Finite Group Databasebeta

← C2×#22574599 #31763532

Subgroups — C2×#22574599 #31763532

Order 17152.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574599C2132yesmaximal, direct product factor
2C2×#16864142C214yesmaximal, complemented
3C2×#16864112C211yesmaximal, characteristic, complemented
4C2×#16864111C212yesmaximal, complemented
5C2×#16864099C212yesmaximal, complemented
6C2×#16864081C212yesmaximal, complemented
7C2×Q8×D268C211yesmaximal, characteristic, complemented
8C2×#16864056C212yesmaximal, complemented
9C2×#16864051C211yesmaximal, characteristic, complemented
10C2×#16864026C212yesmaximal, complemented
11C2×#16864019C214yesmaximal, complemented
12C2×#16863997C212yesmaximal, complemented
13C2×#16863977C212yesmaximal, complemented
14C2×#16863969C212yesmaximal, complemented
15C2×#16863951C211yesmaximal, characteristic, complemented
16C2×#16863943C211yesmaximal, characteristic, complemented
17C2×#16863933C211yesmaximal, characteristic, complemented
18C2×#554×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2212yes—
20C22×#11761628C2212yes—
21C22×Q8×D67C2212yes—
22#16864142C22164yescomplemented
23#16864112C22116yescomplemented
24#16864111C22132yescomplemented
25#16864099C22132yescomplemented
26#16864081C22132yescomplemented
27Q8×D268C22116yescomplemented
28#16864056C22132yescomplemented
29#16864051C22116yescomplemented
30#16864026C22132yescomplemented
31#16864019C22164yescomplemented
32#16863997C22132yescomplemented
33#16863977C22132yescomplemented
34#16863969C22132yescomplemented
35#16863951C22116yescomplemented
36#16863943C22116yescomplemented
37C2×#14524043C2212yes—
38C2×#14524043C2211yescharacteristic
39C2×#14524042C2214yes—
40C2×#14524042C2211yescharacteristic
41C2×#14524039C2211yescharacteristic
42#16863933C22116yescomplemented
43C2×#14524038C2212yes—
44C2×#14524038C2214yes—
45C2×#14524034C2212yes—
46C2×#14524034C2211yescharacteristic
47C2×#14524033C2214yes—
48C2×#14524032C2214yes—
49C2×#14524032C2211yescharacteristic
50C2×#14524029C2212yes—
51C2×#14524029C2214yes—
52C2×#14524029C2214yes—
53C2×#14524028C2212yes—
54C2×#14524028C2214yes—
55C2×#14524026C2214yes—
56C2×#14524025C2214yes—
57C2×#14524025C2214yes—
58C2×#14524023C2214yes—
59C2×#14524023C2214yes—
60C2×#14524023C2212yes—
61C2×#14524023C2212yes—
62C2×#14524022C2212yes—
63C2×#14524021C2214yes—
64C2×#14524019C2211yescharacteristic
65C2×#14524019C2212yes—
66C2×#14524018C2212yes—
67C2×#14524018C2211yescharacteristic
68C2×#14524018C2211yescharacteristic
69C2×#14524018C2212yes—
70C2×#14524018C2214yes—
71C2×#14524017C2214yes—
72C2×#14524017C2214yes—
73C2×#14524016C2214yes—
74C2×#14524016C2212yes—
75C2×#14524014C2212yes—
76C2×#14524014C2211yescharacteristic
77C2×Q8×Dic67C2212yes—
78C2×#14524008C2212yes—
79C2×C4×D268C2211yescharacteristic
80C2×C4×D268C2212yes—
81C2×C4×D268C2211yescharacteristic
82C2×C4×D268C2212yes—
83C2×#14524005C2214yes—
84C2×C4×C22⋊D67C2212yes—
85C2×#14524002C2214yes—
86C2×#14524001C2212yes—
87C2×#14524001C2212yes—
88C2×#14524001C2212yes—
89C2×#14524000C2212yes—
90C2×C4⋊C4×D67C2212yes—
91C2×C42×D67C2211yescharacteristic
92#554×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×#125×C67C2212yes—
95C2×C22⋊Q8×C67C2214yes—
96C2×C22⋊Q8×C67C2212yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×D4×C67C2211yescharacteristic
99C2×C4×D4×C67C2212yes—
100C22×C4⋊C4×C67C2212yes—
101C2×#11761628—48no—
102C2×#11761628—48no—
103C2×#11761628C23116yes—
104C2×#11761628C23116yes—
105C22×Dic134C2312yes—
106C22×Dic134C2314yes—
107C22×Dic134C2312yes—
108C2×Q8×D67—48no—
109C2×Q8×D67C23116yes—
110C22×D268C2311yescharacteristic
111C22×D268C2311yescharacteristic
112C22×D268C2314yes—
113C22×D268C2312yes—
114C22×D268C2312yes—
115C22×C22⋊D67C2312yes—
116C22×C22⋊D67C2314yes—
117C22×C22⋊D67C2312yes—
118C22×C22⋊D67C2312yes—
119C22×C4×D67C2311yescharacteristic
120C22×C4×D67C2311yescharacteristic
121C22×C4×D67C2312yes—
122C22×C4×D67C2312yes—
123C22×C4×D67C2311yescharacteristic
124C22×C4×D67C2314yes—
125C22×C4×D67C2314yes—
126#14524043C23116yes—
127#14524043C2318yes—
128#14524042C23132yes—
129#14524042C2318yes—
130#14524039C2318yes—
131#14524038C23116yes—
132#14524038C23132yes—
133#14524034C23116yes—
134#14524034C2318yes—
135#14524033C23132yes—
136#14524032C23132yes—
137#14524032C2318yes—
138#14524029C23116yes—
139#14524029C23132yes—
140#14524029C23132yes—
141#14524028C23132yes—
142#14524028C23116yes—
143#14524026C23132yes—
144#14524025C23132yes—
145#14524025C23132yes—
146#14524023C23132yes—
147#14524023C23132yes—
148#14524023C23116yes—
149#14524023C23116yes—
150#14524022C23116yes—
151#14524021C23132yes—
152#14524019C23116yes—
153#14524019C2318yes—
154#14524018C23116yes—
155#14524018C2318yes—
156#14524018C23116yes—
157#14524018C23132yes—
158#14524018C2318yes—
159#14524017C23132yes—
160#14524017C23132yes—
161#14524016C23132yes—
162#14524016C23116yes—
163#14524014C23116yes—
164#14524014C2318yes—
165Q8×Dic67C23116yes—
166#14524008C23116yes—
167C4×D268C2318yes—
168C4×D268C23116yes—
169C4×D268C2318yes—
170C4×D268C23116yes—
171#14524005C23132yes—
172C4×C22⋊D67C23116yes—
173#14524002C23132yes—
174#14524001C23116yes—
175#14524001C23116yes—
176#14524001C23116yes—
177#14524000C23116yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2311yescharacteristic
180C2×C4⋊Dic67C2311yescharacteristic
181C2×C4⋊Dic67C2312yes—
182C2×C4⋊Dic67C2314yes—
183C2×C4⋊Dic67C2314yes—
184C2×C4⋊Dic67C2312yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C2×Dic67⋊C4C2312yes—
189C2×Dic67⋊C4C2314yes—
190C4⋊C4×D67C23116yes—
191C2×C22⋊Dic67C2312yes—
192C2×C22⋊Dic67C2314yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2312yes—
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×Dic67C2311yescharacteristic
206C2×C4×Dic67C2311yescharacteristic
207C2×C4×Dic67C2314yes—
208C2×C4×Dic67C2314yes—
209C42×D67C2318yes—
210C22×Q8×C67C2311yescharacteristic
211C22×Q8×C67C2312yes—
212C22×D4×C67C2311yescharacteristic
213C23×C4×C67C2312yes—
214C23×C4×C67C2314yes—
215C4⋊Q8×C67C2318yes—
216#125×C67C23116yes—
217C22⋊Q8×C67C23132yes—
218C22⋊Q8×C67C23116yes—
219C4×Q8×C67C2318yes—
220C4×D4×C67C2318yes—
221C4×D4×C67C23116yes—
222C2×C4⋊C4×C67C2311yescharacteristic
223C2×C4⋊C4×C67C2314yes—
224C2×C4⋊C4×C67C2312yes—
225C2×C4⋊C4×C67C23116yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2311yescharacteristic
234C23×D67C2412yes—
235C23×D67C2411yescharacteristic
236C23×D67C2412yes—
237#11761628—432no—
238#11761628—432no—
239C2×Dic134—28no—
240C2×Dic134—48no—
241C2×Dic134—44no—
242C2×Dic134C2418yes—
243C2×Dic134C24116yes—
244C2×Dic134C2418yes—
245Q8×D67—432no—
246C2×D268—24no—
247C2×D268—24no—
248C2×D268—44no—
249C2×D268—48no—
250C2×D268—44no—
251C2×D268C2414yes—
252C2×D268C2414yes—
253C2×D268C24116yes—
254C2×D268C2418yes—
255C2×D268C2418yes—
256C2×C22⋊D67—44no—
257C2×C22⋊D67—44no—
258C2×C22⋊D67—44no—
259C2×C22⋊D67—48no—
260C2×C22⋊D67C2418yes—
261C2×C22⋊D67C24116yes—
262C2×C22⋊D67C2418yes—
263C2×C22⋊D67C2418yes—
264C22×Dic67C2411yescharacteristic
265C22×Dic67C2412yes—
266C22×Dic67C2412yes—
267C22×Dic67C2411yescharacteristic
268C22×Dic67C2411yescharacteristic
269C22×Dic67C2414yes—
270C2×C4×D67—28no—
271C2×C4×D67—24no—
272C2×C4×D67—24no—
273C2×C4×D67—28no—
274C2×C4×D67—42no—
275C2×C4×D67—48no—
276C2×C4×D67—48no—
277C2×C4×D67C2414yes—
278C2×C4×D67C2414yes—
279C2×C4×D67C2418yes—
280C2×C4×D67C2418yes—
281C2×C4×D67C2414yes—
282C2×C4×D67C24116yes—
283C2×C4×D67C24116yes—
284C4⋊Dic67C2418yes—
285C4⋊Dic67C2414yes—
286C4⋊Dic67C2414yes—
287C4⋊Dic67C2418yes—
288C4⋊Dic67C24116yes—
289C4⋊Dic67C24116yes—
290C4⋊Dic67C2418yes—
291Dic67⋊C4C24116yes—
292Dic67⋊C4C2418yes—
293Dic67⋊C4C2418yes—
294Dic67⋊C4C2418yes—
295Dic67⋊C4C24116yes—
296C22⋊Dic67C2418yes—
297C22⋊Dic67C24116yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C24116yes—
303(C2×D67)⋊C4C2418yes—
304(C2×D67)⋊C4C2418yes—
305(C2×D67)⋊C4C2418yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C2418yes—
308(C2×D67)⋊C4C2418yes—
309C4×Dic67C2414yes—
310C4×Dic67C2414yes—
311C4×Dic67C2414yes—
312C4×Dic67C24116yes—
313C4×Dic67C24116yes—
314C24×C67C2412yes—
315C2×Q8×C67—24no—
316C2×Q8×C67—44no—
317C2×Q8×C67C2414yes—
318C2×Q8×C67C2418yes—
319C2×D4×C67—24no—
320C2×D4×C67C2414yes—
321C22×C4×C67—28no—
322C22×C4×C67—48no—
323C22×C4×C67C2412yes—
324C22×C4×C67C2411yescharacteristic
325C22×C4×C67C2412yes—
326C22×C4×C67C2412yes—
327C22×C4×C67C2414yes—
328C22×C4×C67C2418yes—
329C22×C4×C67C24116yes—
330C22×C4×C67C2411yescharacteristic
331C22×C4×C67C2411yescharacteristic
332C4⋊C4×C67C2414yes—
333C4⋊C4×C67C24116yes—
334C4⋊C4×C67C2418yes—
335C4⋊C4×C67C2414yes—
336C4⋊C4×C67C2418yes—
337C4⋊C4×C67C2418yes—
338C4⋊C4×C67C24116yes—
339C22⋊C4×C67C2418yes—
340C22⋊C4×C67C24116yes—
341C42×C67C2418yes—
342C42×C67C2414yes—
343C23×C67—24no—
344C23×C67—24no—
345C23×C67—24no—
346C23×C67C2514yes—
347C23×C67C2511yescharacteristic
348C22×D67—24no—
349C22×D67—22no—
350C22×D67—24no—
351C22×D67—22no—
352C22×D67—24no—
353C22×D67—24no—
354C22×D67—22no—
355C22×D67—24no—
356C22×D67—24no—
357C22×D67C2514yes—
358C22×D67C2512yes—
359C22×D67C2514yes—
360Q8×C67—28no—
361Q8×C67—48no—
362D4×C67—28no—
363C2×C4×C67—24no—
364C2×C4×C67—24no—
365C2×C4×C67—24no—
366C2×C4×C67—28no—
367C2×C4×C67—22no—
368C2×C4×C67—216no—
369C2×C4×C67—416no—
370C2×C4×C67H(5,𝔽2)14yes—
371C2×C4×C672−1+414yes—
372C2×C4×C67C2514yes—
373C2×C4×C67C2512yes—
374C2×C4×C67C2514yes—
375C2×C4×C67C2514yes—
376C2×C4×C67C2518yes—
377C2×C4×C67C2512yes—
378C2×C4×C67C2512yes—
379C22⋊D67—48no—
380C22⋊D67—416no—
381C22⋊D67—48no—
382C22⋊D67—48no—
383C2×Dic67—22no—
384C2×Dic67—24no—
385C2×Dic67—28no—
386C2×Dic67—22no—
387C2×Dic67—24no—
388C2×Dic67—22no—
389C2×Dic67C2512yes—
390C2×Dic67C2514yes—
391C2×Dic67C2514yes—
392C2×Dic67C2512yes—
393C2×Dic67C2512yes—
394C2×Dic67C2518yes—
395D268—28no—
396D268—28no—
397D268—48no—
398D268—416no—
399D268—48no—
400C4×D67—216no—
401C4×D67—28no—
402C4×D67—28no—
403C4×D67—216no—
404C4×D67—44no—
405C4×D67—416no—
406C4×D67—416no—
407Dic134—216no—
408Dic134—416no—
409Dic134—48no—
410C22×C67—24no—
411C22×C67—24no—
412C22×C67—24no—
413C22×C67—48no—
414C22×C67C2×H(5,𝔽2)12yes—
415C22×C67C2×2−1+412yes—
416C22×C67#58512yes—
417C22×C67C2611yescharacteristic
418C2×D67—24no—
419C2×D67—22no—
420C2×D67—24no—
421C2×D67—22no—
422C2×D67—24no—
423C2×D67—24no—
424C2×D67—22no—
425C2×D67—24no—
426C2×D67—24no—
427C2×D67—48no—
428C2×D67—44no—
429C2×D67—48no—
430C4×C67—24no—
431C4×C67—24no—
432C4×C67—22no—
433C4×C67—24no—
434C4×C67—28no—
435C4×C67C2×H(5,𝔽2)14yes—
436C4×C67C2×2−1+414yes—
437Dic67—28no—
438Dic67—24no—
439Dic67—22no—
440Dic67—22no—
441Dic67—24no—
442Dic67—22no—
443C2×#3547—671nomaximal, Sylow
444C2×C67—44no—
445C2×C67#354714yescomplemented
446C2×C67C22×H(5,𝔽2)11yescharacteristic
447C2×C67C22×2−1+411yescharacteristic
448C2×C67C2×#58511yescharacteristic
449D67—44no—
450D67—42no—
451D67—44no—
452#3547—6732no—
453C2×#562—674no—
454C2×#555—671no—
455C2×#555—672no—
456C2×#554D6711yescharacteristic, complemented
457C2×#553—672no—
458C2×#552—672no—
459C2×D4×Q8—671no—
460C2×#548—672no—
461C2×#547—671no—
462C2×#544—672no—
463C2×#542—674no—
464C2×#540—672no—
465C2×#537—672no—
466C2×#536—672no—
467C2×#533—671no—
468C2×#532—671no—
469C2×#529—671no—
470C67C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—672no—
472C22×#41—672no—
473C23×Q8—672no—
474#562—6764no—
475#555—6716no—
476#555—6732no—
477#554C2×D67116yescomplemented
478#553—6732no—
479#552—6732no—
480D4×Q8—6716no—
481#548—6732no—
482#547—6716no—
483#544—6732no—
484#542—6764no—
485#540—6732no—
486#537—6732no—
487#536—6732no—
488#533—6716no—
489#532—6716no—
490C2×C4⋊Q8—671no—
491C2×C4⋊Q8—674no—
492C2×C4⋊Q8—671no—
493C2×C4⋊Q8—672no—
494C2×C4⋊Q8C2×D6711yescharacteristic
495C2×#127—671no—
496#529—6716no—
497C2×#126—672no—
498C2×#126—674no—
499C2×#125—671no—
500C2×#125—672no—
501C2×#125—674no—
502C2×#125C2×D6712yes—
503C2×#124—671no—
504C2×#124—674no—
505C2×#124—672no—
506C2×#124—674no—
507C2×#124—674no—
508C2×#123—674no—
509C2×#123—672no—
510C2×#123—674no—
511C2×#123—674no—
512C2×#123—674no—
513C2×C22⋊Q8—671no—
514C2×C22⋊Q8—672no—
515C2×C22⋊Q8—672no—
516C2×C22⋊Q8—672no—
517C2×C22⋊Q8—674no—
518C2×C22⋊Q8—672no—
519C2×C22⋊Q8—674no—
520C2×C22⋊Q8—674no—
521C2×C22⋊Q8C2×D6712yes—
522C2×C22⋊Q8C2×D6714yes—
523C2×#121—671no—
524C2×#121—672no—
525C2×#121—674no—
526C2×#121—674no—
527C2×#121—671no—
528C2×#121—671no—
529C2×#121—672no—
530C2×#121—674no—
531C2×#121—672no—
532C2×#121—672no—
533C2×#121—674no—
534C2×C4×Q8—672no—
535C2×C4×Q8—672no—
536C2×C4×Q8C2×D6711yescharacteristic
537C2×C4×D4—672no—
538C2×C4×D4—674no—
539C2×C4×D4—671no—
540C2×C4×D4—672no—
541C2×C4×D4—671no—
542C2×C4×D4—672no—
543C2×C4×D4C2×D6711yescharacteristic
544C2×C4×D4C2×D6712yes—
545C2×#117—674no—
546C2×#117—672no—
547C2×#117—672no—
548C2×#117—672no—
549C2×#117—672no—
550C22×C4⋊C4—672no—
551C22×C4⋊C4C2×D6712yes—
552C22×C42—671no—
553C2×#41—2688no—
554C2×#41—2688no—
555C2×#41—6716no—
556C2×#41—6716no—
557C22×Q8—2688no—
558C22×Q8—6716no—
559C22×Q8—674no—
560C22×Q8—672no—
561C22×Q8—672no—
562C22×Q8C22×D6711yescharacteristic
563C22×Q8C22×D6712yes—
564C22×D4—672no—
565C22×D4—674no—
566C22×D4—672no—
567C22×D4—672no—
568C22×D4—672no—
569C22×D4—674no—
570C22×D4—672no—
571C22×D4—671no—
572C22×D4—671no—
573C22×D4C22×D6711yescharacteristic
574C23×C4—674no—
575C23×C4—674no—
576C23×C4—671no—
577C23×C4—672no—
578C23×C4—671no—
579C23×C4—672no—
580C23×C4—671no—
581C23×C4C22×D6712yes—
582C23×C4C22×D6714yes—
583C4⋊Q8—678no—
584C4⋊Q8—6732no—
585C4⋊Q8—678no—
586C4⋊Q8—6716no—
587C4⋊Q8C22×D6718yes—
588#127—678no—
589#126—6716no—
590#126—6732no—
591#125—678no—
592#125—6716no—
593#125—6732no—
594#125C22×D67116yes—
595#124—678no—
596#124—6732no—
597#124—6716no—
598#124—6732no—
599#124—6732no—
600#123—6732no—
601#123—6716no—
602#123—6732no—
603#123—6732no—
604#123—6732no—
605C22⋊Q8—678no—
606C22⋊Q8—6716no—
607C22⋊Q8—6716no—
608C22⋊Q8—6716no—
609C22⋊Q8—6732no—
610C22⋊Q8—6716no—
611C22⋊Q8—6732no—
612C22⋊Q8—6732no—
613C22⋊Q8C22×D67116yes—
614C22⋊Q8C22×D67132yes—
615#121—678no—
616#121—6716no—
617#121—6732no—
618#121—6732no—
619#121—678no—
620#121—678no—
621#121—6716no—
622#121—6732no—
623#121—6716no—
624#121—6716no—
625#121—6732no—
626C4×Q8—6716no—
627C4×Q8—6716no—
628C4×Q8C22×D6718yes—
629C4×D4—6716no—
630C4×D4—6732no—
631C4×D4—678no—
632C4×D4—6716no—
633C4×D4—678no—
634C4×D4—6716no—
635C4×D4C22×D6718yes—
636C4×D4C22×D67116yes—
637#117—6732no—
638#117—6716no—
639#117—6716no—
640#117—6716no—
641#117—6716no—
642C2×C4⋊C4—672no—
643C2×C4⋊C4—674no—
644C2×C4⋊C4—671no—
645C2×C4⋊C4—671no—
646C2×C4⋊C4—672no—
647C2×C4⋊C4—674no—
648C2×C4⋊C4—672no—
649C2×C4⋊C4—672no—
650C2×C4⋊C4—672no—
651C2×C4⋊C4—674no—
652C2×C4⋊C4—674no—
653C2×C4⋊C4—672no—
654C2×C4⋊C4—6716no—
655C2×C4⋊C4C22×D6711yescharacteristic
656C2×C4⋊C4C22×D6711yescharacteristic
657C2×C4⋊C4C22×D6712yes—
658C2×C4⋊C4C22×D6714yes—
659C2×C4⋊C4C22×D67116yes—
660C2×C4⋊C4C22×D6712yes—
661C2×C4⋊C4C22×D6714yes—
662C2×C4⋊C4C22×D6712yes—
663C2×C22⋊C4—672no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4—672no—
666C2×C22⋊C4—672no—
667C2×C22⋊C4—674no—
668C2×C22⋊C4—674no—
669C2×C22⋊C4—674no—
670C2×C22⋊C4—672no—
671C2×C22⋊C4—672no—
672C2×C22⋊C4—674no—
673C2×C22⋊C4—672no—
674C2×C22⋊C4—672no—
675C2×C22⋊C4—672no—
676C2×C22⋊C4C22×D6712yes—
677C2×C22⋊C4C22×D6714yes—
678C2×C42—674no—
679C2×C42—674no—
680C2×C42—671no—
681C2×C42—671no—
682C2×C42—671no—
683C2×C42—678no—
684C2×C42C22×D6712yes—
685C2×C42C22×D6711yescharacteristic
686C24—672no—
687C24—672no—
688C24—671no—
689C24C23×D6712yes—
690#41—26832no—
691#41—26832no—
692C2×Q8—24no—
693C2×Q8—44no—
694C2×Q8—2688no—
695C2×Q8—2684no—
696C2×Q8—26832no—
697C2×Q8—6716no—
698C2×Q8—678no—
699C2×Q8—678no—
700C2×Q8—1348no—
701C2×Q8C23×D6714yes—
702C2×Q8C23×D6718yes—
703C2×D4—24no—
704C2×D4—2684no—
705C2×D4—2684no—
706C2×D4—2688no—
707C2×D4—2688no—
708C2×D4—2684no—
709C2×D4—2684no—
710C2×D4—2684no—
711C2×D4—678no—
712C2×D4—6716no—
713C2×D4—678no—
714C2×D4—678no—
715C2×D4—678no—
716C2×D4—6716no—
717C2×D4—678no—
718C2×D4—674no—
719C2×D4—674no—
720C2×D4—1344no—
721C2×D4—1344no—
722C2×D4C23×D6714yes—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—2688no—
726C22×C4—2688no—
727C22×C4—2682no—
728C22×C4—674no—
729C22×C4—6716no—
730C22×C4—6716no—
731C22×C4—671no—
732C22×C4—672no—
733C22×C4—672no—
734C22×C4—671no—
735C22×C4—671no—
736C22×C4—674no—
737C22×C4—674no—
738C22×C4—674no—
739C22×C4—678no—
740C22×C4—678no—
741C22×C4—1348no—
742C22×C4—1344no—
743C22×C4—1348no—
744C22×C4—1344no—
745C22×C4C23×D6718yes—
746C22×C4C23×D6714yes—
747C22×C4C23×D6711yescharacteristic
748C22×C4C23×D6712yes—
749C22×C4C23×D6712yes—
750C22×C4C23×D6712yes—
751C22×C4C23×D67116yes—
752C22×C4C23×D6711yescharacteristic
753C22×C4C23×D6711yescharacteristic
754C4⋊C4—678no—
755C4⋊C4—6716no—
756C4⋊C4—674no—
757C4⋊C4—674no—
758C4⋊C4—678no—
759C4⋊C4—6716no—
760C4⋊C4—678no—
761C4⋊C4—678no—
762C4⋊C4—678no—
763C4⋊C4—6716no—
764C4⋊C4—6716no—
765C4⋊C4—678no—
766C4⋊C4C23×D6714yes—
767C4⋊C4C23×D6714yes—
768C4⋊C4C23×D6718yes—
769C4⋊C4C23×D67116yes—
770C4⋊C4C23×D6718yes—
771C4⋊C4C23×D67116yes—
772C4⋊C4C23×D6718yes—
773C22⋊C4—678no—
774C22⋊C4—6716no—
775C22⋊C4—678no—
776C22⋊C4—678no—
777C22⋊C4—6716no—
778C22⋊C4—6716no—
779C22⋊C4—6716no—
780C22⋊C4—678no—
781C22⋊C4—678no—
782C22⋊C4—6716no—
783C22⋊C4—678no—
784C22⋊C4—678no—
785C22⋊C4—678no—
786C22⋊C4C23×D6718yes—
787C22⋊C4C23×D67116yes—
788C42—674no—
789C42—674no—
790C42—674no—
791C42—6716no—
792C42—6716no—
793C42C23×D6714yes—
794C42C23×D6718yes—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—674no—
799C23—674no—
800C23—672no—
801C23—1344no—
802C23—1344no—
803C23—1342no—
804C23—1344no—
805C23—1342no—
806C23—1344no—
807C23—1342no—
808C23—1344no—
809C23—1344no—
810C23C24×D6714yes—
811C23C24×D6711yescharacteristic
812Q8—28no—
813Q8—48no—
814Q8—26816no—
815Q8—2688no—
816Q8—13416no—
817D4—28no—
818D4—2688no—
819D4—2688no—
820D4—26816no—
821D4—26816no—
822D4—2688no—
823D4—2688no—
824D4—2688no—
825D4—1348no—
826D4—1348no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—26816no—
835C2×C4—26816no—
836C2×C4—2684no—
837C2×C4—672no—
838C2×C4—674no—
839C2×C4—674no—
840C2×C4—672no—
841C2×C4—672no—
842C2×C4—678no—
843C2×C4—1348no—
844C2×C4—1342no—
845C2×C4—1344no—
846C2×C4—1342no—
847C2×C4—1344no—
848C2×C4—1342no—
849C2×C4—13416no—
850C2×C4—1348no—
851C2×C4—1348no—
852C2×C4—13416no—
853C2×C4#1452408914yes—
854C2×C4#1452409114yes—
855C2×C4C24×D6718yes—
856C2×C4C24×D6712yes—
857C2×C4C24×D6714yes—
858C2×C4C24×D6714yes—
859C2×C4C24×D6714yes—
860C2×C4C24×D6712yes—
861C2×C4C24×D6712yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—48no—
866C22—2688no—
867C22—2688no—
868C22—2684no—
869C22—1344no—
870C22—1344no—
871C22—1342no—
872C22—1344no—
873C22—1342no—
874C22—1344no—
875C22—1342no—
876C22—1344no—
877C22—1344no—
878C22C2×#1452408912yes—
879C22C2×#1452409112yes—
880C22#1686423112yes—
881C22C25×D6711yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—22no—
887C4—1348no—
888C4—1342no—
889C4—1344no—
890C4—1342no—
891C4—1344no—
892C4—1342no—
893C4C2×#1452408914yes—
894C4C2×#1452409114yes—
895C2—44no—
896C2—2684no—
897C2—2684no—
898C2—2682no—
899C2#2257459914yesdirect product factor
900C2C22×#1452408911yescharacteristic
901C2C22×#1452409111yescharacteristic
902C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#554×C67C2
socleC23×C67C25
hypercenterC2×#554D67
hypocenterC67C2×#3547
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22574599C2direct (N × H)
2. C2×#16864142C2semidirect
3. C2×#16864112C2semidirect
4. C2×#16864111C2semidirect
5. C2×#16864099C2semidirect
6. C2×#16864081C2semidirect
7. C2×Q8×D268C2semidirect
8. C2×#16864056C2semidirect
9. C2×#16864051C2semidirect
10. C2×#16864026C2semidirect
11. C2×#16864019C2semidirect
12. C2×#16863997C2semidirect
13. C2×#16863977C2semidirect
14. C2×#16863969C2semidirect
15. C2×#16863951C2semidirect
16. C2×#16863943C2semidirect
17. C2×#16863933C2semidirect
18. C2×#554×C67C2semidirect
22. #16864142C22semidirect
23. #16864112C22semidirect
24. #16864111C22semidirect
25. #16864099C22semidirect
26. #16864081C22semidirect
27. Q8×D268C22semidirect
28. #16864056C22semidirect
29. #16864051C22semidirect
30. #16864026C22semidirect
31. #16864019C22semidirect
32. #16863997C22semidirect
33. #16863977C22semidirect
34. #16863969C22semidirect
35. #16863951C22semidirect
36. #16863943C22semidirect
42. #16863933C22semidirect
92. #554×C67C22semidirect
445. C2×C67#3547semidirect
456. C2×#554D67semidirect
470. C67C2×#3547semidirect
477. #554C2×D67semidirect
899. C2#22574599direct (N × H)

Maximal subgroups

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

subgroupindex
#225745992
C2×#168641422
C2×#168641122
C2×#168641112
C2×#168640992
C2×#168640812
C2×Q8×D2682
C2×#168640562
C2×#168640512
C2×#168640262
C2×#168640192
C2×#168639972
C2×#168639772
C2×#168639692
C2×#168639512
C2×#168639432
C2×#168639332
C2×#554×C672
C2×#354767