Finite Group Databasebeta

← C2×#22574113 #31764199

Subgroups — C2×#22574113 #31764199

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574113C2132yesmaximal, direct product factor
2C2×#16864119C211yesmaximal, characteristic, complemented
3C2×#16864109C212yesmaximal, complemented
4C2×#16864104C212yesmaximal, complemented
5C2×#16864097C214yesmaximal, complemented
6C2×#16864058C212yesmaximal, complemented
7C2×#16864054C212yesmaximal, complemented
8C2×#16864050C211yesmaximal, characteristic, complemented
9C2×#16864049C211yesmaximal, characteristic, complemented
10C2×#16864012C214yesmaximal, complemented
11C2×#16863976C212yesmaximal, complemented
12C2×#16863950C212yesmaximal, complemented
13C2×#16863945C212yesmaximal, complemented
14C2×#16863943C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863876C212yesmaximal, complemented
17C2×C4×#11761629C211yesmaximal, characteristic, complemented
18C2×#556×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2211yescharacteristic
20C22×#11761629C2212yes—
21C22×#11761628C2212yes—
22C22×#11761627C2212yes—
23C22×Q8×D67C2212yes—
24#16864119C22116yescomplemented
25#16864109C22132yescomplemented
26#16864104C22132yescomplemented
27#16864097C22164yescomplemented
28#16864058C22132yescomplemented
29#16864054C22132yescomplemented
30#16864050C22116yescomplemented
31#16864049C22116yescomplemented
32#16864012C22164yescomplemented
33#16863976C22132yescomplemented
34#16863950C22132yescomplemented
35#16863945C22132yescomplemented
36#16863943C22116yescomplemented
37C2×#14524043C2211yescharacteristic
38C2×#14524042C2212yes—
39C2×#14524042C2212yes—
40C2×#14524042C2211yescharacteristic
41C2×#14524041C2212yes—
42C4⋊Q8×D67C22116yescomplemented
43C2×#14524039C2211yescharacteristic
44C2×#14524038C2214yes—
45C2×#14524033C2214yes—
46C2×#14524031C2214yes—
47C2×#14524031C2212yes—
48C2×#14524029C2212yes—
49C2×#14524029C2214yes—
50C2×#14524028C2214yes—
51C2×#14524027C2214yes—
52C2×#14524023C2214yes—
53C2×#14524023C2212yes—
54C2×#14524021C2214yes—
55C2×#14524020C2214yes—
56C2×#14524019C2212yes—
57C2×#14524019C2212yes—
58C2×#14524018C2212yes—
59C2×#14524018C2211yescharacteristic
60C2×#14524018C2214yes—
61C2×#14524017C2212yes—
62C2×#14524016C2214yes—
63C2×#14524016C2214yes—
64C2×#14524016C2212yes—
65C2×#14524016C2214yes—
66C2×#14524014C2211yescharacteristic
67#16863876C22132yescomplemented
68C4×#11761629C22116yescomplemented
69C2×Q8×Dic67C2211yescharacteristic
70C2×C4×Dic134C2214yes—
71C2×C4×Dic134C2212yes—
72C2×C4×D268C2211yescharacteristic
73C2×C4×D268C2212yes—
74C2×C4×D268C2214yes—
75C2×C4×D268C2211yescharacteristic
76C2×#14524005C2212yes—
77C2×#14524005C2211yescharacteristic
78C2×C4×C22⋊D67C2212yes—
79C2×(C22⋊D67)⋊C4C2214yes—
80C2×(C22⋊D67)⋊C4C2214yes—
81C2×(C22⋊D67)⋊C4C2214yes—
82C2×#14524001C2212yes—
83C2×#14524001C2211yescharacteristic
84C2×#14524001C2212yes—
85C2×#14524000C2214yes—
86C22×C4⋊Dic67C2212yes—
87C2×C4⋊C4×D67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C42×D67C2211yescharacteristic
91C2×C42×D67C2212yes—
92#556×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×#126×C67C2214yes—
95C2×#124×C67C2212yes—
96C2×C22⋊Q8×C67C2212yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×Q8×C67C2212yes—
99C2×C4×D4×C67C2211yescharacteristic
100C2×#117×C67C2212yes—
101C2×#11761629—28no—
102C2×#11761629—48no—
103C2×#11761629C2318yes—
104C2×#11761629C23116yes—
105C2×#11761628—216no—
106C2×#11761628C23116yes—
107C2×#11761627—48no—
108C2×#11761627C23116yes—
109C22×Dic134C2312yes—
110C22×Dic134C2312yes—
111C22×Dic134C2314yes—
112C2×Q8×D67—48no—
113C2×Q8×D67C23116yes—
114C22×D268C2312yes—
115C22×D268C2311yescharacteristic
116C22×D268C2312yes—
117C22×D268C2311yescharacteristic
118C22×D268C2314yes—
119C22×C22⋊D67C2312yes—
120C22×C22⋊D67C2312yes—
121C22×C22⋊D67C2312yes—
122C22×C22⋊D67C2314yes—
123C23×Dic67C2314yes—
124C22×C4×D67C2311yescharacteristic
125C22×C4×D67C2312yes—
126C22×C4×D67C2312yes—
127C22×C4×D67C2311yescharacteristic
128C22×C4×D67C2312yes—
129C22×C4×D67C2312yes—
130C22×C4×D67C2314yes—
131C22×C4×D67C2314yes—
132C22×C4×D67C2311yescharacteristic
133#14524043C2318yes—
134#14524042C23116yes—
135#14524042C23116yes—
136#14524042C2318yes—
137#14524041C23116yes—
138#14524039C2318yes—
139#14524038C23132yes—
140#14524033C23132yes—
141#14524031C23132yes—
142#14524031C23116yes—
143#14524029C23116yes—
144#14524029C23132yes—
145#14524028C23132yes—
146#14524027C23132yes—
147#14524023C23132yes—
148#14524023C23116yes—
149#14524021C23132yes—
150#14524020C23132yes—
151#14524019C23116yes—
152#14524019C23116yes—
153#14524018C23116yes—
154#14524018C2318yes—
155#14524018C23132yes—
156#14524017C23116yes—
157#14524016C23132yes—
158#14524016C23132yes—
159#14524016C23116yes—
160#14524016C23132yes—
161#14524014C2318yes—
162Q8×Dic67C2318yes—
163C4×Dic134C23132yes—
164C4×Dic134C23116yes—
165C4×D268C2318yes—
166C4×D268C2318yes—
167C4×D268C23116yes—
168C4×D268C23132yes—
169#14524005C23116yes—
170#14524005C2318yes—
171C4×C22⋊D67C23116yes—
172(C22⋊D67)⋊C4C23132yes—
173(C22⋊D67)⋊C4C23132yes—
174(C22⋊D67)⋊C4C23132yes—
175#14524001C23116yes—
176#14524001C23116yes—
177#14524001C2318yes—
178#14524000C23132yes—
179C2×C4⋊Dic67C23116yes—
180C2×C4⋊Dic67C2311yescharacteristic
181C2×C4⋊Dic67C2312yes—
182C2×C4⋊Dic67C2312yes—
183C2×C4⋊Dic67C2314yes—
184C2×C4⋊Dic67C2312yes—
185C2×C4⋊Dic67C2311yescharacteristic
186C2×Dic67⋊C4C2314yes—
187C2×Dic67⋊C4C2314yes—
188C2×Dic67⋊C4C2314yes—
189C2×Dic67⋊C4C2312yes—
190C2×Dic67⋊C4C2314yes—
191C4⋊C4×D67C23116yes—
192C4⋊C4×D67C23116yes—
193C4⋊C4×D67C23116yes—
194C2×C22⋊Dic67C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2312yes—
200C2×(C2×D67)⋊C4C2312yes—
201C2×(C2×D67)⋊C4C2314yes—
202C2×(C2×D67)⋊C4C2312yes—
203C2×(C2×D67)⋊C4C2312yes—
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2312yes—
206C2×C4×Dic67C2311yescharacteristic
207C2×C4×Dic67C2312yes—
208C2×C4×Dic67C2311yescharacteristic
209C2×C4×Dic67C2314yes—
210C42×D67C2318yes—
211C42×D67C23116yes—
212C22×Q8×C67C2311yescharacteristic
213C22×Q8×C67C2312yes—
214C22×D4×C67C2311yescharacteristic
215C23×C4×C67C2312yes—
216C4⋊Q8×C67C2318yes—
217#126×C67C23132yes—
218#124×C67C23116yes—
219C22⋊Q8×C67C23116yes—
220C4×Q8×C67C23116yes—
221C4×Q8×C67C2318yes—
222C4×D4×C67C2318yes—
223#117×C67C23116yes—
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2314yes—
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2312yes—
230C2×C22⋊C4×C67C2314yes—
231C2×C22⋊C4×C67C2312yes—
232C2×C22⋊C4×C67C2314yes—
233C2×C42×C67C2314yes—
234C2×C42×C67C2311yescharacteristic
235C2×C42×C67C2312yes—
236C23×D67C2412yes—
237C23×D67C2412yes—
238C23×D67C2411yescharacteristic
239#11761629—232no—
240#11761629—432no—
241#11761628—264no—
242#11761627—432no—
243C2×Dic134—28no—
244C2×Dic134—28no—
245C2×Dic134—48no—
246C2×Dic134C2418yes—
247C2×Dic134C2418yes—
248C2×Dic134C24116yes—
249Q8×D67—432no—
250C2×D268—28no—
251C2×D268—28no—
252C2×D268—24no—
253C2×D268—24no—
254C2×D268—48no—
255C2×D268C2418yes—
256C2×D268C2414yes—
257C2×D268C2418yes—
258C2×D268C2414yes—
259C2×D268C24116yes—
260C2×C22⋊D67—28no—
261C2×C22⋊D67—28no—
262C2×C22⋊D67—28no—
263C2×C22⋊D67—48no—
264C2×C22⋊D67C2418yes—
265C2×C22⋊D67C2418yes—
266C2×C22⋊D67C2418yes—
267C2×C22⋊D67C24116yes—
268C22×Dic67—48no—
269C22×Dic67C2411yescharacteristic
270C22×Dic67C2412yes—
271C22×Dic67C2412yes—
272C22×Dic67C2414yes—
273C22×Dic67C24116yes—
274C22×Dic67C2411yescharacteristic
275C22×Dic67C2411yescharacteristic
276C2×C4×D67—28no—
277C2×C4×D67—24no—
278C2×C4×D67—28no—
279C2×C4×D67—28no—
280C2×C4×D67—24no—
281C2×C4×D67—28no—
282C2×C4×D67—48no—
283C2×C4×D67—48no—
284C2×C4×D67#4118yescomplemented
285C2×C4×D67C2414yes—
286C2×C4×D67C2418yes—
287C2×C4×D67C2418yes—
288C2×C4×D67C2414yes—
289C2×C4×D67C2418yes—
290C2×C4×D67C2418yes—
291C2×C4×D67C24116yes—
292C2×C4×D67C24116yes—
293C2×C4×D67C2414yes—
294C4⋊Dic67C2414yes—
295C4⋊Dic67C2418yes—
296C4⋊Dic67C2418yes—
297C4⋊Dic67C24116yes—
298C4⋊Dic67C2418yes—
299C4⋊Dic67C2414yes—
300Dic67⋊C4C24116yes—
301Dic67⋊C4C24116yes—
302Dic67⋊C4C24116yes—
303Dic67⋊C4C2418yes—
304Dic67⋊C4C24116yes—
305C22⋊Dic67C2418yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C24116yes—
308(C2×D67)⋊C4C2418yes—
309(C2×D67)⋊C4C24116yes—
310(C2×D67)⋊C4C2418yes—
311(C2×D67)⋊C4C2418yes—
312(C2×D67)⋊C4C24116yes—
313(C2×D67)⋊C4C2418yes—
314(C2×D67)⋊C4C2418yes—
315C4×Dic67C2414yes—
316C4×Dic67C2418yes—
317C4×Dic67C2414yes—
318C4×Dic67C2418yes—
319C4×Dic67C2414yes—
320C4×Dic67C24116yes—
321C24×C67C2412yes—
322C2×Q8×C67—24no—
323C2×Q8×C67—28no—
324C2×Q8×C67C2414yes—
325C2×Q8×C67C2418yes—
326C2×D4×C67—24no—
327C2×D4×C67C2414yes—
328C22×C4×C67—28no—
329C22×C4×C67C2412yes—
330C22×C4×C67C2412yes—
331C22×C4×C67C2411yescharacteristic
332C22×C4×C67C2412yes—
333C22×C4×C67C2414yes—
334C22×C4×C67C2418yes—
335C22×C4×C67C2411yescharacteristic
336C22×C4×C67C2411yescharacteristic
337C4⋊C4×C67C2414yes—
338C4⋊C4×C67C2418yes—
339C4⋊C4×C67C2414yes—
340C4⋊C4×C67C24116yes—
341C4⋊C4×C67C2418yes—
342C4⋊C4×C67C2418yes—
343C22⋊C4×C67C24116yes—
344C22⋊C4×C67C2418yes—
345C22⋊C4×C67C24116yes—
346C42×C67C24116yes—
347C42×C67C2414yes—
348C42×C67C2418yes—
349C23×C67—24no—
350C23×C67—24no—
351C23×C67—24no—
352C23×C67C2514yes—
353C23×C67C2511yescharacteristic
354C22×D67—22no—
355C22×D67—22no—
356C22×D67—24no—
357C22×D67—24no—
358C22×D67—24no—
359C22×D67—24no—
360C22×D67—24no—
361C22×D67—24no—
362C22×D67C2×#4114yes—
363C22×D67C2514yes—
364C22×D67C2514yes—
365C22×D67C2512yes—
366Q8×C67—28no—
367Q8×C67—216no—
368D4×C67—28no—
369C2×C4×C67—24no—
370C2×C4×C67—24no—
371C2×C4×C67—28no—
372C2×C4×C67—24no—
373C2×C4×C67—22no—
374C2×C4×C67—216no—
375C2×C4×C67C2×#4114yes—
376C2×C4×C67H(5,𝔽2)14yes—
377C2×C4×C67C2514yes—
378C2×C4×C67C2514yes—
379C2×C4×C67C2512yes—
380C2×C4×C67C2514yes—
381C2×C4×C67C2518yes—
382C2×C4×C67C2512yes—
383C2×C4×C67C2512yes—
384C22⋊D67—216no—
385C22⋊D67—216no—
386C22⋊D67—216no—
387C22⋊D67—416no—
388C2×Dic67—24no—
389C2×Dic67—24no—
390C2×Dic67—22no—
391C2×Dic67—28no—
392C2×Dic67—416no—
393C2×Dic67C2×#4114yes—
394C2×Dic672−1+414yes—
395C2×Dic67C2512yes—
396C2×Dic67C2514yes—
397C2×Dic67C2514yes—
398C2×Dic67C2518yes—
399C2×Dic67C2512yes—
400C2×Dic67C2512yes—
401D268—216no—
402D268—216no—
403D268—28no—
404D268—28no—
405D268—416no—
406C4×D67—216no—
407C4×D67—28no—
408C4×D67—216no—
409C4×D67—216no—
410C4×D67—28no—
411C4×D67—216no—
412C4×D67—416no—
413C4×D67—416no—
414C4×D67C2×#41116yescomplemented
415Dic134—216no—
416Dic134—216no—
417Dic134—416no—
418C22×C67—24no—
419C22×C67—24no—
420C22×C67—24no—
421C22×C67—48no—
422C22×C67C22×#4112yes—
423C22×C67C2×H(5,𝔽2)12yes—
424C22×C67C2×2−1+412yes—
425C22×C67C2611yescharacteristic
426C2×D67—22no—
427C2×D67—22no—
428C2×D67—28no—
429C2×D67—24no—
430C2×D67—24no—
431C2×D67—24no—
432C2×D67—24no—
433C2×D67—24no—
434C2×D67—24no—
435C2×D67—48no—
436C2×D67—48no—
437C2×D67C22×#4114yes—
438C4×C67—24no—
439C4×C67—24no—
440C4×C67—28no—
441C4×C67—24no—
442C4×C67—22no—
443C4×C67C22×#4114yes—
444C4×C67C2×H(5,𝔽2)14yes—
445Dic67—24no—
446Dic67—28no—
447Dic67—22no—
448Dic67—24no—
449Dic67C22×#4114yes—
450Dic67C2×2−1+414yes—
451C2×#3511—671nomaximal, Sylow
452C2×C67—44no—
453C2×C67#351114yescomplemented
454C2×C67C23×#4111yescharacteristic
455C2×C67C22×H(5,𝔽2)11yescharacteristic
456C2×C67C22×2−1+411yescharacteristic
457D67—24no—
458D67—44no—
459D67—44no—
460#3511—6732no—
461C2×#556—671no—
462C2×#556D6711yescharacteristic, complemented
463C2×#555—672no—
464C2×#554—672no—
465C2×#553—674no—
466C2×#548—672no—
467C2×#548—672no—
468C2×#547—671no—
469C2×#547—671no—
470C2×#542—674no—
471C2×#537—672no—
472C2×#533—672no—
473C2×#532—672no—
474C2×#532—671no—
475C22×C4⋊Q8—671no—
476C2×#520—672no—
477C2×C4×#41—671no—
478C67C2×#351111yescharacteristic, complemented, Sylow
479C22×#41—672no—
480C22×#41—671no—
481C22×#41—672no—
482C22×#41—672no—
483C23×Q8—672no—
484#556—6716no—
485#556C2×D67116yescomplemented
486#555—6732no—
487#554—6732no—
488#553—6764no—
489#548—6732no—
490#548—6732no—
491#547—6716no—
492#547—6716no—
493#542—6764no—
494#537—6732no—
495#533—6732no—
496#532—6732no—
497#532—6716no—
498C2×C4⋊Q8—672no—
499C2×C4⋊Q8—6716no—
500C2×C4⋊Q8—672no—
501C2×C4⋊Q8—672no—
502C2×C4⋊Q8—671no—
503C2×C4⋊Q8—671no—
504C2×C4⋊Q8C2×D6711yescharacteristic
505C2×#127—671no—
506C2×#126—674no—
507C2×#126C2×D6714yes—
508C2×#125—674no—
509C2×#124—672no—
510C2×#124—674no—
511C2×#124—672no—
512C2×#124—674no—
513C2×#124C2×D6712yes—
514C2×#123—674no—
515C2×#123—674no—
516C2×C22⋊Q8—672no—
517C2×C22⋊Q8—672no—
518C2×C22⋊Q8—674no—
519C2×C22⋊Q8—672no—
520C2×C22⋊Q8—674no—
521C2×C22⋊Q8—674no—
522C2×C22⋊Q8C2×D6712yes—
523C2×#121—671no—
524C2×#121—672no—
525C2×#121—671no—
526C2×#121—672no—
527C2×#121—674no—
528C2×#121—674no—
529C2×#121—672no—
530C2×#121—674no—
531C2×#121—674no—
532#520—6732no—
533C4×#41—6716no—
534C2×C4×Q8—671no—
535C2×C4×Q8—674no—
536C2×C4×Q8—672no—
537C2×C4×Q8C2×D6711yescharacteristic
538C2×C4×Q8C2×D6712yes—
539C2×C4×D4—672no—
540C2×C4×D4—672no—
541C2×C4×D4—671no—
542C2×C4×D4—674no—
543C2×C4×D4—674no—
544C2×C4×D4—674no—
545C2×C4×D4—671no—
546C2×C4×D4—672no—
547C2×C4×D4—674no—
548C2×C4×D4—671no—
549C2×C4×D4C2×D6711yescharacteristic
550C2×#117—671no—
551C2×#117—672no—
552C2×#117—672no—
553C2×#117—674no—
554C2×#117C2×D6712yes—
555C22×C4⋊C4—672no—
556C22×C4⋊C4—672no—
557C22×C4⋊C4—672no—
558C22×C4⋊C4—672no—
559C22×C42—671no—
560C22×C42—672no—
561C2×#41—2688no—
562C2×#41—2688no—
563C2×#41—6716no—
564C2×#41—678no—
565C2×#41—6716no—
566C2×#41—6716no—
567C2×#41—13416no—
568C2×#41—1348no—
569C22×Q8—2688no—
570C22×Q8—6716no—
571C22×Q8—674no—
572C22×Q8—672no—
573C22×Q8—672no—
574C22×Q8C22×D6711yescharacteristic
575C22×Q8C22×D6712yes—
576C22×D4—674no—
577C22×D4—672no—
578C22×D4—672no—
579C22×D4—672no—
580C22×D4—674no—
581C22×D4—672no—
582C22×D4—672no—
583C22×D4—671no—
584C22×D4—671no—
585C22×D4C22×D6711yescharacteristic
586C23×C4—674no—
587C23×C4—674no—
588C23×C4—674no—
589C23×C4—671no—
590C23×C4—671no—
591C23×C4—672no—
592C23×C4—672no—
593C23×C4—672no—
594C23×C4—671no—
595C23×C4—672no—
596C23×C4C22×D6712yes—
597C4⋊Q8—6716no—
598C4⋊Q8—6716no—
599C4⋊Q8—6716no—
600C4⋊Q8—678no—
601C4⋊Q8—678no—
602C4⋊Q8C22×D6718yes—
603#127—678no—
604#126—6732no—
605#126C22×D67132yes—
606#125—6732no—
607#124—6716no—
608#124—6732no—
609#124—6716no—
610#124—6732no—
611#124C22×D67116yes—
612#123—6732no—
613#123—6732no—
614C22⋊Q8—6716no—
615C22⋊Q8—6716no—
616C22⋊Q8—6732no—
617C22⋊Q8—6716no—
618C22⋊Q8—6732no—
619C22⋊Q8—6732no—
620C22⋊Q8C22×D67116yes—
621#121—678no—
622#121—6716no—
623#121—678no—
624#121—6716no—
625#121—6732no—
626#121—6732no—
627#121—6716no—
628#121—6732no—
629#121—6732no—
630C4×Q8—678no—
631C4×Q8—6732no—
632C4×Q8—6716no—
633C4×Q8C22×D6718yes—
634C4×Q8C22×D67116yes—
635C4×D4—6716no—
636C4×D4—6716no—
637C4×D4—678no—
638C4×D4—6732no—
639C4×D4—6732no—
640C4×D4—6732no—
641C4×D4—678no—
642C4×D4—6716no—
643C4×D4—6732no—
644C4×D4—678no—
645C4×D4C22×D6718yes—
646#117—678no—
647#117—6716no—
648#117—6716no—
649#117—6732no—
650#117C22×D67116yes—
651C2×C4⋊C4—671no—
652C2×C4⋊C4—672no—
653C2×C4⋊C4—674no—
654C2×C4⋊C4—674no—
655C2×C4⋊C4—674no—
656C2×C4⋊C4—674no—
657C2×C4⋊C4—6716no—
658C2×C4⋊C4—672no—
659C2×C4⋊C4—672no—
660C2×C4⋊C4—672no—
661C2×C4⋊C4—671no—
662C2×C4⋊C4—674no—
663C2×C4⋊C4—6716no—
664C2×C4⋊C4—6716no—
665C2×C4⋊C4—6716no—
666C2×C4⋊C4C22×D6712yes—
667C2×C4⋊C4C22×D6712yes—
668C2×C4⋊C4C22×D6711yescharacteristic
669C2×C4⋊C4C22×D6712yes—
670C2×C4⋊C4C22×D6711yescharacteristic
671C2×C4⋊C4C22×D6714yes—
672C2×C22⋊C4—672no—
673C2×C22⋊C4—672no—
674C2×C22⋊C4—674no—
675C2×C22⋊C4—672no—
676C2×C22⋊C4—672no—
677C2×C22⋊C4—674no—
678C2×C22⋊C4—674no—
679C2×C22⋊C4—674no—
680C2×C22⋊C4—672no—
681C2×C22⋊C4—672no—
682C2×C22⋊C4C22×D6714yes—
683C2×C22⋊C4C22×D6714yes—
684C2×C22⋊C4C22×D6712yes—
685C2×C42—672no—
686C2×C42—674no—
687C2×C42—671no—
688C2×C42—672no—
689C2×C42—671no—
690C2×C42—671no—
691C2×C42—678no—
692C2×C42—6716no—
693C2×C42C22×D6714yes—
694C2×C42C22×D6711yescharacteristic
695C2×C42C22×D6712yes—
696C24—671no—
697C24—672no—
698C24—672no—
699C24C23×D6712yes—
700#41—26832no—
701#41—26832no—
702#41—13464no—
703#41—13432no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—2688no—
707C2×Q8—26832no—
708C2×Q8—6716no—
709C2×Q8—678no—
710C2×Q8—678no—
711C2×Q8—1348no—
712C2×Q8—1348no—
713C2×Q8C23×D6714yes—
714C2×Q8C23×D6718yes—
715C2×D4—24no—
716C2×D4—2688no—
717C2×D4—2688no—
718C2×D4—6716no—
719C2×D4—678no—
720C2×D4—678no—
721C2×D4—678no—
722C2×D4—6716no—
723C2×D4—678no—
724C2×D4—678no—
725C2×D4—674no—
726C2×D4—674no—
727C2×D4—1348no—
728C2×D4—1348no—
729C2×D4—1348no—
730C2×D4—1348no—
731C2×D4—1348no—
732C2×D4—1344no—
733C2×D4—1344no—
734C2×D4C23×D6714yes—
735C22×C4—28no—
736C22×C4—2688no—
737C22×C4—2688no—
738C22×C4—2688no—
739C22×C4—6716no—
740C22×C4—6716no—
741C22×C4—6716no—
742C22×C4—671no—
743C22×C4—671no—
744C22×C4—678no—
745C22×C4—674no—
746C22×C4—671no—
747C22×C4—672no—
748C22×C4—672no—
749C22×C4—674no—
750C22×C4—674no—
751C22×C4—678no—
752C22×C4—678no—
753C22×C4—674no—
754C22×C4—678no—
755C22×C4—678no—
756C22×C4—1348no—
757C22×C4—1348no—
758C22×C4—1344no—
759C22×C4—1348no—
760C22×C4—1344no—
761C22×C4—1348no—
762C22×C4C23×D6718yes—
763C22×C4C23×D6712yes—
764C22×C4C23×D6711yescharacteristic
765C22×C4C23×D6712yes—
766C22×C4C23×D6712yes—
767C22×C4C23×D6714yes—
768C22×C4C23×D6711yescharacteristic
769C22×C4C23×D6711yescharacteristic
770C4⋊C4—674no—
771C4⋊C4—678no—
772C4⋊C4—6716no—
773C4⋊C4—6716no—
774C4⋊C4—6716no—
775C4⋊C4—6716no—
776C4⋊C4—678no—
777C4⋊C4—678no—
778C4⋊C4—678no—
779C4⋊C4—674no—
780C4⋊C4—6716no—
781C4⋊C4C23×D6718yes—
782C4⋊C4C23×D6718yes—
783C4⋊C4C23×D6714yes—
784C4⋊C4C23×D6718yes—
785C4⋊C4C23×D6714yes—
786C4⋊C4C23×D67116yes—
787C22⋊C4—678no—
788C22⋊C4—678no—
789C22⋊C4—6716no—
790C22⋊C4—678no—
791C22⋊C4—678no—
792C22⋊C4—6716no—
793C22⋊C4—6716no—
794C22⋊C4—6716no—
795C22⋊C4—678no—
796C22⋊C4—678no—
797C22⋊C4C23×D67116yes—
798C22⋊C4C23×D67116yes—
799C22⋊C4C23×D6718yes—
800C42—674no—
801C42—678no—
802C42—674no—
803C42—678no—
804C42—674no—
805C42—6716no—
806C42C23×D6714yes—
807C42C23×D6718yes—
808C42C23×D67116yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—674no—
813C23—672no—
814C23—674no—
815C23—674no—
816C23—1344no—
817C23—1344no—
818C23—1344no—
819C23—1344no—
820C23—1344no—
821C23—1344no—
822C23—1342no—
823C23—1342no—
824C23C24×D6714yes—
825C23C24×D6711yescharacteristic
826Q8—28no—
827Q8—216no—
828Q8—26816no—
829Q8—13416no—
830Q8—13416no—
831D4—28no—
832D4—26816no—
833D4—26816no—
834D4—13416no—
835D4—13416no—
836D4—13416no—
837D4—13416no—
838D4—13416no—
839D4—1348no—
840D4—1348no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—216no—
847C2×C4—26816no—
848C2×C4—26816no—
849C2×C4—26816no—
850C2×C4—674no—
851C2×C4—674no—
852C2×C4—672no—
853C2×C4—672no—
854C2×C4—6716no—
855C2×C4—672no—
856C2×C4—674no—
857C2×C4—674no—
858C2×C4—678no—
859C2×C4—13416no—
860C2×C4—13416no—
861C2×C4—1348no—
862C2×C4—1344no—
863C2×C4—1344no—
864C2×C4—1348no—
865C2×C4—1342no—
866C2×C4—13416no—
867C2×C4—1348no—
868C2×C4—13416no—
869C2×C4#41×D6714yes—
870C2×C4#1452408914yes—
871C2×C4C24×D6714yes—
872C2×C4C24×D6712yes—
873C2×C4C24×D6714yes—
874C2×C4C24×D6714yes—
875C2×C4C24×D6718yes—
876C2×C4C24×D6712yes—
877C2×C4C24×D6712yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—48no—
882C22—2688no—
883C22—2688no—
884C22—674no—
885C22—1344no—
886C22—1344no—
887C22—1344no—
888C22—1344no—
889C22—1344no—
890C22—1344no—
891C22—1348no—
892C22—1342no—
893C22—1342no—
894C22C2×#41×D6712yes—
895C22C2×#1452408912yes—
896C222−1+4×D6712yes—
897C22C25×D6711yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—24no—
902C4—22no—
903C4—674no—
904C4—674no—
905C4—1344no—
906C4—1344no—
907C4—1348no—
908C4—1342no—
909C4C2×#41×D6714yes—
910C4C2×#1452408914yes—
911C2—44no—
912C2—2684no—
913C2—2684no—
914C2—1344no—
915C2#2257411314yesdirect product factor
916C2C22×#41×D6711yescharacteristic
917C2C22×#1452408911yescharacteristic
918C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#556×C67C2
socleC23×C67C25
hypercenterC2×#556D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22574113C2direct (N × H)
2. C2×#16864119C2semidirect
3. C2×#16864109C2semidirect
4. C2×#16864104C2semidirect
5. C2×#16864097C2semidirect
6. C2×#16864058C2semidirect
7. C2×#16864054C2semidirect
8. C2×#16864050C2semidirect
9. C2×#16864049C2semidirect
10. C2×#16864012C2semidirect
11. C2×#16863976C2semidirect
12. C2×#16863950C2semidirect
13. C2×#16863945C2semidirect
14. C2×#16863943C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
16. C2×#16863876C2semidirect
17. C2×C4×#11761629C2semidirect
18. C2×#556×C67C2semidirect
24. #16864119C22semidirect
25. #16864109C22semidirect
26. #16864104C22semidirect
27. #16864097C22semidirect
28. #16864058C22semidirect
29. #16864054C22semidirect
30. #16864050C22semidirect
31. #16864049C22semidirect
32. #16864012C22semidirect
33. #16863976C22semidirect
34. #16863950C22semidirect
35. #16863945C22semidirect
36. #16863943C22semidirect
42. C4⋊Q8×D67C22semidirect
67. #16863876C22semidirect
68. C4×#11761629C22semidirect
92. #556×C67C22semidirect
284. C2×C4×D67#41semidirect
414. C4×D67C2×#41semidirect
453. C2×C67#3511semidirect
462. C2×#556D67semidirect
478. C67C2×#3511semidirect
485. #556C2×D67semidirect
915. C2#22574113direct (N × H)

Maximal subgroups

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

subgroupindex
#225741132
C2×#168641192
C2×#168641092
C2×#168641042
C2×#168640972
C2×#168640582
C2×#168640542
C2×#168640502
C2×#168640492
C2×#168640122
C2×#168639762
C2×#168639502
C2×#168639452
C2×#168639432
C2×C4⋊Q8×D672
C2×#168638762
C2×C4×#117616292
C2×#556×C672
C2×#351167