Finite Group Databasebeta

← C2×#22573799 #31762885

Subgroups — C2×#22573799 #31762885

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#22573799C2132yesmaximal, direct product factor
2C2×#16864128C213yesmaximal, complemented
3C2×#16864122C211yesmaximal, characteristic, complemented
4C2×#16864117C213yesmaximal, complemented
5C2×#16864098C213yesmaximal, complemented
6C2×#16864092C213yesmaximal, complemented
7C2×#16864065C211yesmaximal, characteristic, complemented
8C2×#16864057C211yesmaximal, characteristic, complemented
9C2×#16863941C213yesmaximal, complemented
10C2×#16863932C213yesmaximal, complemented
11C2×#16863925C213yesmaximal, complemented
12C2×#41×Dic67C211yesmaximal, characteristic, complemented
13C2×C4×#11761629C211yesmaximal, characteristic, complemented
14C2×C4×#11761627C213yesmaximal, complemented
15C22×Q8×Dic67C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761627C2213yes—
19#16864128C22148yescomplemented
20#16864122C22116yescomplemented
21#16864117C22148yescomplemented
22#16864098C22148yescomplemented
23#16864092C22148yescomplemented
24#16864065C22116yescomplemented
25#16864057C22116yescomplemented
26#16863941C22148yescomplemented
27C2×#14524042C2213yes—
28C2×#14524039C2213yes—
29#16863932C22148yescomplemented
30#16863925C22148yescomplemented
31C2×#14524038C2216yes—
32C2×#14524036C2216yes—
33C2×#14524035C2213yes—
34C2×#14524034C2213yes—
35C2×#14524032C2213yes—
36C2×#14524029C2216yes—
37C2×#14524027C2216yes—
38C2×#14524025C2216yes—
39C2×#14524019C2213yes—
40C2×#14524017C2213yes—
41C2×#14524017C2213yes—
42C2×#14524015C2216yes—
43C2×#14524014C2213yes—
44#41×Dic67C22116yescomplemented
45C4×#11761629C22116yescomplemented
46C4×#11761627C22148yescomplemented
47C2×Q8×Dic67C2211yescharacteristic
48C2×Q8×Dic67C2211yescharacteristic
49C2×Q8×Dic67C2213yes—
50C2×Q8×Dic67C2213yes—
51C2×Q8×Dic67C2211yescharacteristic
52C2×Q8×Dic67C22116yescomplemented
53C2×C4×Dic134C2213yes—
54C2×#14524008C2213yes—
55C2×C4×D268C2213yes—
56C2×D4×Dic67C2213yes—
57C2×D4×Dic67C2213yes—
58C2×D4×Dic67C2213yes—
59C2×#14524005C2213yes—
60C2×C4×C22⋊D67C2213yes—
61C2×C4×C22⋊D67C2213yes—
62C2×(C22⋊D67)⋊C4C2213yes—
63C2×(C22⋊D67)⋊C4C2213yes—
64C2×(C22⋊D67)⋊C4C2216yes—
65C2×#14524002C2213yes—
66C2×#14524001C2213yes—
67C2×#14524001C2213yes—
68C2×#14523999C2211yescharacteristic
69C2×#14523999C2213yes—
70C22×C4⋊Dic67C2213yes—
71C22×C4×Dic67C2213yes—
72C22×C4×Dic67C2213yes—
73C2×C42×D67C2213yes—
74C22×#41×C67C2211yescharacteristic
75C23×Q8×C67C2211yescharacteristic
76#548×C67C22116yescomplemented
77C2×#124×C67C2213yes—
78C2×C22⋊Q8×C67C2213yes—
79C2×#121×C67C2213yes—
80C2×C4×Q8×C67C2211yescharacteristic
81C2×C4×D4×C67C2213yes—
82C2×#11761629—28no—
83C2×#11761629C2318yes—
84C2×#11761627—224no—
85C2×#11761627C23124yes—
86C22×Dic134C2313yes—
87C22×D268C2313yes—
88C22×C22⋊D67C2313yes—
89C22×C22⋊D67C2313yes—
90C22×C22⋊D67C2316yes—
91C23×Dic67C2313yes—
92C23×Dic67C2313yes—
93C23×Dic67C2313yes—
94C23×Dic67C2311yescharacteristic
95C22×C4×D67C2313yes—
96C22×C4×D67C2313yes—
97C22×C4×D67C2313yes—
98#14524042C23124yes—
99#14524039C23124yes—
100#14524038C23148yes—
101#14524036C23148yes—
102#14524035C23124yes—
103#14524034C23124yes—
104#14524032C23124yes—
105#14524029C23148yes—
106#14524027C23148yes—
107#14524025C23148yes—
108#14524019C23124yes—
109#14524017C23124yes—
110#14524017C23124yes—
111#14524015C23148yes—
112#14524014C23124yes—
113Q8×Dic67C2318yes—
114Q8×Dic67C2318yes—
115Q8×Dic67C23124yes—
116Q8×Dic67C2318yes—
117Q8×Dic67C23124yes—
118C4×Dic134C23124yes—
119#14524008C23124yes—
120C4×D268C23124yes—
121D4×Dic67C23124yes—
122D4×Dic67C23124yes—
123D4×Dic67C23124yes—
124#14524005C23124yes—
125C4×C22⋊D67C23124yes—
126C4×C22⋊D67C23124yes—
127(C22⋊D67)⋊C4C23124yes—
128(C22⋊D67)⋊C4C23124yes—
129(C22⋊D67)⋊C4C23148yes—
130#14524002C23124yes—
131#14524001C23124yes—
132#14524001C23124yes—
133#14523999C2318yes—
134#14523999C23124yes—
135C2×C4⋊Dic67C23124yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2313yes—
138C2×C4⋊Dic67C2316yes—
139C2×C4⋊Dic67C2313yes—
140C2×C4⋊Dic67C2313yes—
141C2×Dic67⋊C4C2311yescharacteristic
142C2×Dic67⋊C4C2313yes—
143C2×Dic67⋊C4C2311yescharacteristic
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2316yes—
146C2×C22⋊Dic67C2311yescharacteristic
147C2×C22⋊Dic67C2313yes—
148C2×C22⋊Dic67C2316yes—
149C2×(C2×D67)⋊C4C2313yes—
150C2×(C2×D67)⋊C4C2313yes—
151C2×(C2×D67)⋊C4C2316yes—
152C2×(C2×D67)⋊C4C2316yes—
153C2×C4×Dic67C2311yescharacteristic
154C2×C4×Dic67C2313yes—
155C2×C4×Dic67C2313yes—
156C2×C4×Dic67C2311yescharacteristic
157C2×C4×Dic67C2313yes—
158C2×C4×Dic67C2313yes—
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C2313yes—
162C2×C4×Dic67C23124yes—
163C2×C4×Dic67C23124yes—
164C42×D67C23124yes—
165C2×#41×C67—28no—
166C2×#41×C67C2318yes—
167C22×Q8×C67—28no—
168C22×Q8×C67C2318yes—
169C22×Q8×C67C2313yes—
170C22×Q8×C67C2311yescharacteristic
171C22×D4×C67C2313yes—
172C22×D4×C67C2313yes—
173C23×C4×C67C2313yes—
174C23×C4×C67C2313yes—
175#124×C67C23124yes—
176C22⋊Q8×C67C23124yes—
177#121×C67C23124yes—
178C4×Q8×C67C2318yes—
179C4×D4×C67C23124yes—
180C2×C4⋊C4×C67C2313yes—
181C2×C4⋊C4×C67C2313yes—
182C2×C22⋊C4×C67C2311yescharacteristic
183C2×C22⋊C4×C67C2313yes—
184C2×C22⋊C4×C67C2316yes—
185C2×C42×C67C2313yes—
186C23×D67C2413yes—
187#11761629—232no—
188#11761627—296no—
189C2×Dic134—212no—
190C2×Dic134C24112yes—
191C2×D268—212no—
192C2×D268C24112yes—
193C2×C22⋊D67—212no—
194C2×C22⋊D67—212no—
195C2×C22⋊D67—412no—
196C2×C22⋊D67C24112yes—
197C2×C22⋊D67C24112yes—
198C2×C22⋊D67C24124yes—
199C22×Dic67—212no—
200C22×Dic67—46no—
201C22×Dic67—46no—
202C22×Dic67#4118yescomplemented
203C22×Dic67C2411yescharacteristic
204C22×Dic67C2413yes—
205C22×Dic67C2411yescharacteristic
206C22×Dic67C2413yes—
207C22×Dic67C2413yes—
208C22×Dic67C24112yes—
209C22×Dic67C24112yes—
210C22×Dic67C24112yes—
211C22×Dic67C2411yescharacteristic
212C22×Dic67C2411yescharacteristic
213C22×Dic67C2414yes—
214C2×C4×D67—212no—
215C2×C4×D67—212no—
216C2×C4×D67—46no—
217C2×C4×D67C24112yes—
218C2×C4×D67C24112yes—
219C2×C4×D67C24112yes—
220C4⋊Dic67C24112yes—
221C4⋊Dic67C24112yes—
222C4⋊Dic67C24124yes—
223C4⋊Dic67C24112yes—
224C4⋊Dic67C24112yes—
225Dic67⋊C4C2414yes—
226Dic67⋊C4C24112yes—
227Dic67⋊C4C2414yes—
228Dic67⋊C4C24112yes—
229Dic67⋊C4C24124yes—
230C22⋊Dic67C2414yes—
231C22⋊Dic67C24112yes—
232C22⋊Dic67C24124yes—
233(C2×D67)⋊C4C24112yes—
234(C2×D67)⋊C4C24112yes—
235(C2×D67)⋊C4C24124yes—
236(C2×D67)⋊C4C24124yes—
237C4×Dic67C2414yes—
238C4×Dic67C24112yes—
239C4×Dic67C24112yes—
240C4×Dic67C2414yes—
241C4×Dic67C24112yes—
242C4×Dic67C24112yes—
243C4×Dic67C24112yes—
244C4×Dic67C24112yes—
245C4×Dic67C24112yes—
246C24×C67C2413yes—
247C24×C67C2411yescharacteristic
248#41×C67—232no—
249C2×Q8×C67—232no—
250C2×Q8×C67—212no—
251C2×Q8×C67#4118yescomplemented
252C2×Q8×C67C24112yes—
253C2×Q8×C67C2414yes—
254C2×D4×C67—212no—
255C2×D4×C67—212no—
256C2×D4×C67C24112yes—
257C2×D4×C67C24112yes—
258C22×C4×C67—212no—
259C22×C4×C67—212no—
260C22×C4×C67C2411yescharacteristic
261C22×C4×C67C2413yes—
262C22×C4×C67C2413yes—
263C22×C4×C67C2411yescharacteristic
264C22×C4×C67C24112yes—
265C22×C4×C67C24112yes—
266C22×C4×C67C2413yes—
267C4⋊C4×C67C24112yes—
268C4⋊C4×C67C24112yes—
269C22⋊C4×C67C2414yes—
270C22⋊C4×C67C24112yes—
271C22⋊C4×C67C24124yes—
272C42×C67C24112yes—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—26no—
276C23×C67—26no—
277C23×C67—26no—
278C23×C67C2×#4114yes—
279C23×C67C2516yes—
280C23×C67C2512yes—
281C23×C67C2511yescharacteristic
282C22×D67—26no—
283C22×D67—26no—
284C22×D67—26no—
285C22×D67C2516yes—
286Q8×C67—224no—
287Q8×C67C2×#41116yescomplemented
288D4×C67—224no—
289D4×C67—224no—
290C2×C4×C67—22no—
291C2×C4×C67—26no—
292C2×C4×C67—26no—
293C2×C4×C67—22no—
294C2×C4×C67—224no—
295C2×C4×C67—224no—
296C2×C4×C67C2×#41112yes—
297C2×C4×C67C2512yes—
298C2×C4×C67C2516yes—
299C2×C4×C67C2516yes—
300C2×C4×C67C2512yes—
301C2×C4×C67C2516yes—
302C22⋊D67—224no—
303C22⋊D67—224no—
304C22⋊D67—424no—
305C2×Dic67—22no—
306C2×Dic67—26no—
307C2×Dic67—26no—
308C2×Dic67—22no—
309C2×Dic67—26no—
310C2×Dic67—224no—
311C2×Dic67—412no—
312C2×Dic67—412no—
313C2×Dic67C2×#4114yes—
314C2×Dic67C2×#4114yes—
315C2×Dic67C2×#41116yescomplemented
316C2×Dic67C2512yes—
317C2×Dic67C2516yes—
318C2×Dic67C2512yes—
319C2×Dic67C2516yes—
320C2×Dic67C2516yes—
321C2×Dic67C2512yes—
322C2×Dic67C2512yes—
323D268—224no—
324C4×D67—224no—
325C4×D67—224no—
326C4×D67—412no—
327Dic134—224no—
328C22×C67—22no—
329C22×C67—22no—
330C22×C67—28no—
331C22×C67—26no—
332C22×C67—26no—
333C22×C67—26no—
334C22×C67—412no—
335C22×C67C22×#4114yes—
336C22×C67C22×#4112yes—
337C22×C67C22×#4112yes—
338C22×C67#58512yes—
339C22×C67C2611yescharacteristic
340C2×D67—26no—
341C2×D67—26no—
342C2×D67—26no—
343C2×D67—412no—
344C4×C67—26no—
345C4×C67—22no—
346C4×C67—26no—
347C4×C67—22no—
348C4×C67C22×#41112yes—
349Dic67—26no—
350Dic67—22no—
351Dic67—26no—
352Dic67—22no—
353Dic67—26no—
354Dic67C22×#4114yes—
355Dic67C22×#4114yes—
356C2×#3480—671nomaximal, Sylow
357C2×C67—24no—
358C2×C67—46no—
359C2×C67#348014yescomplemented
360C2×C67C23×#4111yescharacteristic
361C2×C67C23×#4111yescharacteristic
362C2×C67C2×#58511yescharacteristic
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×#548D6711yescharacteristic, complemented
373C2×#532—673no—
374C2×#529—673no—
375C2×#529—673no—
376C2×C4×#41—671no—
377C2×C4×#41—671no—
378C2×C4×#41—673no—
379C22×C4×Q8—671no—
380C67C2×#348011yescharacteristic, complemented, Sylow
381C22×#41—671no—
382C22×#41—673no—
383C22×#41C2×D6711yescharacteristic
384C23×Q8C2×D6711yescharacteristic
385#559—6748no—
386#557—6716no—
387#556—6748no—
388#553—6748no—
389#553—6748no—
390#550—6716no—
391#548—6716no—
392#548C2×D67116yescomplemented
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×#124C2×D6713yes—
405C2×#123—676no—
406C2×#123—676no—
407C2×C22⋊Q8—673no—
408C2×C22⋊Q8C2×D6713yes—
409C2×#121—673no—
410C2×#121—676no—
411C2×#121—673no—
412C2×#121—673no—
413C2×#121C2×D6713yes—
414C4×#41—6716no—
415C4×#41—6716no—
416C4×#41—6748no—
417C2×C4×Q8—671no—
418C2×C4×Q8—673no—
419C2×C4×Q8—671no—
420C2×C4×Q8—673no—
421C2×C4×Q8—6716no—
422C2×C4×Q8—671no—
423C2×C4×Q8—673no—
424C2×C4×Q8—673no—
425C2×C4×Q8C2×D6711yescharacteristic
426C2×C4×D4—673no—
427C2×C4×D4—673no—
428C2×C4×D4—673no—
429C2×C4×D4—673no—
430C2×C4×D4—673no—
431C2×C4×D4—673no—
432C2×C4×D4—673no—
433C2×C4×D4—673no—
434C2×C4×D4—676no—
435C2×C4×D4—673no—
436C2×C4×D4C2×D6713yes—
437C2×#117—673no—
438C2×#117—673no—
439C2×#117—673no—
440C2×#117—671no—
441C2×#117—673no—
442C22×C4⋊C4—673no—
443C22×C42—673no—
444C22×C42—673no—
445C22×C42—673no—
446C2×#41—28no—
447C2×#41—678no—
448C2×#41—6724no—
449C2×#41—13424no—
450C2×#41—1348no—
451C2×#41C22×D6718yes—
452C22×Q8—28no—
453C22×Q8—673no—
454C22×Q8C22×D6713yes—
455C22×Q8C22×D6718yes—
456C22×Q8C22×D6711yescharacteristic
457C22×D4—676no—
458C22×D4—673no—
459C22×D4—673no—
460C22×D4—673no—
461C22×D4C22×D6713yes—
462C22×D4C22×D6713yes—
463C23×C4—673no—
464C23×C4—673no—
465C23×C4—673no—
466C23×C4—671no—
467C23×C4—673no—
468C23×C4—673no—
469C23×C4—673no—
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#124C22×D67124yes—
481#123—6748no—
482#123—6748no—
483C22⋊Q8—6724no—
484C22⋊Q8C22×D67124yes—
485#121—6724no—
486#121—6748no—
487#121—6724no—
488#121—6724no—
489#121C22×D67124yes—
490C4×Q8—678no—
491C4×Q8—6724no—
492C4×Q8—678no—
493C4×Q8—6724no—
494C4×Q8—678no—
495C4×Q8—6724no—
496C4×Q8—6724no—
497C4×Q8C22×D6718yes—
498C4×D4—6724no—
499C4×D4—6724no—
500C4×D4—6724no—
501C4×D4—6724no—
502C4×D4—6724no—
503C4×D4—6724no—
504C4×D4—6724no—
505C4×D4—6724no—
506C4×D4—6748no—
507C4×D4—6724no—
508C4×D4C22×D67124yes—
509#117—6724no—
510#117—6724no—
511#117—6724no—
512#117—678no—
513#117—6724no—
514C2×C4⋊C4—673no—
515C2×C4⋊C4—673no—
516C2×C4⋊C4—676no—
517C2×C4⋊C4—6724no—
518C2×C4⋊C4—671no—
519C2×C4⋊C4—671no—
520C2×C4⋊C4—673no—
521C2×C4⋊C4—673no—
522C2×C4⋊C4—673no—
523C2×C4⋊C4—673no—
524C2×C4⋊C4—676no—
525C2×C4⋊C4C22×D6713yes—
526C2×C4⋊C4C22×D6713yes—
527C2×C22⋊C4—671no—
528C2×C22⋊C4—673no—
529C2×C22⋊C4—676no—
530C2×C22⋊C4—673no—
531C2×C22⋊C4—676no—
532C2×C22⋊C4—673no—
533C2×C22⋊C4—676no—
534C2×C22⋊C4C22×D6711yescharacteristic
535C2×C22⋊C4C22×D6713yes—
536C2×C22⋊C4C22×D6716yes—
537C2×C42—671no—
538C2×C42—671no—
539C2×C42—673no—
540C2×C42—673no—
541C2×C42—673no—
542C2×C42—673no—
543C2×C42—673no—
544C2×C42—673no—
545C2×C42—673no—
546C2×C42—6724no—
547C2×C42—6724no—
548C2×C42—6724no—
549C2×C42C22×D6713yes—
550C24—673no—
551C24C23×D6713yes—
552C24C23×D6711yescharacteristic
553#41—232no—
554#41—13496no—
555#41—13432no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—6712no—
559C2×Q8—13412no—
560C2×Q8#1176162718yescomplemented
561C2×Q8C23×D67112yes—
562C2×Q8C23×D6714yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—26812no—
566C2×D4—6724no—
567C2×D4—6712no—
568C2×D4—6712no—
569C2×D4—6712no—
570C2×D4—13412no—
571C2×D4—13412no—
572C2×D4—13412no—
573C2×D4C23×D67112yes—
574C2×D4C23×D67112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—2686no—
578C22×C4—2686no—
579C22×C4—2686no—
580C22×C4—6712no—
581C22×C4—6712no—
582C22×C4—6712no—
583C22×C4—678no—
584C22×C4—674no—
585C22×C4—671no—
586C22×C4—671no—
587C22×C4—6712no—
588C22×C4—671no—
589C22×C4—671no—
590C22×C4—673no—
591C22×C4—673no—
592C22×C4—673no—
593C22×C4—6712no—
594C22×C4—6712no—
595C22×C4—13412no—
596C22×C4—13412no—
597C22×C4—13412no—
598C22×C4C23×D67112yes—
599C22×C4C23×D67112yes—
600C22×C4C23×D6711yescharacteristic
601C22×C4C23×D6713yes—
602C22×C4C23×D6711yescharacteristic
603C22×C4C23×D6713yes—
604C22×C4C23×D6713yes—
605C4⋊C4—6712no—
606C4⋊C4—6712no—
607C4⋊C4—6724no—
608C4⋊C4—674no—
609C4⋊C4—674no—
610C4⋊C4—6712no—
611C4⋊C4—6712no—
612C4⋊C4—6712no—
613C4⋊C4—6712no—
614C4⋊C4—6724no—
615C4⋊C4C23×D67112yes—
616C4⋊C4C23×D67112yes—
617C22⋊C4—674no—
618C22⋊C4—6712no—
619C22⋊C4—6724no—
620C22⋊C4—6712no—
621C22⋊C4—6724no—
622C22⋊C4—6712no—
623C22⋊C4—6724no—
624C22⋊C4C23×D6714yes—
625C22⋊C4C23×D67112yes—
626C22⋊C4C23×D67124yes—
627C42—674no—
628C42—674no—
629C42—6712no—
630C42—6712no—
631C42—6712no—
632C42—6712no—
633C42—6712no—
634C42—6712no—
635C42—6712no—
636C42C23×D67112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—676no—
643C23—1346no—
644C23—1346no—
645C23—1346no—
646C23#41×D6714yes—
647C23C24×D6716yes—
648C23C24×D6712yes—
649C23C24×D6711yescharacteristic
650Q8—224no—
651Q8—13424no—
652Q8C2×#11761627116yescomplemented
653D4—224no—
654D4—224no—
655D4—26824no—
656D4—13424no—
657D4—13424no—
658D4—13424no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—26812no—
666C2×C4—26812no—
667C2×C4—26812no—
668C2×C4—674no—
669C2×C4—674no—
670C2×C4—6716no—
671C2×C4—672no—
672C2×C4—672no—
673C2×C4—672no—
674C2×C4—672no—
675C2×C4—676no—
676C2×C4—676no—
677C2×C4—676no—
678C2×C4—13424no—
679C2×C4—13424no—
680C2×C4—1346no—
681C2×C4—1342no—
682C2×C4—1346no—
683C2×C4—1342no—
684C2×C4—1346no—
685C2×C4—13424no—
686C2×C4C2×#11761627112yes—
687C2×C4C24×D6712yes—
688C2×C4C24×D6716yes—
689C2×C4C24×D6712yes—
690C2×C4C24×D6716yes—
691C2×C4C24×D6716yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—26812no—
700C22—1346no—
701C22—1346no—
702C22—1346no—
703C22C2×#41×D6714yes—
704C22C2×#41×D6712yes—
705C22C22×#1176162712yes—
706C22#1686423312yes—
707C22C25×D6711yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—674no—
713C4—674no—
714C4—1346no—
715C4—1342no—
716C4—1346no—
717C4—1342no—
718C4—1346no—
719C4C22×#11761627112yes—
720C2—24no—
721C2—46no—
722C2—2686no—
723C2#2257379914yesdirect product factor
724C2C22×#41×D6711yescharacteristic
725C2C23×#1176162711yescharacteristic
726C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#548×C67C2
socleC23×C67C25
hypercenterC2×#548D67
hypocenterC67C2×#3480
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22573799C2direct (N × H)
2. C2×#16864128C2semidirect
3. C2×#16864122C2semidirect
4. C2×#16864117C2semidirect
5. C2×#16864098C2semidirect
6. C2×#16864092C2semidirect
7. C2×#16864065C2semidirect
8. C2×#16864057C2semidirect
9. C2×#16863941C2semidirect
10. C2×#16863932C2semidirect
11. C2×#16863925C2semidirect
12. C2×#41×Dic67C2semidirect
13. C2×C4×#11761629C2semidirect
14. C2×C4×#11761627C2semidirect
15. C22×Q8×Dic67C2semidirect
16. C2×#548×C67C2semidirect
19. #16864128C22semidirect
20. #16864122C22semidirect
21. #16864117C22semidirect
22. #16864098C22semidirect
23. #16864092C22semidirect
24. #16864065C22semidirect
25. #16864057C22semidirect
26. #16863941C22semidirect
29. #16863932C22semidirect
30. #16863925C22semidirect
44. #41×Dic67C22semidirect
45. C4×#11761629C22semidirect
46. C4×#11761627C22semidirect
52. C2×Q8×Dic67C22semidirect
76. #548×C67C22semidirect
202. C22×Dic67#41semidirect
251. C2×Q8×C67#41semidirect
287. Q8×C67C2×#41semidirect
315. C2×Dic67C2×#41semidirect
359. C2×C67#3480semidirect
372. C2×#548D67semidirect
380. C67C2×#3480semidirect
392. #548C2×D67semidirect
560. C2×Q8#11761627semidirect
652. Q8C2×#11761627semidirect
723. C2#22573799direct (N × H)

Maximal subgroups

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

subgroupindex
#225737992
C2×#168641282
C2×#168641222
C2×#168641172
C2×#168640982
C2×#168640922
C2×#168640652
C2×#168640572
C2×#168639412
C2×#168639322
C2×#168639252
C2×#41×Dic672
C2×C4×#117616292
C2×C4×#117616272
C22×Q8×Dic672
C2×#548×C672
C2×#348067