes—
227Dic67⋊C4C24124yes—
228Dic67⋊C4C2414yes—
229Dic67⋊C4C2414yes—
230Dic67⋊C4C24112yes—
231Dic67⋊C4C24112yes—
232Dic67⋊C4C24124yes—
233C22⋊Dic67C24112yes—
234C22⋊Dic67C24112yes—
235C22⋊Dic67C24124yes—
236(C2×D67)⋊C4C2414yes—
237(C2×D67)⋊C4C2414yes—
238(C2×D67)⋊C4C24112yes—
239(C2×D67)⋊C4C24112yes—
240(C2×D67)⋊C4C24124yes—
241(C2×D67)⋊C4C24124yes—
242C4×Dic67C2414yes—
243C4×Dic67C24112yes—
244C4×Dic67C24112yes—
245C4×Dic67C24112yes—
246C4×Dic67C24112yes—
247C4×Dic67C24112yes—
248C24×C67C2413yes—
249#41×C67—232no—
250C2×Q8×C67#4118yescomplemented
251C2×Q8×C67C2414yes—
252C2×D4×C67—212no—
253C2×D4×C67C24112yes—
254C22×C4×C67—212no—
255C22×C4×C67—212no—
256C22×C4×C67—46no—
257C22×C4×C67C2411yescharacteristic
258C22×C4×C67C2411yescharacteristic
259C22×C4×C67C2413yes—
260C22×C4×C67C2413yes—
261C22×C4×C67C24112yes—
262C22×C4×C67C24112yes—
263C22×C4×C67C24112yes—
264C22×C4×C67C2413yes—
265C22×C4×C67C2411yescharacteristic
266C4⋊C4×C67C24112yes—
267C4⋊C4×C67C24112yes—
268C22⋊C4×C67C24124yes—
269C42×C67C2414yes—
270C42×C67C24112yes—
271C42×C67C24112yes—
272C42×C67C24112yes—
273C23×C67—26no—
274C23×C67—26no—
275C23×C67—26no—
276C23×C67C2516yes—
277C23×C67C2511yescharacteristic
278C22×D67—22no—
279C22×D67—22no—
280C22×D67—26no—
281C22×D67—26no—
282C22×D67—26no—
283C22×D67C2×#4114yes—
284C22×D67C2516yes—
285C22×D67C2512yes—
286Q8×C67C2×#41116yescomplemented
287D4×C67—224no—
288C2×C4×C67—22no—
289C2×C4×C67—26no—
290C2×C4×C67—22no—
291C2×C4×C67—26no—
292C2×C4×C67—224no—
293C2×C4×C67—224no—
294C2×C4×C67—412no—
295C2×C4×C67C2×#4114yes—
296C2×C4×C67C2×#41112yes—
297C2×C4×C67C2512yes—
298C2×C4×C67C2512yes—
299C2×C4×C67C2516yes—
300C2×C4×C67C2516yes—
301C2×C4×C67C2512yes—
302C2×C4×C67C2516yes—
303C22⋊D67—224no—
304C22⋊D67—224no—
305C22⋊D67—424no—
306C2×Dic67—22no—
307C2×Dic67—26no—
308C2×Dic67—26no—
309C2×Dic67—22no—
310C2×Dic67—26no—
311C2×Dic67C2×#4114yes—
312C2×Dic67C2512yes—
313C2×Dic67C2512yes—
314C2×Dic67C2516yes—
315C2×Dic67C2516yes—
316C2×Dic67C2516yes—
317C2×Dic67C2512yes—
318D268—224no—
319D268—224no—
320C4×D67—224no—
321C4×D67—224no—
322C4×D67—224no—
323C4×D67—412no—
324C4×D67—412no—
325C4×D67C2×#41116yescomplemented
326Dic134—224no—
327Dic134—224no—
328C22×C67—26no—
329C22×C67—26no—
330C22×C67—26no—
331C22×C67—412no—
332C22×C67C22×#4112yes—
333C22×C67C22×#4112yes—
334C22×C67#58512yes—
335C22×C67C2611yescharacteristic
336C2×D67—22no—
337C2×D67—22no—
338C2×D67—28no—
339C2×D67—26no—
340C2×D67—26no—
341C2×D67—26no—
342C2×D67—412no—
343C2×D67C22×#4114yes—
344C4×C67—26no—
345C4×C67—22no—
346C4×C67—26no—
347C4×C67—22no—
348C4×C67C22×#4114yes—
349C4×C67C22×#41112yes—
350Dic67—26no—
351Dic67—26no—
352Dic67—22no—
353Dic67—22no—
354Dic67—26no—
355Dic67C22×#4114yes—
356C2×#3480—671nomaximal, Sylow
357C2×C67—46no—
358C2×C67#348014yescomplemented
359C2×C67C23×#4111yescharacteristic
360C2×C67C23×#4111yescharacteristic
361C2×C67C2×#58511yescharacteristic
362D67—24no—
363D67—46no—
364#3480—6732no—
365C2×#559—673no—
366C2×#557—671no—
367C2×#556—673no—
368C2×#553—673no—
369C2×#553—673no—
370C2×#550—671no—
371C2×#548—671no—
372C2×#548—671no—
373C2×#532—673no—
374C2×#529—673no—
375C2×#529—673no—
376C2×C4×#41—673no—
377C2×C4×#41—671no—
378C2×C4×#41D6711yescharacteristic, complemented
379C22×C4×Q8—671no—
380C67C2×#348011yescharacteristic, complemented, Sylow
381C22×#41—671no—
382C22×#41—673no—
383C22×#41C2×D6711yescharacteristic
384C23×Q8—671no—
385#559—6748no—
386#557—6716no—
387#556—6748no—
388#553—6748no—
389#553—6748no—
390#550—6716no—
391#548—6716no—
392#548—6716no—
393#532—6748no—
394C2×C4⋊Q8—673no—
395C2×#127—673no—
396#529—6748no—
397#529—6748no—
398C2×#126—676no—
399C2×#126—676no—
400C2×#125—673no—
401C2×#125—673no—
402C2×#124—673no—
403C2×#124—676no—
404C2×#124—673no—
405C2×#123—676no—
406C2×#123—676no—
407C2×C22⋊Q8—673no—
408C2×C22⋊Q8—673no—
409C2×#121—673no—
410C2×#121—673no—
411C2×#121—673no—
412C2×#121—673no—
413C2×#121—676no—
414C4×#41—6716no—
415C4×#41—6748no—
416C4×#41C2×D67116yescomplemented
417C2×C4×Q8—671no—
418C2×C4×Q8—671no—
419C2×C4×Q8—6716no—
420C2×C4×Q8—673no—
421C2×C4×Q8—673no—
422C2×C4×Q8—673no—
423C2×C4×Q8—673no—
424C2×C4×Q8C2×D6711yescharacteristic
425C2×C4×Q8C2×D6711yescharacteristic
426C2×C4×D4—673no—
427C2×C4×D4—673no—
428C2×C4×D4—673no—
429C2×C4×D4—673no—
430C2×C4×D4—676no—
431C2×C4×D4—673no—
432C2×C4×D4—673no—
433C2×C4×D4—673no—
434C2×C4×D4—673no—
435C2×C4×D4C2×D6713yes—
436C2×C4×D4C2×D6713yes—
437C2×#117—673no—
438C2×#117—673no—
439C2×#117—671no—
440C2×#117—673no—
441C2×#117C2×D6713yes—
442C22×C4⋊C4—673no—
443C22×C42—673no—
444C22×C42—673no—
445C22×C42C2×D6713yes—
446C2×#41—28no—
447C2×#41—678no—
448C2×#41—6724no—
449C2×#41—13424no—
450C2×#41—1348no—
451C2×#41C22×D6718yes—
452C22×Q8—678no—
453C22×Q8—673no—
454C22×Q8—673no—
455C22×Q8—1348no—
456C22×Q8C22×D6711yescharacteristic
457C22×D4—676no—
458C22×D4—673no—
459C22×D4—673no—
460C22×D4—673no—
461C22×D4—673no—
462C22×D4C22×D6713yes—
463C23×C4—673no—
464C23×C4—673no—
465C23×C4—671no—
466C23×C4—673no—
467C23×C4—673no—
468C23×C4—673no—
469C23×C4C22×D6713yes—
470C23×C4C22×D6713yes—
471C23×C4C22×D6713yes—
472C4⋊Q8—6724no—
473#127—6724no—
474#126—6748no—
475#126—6748no—
476#125—6724no—
477#125—6724no—
478#124—6724no—
479#124—6748no—
480#124—6724no—
481#123—6748no—
482#123—6748no—
483C22⋊Q8—6724no—
484C22⋊Q8—6724no—
485#121—6724no—
486#121—6724no—
487#121—6724no—
488#121—6724no—
489#121—6748no—
490C4×Q8—678no—
491C4×Q8—678no—
492C4×Q8—6724no—
493C4×Q8—6724no—
494C4×Q8—6724no—
495C4×Q8—6724no—
496C4×Q8C22×D6718yes—
497C4×Q8C22×D6718yes—
498C4×D4—6724no—
499C4×D4—6724no—
500C4×D4—6724no—
501C4×D4—6724no—
502C4×D4—6748no—
503C4×D4—6724no—
504C4×D4—6724no—
505C4×D4—6724no—
506C4×D4—6724no—
507C4×D4C22×D67124yes—
508C4×D4C22×D67124yes—
509#117—6724no—
510#117—6724no—
511#117—678no—
512#117—6724no—
513#117C22×D67124yes—
514C2×C4⋊C4—673no—
515C2×C4⋊C4—676no—
516C2×C4⋊C4—671no—
517C2×C4⋊C4—671no—
518C2×C4⋊C4—673no—
519C2×C4⋊C4—673no—
520C2×C4⋊C4—673no—
521C2×C4⋊C4—673no—
522C2×C4⋊C4—673no—
523C2×C4⋊C4—676no—
524C2×C4⋊C4—6724no—
525C2×C4⋊C4C22×D6713yes—
526C2×C4⋊C4C22×D6713yes—
527C2×C22⋊C4—673no—
528C2×C22⋊C4—673no—
529C2×C22⋊C4—676no—
530C2×C22⋊C4—671no—
531C2×C22⋊C4—671no—
532C2×C22⋊C4—673no—
533C2×C22⋊C4—676no—
534C2×C22⋊C4—673no—
535C2×C22⋊C4—676no—
536C2×C22⋊C4C22×D6716yes—
537C2×C42—673no—
538C2×C42—673no—
539C2×C42—673no—
540C2×C42—673no—
541C2×C42—671no—
542C2×C42—673no—
543C2×C42—6724no—
544C2×C42—6724no—
545C2×C42C22×D6713yes—
546C2×C42C22×D6713yes—
547C2×C42C22×D67124yes—
548C2×C42C22×D6711yescharacteristic
549C2×C42C22×D6713yes—
550C24—671no—
551C24—673no—
552C24C23×D6713yes—
553#41—232no—
554#41—13496no—
555#41—13432no—
556C2×Q8—6712no—
557C2×Q8—6712no—
558C2×Q8—13412no—
559C2×Q8—13432no—
560C2×Q8—13412no—
561C2×Q8#1176162818yescomplemented
562C2×Q8C23×D6714yes—
563C2×D4—212no—
564C2×D4—26812no—
565C2×D4—6724no—
566C2×D4—6712no—
567C2×D4—6712no—
568C2×D4—6712no—
569C2×D4—6712no—
570C2×D4—13412no—
571C2×D4—13412no—
572C2×D4—13412no—
573C2×D4—13412no—
574C2×D4C23×D67112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—2686no—
579C22×C4—2686no—
580C22×C4—6712no—
581C22×C4—6712no—
582C22×C4—671no—
583C22×C4—678no—
584C22×C4—674no—
585C22×C4—671no—
586C22×C4—671no—
587C22×C4—673no—
588C22×C4—673no—
589C22×C4—673no—
590C22×C4—6712no—
591C22×C4—6712no—
592C22×C4—6712no—
593C22×C4—13412no—
594C22×C4—13412no—
595C22×C4—13412no—
596C22×C4C23×D6713yes—
597C22×C4C23×D6711yescharacteristic
598C22×C4C23×D6711yescharacteristic
599C22×C4C23×D6713yes—
600C22×C4C23×D67112yes—
601C22×C4C23×D67112yes—
602C22×C4C23×D67112yes—
603C22×C4C23×D6713yes—
604C22×C4C23×D6711yescharacteristic
605C4⋊C4—6712no—
606C4⋊C4—6724no—
607C4⋊C4—674no—
608C4⋊C4—674no—
609C4⋊C4—6712no—
610C4⋊C4—6712no—
611C4⋊C4—6712no—
612C4⋊C4—6712no—
613C4⋊C4—6712no—
614C4⋊C4—6724no—
615C4⋊C4C23×D67112yes—
616C4⋊C4C23×D67112yes—
617C22⋊C4—6712no—
618C22⋊C4—6712no—
619C22⋊C4—6724no—
620C22⋊C4—674no—
621C22⋊C4—674no—
622C22⋊C4—6712no—
623C22⋊C4—6724no—
624C22⋊C4—6712no—
625C22⋊C4—6724no—
626C22⋊C4C23×D67124yes—
627C42—674no—
628C42—6712no—
629C42—6712no—
630C42—6712no—
631C42—6712no—
632C42—6712no—
633C42C23×D67112yes—
634C42C23×D6714yes—
635C42C23×D67112yes—
636C42C23×D67112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—674no—
641C23—672no—
642C23—676no—
643C23—1346no—
644C23—1346no—
645C23—1346no—
646C23—1342no—
647C23—1342no—
648C23C24×D6716yes—
649C23C24×D6711yescharacteristic
650Q8—13424no—
651Q8—13424no—
652Q8C2×#11761628116yescomplemented
653D4—224no—
654D4—26824no—
655D4—13424no—
656D4—13424no—
657D4—13424no—
658D4—13424no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—26812no—
667C2×C4—26812no—
668C2×C4—674no—
669C2×C4—672no—
670C2×C4—6716no—
671C2×C4—672no—
672C2×C4—672no—
673C2×C4—676no—
674C2×C4—676no—
675C2×C4—676no—
676C2×C4—1346no—
677C2×C4—1342no—
678C2×C4—1346no—
679C2×C4—1342no—
680C2×C4—1346no—
681C2×C4—13424no—
682C2×C4—13424no—
683C2×C4—13424no—
684C2×C4#41×D6714yes—
685C2×C4C2×#11761628112yes—
686C2×C4C24×D6716yes—
687C2×C4C24×D6712yes—
688C2×C4C24×D6712yes—
689C2×C4C24×D6716yes—
690C2×C4C24×D6712yes—
691C2×C4C24×D6716yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—26812no—
697C22—674no—
698C22—1346no—
699C22—1346no—
700C22—1346no—
701C22—1342no—
702C22—1342no—
703C22—1348no—
704C22C2×#41×D6712yes—
705C22C22×#1176162812yes—
706C22#1686423212yes—
707C22C25×D6711yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—674no—
713C4—1346no—
714C4—1342no—
715C4—1346no—
716C4—1342no—
717C4—1346no—
718C4C2×#41×D6714yes—
719C4C22×#11761628112yes—
720C2—46no—
721C2—2686no—
722C2—1344no—
723C2#2257380714yesdirect product factor
724C2C22×#41×D6711yescharacteristic
725C2C23×#1176162811yescharacteristic
726C2C2×#1686423211yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
socleC23×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×#3480
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22573807C2direct (N × H)
2. C2×#16864129C2semidirect
3. C2×#16864122C2semidirect
4. C2×#16864114C2semidirect
5. C2×#16864096C2semidirect
6. C2×#16864090C2semidirect
7. C2×#16864065C2semidirect
8. C2×#16864058C2semidirect
9. C2×#16864053C2semidirect
10. C2×#16863943C2semidirect
11. C2×#16863930C2semidirect
12. C2×#16863928C2semidirect
13. C2×C4×#11761629C2semidirect
14. C2×C4×#11761628C2semidirect
15. C2×C4×Q8×D67C2semidirect
16. C2×C4×#41×C67C2semidirect
20. #16864129C22semidirect
21. #16864122C22semidirect
22. #16864114C22semidirect
23. #16864096C22semidirect
24. #16864090C22semidirect
25. #16864065C22semidirect
26. #16864058C22semidirect
27. #16864053C22semidirect
28. #16863943C22semidirect
31. #16863930C22semidirect
32. #16863928C22semidirect
49. C4×#11761629C22semidirect
50. C4×#11761628C22semidirect
57. C4×Q8×D67C22semidirect
75. C4×#41×C67C22semidirect
216. C2×C4×D67#41semidirect
250. C2×Q8×C67#41semidirect
286. Q8×C67C2×#41semidirect
325. C4×D67C2×#41semidirect
358. C2×C67#3480semidirect
378. C2×C4×#41D67semidirect
380. C67C2×#3480semidirect
416. C4×#41C2×D67semidirect
561. C2×Q8#11761628semidirect
652. Q8C2×#11761628semidirect
723. C2#22573807direct (N × H)

Maximal subgroups

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

subgroupindex
#225738072
C2×#168641292
C2×#168641222
C2×#168641142
C2×#168640962
C2×#168640902
C2×#168640652
C2×#168640582
C2×#168640532
C2×#168639432
C2×#168639302
C2×#168639282
C2×C4×#117616292
C2×C4×#117616282
C2×C4×Q8×D672
C2×C4×#41×C672
C2×#348067