Finite Group Databasebeta

← C2×#22574600 #31763525

Subgroups — C2×#22574600 #31763525

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#22574600C2132yesmaximal, direct product factor
2C2×#16864143C214yesmaximal, complemented
3C2×#16864111C211yesmaximal, characteristic, complemented
4C2×#16864111C212yesmaximal, complemented
5C2×#16864106C211yesmaximal, characteristic, complemented
6C2×#16864092C212yesmaximal, complemented
7C2×#16864084C212yesmaximal, complemented
8C2×Q8×D268C211yesmaximal, characteristic, complemented
9C2×#16864054C212yesmaximal, complemented
10C2×#16864050C211yesmaximal, characteristic, complemented
11C2×#16864024C212yesmaximal, complemented
12C2×#16864012C214yesmaximal, complemented
13C2×#16864001C212yesmaximal, complemented
14C2×#16863975C212yesmaximal, complemented
15C2×#16863969C212yesmaximal, complemented
16C2×#16863953C211yesmaximal, characteristic, complemented
17C2×#16863946C211yesmaximal, characteristic, complemented
18C2×#529×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2212yes—
20C22×#11761627C2212yes—
21C22×Q8×D67C2212yes—
22#16864143C22164yescomplemented
23#16864111C22116yescomplemented
24#16864111C22132yescomplemented
25#16864106C22116yescomplemented
26#16864092C22132yescomplemented
27#16864084C22132yescomplemented
28Q8×D268C22116yescomplemented
29#16864054C22132yescomplemented
30#16864050C22116yescomplemented
31#16864024C22132yescomplemented
32#16864012C22164yescomplemented
33#16864001C22132yescomplemented
34#16863975C22132yescomplemented
35#16863969C22132yescomplemented
36#16863953C22116yescomplemented
37#16863946C22116yescomplemented
38C2×#14524043C2211yescharacteristic
39C2×#14524043C2212yes—
40C2×#14524043C2211yescharacteristic
41C2×#14524043C2211yescharacteristic
42C2×#14524042C2214yes—
43C2×#14524040C2211yescharacteristic
44C2×#14524038C2214yes—
45C2×#14524035C2212yes—
46C2×#14524035C2212yes—
47C2×#14524034C2214yes—
48C2×#14524031C2212yes—
49C2×#14524029C2214yes—
50C2×#14524029C2214yes—
51C2×#14524029C2214yes—
52C2×#14524028C2214yes—
53C2×#14524028C2214yes—
54C2×#14524027C2214yes—
55C2×#14524025C2214yes—
56C2×#14524023C2214yes—
57C2×#14524023C2212yes—
58C2×#14524023C2212yes—
59C2×#14524022C2212yes—
60C2×#14524022C2212yes—
61C2×#14524021C2214yes—
62C2×#14524020C2214yes—
63C2×#14524020C2214yes—
64C2×#14524019C2212yes—
65C2×#14524017C2212yes—
66C2×#14524017C2212yes—
67C2×#14524017C2211yescharacteristic
68C2×#14524017C2211yescharacteristic
69C2×#14524017C2212yes—
70C2×#14524016C2214yes—
71C2×#14524016C2214yes—
72C2×#14524015C2214yes—
73C2×#14524014C2212yes—
74C2×#14524014C2214yes—
75C2×C4×Dic134C2212yes—
76C2×C4×Dic134C2212yes—
77C2×C4×D268C2212yes—
78C2×C4×D268C2212yes—
79C2×C4×D268C2211yescharacteristic
80C2×C4×D268C2212yes—
81C2×C4×D268C2211yescharacteristic
82C2×(C22⋊D67)⋊C4C2214yes—
83C2×#14524002C2212yes—
84C2×#14524002C2212yes—
85C2×#14524001C2214yes—
86C2×#14524001C2212yes—
87C22×C4⋊Dic67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89#529×C67C22116yescomplemented
90C2×#126×C67C2212yes—
91C2×#125×C67C2211yescharacteristic
92C2×#124×C67C2211yescharacteristic
93C2×#123×C67C2212yes—
94C2×C22⋊Q8×C67C2211yescharacteristic
95C2×#121×C67C2211yescharacteristic
96C2×C4×Q8×C67C2211yescharacteristic
97C2×C4×D4×C67C2211yescharacteristic
98C2×C4×D4×C67C2212yes—
99C2×#117×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C2×#11761628—48no—
102C2×#11761628C23116yes—
103C2×#11761627—48no—
104C2×#11761627C23116yes—
105C22×Dic134C2312yes—
106C22×Dic134C2312yes—
107C22×Dic134C2312yes—
108C22×Dic134C2314yes—
109C2×Q8×D67—48no—
110C2×Q8×D67C23116yes—
111C22×D268C2311yescharacteristic
112C22×D268C2311yescharacteristic
113C22×D268C2312yes—
114C22×D268C2312yes—
115C22×C22⋊D67C2314yes—
116C22×C22⋊D67C2312yes—
117C22×C22⋊D67C2314yes—
118C22×C22⋊D67C2312yes—
119C23×Dic67C2314yes—
120C22×C4×D67C2312yes—
121C22×C4×D67C2312yes—
122C22×C4×D67C2314yes—
123C22×C4×D67C2314yes—
124#14524043C2318yes—
125#14524043C23116yes—
126#14524043C2318yes—
127#14524043C2318yes—
128#14524042C23132yes—
129#14524040C2318yes—
130#14524038C23132yes—
131#14524035C23116yes—
132#14524035C23116yes—
133#14524034C23132yes—
134#14524031C23116yes—
135#14524029C23132yes—
136#14524029C23132yes—
137#14524029C23132yes—
138#14524028C23132yes—
139#14524028C23132yes—
140#14524027C23132yes—
141#14524025C23132yes—
142#14524023C23132yes—
143#14524023C23116yes—
144#14524023C23116yes—
145#14524022C23116yes—
146#14524022C23116yes—
147#14524021C23132yes—
148#14524020C23132yes—
149#14524020C23132yes—
150#14524019C23116yes—
151#14524017C23116yes—
152#14524017C23116yes—
153#14524017C2318yes—
154#14524017C2318yes—
155#14524017C23116yes—
156#14524016C23132yes—
157#14524016C23132yes—
158#14524015C23132yes—
159#14524014C23116yes—
160#14524014C23132yes—
161C4×Dic134C23116yes—
162C4×Dic134C23116yes—
163C4×D268C23116yes—
164C4×D268C23116yes—
165C4×D268C2318yes—
166C4×D268C23116yes—
167C4×D268C2318yes—
168(C22⋊D67)⋊C4C23132yes—
169#14524002C23116yes—
170#14524002C23116yes—
171#14524001C23132yes—
172#14524001C23116yes—
173C2×C4⋊Dic67C23116yes—
174C2×C4⋊Dic67C2312yes—
175C2×C4⋊Dic67C2311yescharacteristic
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2314yes—
178C2×C4⋊Dic67C2314yes—
179C2×C4⋊Dic67C2312yes—
180C2×C4⋊Dic67C2311yescharacteristic
181C2×C4⋊Dic67C2312yes—
182C2×C4⋊Dic67C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2314yes—
187C4⋊C4×D67C23116yes—
188C2×C22⋊Dic67C2314yes—
189C2×C22⋊Dic67C2314yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2314yes—
192C2×(C2×D67)⋊C4C2314yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×C4×Dic67C2314yes—
199C2×C4×Dic67C2314yes—
200C22×Q8×C67C2311yescharacteristic
201C22×D4×C67C2311yescharacteristic
202C22×D4×C67C2312yes—
203C23×C4×C67C2311yescharacteristic
204C23×C4×C67C2311yescharacteristic
205C23×C4×C67C2312yes—
206C23×C4×C67C2311yescharacteristic
207#126×C67C23116yes—
208#125×C67C2318yes—
209#124×C67C2318yes—
210#123×C67C23116yes—
211C22⋊Q8×C67C2318yes—
212#121×C67C2318yes—
213C4×Q8×C67C2318yes—
214C4×D4×C67C2318yes—
215C4×D4×C67C23116yes—
216#117×C67C23116yes—
217C2×C4⋊C4×C67C2312yes—
218C2×C4⋊C4×C67C2312yes—
219C2×C4⋊C4×C67C2311yescharacteristic
220C2×C4⋊C4×C67C2312yes—
221C2×C4⋊C4×C67C2311yescharacteristic
222C2×C4⋊C4×C67C2312yes—
223C2×C22⋊C4×C67C2312yes—
224C2×C22⋊C4×C67C2312yes—
225C2×C22⋊C4×C67C2312yes—
226C2×C22⋊C4×C67C2312yes—
227C2×C22⋊C4×C67C2312yes—
228C2×C42×C67C2311yescharacteristic
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2311yescharacteristic
231C2×C42×C67C2311yescharacteristic
232C2×C42×C67C2318yes—
233C2×C42×C67C2312yes—
234C23×D67C2412yes—
235C23×D67C2412yes—
236#11761628—432no—
237#11761627—432no—
238C2×Dic134—28no—
239C2×Dic134—48no—
240C2×Dic134—44no—
241C2×Dic134—44no—
242C2×Dic134C2418yes—
243C2×Dic134C2418yes—
244C2×Dic134C2418yes—
245C2×Dic134C24116yes—
246Q8×D67—432no—
247C2×D268—24no—
248C2×D268—24no—
249C2×D268—44no—
250C2×D268—44no—
251C2×D268C2414yes—
252C2×D268C2414yes—
253C2×D268C2418yes—
254C2×D268C2418yes—
255C2×C22⋊D67—48no—
256C2×C22⋊D67—48no—
257C2×C22⋊D67—44no—
258C2×C22⋊D67—44no—
259C2×C22⋊D67C24116yes—
260C2×C22⋊D67C2418yes—
261C2×C22⋊D67C24116yes—
262C2×C22⋊D67C2418yes—
263C22×Dic67—48no—
264C22×Dic67C2414yes—
265C22×Dic67C2412yes—
266C22×Dic67C2414yes—
267C22×Dic67C2412yes—
268C22×Dic67C24116yes—
269C2×C4×D67—28no—
270C2×C4×D67—28no—
271C2×C4×D67—48no—
272C2×C4×D67—48no—
273C2×C4×D67C2418yes—
274C2×C4×D67C2418yes—
275C2×C4×D67C24116yes—
276C2×C4×D67C24116yes—
277C4⋊Dic67C2418yes—
278C4⋊Dic67C2414yes—
279C4⋊Dic67C2418yes—
280C4⋊Dic67C24116yes—
281C4⋊Dic67C24116yes—
282C4⋊Dic67C2418yes—
283C4⋊Dic67C2414yes—
284C4⋊Dic67C2418yes—
285C4⋊Dic67C2418yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C24116yes—
290C22⋊Dic67C24116yes—
291C22⋊Dic67C24116yes—
292(C2×D67)⋊C4C2418yes—
293(C2×D67)⋊C4C24116yes—
294(C2×D67)⋊C4C24116yes—
295(C2×D67)⋊C4C2418yes—
296(C2×D67)⋊C4C24116yes—
297(C2×D67)⋊C4C24116yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300C4×Dic67C24116yes—
301C4×Dic67C24116yes—
302C24×C67C2412yes—
303C24×C67C2411yescharacteristic
304C2×Q8×C67—24no—
305C2×Q8×C67C2414yes—
306C2×D4×C67—24no—
307C2×D4×C67—44no—
308C2×D4×C67C2414yes—
309C2×D4×C67C2418yes—
310C22×C4×C67—24no—
311C22×C4×C67—24no—
312C22×C4×C67—28no—
313C22×C4×C67—42no—
314C22×C4×C67C2411yescharacteristic
315C22×C4×C67C2411yescharacteristic
316C22×C4×C67C2411yescharacteristic
317C22×C4×C67C2411yescharacteristic
318C22×C4×C67C2414yes—
319C22×C4×C67C2414yes—
320C22×C4×C67C2412yes—
321C22×C4×C67C2412yes—
322C22×C4×C67C2412yes—
323C22×C4×C67C2418yes—
324C22×C4×C67C2414yes—
325C22×C4×C67C2411yescharacteristic
326C22×C4×C67C2411yescharacteristic
327C4⋊C4×C67C2418yes—
328C4⋊C4×C67C2418yes—
329C4⋊C4×C67C2414yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C2414yes—
332C4⋊C4×C67C2418yes—
333C22⋊C4×C67C2418yes—
334C22⋊C4×C67C2418yes—
335C22⋊C4×C67C2418yes—
336C22⋊C4×C67C2418yes—
337C22⋊C4×C67C2418yes—
338C42×C67C2414yes—
339C42×C67C2414yes—
340C42×C67C2414yes—
341C42×C67C2414yes—
342C42×C67C2418yes—
343C23×C67—22no—
344C23×C67—24no—
345C23×C67—24no—
346C23×C67—22no—
347C23×C67—22no—
348C23×C67—24no—
349C23×C67C2514yes—
350C23×C67C2512yes—
351C23×C67C2511yescharacteristic
352C22×D67—24no—
353C22×D67—24no—
354C22×D67—24no—
355C22×D67—24no—
356C22×D67—24no—
357C22×D67—24no—
358C22×D67C2514yes—
359C22×D67C2514yes—
360Q8×C67—28no—
361D4×C67—28no—
362D4×C67—48no—
363C2×C4×C67—22no—
364C2×C4×C67—24no—
365C2×C4×C67—22no—
366C2×C4×C67—24no—
367C2×C4×C67—22no—
368C2×C4×C67—22no—
369C2×C4×C67—24no—
370C2×C4×C67—28no—
371C2×C4×C67—28no—
372C2×C4×C67—216no—
373C2×C4×C67—44no—
374C2×C4×C67H(5,𝔽2)14yes—
375C2×C4×C672−1+414yes—
376C2×C4×C67C2512yes—
377C2×C4×C67C2512yes—
378C2×C4×C67C2512yes—
379C2×C4×C67C2512yes—
380C2×C4×C67C2514yes—
381C2×C4×C67C2514yes—
382C2×C4×C67C2514yes—
383C2×C4×C67C2512yes—
384C2×C4×C67C2512yes—
385C22⋊D67—416no—
386C22⋊D67—416no—
387C22⋊D67—48no—
388C22⋊D67—48no—
389C2×Dic67—24no—
390C2×Dic67—24no—
391C2×Dic67—28no—
392C2×Dic67—28no—
393C2×Dic67—416no—
394C2×Dic67C2518yes—
395C2×Dic67C2514yes—
396C2×Dic67C2518yes—
397C2×Dic67C2514yes—
398D268—28no—
399D268—28no—
400D268—48no—
401D268—48no—
402C4×D67—216no—
403C4×D67—216no—
404C4×D67—416no—
405C4×D67—416no—
406Dic134—216no—
407Dic134—416no—
408Dic134—48no—
409Dic134—48no—
410C22×C67—24no—
411C22×C67—22no—
412C22×C67—24no—
413C22×C67—22no—
414C22×C67—24no—
415C22×C67—22no—
416C22×C67—44no—
417C22×C67—48no—
418C22×C67C2×H(5,𝔽2)12yes—
419C22×C67C2×2−1+412yes—
420C22×C67#58512yes—
421C22×C67C2611yescharacteristic
422C2×D67—24no—
423C2×D67—24no—
424C2×D67—24no—
425C2×D67—24no—
426C2×D67—24no—
427C2×D67—24no—
428C2×D67—48no—
429C2×D67—48no—
430C4×C67—24no—
431C4×C67—22no—
432C4×C67—22no—
433C4×C67—24no—
434C4×C67—22no—
435C4×C67—24no—
436C4×C67—22no—
437C4×C67C2×H(5,𝔽2)14yes—
438C4×C67C2×2−1+414yes—
439Dic67—28no—
440Dic67—24no—
441Dic67—24no—
442Dic67—28no—
443C2×#3547—671nomaximal, Sylow
444C2×C67—44no—
445C2×C67—42no—
446C2×C67#354714yescomplemented
447C2×C67C22×H(5,𝔽2)11yescharacteristic
448C2×C67C22×2−1+411yescharacteristic
449C2×C67C2×#58511yescharacteristic
450D67—44no—
451D67—44no—
452#3547—6732no—
453C2×#562—674no—
454C2×#555—672no—
455C2×#555—671no—
456C2×#554—671no—
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×#529D6711yescharacteristic, complemented
470C67C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—672no—
472C22×#41—672no—
473C23×Q8—672no—
474#562—6764no—
475#555—6732no—
476#555—6716no—
477#554—6716no—
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—674no—
491C2×C4⋊Q8—671no—
492C2×C4⋊Q8—671no—
493C2×C4⋊Q8—671no—
494C2×C4⋊Q8—672no—
495C2×#127—671no—
496#529C2×D67116yescomplemented
497C2×#126—674no—
498C2×#126C2×D6712yes—
499C2×#125—674no—
500C2×#125—672no—
501C2×#125—672no—
502C2×#125C2×D6711yescharacteristic
503C2×#124—674no—
504C2×#124—674no—
505C2×#124—674no—
506C2×#124—672no—
507C2×#124C2×D6711yescharacteristic
508C2×#123—674no—
509C2×#123—674no—
510C2×#123—674no—
511C2×#123—674no—
512C2×#123C2×D6712yes—
513C2×C22⋊Q8—672no—
514C2×C22⋊Q8—672no—
515C2×C22⋊Q8—672no—
516C2×C22⋊Q8—672no—
517C2×C22⋊Q8—672no—
518C2×C22⋊Q8—674no—
519C2×C22⋊Q8—674no—
520C2×C22⋊Q8—674no—
521C2×C22⋊Q8—674no—
522C2×C22⋊Q8C2×D6711yescharacteristic
523C2×#121—672no—
524C2×#121—674no—
525C2×#121—674no—
526C2×#121—671no—
527C2×#121—671no—
528C2×#121—672no—
529C2×#121—672no—
530C2×#121—672no—
531C2×#121—674no—
532C2×#121—674no—
533C2×#121C2×D6711yescharacteristic
534C2×C4×Q8—672no—
535C2×C4×Q8—672no—
536C2×C4×Q8C2×D6711yescharacteristic
537C2×C4×D4—674no—
538C2×C4×D4—671no—
539C2×C4×D4—672no—
540C2×C4×D4—671no—
541C2×C4×D4—672no—
542C2×C4×D4—672no—
543C2×C4×D4C2×D6711yescharacteristic
544C2×C4×D4C2×D6712yes—
545C2×#117—672no—
546C2×#117—672no—
547C2×#117—672no—
548C2×#117—674no—
549C2×#117C2×D6712yes—
550C22×C4⋊C4—672no—
551C22×C4⋊C4—672no—
552C22×C42C2×D6711yescharacteristic
553C2×#41—2688no—
554C2×#41—2688no—
555C2×#41—6716no—
556C2×#41—6716no—
557C22×Q8—2688no—
558C22×Q8—6716no—
559C22×Q8—672no—
560C22×Q8—674no—
561C22×Q8—672no—
562C22×Q8—672no—
563C22×Q8C22×D6711yescharacteristic
564C22×D4—674no—
565C22×D4—672no—
566C22×D4—674no—
567C22×D4—672no—
568C22×D4—672no—
569C22×D4—672no—
570C22×D4—671no—
571C22×D4—671no—
572C22×D4C22×D6711yescharacteristic
573C22×D4C22×D6712yes—
574C23×C4—674no—
575C23×C4—674no—
576C23×C4—674no—
577C23×C4—672no—
578C23×C4—672no—
579C23×C4C22×D6712yes—
580C23×C4C22×D6711yescharacteristic
581C23×C4C22×D6711yescharacteristic
582C23×C4C22×D6711yescharacteristic
583C4⋊Q8—6732no—
584C4⋊Q8—678no—
585C4⋊Q8—678no—
586C4⋊Q8—678no—
587C4⋊Q8—6716no—
588#127—678no—
589#126—6732no—
590#126C22×D67116yes—
591#125—6732no—
592#125—6716no—
593#125—6716no—
594#125C22×D6718yes—
595#124—6732no—
596#124—6732no—
597#124—6732no—
598#124—6716no—
599#124C22×D6718yes—
600#123—6732no—
601#123—6732no—
602#123—6732no—
603#123—6732no—
604#123C22×D67116yes—
605C22⋊Q8—6716no—
606C22⋊Q8—6716no—
607C22⋊Q8—6716no—
608C22⋊Q8—6716no—
609C22⋊Q8—6716no—
610C22⋊Q8—6732no—
611C22⋊Q8—6732no—
612C22⋊Q8—6732no—
613C22⋊Q8—6732no—
614C22⋊Q8C22×D6718yes—
615#121—6716no—
616#121—6732no—
617#121—6732no—
618#121—678no—
619#121—678no—
620#121—6716no—
621#121—6716no—
622#121—6716no—
623#121—6732no—
624#121—6732no—
625#121C22×D6718yes—
626C4×Q8—6716no—
627C4×Q8—6716no—
628C4×Q8C22×D6718yes—
629C4×D4—6732no—
630C4×D4—678no—
631C4×D4—6716no—
632C4×D4—678no—
633C4×D4—6716no—
634C4×D4—6716no—
635C4×D4C22×D6718yes—
636C4×D4C22×D67116yes—
637#117—6716no—
638#117—6716no—
639#117—6716no—
640#117—6732no—
641#117C22×D67116yes—
642C2×C4⋊C4—671no—
643C2×C4⋊C4—672no—
644C2×C4⋊C4—672no—
645C2×C4⋊C4—674no—
646C2×C4⋊C4—674no—
647C2×C4⋊C4—6716no—
648C2×C4⋊C4—672no—
649C2×C4⋊C4—671no—
650C2×C4⋊C4—674no—
651C2×C4⋊C4—672no—
652C2×C4⋊C4—674no—
653C2×C4⋊C4—674no—
654C2×C4⋊C4—674no—
655C2×C4⋊C4—672no—
656C2×C4⋊C4—6716no—
657C2×C4⋊C4C22×D6711yescharacteristic
658C2×C4⋊C4C22×D6711yescharacteristic
659C2×C4⋊C4C22×D6712yes—
660C2×C4⋊C4C22×D6712yes—
661C2×C4⋊C4C22×D6712yes—
662C2×C4⋊C4C22×D6712yes—
663C2×C22⋊C4—674no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4—672no—
666C2×C22⋊C4—674no—
667C2×C22⋊C4—674no—
668C2×C22⋊C4—672no—
669C2×C22⋊C4—674no—
670C2×C22⋊C4—672no—
671C2×C22⋊C4—674no—
672C2×C22⋊C4—672no—
673C2×C22⋊C4C22×D6712yes—
674C2×C22⋊C4C22×D6712yes—
675C2×C22⋊C4C22×D6712yes—
676C2×C22⋊C4C22×D6712yes—
677C2×C22⋊C4C22×D6712yes—
678C2×C42—674no—
679C2×C42—674no—
680C2×C42C22×D6711yescharacteristic
681C2×C42C22×D6712yes—
682C2×C42C22×D6711yescharacteristic
683C2×C42C22×D6711yescharacteristic
684C2×C42C22×D6711yescharacteristic
685C2×C42C22×D6718yes—
686C24—672no—
687C24—672no—
688C24C23×D6711yescharacteristic
689C24C23×D6712yes—
690#41—26832no—
691#41—26832no—
692C2×Q8—24no—
693C2×Q8—2688no—
694C2×Q8—2684no—
695C2×Q8—2684no—
696C2×Q8—26832no—
697C2×Q8—678no—
698C2×Q8—6716no—
699C2×Q8—678no—
700C2×Q8—678no—
701C2×Q8—1348no—
702C2×Q8C23×D6714yes—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—2684no—
706C2×D4—2684no—
707C2×D4—2684no—
708C2×D4—2688no—
709C2×D4—2684no—
710C2×D4—2688no—
711C2×D4—6716no—
712C2×D4—678no—
713C2×D4—6716no—
714C2×D4—678no—
715C2×D4—678no—
716C2×D4—678no—
717C2×D4—674no—
718C2×D4—674no—
719C2×D4—1344no—
720C2×D4—1344no—
721C2×D4C23×D6714yes—
722C2×D4C23×D6718yes—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—2688no—
728C22×C4—2688no—
729C22×C4—2688no—
730C22×C4—6716no—
731C22×C4—6716no—
732C22×C4—6716no—
733C22×C4—674no—
734C22×C4—672no—
735C22×C4—674no—
736C22×C4—672no—
737C22×C4—678no—
738C22×C4—678no—
739C22×C4—1348no—
740C22×C4—1348no—
741C22×C4C23×D6714yes—
742C22×C4C23×D6714yes—
743C22×C4C23×D6718yes—
744C22×C4C23×D6711yescharacteristic
745C22×C4C23×D6712yes—
746C22×C4C23×D6711yescharacteristic
747C22×C4C23×D6711yescharacteristic
748C22×C4C23×D6711yescharacteristic
749C22×C4C23×D6712yes—
750C22×C4C23×D6712yes—
751C22×C4C23×D6714yes—
752C22×C4C23×D6711yescharacteristic
753C22×C4C23×D6711yescharacteristic
754C4⋊C4—674no—
755C4⋊C4—678no—
756C4⋊C4—678no—
757C4⋊C4—6716no—
758C4⋊C4—6716no—
759C4⋊C4—678no—
760C4⋊C4—674no—
761C4⋊C4—6716no—
762C4⋊C4—678no—
763C4⋊C4—6716no—
764C4⋊C4—6716no—
765C4⋊C4—6716no—
766C4⋊C4—678no—
767C4⋊C4C23×D6714yes—
768C4⋊C4C23×D6714yes—
769C4⋊C4C23×D6718yes—
770C4⋊C4C23×D6718yes—
771C4⋊C4C23×D6718yes—
772C4⋊C4C23×D6718yes—
773C22⋊C4—6716no—
774C22⋊C4—6716no—
775C22⋊C4—678no—
776C22⋊C4—6716no—
777C22⋊C4—6716no—
778C22⋊C4—678no—
779C22⋊C4—6716no—
780C22⋊C4—678no—
781C22⋊C4—6716no—
782C22⋊C4—678no—
783C22⋊C4C23×D6718yes—
784C22⋊C4C23×D6718yes—
785C22⋊C4C23×D6718yes—
786C22⋊C4C23×D6718yes—
787C22⋊C4C23×D6718yes—
788C42—6716no—
789C42—6716no—
790C42C23×D6714yes—
791C42C23×D6714yes—
792C42C23×D6714yes—
793C42C23×D6714yes—
794C42C23×D6718yes—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—674no—
802C23—674no—
803C23—1344no—
804C23—1344no—
805C23—1344no—
806C23—1344no—
807C23—1344no—
808C23—1344no—
809C23C24×D6712yes—
810C23C24×D6714yes—
811C23C24×D6711yescharacteristic
812Q8—28no—
813Q8—26816no—
814Q8—2688no—
815Q8—2688no—
816Q8—13416no—
817D4—28no—
818D4—48no—
819D4—2688no—
820D4—2688no—
821D4—2688no—
822D4—26816no—
823D4—2688no—
824D4—26816no—
825D4—1348no—
826D4—1348no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—26816no—
839C2×C4—26816no—
840C2×C4—26816no—
841C2×C4—678no—
842C2×C4—674no—
843C2×C4—678no—
844C2×C4—674no—
845C2×C4—1344no—
846C2×C4—1348no—
847C2×C4—1344no—
848C2×C4—1348no—
849C2×C4—13416no—
850C2×C4—13416no—
851C2×C4#1452408914yes—
852C2×C4#1452409014yes—
853C2×C4C24×D6712yes—
854C2×C4C24×D6714yes—
855C2×C4C24×D6712yes—
856C2×C4C24×D6712yes—
857C2×C4C24×D6712yes—
858C2×C4C24×D6714yes—
859C2×C4C24×D6714yes—
860C2×C4C24×D6712yes—
861C2×C4C24×D6712yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—2688no—
871C22—2688no—
872C22—1344no—
873C22—1344no—
874C22—1344no—
875C22—1344no—
876C22—1344no—
877C22—1344no—
878C22C2×#1452408912yes—
879C22C2×#1452409012yes—
880C22#1686423212yes—
881C22C25×D6711yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—1344no—
890C4—1348no—
891C4—1344no—
892C4—1348no—
893C4C2×#1452408914yes—
894C4C2×#1452409014yes—
895C2—42no—
896C2—44no—
897C2—2684no—
898C2—2684no—
899C2#2257460014yesdirect product factor
900C2C22×#1452408911yescharacteristic
901C2C22×#1452409011yescharacteristic
902C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
hypercenterC2×#529D67
hypocenterC67C2×#3547
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574600C2direct (N × H)
2. C2×#16864143C2semidirect
3. C2×#16864111C2semidirect
4. C2×#16864111C2semidirect
5. C2×#16864106C2semidirect
6. C2×#16864092C2semidirect
7. C2×#16864084C2semidirect
8. C2×Q8×D268C2semidirect
9. C2×#16864054C2semidirect
10. C2×#16864050C2semidirect
11. C2×#16864024C2semidirect
12. C2×#16864012C2semidirect
13. C2×#16864001C2semidirect
14. C2×#16863975C2semidirect
15. C2×#16863969C2semidirect
16. C2×#16863953C2semidirect
17. C2×#16863946C2semidirect
18. C2×#529×C67C2semidirect
22. #16864143C22semidirect
23. #16864111C22semidirect
24. #16864111C22semidirect
25. #16864106C22semidirect
26. #16864092C22semidirect
27. #16864084C22semidirect
28. Q8×D268C22semidirect
29. #16864054C22semidirect
30. #16864050C22semidirect
31. #16864024C22semidirect
32. #16864012C22semidirect
33. #16864001C22semidirect
34. #16863975C22semidirect
35. #16863969C22semidirect
36. #16863953C22semidirect
37. #16863946C22semidirect
89. #529×C67C22semidirect
446. C2×C67#3547semidirect
469. C2×#529D67semidirect
470. C67C2×#3547semidirect
496. #529C2×D67semidirect
899. C2#22574600direct (N × H)

Maximal subgroups

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

subgroupindex
#225746002
C2×#168641432
C2×#168641112
C2×#168641062
C2×#168640922
C2×#168640842
C2×Q8×D2682
C2×#168640542
C2×#168640502
C2×#168640242
C2×#168640122
C2×#168640012
C2×#168639752
C2×#168639692
C2×#168639532
C2×#168639462
C2×#529×C672
C2×#354767