Finite Group Databasebeta

← C2×#22574121 #31764195

Subgroups — C2×#22574121 #31764195

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574121C2132yesmaximal, direct product factor
2C2×#16864118C212yesmaximal, complemented
3C2×#16864109C212yesmaximal, complemented
4C2×#16864102C212yesmaximal, complemented
5C2×#16864099C212yesmaximal, complemented
6C2×#16864090C212yesmaximal, complemented
7C2×#16864058C212yesmaximal, complemented
8C2×#16864056C212yesmaximal, complemented
9C2×#16864048C212yesmaximal, complemented
10C2×#16864019C212yesmaximal, complemented
11C2×#16864018C212yesmaximal, complemented
12C2×#16863976C212yesmaximal, complemented
13C2×#16863951C211yesmaximal, characteristic, complemented
14C2×#16863947C211yesmaximal, characteristic, complemented
15C2×#16863947C211yesmaximal, characteristic, complemented
16C2×#16863946C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
18C2×#16863878C212yesmaximal, complemented
19C2×C4×#11761628C211yesmaximal, characteristic, complemented
20C2×#533×C67C211yesmaximal, characteristic, complemented
21C22×#11761629C2212yes—
22C22×#11761629C2212yes—
23C22×#11761628C2211yescharacteristic
24C22×#11761628C2212yes—
25C22×Q8×D67C2212yes—
26#16864118C22132yescomplemented
27#16864109C22132yescomplemented
28#16864102C22132yescomplemented
29#16864099C22132yescomplemented
30#16864090C22132yescomplemented
31#16864058C22132yescomplemented
32#16864056C22132yescomplemented
33#16864048C22132yescomplemented
34#16864019C22132yescomplemented
35#16864018C22132yescomplemented
36#16863976C22132yescomplemented
37#16863951C22116yescomplemented
38#16863947C22116yescomplemented
39#16863947C22116yescomplemented
40#16863946C22116yescomplemented
41C2×#14524043C2211yescharacteristic
42C2×#14524042C2212yes—
43C2×#14524042C2212yes—
44C2×#14524041C2212yes—
45C4⋊Q8×D67C22116yescomplemented
46C2×#14524040C2211yescharacteristic
47C2×#14524038C2214yes—
48C2×#14524037C2214yes—
49C2×#14524034C2212yes—
50C2×#14524032C2212yes—
51C2×#14524032C2212yes—
52C2×#14524031C2214yes—
53C2×#14524031C2212yes—
54C2×#14524029C2214yes—
55C2×#14524028C2214yes—
56C2×#14524025C2214yes—
57C2×#14524023C2214yes—
58C2×#14524023C2212yes—
59C2×#14524021C2214yes—
60C2×#14524021C2214yes—
61C2×#14524019C2212yes—
62C2×#14524018C2212yes—
63C2×#14524018C2212yes—
64C2×#14524018C2214yes—
65C2×#14524018C2212yes—
66C2×#14524018C2212yes—
67C2×#14524017C2212yes—
68C2×#14524017C2212yes—
69C2×#14524016C2214yes—
70C2×#14524016C2214yes—
71#16863878C22132yescomplemented
72C4×#11761628C22116yescomplemented
73C2×Q8×Dic67C2212yes—
74C2×C4×Dic134C2211yescharacteristic
75C2×C4×Dic134C2211yescharacteristic
76C2×#14524008C2212yes—
77C2×C4×D268C2212yes—
78C2×C4×D268C2211yescharacteristic
79C2×C4×D268C2211yescharacteristic
80C2×C4×D268C2214yes—
81C2×C4×D268C2212yes—
82C2×#14524005C2212yes—
83C2×#14524005C2214yes—
84C2×#14524005C2212yes—
85C2×#14524005C2212yes—
86C2×#14524005C2212yes—
87C2×C4×C22⋊D67C2211yescharacteristic
88C2×C4×C22⋊D67C2211yescharacteristic
89C2×C4×C22⋊D67C2211yescharacteristic
90C2×C4×C22⋊D67C2211yescharacteristic
91C2×#14524002C2211yescharacteristic
92C2×#14524001C2212yes—
93C2×#14524000C2211yescharacteristic
94C2×#14524000C2211yescharacteristic
95C2×#14524000C2214yes—
96C2×C4⋊C4×D67C2214yes—
97C2×C4⋊C4×D67C2212yes—
98C2×C4⋊C4×D67C2212yes—
99C2×C42×D67C2211yescharacteristic
100C2×C42×D67C2211yescharacteristic
101#533×C67C22116yescomplemented
102C2×C4⋊Q8×C67C2211yescharacteristic
103C2×C4⋊Q8×C67C2211yescharacteristic
104C2×#125×C67C2212yes—
105C2×C22⋊Q8×C67C2212yes—
106C2×C22⋊Q8×C67C2212yes—
107C2×C4×Q8×C67C2212yes—
108C2×C4×Q8×C67C2212yes—
109C2×#117×C67C2212yes—
110C22×C42×C67C2211yescharacteristic
111C2×#11761629—216no—
112C2×#11761629—48no—
113C2×#11761629C23116yes—
114C2×#11761629C23116yes—
115C2×#11761628—28no—
116C2×#11761628—48no—
117C2×#11761628C2318yes—
118C2×#11761628C23116yes—
119C22×Dic134C2312yes—
120C22×Dic134C2311yescharacteristic
121C22×Dic134C2314yes—
122C2×Q8×D67—48no—
123C2×Q8×D67C23116yes—
124C22×D268C2312yes—
125C22×D268C2314yes—
126C22×D268C2312yes—
127C22×D268C2312yes—
128C22×D268C2311yescharacteristic
129C22×D268C2314yes—
130C22×C22⋊D67C2311yescharacteristic
131C22×C22⋊D67C2311yescharacteristic
132C22×C22⋊D67C2314yes—
133C22×C4×D67C2311yescharacteristic
134C22×C4×D67C2311yescharacteristic
135C22×C4×D67C2311yescharacteristic
136C22×C4×D67C2311yescharacteristic
137C22×C4×D67C2311yescharacteristic
138C22×C4×D67C2314yes—
139C22×C4×D67C2314yes—
140C22×C4×D67C2314yes—
141C22×C4×D67C2314yes—
142C22×C4×D67C2311yescharacteristic
143#14524043C2318yes—
144#14524042C23116yes—
145#14524042C23116yes—
146#14524041C23116yes—
147#14524040C2318yes—
148#14524038C23132yes—
149#14524037C23132yes—
150#14524034C23116yes—
151#14524032C23116yes—
152#14524032C23116yes—
153#14524031C23132yes—
154#14524031C23116yes—
155#14524029C23132yes—
156#14524028C23132yes—
157#14524025C23132yes—
158#14524023C23132yes—
159#14524023C23116yes—
160#14524021C23132yes—
161#14524021C23132yes—
162#14524019C23116yes—
163#14524018C23116yes—
164#14524018C23116yes—
165#14524018C23132yes—
166#14524018C23116yes—
167#14524018C23116yes—
168#14524017C23116yes—
169#14524017C23116yes—
170#14524016C23132yes—
171#14524016C23132yes—
172Q8×Dic67C23116yes—
173C4×Dic134C2318yes—
174C4×Dic134C2318yes—
175#14524008C23116yes—
176C4×D268C23116yes—
177C4×D268C2318yes—
178C4×D268C23132yes—
179C4×D268C2318yes—
180C4×D268C23116yes—
181#14524005C23116yes—
182#14524005C23116yes—
183#14524005C23132yes—
184#14524005C23116yes—
185#14524005C23116yes—
186C4×C22⋊D67C2318yes—
187C4×C22⋊D67C2318yes—
188C4×C22⋊D67C2318yes—
189C4×C22⋊D67C2318yes—
190#14524002C2318yes—
191#14524001C23116yes—
192#14524000C2318yes—
193#14524000C23132yes—
194#14524000C2318yes—
195C2×C4⋊Dic67C2312yes—
196C2×C4⋊Dic67C2312yes—
197C2×C4⋊Dic67C2314yes—
198C2×C4⋊Dic67C2311yescharacteristic
199C2×C4⋊Dic67C2311yescharacteristic
200C2×Dic67⋊C4C2311yescharacteristic
201C2×Dic67⋊C4C2314yes—
202C2×Dic67⋊C4C2314yes—
203C2×Dic67⋊C4C2311yescharacteristic
204C2×Dic67⋊C4C2311yescharacteristic
205C2×Dic67⋊C4C2311yescharacteristic
206C2×Dic67⋊C4C2314yes—
207C4⋊C4×D67C23132yes—
208C4⋊C4×D67C23116yes—
209C4⋊C4×D67C23116yes—
210C2×C22⋊Dic67C2311yescharacteristic
211C2×C22⋊Dic67C2311yescharacteristic
212C2×(C2×D67)⋊C4C2311yescharacteristic
213C2×(C2×D67)⋊C4C2311yescharacteristic
214C2×(C2×D67)⋊C4C2311yescharacteristic
215C2×(C2×D67)⋊C4C2311yescharacteristic
216C2×(C2×D67)⋊C4C2314yes—
217C2×(C2×D67)⋊C4C2314yes—
218C2×(C2×D67)⋊C4C2314yes—
219C2×(C2×D67)⋊C4C2314yes—
220C2×(C2×D67)⋊C4C2314yes—
221C2×(C2×D67)⋊C4C2314yes—
222C2×(C2×D67)⋊C4C2314yes—
223C2×C4×Dic67C2311yescharacteristic
224C2×C4×Dic67C2311yescharacteristic
225C2×C4×Dic67C2311yescharacteristic
226C2×C4×Dic67C2311yescharacteristic
227C2×C4×Dic67C2311yescharacteristic
228C2×C4×Dic67C2311yescharacteristic
229C2×C4×Dic67C2314yes—
230C42×D67C2318yes—
231C42×D67C2318yes—
232C22×Q8×C67C2312yes—
233C22×Q8×C67C2312yes—
234C23×C4×C67C2311yescharacteristic
235C23×C4×C67C2311yescharacteristic
236C23×C4×C67C2311yescharacteristic
237C4⋊Q8×C67C2318yes—
238C4⋊Q8×C67C2318yes—
239#125×C67C23116yes—
240C22⋊Q8×C67C23116yes—
241C22⋊Q8×C67C23116yes—
242C4×Q8×C67C23116yes—
243C4×Q8×C67C23116yes—
244#117×C67C23116yes—
245C2×C4⋊C4×C67C2312yes—
246C2×C4⋊C4×C67C2312yes—
247C2×C4⋊C4×C67C2314yes—
248C2×C4⋊C4×C67C2314yes—
249C2×C4⋊C4×C67C2312yes—
250C2×C4⋊C4×C67C2312yes—
251C2×C22⋊C4×C67C2314yes—
252C2×C42×C67C2311yescharacteristic
253C2×C42×C67C2311yescharacteristic
254C2×C42×C67C2311yescharacteristic
255C2×C42×C67C2311yescharacteristic
256C2×C42×C67C2318yes—
257C2×C42×C67C2314yes—
258C23×D67C2411yescharacteristic
259C23×D67C2414yes—
260C23×D67C2411yescharacteristic
261#11761629—264no—
262#11761629—432no—
263#11761628—232no—
264#11761628—432no—
265C2×Dic134—28no—
266C2×Dic134—24no—
267C2×Dic134—48no—
268C2×Dic134C2418yes—
269C2×Dic134C2414yes—
270C2×Dic134C24116yes—
271Q8×D67—432no—
272C2×D268—24no—
273C2×D268—216no—
274C2×D268—28no—
275C2×D268—28no—
276C2×D268—28no—
277C2×D268—48no—
278C2×D268C2418yes—
279C2×D268C24116yes—
280C2×D268C2418yes—
281C2×D268C2418yes—
282C2×D268C2414yes—
283C2×D268C24116yes—
284C2×C22⋊D67—24no—
285C2×C22⋊D67—24no—
286C2×C22⋊D67—48no—
287C2×C22⋊D67C2414yes—
288C2×C22⋊D67C2414yes—
289C2×C22⋊D67C24116yes—
290C22×Dic67C2411yescharacteristic
291C22×Dic67C2411yescharacteristic
292C22×Dic67C2411yescharacteristic
293C22×Dic67C2411yescharacteristic
294C22×Dic67C2411yescharacteristic
295C22×Dic67C2414yes—
296C22×Dic67C2411yescharacteristic
297C2×C4×D67—24no—
298C2×C4×D67—24no—
299C2×C4×D67—24no—
300C2×C4×D67—24no—
301C2×C4×D67—24no—
302C2×C4×D67—216no—
303C2×C4×D67—48no—
304C2×C4×D67—48no—
305C2×C4×D67—48no—
306C2×C4×D67#4118yescomplemented
307C2×C4×D67C2414yes—
308C2×C4×D67C2414yes—
309C2×C4×D67C2414yes—
310C2×C4×D67C2414yes—
311C2×C4×D67C2414yes—
312C2×C4×D67C24116yes—
313C2×C4×D67C24116yes—
314C2×C4×D67C24116yes—
315C2×C4×D67C24116yes—
316C2×C4×D67C2414yes—
317C4⋊Dic67C2418yes—
318C4⋊Dic67C2418yes—
319C4⋊Dic67C24116yes—
320C4⋊Dic67C2414yes—
321C4⋊Dic67C2414yes—
322Dic67⋊C4C2414yes—
323Dic67⋊C4C24116yes—
324Dic67⋊C4C24116yes—
325Dic67⋊C4C2414yes—
326Dic67⋊C4C2414yes—
327Dic67⋊C4C2414yes—
328Dic67⋊C4C24116yes—
329C22⋊Dic67C2414yes—
330C22⋊Dic67C2414yes—
331(C2×D67)⋊C4C2414yes—
332(C2×D67)⋊C4C2414yes—
333(C2×D67)⋊C4C2414yes—
334(C2×D67)⋊C4C2414yes—
335(C2×D67)⋊C4C24116yes—
336(C2×D67)⋊C4C24116yes—
337(C2×D67)⋊C4C24116yes—
338(C2×D67)⋊C4C24116yes—
339(C2×D67)⋊C4C24116yes—
340(C2×D67)⋊C4C24116yes—
341(C2×D67)⋊C4C24116yes—
342C4×Dic67C2414yes—
343C4×Dic67C2414yes—
344C4×Dic67C2414yes—
345C4×Dic67C2414yes—
346C4×Dic67C2414yes—
347C4×Dic67C2414yes—
348C4×Dic67C24116yes—
349C24×C67C2411yescharacteristic
350C2×Q8×C67—28no—
351C2×Q8×C67—28no—
352C2×Q8×C67C2418yes—
353C2×Q8×C67C2418yes—
354C22×C4×C67—24no—
355C22×C4×C67—24no—
356C22×C4×C67—24no—
357C22×C4×C67C2411yescharacteristic
358C22×C4×C67C2411yescharacteristic
359C22×C4×C67C2411yescharacteristic
360C22×C4×C67C2414yes—
361C22×C4×C67C2414yes—
362C22×C4×C67C2414yes—
363C22×C4×C67C2414yes—
364C22×C4×C67C2414yes—
365C22×C4×C67C2411yescharacteristic
366C22×C4×C67C2411yescharacteristic
367C22×C4×C67C2411yescharacteristic
368C4⋊C4×C67C2418yes—
369C4⋊C4×C67C2418yes—
370C4⋊C4×C67C24116yes—
371C4⋊C4×C67C24116yes—
372C4⋊C4×C67C2418yes—
373C4⋊C4×C67C2418yes—
374C22⋊C4×C67C24116yes—
375C42×C67C2414yes—
376C42×C67C2414yes—
377C42×C67C2414yes—
378C42×C67C2414yes—
379C42×C67C24116yes—
380C23×C67—22no—
381C23×C67—22no—
382C23×C67—22no—
383C23×C67C2512yes—
384C23×C67C2511yescharacteristic
385C22×D67—22no—
386C22×D67—22no—
387C22×D67—22no—
388C22×D67—28no—
389C22×D67—22no—
390C22×D67—28no—
391C22×D67—22no—
392C22×D67—28no—
393C22×D67C2×#4114yes—
394C22×D67C2518yes—
395C22×D67C2512yes—
396C22×D67C2512yes—
397Q8×C67—216no—
398Q8×C67—216no—
399C2×C4×C67—22no—
400C2×C4×C67—28no—
401C2×C4×C67—22no—
402C2×C4×C67—28no—
403C2×C4×C67—22no—
404C2×C4×C67—28no—
405C2×C4×C67—28no—
406C2×C4×C67—28no—
407C2×C4×C67C2×#4114yes—
408C2×C4×C67H(5,𝔽2)14yes—
409C2×C4×C672−1+414yes—
410C2×C4×C67C2512yes—
411C2×C4×C67C2512yes—
412C2×C4×C67C2512yes—
413C2×C4×C67C2518yes—
414C2×C4×C67C2518yes—
415C2×C4×C67C2512yes—
416C2×C4×C67C2512yes—
417C2×C4×C67C2512yes—
418C22⋊D67—28no—
419C22⋊D67—28no—
420C22⋊D67—416no—
421C2×Dic67—22no—
422C2×Dic67—22no—
423C2×Dic67—22no—
424C2×Dic67—28no—
425C2×Dic67—22no—
426C2×Dic67—22no—
427C2×Dic67C2×#4114yes—
428C2×Dic67C2512yes—
429C2×Dic67C2512yes—
430C2×Dic67C2512yes—
431C2×Dic67C2512yes—
432C2×Dic67C2512yes—
433C2×Dic67C2518yes—
434C2×Dic67C2512yes—
435D268—28no—
436D268—232no—
437D268—216no—
438D268—216no—
439D268—216no—
440D268—416no—
441C4×D67—28no—
442C4×D67—28no—
443C4×D67—28no—
444C4×D67—28no—
445C4×D67—28no—
446C4×D67—232no—
447C4×D67—416no—
448C4×D67—416no—
449C4×D67—416no—
450C4×D67C2×#41116yescomplemented
451Dic134—216no—
452Dic134—28no—
453Dic134—416no—
454C22×C67—22no—
455C22×C67—22no—
456C22×C67—22no—
457C22×C67—44no—
458C22×C67C22×#4112yes—
459C22×C67C2×H(5,𝔽2)12yes—
460C22×C67C2×2−1+412yes—
461C22×C67C2611yescharacteristic
462C2×D67—22no—
463C2×D67—22no—
464C2×D67—28no—
465C2×D67—28no—
466C2×D67—22no—
467C2×D67—22no—
468C2×D67—28no—
469C2×D67—22no—
470C2×D67—28no—
471C2×D67—44no—
472C2×D67—416no—
473C2×D67C22×#4114yes—
474C4×C67—22no—
475C4×C67—28no—
476C4×C67—28no—
477C4×C67—22no—
478C4×C67—22no—
479C4×C67C22×#4114yes—
480C4×C67C2×H(5,𝔽2)14yes—
481C4×C67C2×2−1+414yes—
482Dic67—22no—
483Dic67—28no—
484Dic67—22no—
485Dic67—22no—
486Dic67—22no—
487Dic67—22no—
488Dic67C22×#4114yes—
489C2×#3511—671nomaximal, Sylow
490C2×C67—42no—
491C2×C67#351114yescomplemented
492C2×C67C23×#4111yescharacteristic
493C2×C67C22×H(5,𝔽2)11yescharacteristic
494C2×C67C22×2−1+411yescharacteristic
495D67—24no—
496D67—48no—
497D67—42no—
498#3511—6732no—
499C2×#556—672no—
500C2×#555—672no—
501C2×#554—672no—
502C2×#553—672no—
503C2×#553—672no—
504C2×#548—672no—
505C2×#548—672no—
506C2×#547—672no—
507C2×#542—672no—
508C2×#542—672no—
509C2×#537—672no—
510C2×#533—671no—
511C2×#533D6711yescharacteristic, complemented
512C2×#532—671no—
513C2×#532—671no—
514C2×#532—671no—
515C22×C4⋊Q8—671no—
516C2×#520—672no—
517C2×C4×#41—671no—
518C67C2×#351111yescharacteristic, complemented, Sylow
519C22×#41—672no—
520C22×#41—672no—
521C22×#41—672no—
522C22×#41—671no—
523C23×Q8—672no—
524#556—6732no—
525#555—6732no—
526#554—6732no—
527#553—6732no—
528#553—6732no—
529#548—6732no—
530#548—6732no—
531#547—6732no—
532#542—6732no—
533#542—6732no—
534#537—6732no—
535#533—6716no—
536#533C2×D67116yescomplemented
537#532—6716no—
538#532—6716no—
539#532—6716no—
540C2×C4⋊Q8—672no—
541C2×C4⋊Q8—6716no—
542C2×C4⋊Q8—672no—
543C2×C4⋊Q8—672no—
544C2×C4⋊Q8—671no—
545C2×C4⋊Q8C2×D6711yescharacteristic
546C2×C4⋊Q8C2×D6711yescharacteristic
547C2×#127—671no—
548C2×#126—674no—
549C2×#126—674no—
550C2×#125—672no—
551C2×#125C2×D6712yes—
552C2×#124—672no—
553C2×#124—672no—
554C2×#124—674no—
555C2×#124—672no—
556C2×#124—674no—
557C2×#123—674no—
558C2×#123—674no—
559C2×C22⋊Q8—672no—
560C2×C22⋊Q8—672no—
561C2×C22⋊Q8—674no—
562C2×C22⋊Q8—674no—
563C2×C22⋊Q8—674no—
564C2×C22⋊Q8C2×D6712yes—
565C2×C22⋊Q8C2×D6712yes—
566C2×#121—672no—
567C2×#121—672no—
568C2×#121—672no—
569C2×#121—672no—
570C2×#121—672no—
571C2×#121—672no—
572C2×#121—674no—
573C2×#121—674no—
574C2×#121—674no—
575#520—6732no—
576C4×#41—6716no—
577C2×C4×Q8—672no—
578C2×C4×Q8—672no—
579C2×C4×Q8—671no—
580C2×C4×Q8—671no—
581C2×C4×Q8C2×D6712yes—
582C2×C4×Q8C2×D6712yes—
583C2×C4×D4—671no—
584C2×C4×D4—671no—
585C2×C4×D4—671no—
586C2×C4×D4—671no—
587C2×C4×D4—672no—
588C2×C4×D4—674no—
589C2×C4×D4—672no—
590C2×C4×D4—672no—
591C2×C4×D4—672no—
592C2×C4×D4—671no—
593C2×C4×D4—671no—
594C2×C4×D4—672no—
595C2×C4×D4—674no—
596C2×C4×D4—672no—
597C2×#117—671no—
598C2×#117—672no—
599C2×#117—671no—
600C2×#117—671no—
601C2×#117—674no—
602C2×#117C2×D6712yes—
603C22×C4⋊C4—672no—
604C22×C4⋊C4—674no—
605C22×C4⋊C4—672no—
606C22×C42—671no—
607C22×C42—671no—
608C22×C42C2×D6711yescharacteristic
609C2×#41—2688no—
610C2×#41—2688no—
611C2×#41—6716no—
612C2×#41—6716no—
613C2×#41—6716no—
614C2×#41—678no—
615C2×#41—1348no—
616C2×#41—13416no—
617C22×Q8—2688no—
618C22×Q8—6716no—
619C22×Q8—674no—
620C22×Q8—671no—
621C22×Q8—672no—
622C22×Q8C22×D6712yes—
623C22×Q8C22×D6712yes—
624C22×D4—674no—
625C22×D4—671no—
626C22×D4—671no—
627C22×D4—674no—
628C22×D4—672no—
629C22×D4—674no—
630C22×D4—671no—
631C22×D4—672no—
632C22×D4—672no—
633C23×C4—674no—
634C23×C4—674no—
635C23×C4—674no—
636C23×C4—671no—
637C23×C4—671no—
638C23×C4—674no—
639C23×C4—671no—
640C23×C4—671no—
641C23×C4—671no—
642C23×C4—671no—
643C23×C4C22×D6711yescharacteristic
644C23×C4C22×D6711yescharacteristic
645C23×C4C22×D6711yescharacteristic
646C4⋊Q8—6716no—
647C4⋊Q8—6716no—
648C4⋊Q8—6716no—
649C4⋊Q8—678no—
650C4⋊Q8C22×D6718yes—
651C4⋊Q8C22×D6718yes—
652#127—678no—
653#126—6732no—
654#126—6732no—
655#125—6716no—
656#125C22×D67116yes—
657#124—6716no—
658#124—6716no—
659#124—6732no—
660#124—6716no—
661#124—6732no—
662#123—6732no—
663#123—6732no—
664C22⋊Q8—6716no—
665C22⋊Q8—6716no—
666C22⋊Q8—6732no—
667C22⋊Q8—6732no—
668C22⋊Q8—6732no—
669C22⋊Q8C22×D67116yes—
670C22⋊Q8C22×D67116yes—
671#121—6716no—
672#121—6716no—
673#121—6716no—
674#121—6716no—
675#121—6716no—
676#121—6716no—
677#121—6732no—
678#121—6732no—
679#121—6732no—
680C4×Q8—6716no—
681C4×Q8—6716no—
682C4×Q8—678no—
683C4×Q8—678no—
684C4×Q8C22×D67116yes—
685C4×Q8C22×D67116yes—
686C4×D4—678no—
687C4×D4—678no—
688C4×D4—678no—
689C4×D4—678no—
690C4×D4—6716no—
691C4×D4—6732no—
692C4×D4—6716no—
693C4×D4—6716no—
694C4×D4—6716no—
695C4×D4—678no—
696C4×D4—678no—
697C4×D4—6716no—
698C4×D4—6732no—
699C4×D4—6716no—
700#117—678no—
701#117—6716no—
702#117—678no—
703#117—678no—
704#117—6732no—
705#117C22×D67116yes—
706C2×C4⋊C4—671no—
707C2×C4⋊C4—674no—
708C2×C4⋊C4—672no—
709C2×C4⋊C4—672no—
710C2×C4⋊C4—674no—
711C2×C4⋊C4—674no—
712C2×C4⋊C4—671no—
713C2×C4⋊C4—671no—
714C2×C4⋊C4—671no—
715C2×C4⋊C4—671no—
716C2×C4⋊C4—671no—
717C2×C4⋊C4—674no—
718C2×C4⋊C4—6716no—
719C2×C4⋊C4—6732no—
720C2×C4⋊C4—6716no—
721C2×C4⋊C4C22×D6712yes—
722C2×C4⋊C4C22×D6712yes—
723C2×C4⋊C4C22×D6714yes—
724C2×C4⋊C4C22×D6712yes—
725C2×C4⋊C4C22×D6712yes—
726C2×C4⋊C4C22×D6714yes—
727C2×C22⋊C4—671no—
728C2×C22⋊C4—671no—
729C2×C22⋊C4—671no—
730C2×C22⋊C4—671no—
731C2×C22⋊C4—674no—
732C2×C22⋊C4—674no—
733C2×C22⋊C4—671no—
734C2×C22⋊C4—671no—
735C2×C22⋊C4—674no—
736C2×C22⋊C4—674no—
737C2×C22⋊C4—674no—
738C2×C22⋊C4—674no—
739C2×C22⋊C4—674no—
740C2×C22⋊C4C22×D6714yes—
741C2×C42—671no—
742C2×C42—674no—
743C2×C42—671no—
744C2×C42—671no—
745C2×C42—671no—
746C2×C42—671no—
747C2×C42—671no—
748C2×C42—678no—
749C2×C42—678no—
750C2×C42C22×D6711yescharacteristic
751C2×C42C22×D6714yes—
752C2×C42C22×D6711yescharacteristic
753C2×C42C22×D6711yescharacteristic
754C2×C42C22×D6718yes—
755C2×C42C22×D6711yescharacteristic
756C24—671no—
757C24—674no—
758C24—671no—
759C24C23×D6711yescharacteristic
760#41—26832no—
761#41—26832no—
762#41—13432no—
763#41—13464no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—2688no—
767C2×Q8—26832no—
768C2×Q8—6716no—
769C2×Q8—674no—
770C2×Q8—678no—
771C2×Q8—1344no—
772C2×Q8—1348no—
773C2×Q8C23×D6718yes—
774C2×Q8C23×D6718yes—
775C2×D4—2688no—
776C2×D4—2688no—
777C2×D4—6716no—
778C2×D4—674no—
779C2×D4—674no—
780C2×D4—6716no—
781C2×D4—678no—
782C2×D4—6716no—
783C2×D4—674no—
784C2×D4—678no—
785C2×D4—678no—
786C2×D4—1344no—
787C2×D4—13416no—
788C2×D4—1344no—
789C2×D4—1344no—
790C2×D4—1348no—
791C2×D4—1348no—
792C2×D4—1348no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—2688no—
797C22×C4—2688no—
798C22×C4—2688no—
799C22×C4—6716no—
800C22×C4—6716no—
801C22×C4—6716no—
802C22×C4—671no—
803C22×C4—678no—
804C22×C4—674no—
805C22×C4—671no—
806C22×C4—671no—
807C22×C4—671no—
808C22×C4—671no—
809C22×C4—671no—
810C22×C4—674no—
811C22×C4—674no—
812C22×C4—674no—
813C22×C4—674no—
814C22×C4—674no—
815C22×C4—674no—
816C22×C4—6716no—
817C22×C4—13416no—
818C22×C4—1344no—
819C22×C4—1344no—
820C22×C4—1344no—
821C22×C4—1344no—
822C22×C4—1344no—
823C22×C4C23×D6714yes—
824C22×C4C23×D6714yes—
825C22×C4C23×D6714yes—
826C22×C4C23×D6714yes—
827C22×C4C23×D6711yescharacteristic
828C22×C4C23×D6711yescharacteristic
829C22×C4C23×D6711yescharacteristic
830C22×C4C23×D6714yes—
831C22×C4C23×D6711yescharacteristic
832C22×C4C23×D6711yescharacteristic
833C22×C4C23×D6711yescharacteristic
834C4⋊C4—674no—
835C4⋊C4—6716no—
836C4⋊C4—678no—
837C4⋊C4—678no—
838C4⋊C4—6716no—
839C4⋊C4—6716no—
840C4⋊C4—674no—
841C4⋊C4—674no—
842C4⋊C4—674no—
843C4⋊C4—674no—
844C4⋊C4—674no—
845C4⋊C4—6716no—
846C4⋊C4C23×D6718yes—
847C4⋊C4C23×D6718yes—
848C4⋊C4C23×D67116yes—
849C4⋊C4C23×D6718yes—
850C4⋊C4C23×D6718yes—
851C4⋊C4C23×D67116yes—
852C22⋊C4—674no—
853C22⋊C4—674no—
854C22⋊C4—674no—
855C22⋊C4—674no—
856C22⋊C4—6716no—
857C22⋊C4—6716no—
858C22⋊C4—674no—
859C22⋊C4—674no—
860C22⋊C4—6716no—
861C22⋊C4—6716no—
862C22⋊C4—6716no—
863C22⋊C4—6716no—
864C22⋊C4—6716no—
865C22⋊C4C23×D67116yes—
866C42—674no—
867C42—674no—
868C42—674no—
869C42—674no—
870C42—674no—
871C42—674no—
872C42—6716no—
873C42C23×D6714yes—
874C42C23×D6714yes—
875C42C23×D6714yes—
876C42C23×D6714yes—
877C42C23×D67116yes—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—674no—
882C23—672no—
883C23—678no—
884C23—672no—
885C23—1348no—
886C23—1342no—
887C23—1348no—
888C23—1342no—
889C23—1342no—
890C23—1348no—
891C23—1342no—
892C23—1342no—
893C23C24×D6712yes—
894C23C24×D6711yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—26816no—
898Q8—1348no—
899Q8—13416no—
900D4—26816no—
901D4—26816no—
902D4—1348no—
903D4—13432no—
904D4—1348no—
905D4—1348no—
906D4—13416no—
907D4—13416no—
908D4—13416no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—26816no—
918C2×C4—26816no—
919C2×C4—26816no—
920C2×C4—674no—
921C2×C4—672no—
922C2×C4—6716no—
923C2×C4—672no—
924C2×C4—672no—
925C2×C4—672no—
926C2×C4—672no—
927C2×C4—672no—
928C2×C4—678no—
929C2×C4—13432no—
930C2×C4—1342no—
931C2×C4—1342no—
932C2×C4—1348no—
933C2×C4—1342no—
934C2×C4—1342no—
935C2×C4—1342no—
936C2×C4—1348no—
937C2×C4—1348no—
938C2×C4—1348no—
939C2×C4—1348no—
940C2×C4—1348no—
941C2×C4#41×D6714yes—
942C2×C4#1452408914yes—
943C2×C4#1452409114yes—
944C2×C4C24×D6718yes—
945C2×C4C24×D6712yes—
946C2×C4C24×D6712yes—
947C2×C4C24×D6712yes—
948C2×C4C24×D6718yes—
949C2×C4C24×D6712yes—
950C2×C4C24×D6712yes—
951C2×C4C24×D6712yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—26816no—
957C22—2684no—
958C22—674no—
959C22—1348no—
960C22—1342no—
961C22—1348no—
962C22—1342no—
963C22—1342no—
964C22—1348no—
965C22—1348no—
966C22—1342no—
967C22—1342no—
968C22C2×#41×D6712yes—
969C22C2×#1452408912yes—
970C22C2×#1452409112yes—
971C22C25×D6711yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—674no—
978C4—1342no—
979C4—1342no—
980C4—1348no—
981C4—1342no—
982C4—1342no—
983C4—1342no—
984C4C2×#41×D6714yes—
985C4C2×#1452408914yes—
986C4C2×#1452409114yes—
987C2—42no—
988C2—2688no—
989C2—2682no—
990C2—1344no—
991C2#2257412114yesdirect product factor
992C2C22×#41×D6711yescharacteristic
993C2C22×#1452408911yescharacteristic
994C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#533×C67C2
socleC23×C67C25
hypercenterC2×#533D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22574121C2direct (N × H)
2. C2×#16864118C2semidirect
3. C2×#16864109C2semidirect
4. C2×#16864102C2semidirect
5. C2×#16864099C2semidirect
6. C2×#16864090C2semidirect
7. C2×#16864058C2semidirect
8. C2×#16864056C2semidirect
9. C2×#16864048C2semidirect
10. C2×#16864019C2semidirect
11. C2×#16864018C2semidirect
12. C2×#16863976C2semidirect
13. C2×#16863951C2semidirect
14. C2×#16863947C2semidirect
15. C2×#16863947C2semidirect
16. C2×#16863946C2semidirect
17. C2×C4⋊Q8×D67C2semidirect
18. C2×#16863878C2semidirect
19. C2×C4×#11761628C2semidirect
20. C2×#533×C67C2semidirect
26. #16864118C22semidirect
27. #16864109C22semidirect
28. #16864102C22semidirect
29. #16864099C22semidirect
30. #16864090C22semidirect
31. #16864058C22semidirect
32. #16864056C22semidirect
33. #16864048C22semidirect
34. #16864019C22semidirect
35. #16864018C22semidirect
36. #16863976C22semidirect
37. #16863951C22semidirect
38. #16863947C22semidirect
39. #16863947C22semidirect
40. #16863946C22semidirect
45. C4⋊Q8×D67C22semidirect
71. #16863878C22semidirect
72. C4×#11761628C22semidirect
101. #533×C67C22semidirect
306. C2×C4×D67#41semidirect
450. C4×D67C2×#41semidirect
491. C2×C67#3511semidirect
511. C2×#533D67semidirect
518. C67C2×#3511semidirect
536. #533C2×D67semidirect
991. C2#22574121direct (N × H)

Maximal subgroups

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

subgroupindex
#225741212
C2×#168641182
C2×#168641092
C2×#168641022
C2×#168640992
C2×#168640902
C2×#168640582
C2×#168640562
C2×#168640482
C2×#168640192
C2×#168640182
C2×#168639762
C2×#168639512
C2×#168639472
C2×#168639462
C2×C4⋊Q8×D672
C2×#168638782
C2×C4×#117616282
C2×#533×C672
C2×#351167