Finite Group Databasebeta

← C2×#22574680 #31763460

Subgroups — C2×#22574680 #31763460

Order 17152.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574680C2132yesmaximal, direct product factor
2C2×#16864142C214yesmaximal, complemented
3C2×#16864131C211yesmaximal, characteristic, complemented
4C2×#16864131C212yesmaximal, complemented
5C2×#16864124C211yesmaximal, characteristic, complemented
6C2×#16864106C212yesmaximal, complemented
7C2×#16864068C211yesmaximal, characteristic, complemented
8C2×Q8×D268C211yesmaximal, characteristic, complemented
9C2×#16864056C212yesmaximal, complemented
10C2×#16864048C212yesmaximal, complemented
11C2×#16864020C212yesmaximal, complemented
12C2×#16864017C212yesmaximal, complemented
13C2×#16864001C212yesmaximal, complemented
14C2×#16863994C214yesmaximal, complemented
15C2×#16863971C212yesmaximal, complemented
16C2×#16863946C211yesmaximal, characteristic, complemented
17C2×#16863930C211yesmaximal, characteristic, complemented
18C2×#533×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2212yes—
20C22×#11761628C2212yes—
21C22×Q8×D67C2212yes—
22#16864142C22164yescomplemented
23#16864131C22116yescomplemented
24#16864131C22132yescomplemented
25#16864124C22116yescomplemented
26#16864106C22132yescomplemented
27#16864068C22116yescomplemented
28Q8×D268C22116yescomplemented
29#16864056C22132yescomplemented
30#16864048C22132yescomplemented
31#16864020C22132yescomplemented
32#16864017C22132yescomplemented
33#16864001C22132yescomplemented
34#16863994C22164yescomplemented
35#16863971C22132yescomplemented
36#16863946C22116yescomplemented
37C2×#14524043C2212yes—
38C2×#14524043C2211yescharacteristic
39C2×#14524041C2212yes—
40C2×#14524040C2212yes—
41C2×#14524040C2211yescharacteristic
42#16863930C22116yescomplemented
43C2×#14524038C2214yes—
44C2×#14524037C2212yes—
45C2×#14524035C2212yes—
46C2×#14524035C2211yescharacteristic
47C2×#14524033C2214yes—
48C2×#14524032C2214yes—
49C2×#14524032C2212yes—
50C2×#14524031C2212yes—
51C2×#14524031C2212yes—
52C2×#14524031C2211yescharacteristic
53C2×#14524029C2214yes—
54C2×#14524028C2214yes—
55C2×#14524028C2214yes—
56C2×#14524028C2214yes—
57C2×#14524028C2214yes—
58C2×#14524028C2214yes—
59C2×#14524026C2212yes—
60C2×#14524025C2214yes—
61C2×#14524023C2212yes—
62C2×#14524023C2214yes—
63C2×#14524022C2211yescharacteristic
64C2×#14524021C2214yes—
65C2×#14524021C2214yes—
66C2×#14524021C2214yes—
67C2×#14524019C2214yes—
68C2×#14524018C2212yes—
69C2×#14524018C2214yes—
70C2×#14524017C2211yescharacteristic
71C2×#14524017C2212yes—
72C2×#14524017C2212yes—
73C2×#14524016C2214yes—
74C2×#14524016C2214yes—
75C2×C4×Dic134C2212yes—
76C2×C4×Dic134C2211yescharacteristic
77C2×#14524008C2212yes—
78C2×C4×D268C2212yes—
79C2×C4×D268C2212yes—
80C2×C4×D268C2212yes—
81C2×C4×D268C2211yescharacteristic
82C2×C4×D268C2212yes—
83C2×C4×D268C2212yes—
84C2×#14524005C2212yes—
85C2×#14524005C2214yes—
86C2×C4×C22⋊D67C2212yes—
87C2×#14524000C2212yes—
88C2×C4⋊C4×D67C2214yes—
89#533×C67C22116yescomplemented
90C2×C4⋊Q8×C67C2211yescharacteristic
91C2×C4⋊Q8×C67C2211yescharacteristic
92C2×#125×C67C2212yes—
93C2×C22⋊Q8×C67C2211yescharacteristic
94C2×C22⋊Q8×C67C2211yescharacteristic
95C2×C22⋊Q8×C67C2212yes—
96C2×C4×Q8×C67C2211yescharacteristic
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×Q8×C67C2212yes—
99C2×#117×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C2×#11761629—48no—
102C2×#11761629C23116yes—
103C2×#11761628—48no—
104C2×#11761628C23116yes—
105C22×Dic134C2312yes—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2314yes—
108C2×Q8×D67—48no—
109C2×Q8×D67C23116yes—
110C22×D268C2312yes—
111C22×D268C2311yescharacteristic
112C22×D268C2312yes—
113C22×D268C2314yes—
114C22×D268C2312yes—
115C22×D268C2314yes—
116C22×C22⋊D67C2312yes—
117C22×C22⋊D67C2314yes—
118C22×C4×D67C2312yes—
119C22×C4×D67C2314yes—
120C22×C4×D67C2314yes—
121C22×C4×D67C2314yes—
122C22×C4×D67C2314yes—
123#14524043C23116yes—
124#14524043C2318yes—
125#14524041C23116yes—
126#14524040C23116yes—
127#14524040C2318yes—
128#14524038C23132yes—
129#14524037C23116yes—
130#14524035C23116yes—
131#14524035C2318yes—
132#14524033C23132yes—
133#14524032C23132yes—
134#14524032C23116yes—
135#14524031C23116yes—
136#14524031C23116yes—
137#14524031C2318yes—
138#14524029C23132yes—
139#14524028C23132yes—
140#14524028C23132yes—
141#14524028C23132yes—
142#14524028C23132yes—
143#14524028C23132yes—
144#14524026C23116yes—
145#14524025C23132yes—
146#14524023C23116yes—
147#14524023C23132yes—
148#14524022C2318yes—
149#14524021C23132yes—
150#14524021C23132yes—
151#14524021C23132yes—
152#14524019C23132yes—
153#14524018C23116yes—
154#14524018C23132yes—
155#14524017C2318yes—
156#14524017C23116yes—
157#14524017C23116yes—
158#14524016C23132yes—
159#14524016C23132yes—
160C4×Dic134C23116yes—
161C4×Dic134C2318yes—
162#14524008C23116yes—
163C4×D268C23116yes—
164C4×D268C23116yes—
165C4×D268C23116yes—
166C4×D268C2318yes—
167C4×D268C23116yes—
168C4×D268C23116yes—
169#14524005C23116yes—
170#14524005C23132yes—
171C4×C22⋊D67C23116yes—
172#14524000C23116yes—
173C2×C4⋊Dic67C2314yes—
174C2×C4⋊Dic67C2311yescharacteristic
175C2×C4⋊Dic67C2311yescharacteristic
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2312yes—
178C2×Dic67⋊C4C2312yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C4⋊C4×D67C23132yes—
186C2×C22⋊Dic67C2312yes—
187C2×(C2×D67)⋊C4C2312yes—
188C2×(C2×D67)⋊C4C2312yes—
189C2×(C2×D67)⋊C4C2312yes—
190C2×(C2×D67)⋊C4C2314yes—
191C2×(C2×D67)⋊C4C2314yes—
192C2×(C2×D67)⋊C4C2314yes—
193C2×(C2×D67)⋊C4C2314yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×C4×Dic67C2312yes—
199C2×C4×Dic67C2314yes—
200C22×Q8×C67C2311yescharacteristic
201C22×Q8×C67C2311yescharacteristic
202C22×Q8×C67C2312yes—
203C23×C4×C67C2311yescharacteristic
204C23×C4×C67C2311yescharacteristic
205C23×C4×C67C2311yescharacteristic
206C4⋊Q8×C67C2318yes—
207C4⋊Q8×C67C2318yes—
208#125×C67C23116yes—
209C22⋊Q8×C67C2318yes—
210C22⋊Q8×C67C2318yes—
211C22⋊Q8×C67C23116yes—
212C4×Q8×C67C2318yes—
213C4×Q8×C67C2318yes—
214C4×Q8×C67C23116yes—
215#117×C67C23116yes—
216C2×C4⋊C4×C67C2312yes—
217C2×C4⋊C4×C67C2312yes—
218C2×C4⋊C4×C67C2312yes—
219C2×C4⋊C4×C67C2312yes—
220C2×C4⋊C4×C67C2312yes—
221C2×C4⋊C4×C67C2312yes—
222C2×C4⋊C4×C67C2311yescharacteristic
223C2×C4⋊C4×C67C2311yescharacteristic
224C2×C4⋊C4×C67C2312yes—
225C2×C22⋊C4×C67C2312yes—
226C2×C22⋊C4×C67C2312yes—
227C2×C42×C67C2311yescharacteristic
228C2×C42×C67C2311yescharacteristic
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2311yescharacteristic
231C2×C42×C67C2318yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2312yes—
234C23×D67C2412yes—
235C23×D67C2414yes—
236#11761629—432no—
237#11761628—432no—
238C2×Dic134—28no—
239C2×Dic134—24no—
240C2×Dic134—48no—
241C2×Dic134C2418yes—
242C2×Dic134C2414yes—
243C2×Dic134C24116yes—
244Q8×D67—432no—
245C2×D268—28no—
246C2×D268—24no—
247C2×D268—28no—
248C2×D268—44no—
249C2×D268—48no—
250C2×D268—48no—
251C2×D268C2418yes—
252C2×D268C2414yes—
253C2×D268C2418yes—
254C2×D268C24116yes—
255C2×D268C2418yes—
256C2×D268C24116yes—
257C2×C22⋊D67—44no—
258C2×C22⋊D67—48no—
259C2×C22⋊D67C2418yes—
260C2×C22⋊D67C24116yes—
261C22×Dic67C2412yes—
262C22×Dic67C2412yes—
263C22×Dic67C2414yes—
264C22×Dic67C2412yes—
265C2×C4×D67—28no—
266C2×C4×D67—48no—
267C2×C4×D67—48no—
268C2×C4×D67—48no—
269C2×C4×D67—48no—
270C2×C4×D67C2418yes—
271C2×C4×D67C24116yes—
272C2×C4×D67C24116yes—
273C2×C4×D67C24116yes—
274C2×C4×D67C24116yes—
275C4⋊Dic67C24116yes—
276C4⋊Dic67C2414yes—
277C4⋊Dic67C2414yes—
278C4⋊Dic67C2418yes—
279C4⋊Dic67C2418yes—
280Dic67⋊C4C2418yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C2418yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C2418yes—
287C22⋊Dic67C2418yes—
288(C2×D67)⋊C4C2418yes—
289(C2×D67)⋊C4C2418yes—
290(C2×D67)⋊C4C2418yes—
291(C2×D67)⋊C4C24116yes—
292(C2×D67)⋊C4C24116yes—
293(C2×D67)⋊C4C24116yes—
294(C2×D67)⋊C4C24116yes—
295(C2×D67)⋊C4C24116yes—
296(C2×D67)⋊C4C24116yes—
297(C2×D67)⋊C4C24116yes—
298(C2×D67)⋊C4C2418yes—
299C4×Dic67C2418yes—
300C4×Dic67C24116yes—
301C24×C67C2411yescharacteristic
302C2×Q8×C67—24no—
303C2×Q8×C67—24no—
304C2×Q8×C67—44no—
305C2×Q8×C67C2414yes—
306C2×Q8×C67C2414yes—
307C2×Q8×C67C2418yes—
308C22×C4×C67—24no—
309C22×C4×C67—24no—
310C22×C4×C67—42no—
311C22×C4×C67C2411yescharacteristic
312C22×C4×C67C2411yescharacteristic
313C22×C4×C67C2411yescharacteristic
314C22×C4×C67C2411yescharacteristic
315C22×C4×C67C2414yes—
316C22×C4×C67C2414yes—
317C22×C4×C67C2412yes—
318C22×C4×C67C2412yes—
319C22×C4×C67C2412yes—
320C22×C4×C67C2412yes—
321C22×C4×C67C2414yes—
322C22×C4×C67C2411yescharacteristic
323C22×C4×C67C2411yescharacteristic
324C4⋊C4×C67C2418yes—
325C4⋊C4×C67C2418yes—
326C4⋊C4×C67C2418yes—
327C4⋊C4×C67C2418yes—
328C4⋊C4×C67C2418yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2414yes—
331C4⋊C4×C67C2414yes—
332C4⋊C4×C67C2418yes—
333C22⋊C4×C67C2418yes—
334C22⋊C4×C67C2418yes—
335C42×C67C2414yes—
336C42×C67C2414yes—
337C42×C67C2414yes—
338C42×C67C2414yes—
339C42×C67C2418yes—
340C42×C67C2418yes—
341C23×C67—22no—
342C23×C67—22no—
343C23×C67—22no—
344C23×C67C2512yes—
345C23×C67C2511yescharacteristic
346C22×D67—24no—
347C22×D67—28no—
348C22×D67—24no—
349C22×D67—28no—
350C22×D67—28no—
351C22×D67—24no—
352C22×D67C2514yes—
353C22×D67C2518yes—
354Q8×C67—28no—
355Q8×C67—28no—
356Q8×C67—48no—
357C2×C4×C67—22no—
358C2×C4×C67—24no—
359C2×C4×C67—24no—
360C2×C4×C67—22no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—24no—
364C2×C4×C67—24no—
365C2×C4×C67—28no—
366C2×C4×C67—28no—
367C2×C4×C67—44no—
368C2×C4×C67H(5,𝔽2)14yes—
369C2×C4×C672−1+414yes—
370C2×C4×C67C2512yes—
371C2×C4×C67C2512yes—
372C2×C4×C67C2512yes—
373C2×C4×C67C2512yes—
374C2×C4×C67C2514yes—
375C2×C4×C67C2514yes—
376C2×C4×C67C2514yes—
377C2×C4×C67C2514yes—
378C2×C4×C67C2512yes—
379C2×C4×C67C2512yes—
380C22⋊D67—48no—
381C22⋊D67—416no—
382C2×Dic67—24no—
383C2×Dic67—28no—
384C2×Dic67—24no—
385C2×Dic67—24no—
386C2×Dic67C2514yes—
387C2×Dic67C2514yes—
388C2×Dic67C2518yes—
389C2×Dic67C2514yes—
390D268—216no—
391D268—28no—
392D268—216no—
393D268—48no—
394D268—416no—
395D268—416no—
396C4×D67—216no—
397C4×D67—416no—
398C4×D67—416no—
399C4×D67—416no—
400C4×D67—416no—
401Dic134—216no—
402Dic134—28no—
403Dic134—416no—
404C22×C67—22no—
405C22×C67—22no—
406C22×C67—22no—
407C22×C67—44no—
408C22×C67C2×H(5,𝔽2)12yes—
409C22×C67C2×2−1+412yes—
410C22×C67#58512yes—
411C22×C67C2611yescharacteristic
412C2×D67—24no—
413C2×D67—28no—
414C2×D67—24no—
415C2×D67—28no—
416C2×D67—28no—
417C2×D67—24no—
418C2×D67—48no—
419C2×D67—416no—
420C4×C67—24no—
421C4×C67—22no—
422C4×C67—24no—
423C4×C67—22no—
424C4×C67—24no—
425C4×C67—22no—
426C4×C67—24no—
427C4×C67—22no—
428C4×C67C2×H(5,𝔽2)14yes—
429C4×C67C2×2−1+414yes—
430Dic67—28no—
431Dic67—24no—
432Dic67—24no—
433Dic67—24no—
434C2×#3554—671nomaximal, Sylow
435C2×C67—42no—
436C2×C67#355414yescomplemented
437C2×C67C22×H(5,𝔽2)11yescharacteristic
438C2×C67C22×2−1+411yescharacteristic
439C2×C67C2×#58511yescharacteristic
440D67—44no—
441D67—48no—
442#3554—6732no—
443C2×#562—674no—
444C2×#559—672no—
445C2×#559—671no—
446C2×#557—671no—
447C2×#554—672no—
448C2×#550—671no—
449C2×D4×Q8—671no—
450C2×#548—672no—
451C2×#547—672no—
452C2×#542—672no—
453C2×#542—672no—
454C2×#540—672no—
455C2×#539—674no—
456C2×#536—672no—
457C2×#533D6711yescharacteristic, complemented
458C2×#532—671no—
459C2×#529—671no—
460C67C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—672no—
462C22×#41—672no—
463C23×Q8—672no—
464#562—6764no—
465#559—6732no—
466#559—6716no—
467#557—6716no—
468#554—6732no—
469#550—6716no—
470D4×Q8—6716no—
471#548—6732no—
472#547—6732no—
473#542—6732no—
474#542—6732no—
475#540—6732no—
476#539—6764no—
477#536—6732no—
478#533C2×D67116yescomplemented
479#532—6716no—
480C2×C4⋊Q8—672no—
481C2×C4⋊Q8—671no—
482C2×C4⋊Q8—672no—
483C2×C4⋊Q8C2×D6711yescharacteristic
484C2×C4⋊Q8C2×D6711yescharacteristic
485C2×#127—671no—
486C2×#127—672no—
487#529—6716no—
488C2×#126—674no—
489C2×#126—672no—
490C2×#125—674no—
491C2×#125—671no—
492C2×#125—672no—
493C2×#125C2×D6712yes—
494C2×#124—672no—
495C2×#124—674no—
496C2×#124—674no—
497C2×#124—671no—
498C2×#124—672no—
499C2×#124—672no—
500C2×#123—672no—
501C2×#123—674no—
502C2×#123—674no—
503C2×#123—674no—
504C2×#123—674no—
505C2×#123—674no—
506C2×#123—674no—
507C2×C22⋊Q8—674no—
508C2×C22⋊Q8—671no—
509C2×C22⋊Q8—674no—
510C2×C22⋊Q8—674no—
511C2×C22⋊Q8—674no—
512C2×C22⋊Q8—674no—
513C2×C22⋊Q8—672no—
514C2×C22⋊Q8C2×D6711yescharacteristic
515C2×C22⋊Q8C2×D6711yescharacteristic
516C2×C22⋊Q8C2×D6712yes—
517C2×#121—671no—
518C2×#121—672no—
519C2×#121—672no—
520C2×#121—674no—
521C2×#121—672no—
522C2×#121—674no—
523C2×#121—674no—
524C2×C4×Q8—672no—
525C2×C4×Q8—671no—
526C2×C4×Q8—672no—
527C2×C4×Q8C2×D6711yescharacteristic
528C2×C4×Q8C2×D6711yescharacteristic
529C2×C4×Q8C2×D6712yes—
530C2×C4×D4—672no—
531C2×C4×D4—674no—
532C2×C4×D4—672no—
533C2×C4×D4—671no—
534C2×C4×D4—672no—
535C2×C4×D4—672no—
536C2×C4×D4—672no—
537C2×C4×D4—672no—
538C2×C4×D4—672no—
539C2×#117—672no—
540C2×#117C2×D6712yes—
541C22×C4⋊C4—674no—
542C22×C42C2×D6711yescharacteristic
543C2×#41—2688no—
544C2×#41—2688no—
545C2×#41—6716no—
546C2×#41—6716no—
547C22×Q8—2688no—
548C22×Q8—6716no—
549C22×Q8—674no—
550C22×Q8—671no—
551C22×Q8—672no—
552C22×Q8C22×D6711yescharacteristic
553C22×Q8C22×D6711yescharacteristic
554C22×Q8C22×D6712yes—
555C22×D4—672no—
556C22×D4—674no—
557C22×D4—672no—
558C22×D4—674no—
559C22×D4—674no—
560C22×D4—671no—
561C22×D4—672no—
562C22×D4—672no—
563C23×C4—674no—
564C23×C4—674no—
565C23×C4—674no—
566C23×C4—674no—
567C23×C4—672no—
568C23×C4C22×D6711yescharacteristic
569C23×C4C22×D6711yescharacteristic
570C23×C4C22×D6711yescharacteristic
571C4⋊Q8—6716no—
572C4⋊Q8—678no—
573C4⋊Q8—6716no—
574C4⋊Q8C22×D6718yes—
575C4⋊Q8C22×D6718yes—
576#127—678no—
577#127—6716no—
578#126—6732no—
579#126—6716no—
580#125—6732no—
581#125—678no—
582#125—6716no—
583#125C22×D67116yes—
584#124—6716no—
585#124—6732no—
586#124—6732no—
587#124—678no—
588#124—6716no—
589#124—6716no—
590#123—6716no—
591#123—6732no—
592#123—6732no—
593#123—6732no—
594#123—6732no—
595#123—6732no—
596#123—6732no—
597C22⋊Q8—6732no—
598C22⋊Q8—678no—
599C22⋊Q8—6732no—
600C22⋊Q8—6732no—
601C22⋊Q8—6732no—
602C22⋊Q8—6732no—
603C22⋊Q8—6716no—
604C22⋊Q8C22×D6718yes—
605C22⋊Q8C22×D6718yes—
606C22⋊Q8C22×D67116yes—
607#121—678no—
608#121—6716no—
609#121—6716no—
610#121—6732no—
611#121—6716no—
612#121—6732no—
613#121—6732no—
614C4×Q8—6716no—
615C4×Q8—678no—
616C4×Q8—6716no—
617C4×Q8C22×D6718yes—
618C4×Q8C22×D6718yes—
619C4×Q8C22×D67116yes—
620C4×D4—6716no—
621C4×D4—6732no—
622C4×D4—6716no—
623C4×D4—678no—
624C4×D4—6716no—
625C4×D4—6716no—
626C4×D4—6716no—
627C4×D4—6716no—
628C4×D4—6716no—
629#117—6716no—
630#117C22×D67116yes—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—674no—
633C2×C4⋊C4—674no—
634C2×C4⋊C4—672no—
635C2×C4⋊C4—672no—
636C2×C4⋊C4—671no—
637C2×C4⋊C4—671no—
638C2×C4⋊C4—672no—
639C2×C4⋊C4—672no—
640C2×C4⋊C4—674no—
641C2×C4⋊C4—674no—
642C2×C4⋊C4—672no—
643C2×C4⋊C4—6732no—
644C2×C4⋊C4C22×D6712yes—
645C2×C4⋊C4C22×D6712yes—
646C2×C4⋊C4C22×D6712yes—
647C2×C4⋊C4C22×D6712yes—
648C2×C4⋊C4C22×D6711yescharacteristic
649C2×C4⋊C4C22×D6711yescharacteristic
650C2×C4⋊C4C22×D6712yes—
651C2×C4⋊C4C22×D6712yes—
652C2×C4⋊C4C22×D6712yes—
653C2×C22⋊C4—672no—
654C2×C22⋊C4—672no—
655C2×C22⋊C4—672no—
656C2×C22⋊C4—672no—
657C2×C22⋊C4—672no—
658C2×C22⋊C4—674no—
659C2×C22⋊C4—674no—
660C2×C22⋊C4—674no—
661C2×C22⋊C4—674no—
662C2×C22⋊C4—674no—
663C2×C22⋊C4—674no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4C22×D6712yes—
666C2×C22⋊C4C22×D6712yes—
667C2×C42—672no—
668C2×C42—674no—
669C2×C42C22×D6711yescharacteristic
670C2×C42C22×D6712yes—
671C2×C42C22×D6712yes—
672C2×C42C22×D6711yescharacteristic
673C2×C42C22×D6711yescharacteristic
674C2×C42C22×D6711yescharacteristic
675C2×C42C22×D6718yes—
676C24—672no—
677C24—674no—
678C24C23×D6711yescharacteristic
679#41—26832no—
680#41—26832no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—2688no—
685C2×Q8—26832no—
686C2×Q8—6716no—
687C2×Q8—674no—
688C2×Q8—678no—
689C2×Q8—1348no—
690C2×Q8—1344no—
691C2×Q8C23×D6714yes—
692C2×Q8C23×D6714yes—
693C2×Q8C23×D6718yes—
694C2×D4—2688no—
695C2×D4—2684no—
696C2×D4—2688no—
697C2×D4—2688no—
698C2×D4—2684no—
699C2×D4—678no—
700C2×D4—6716no—
701C2×D4—678no—
702C2×D4—6716no—
703C2×D4—6716no—
704C2×D4—674no—
705C2×D4—678no—
706C2×D4—678no—
707C2×D4—1348no—
708C2×D4—1344no—
709C2×D4—1348no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—2688no—
714C22×C4—2688no—
715C22×C4—2688no—
716C22×C4—2688no—
717C22×C4—6716no—
718C22×C4—6716no—
719C22×C4—6716no—
720C22×C4—6716no—
721C22×C4—672no—
722C22×C4—672no—
723C22×C4—674no—
724C22×C4—672no—
725C22×C4—678no—
726C22×C4—1348no—
727C22×C4C23×D6714yes—
728C22×C4C23×D6714yes—
729C22×C4C23×D6712yes—
730C22×C4C23×D6711yescharacteristic
731C22×C4C23×D6711yescharacteristic
732C22×C4C23×D6711yescharacteristic
733C22×C4C23×D6711yescharacteristic
734C22×C4C23×D6712yes—
735C22×C4C23×D6712yes—
736C22×C4C23×D6712yes—
737C22×C4C23×D6714yes—
738C22×C4C23×D6711yescharacteristic
739C22×C4C23×D6711yescharacteristic
740C4⋊C4—678no—
741C4⋊C4—6716no—
742C4⋊C4—6716no—
743C4⋊C4—678no—
744C4⋊C4—678no—
745C4⋊C4—674no—
746C4⋊C4—674no—
747C4⋊C4—678no—
748C4⋊C4—678no—
749C4⋊C4—6716no—
750C4⋊C4—6716no—
751C4⋊C4—678no—
752C4⋊C4C23×D6718yes—
753C4⋊C4C23×D6718yes—
754C4⋊C4C23×D6718yes—
755C4⋊C4C23×D6718yes—
756C4⋊C4C23×D6714yes—
757C4⋊C4C23×D6714yes—
758C4⋊C4C23×D6718yes—
759C4⋊C4C23×D6718yes—
760C4⋊C4C23×D6718yes—
761C22⋊C4—678no—
762C22⋊C4—678no—
763C22⋊C4—678no—
764C22⋊C4—678no—
765C22⋊C4—678no—
766C22⋊C4—6716no—
767C22⋊C4—6716no—
768C22⋊C4—6716no—
769C22⋊C4—6716no—
770C22⋊C4—6716no—
771C22⋊C4—6716no—
772C22⋊C4—6716no—
773C22⋊C4C23×D6718yes—
774C22⋊C4C23×D6718yes—
775C42—678no—
776C42—6716no—
777C42C23×D6714yes—
778C42C23×D6714yes—
779C42C23×D6714yes—
780C42C23×D6714yes—
781C42C23×D6718yes—
782C42C23×D6718yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—674no—
787C23—678no—
788C23—1344no—
789C23—1348no—
790C23—1344no—
791C23—1348no—
792C23—1348no—
793C23—1344no—
794C23C24×D6712yes—
795C23C24×D6711yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—26816no—
800Q8—13416no—
801Q8—1348no—
802D4—26816no—
803D4—2688no—
804D4—26816no—
805D4—26816no—
806D4—2688no—
807D4—13416no—
808D4—1348no—
809D4—13416no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—26816no—
822C2×C4—26816no—
823C2×C4—26816no—
824C2×C4—26816no—
825C2×C4—674no—
826C2×C4—674no—
827C2×C4—678no—
828C2×C4—674no—
829C2×C4—1344no—
830C2×C4—1348no—
831C2×C4—1344no—
832C2×C4—1344no—
833C2×C4—13416no—
834C2×C4#1452408914yes—
835C2×C4#1452409114yes—
836C2×C4C24×D6714yes—
837C2×C4C24×D6712yes—
838C2×C4C24×D6712yes—
839C2×C4C24×D6712yes—
840C2×C4C24×D6712yes—
841C2×C4C24×D6714yes—
842C2×C4C24×D6714yes—
843C2×C4C24×D6714yes—
844C2×C4C24×D6712yes—
845C2×C4C24×D6712yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—2688no—
851C22—26816no—
852C22—1344no—
853C22—1348no—
854C22—1344no—
855C22—1348no—
856C22—1348no—
857C22—1344no—
858C22C2×#1452408912yes—
859C22C2×#1452409112yes—
860C22#1686423212yes—
861C22C25×D6711yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1344no—
871C4—1348no—
872C4—1344no—
873C4—1344no—
874C4C2×#1452408914yes—
875C4C2×#1452409114yes—
876C2—42no—
877C2—2684no—
878C2—2688no—
879C2#2257468014yesdirect product factor
880C2C22×#1452408911yescharacteristic
881C2C22×#1452409111yescharacteristic
882C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#533×C67C2
socleC23×C67C25
hypercenterC2×#533D67
hypocenterC67C2×#3554
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22574680C2direct (N × H)
2. C2×#16864142C2semidirect
3. C2×#16864131C2semidirect
4. C2×#16864131C2semidirect
5. C2×#16864124C2semidirect
6. C2×#16864106C2semidirect
7. C2×#16864068C2semidirect
8. C2×Q8×D268C2semidirect
9. C2×#16864056C2semidirect
10. C2×#16864048C2semidirect
11. C2×#16864020C2semidirect
12. C2×#16864017C2semidirect
13. C2×#16864001C2semidirect
14. C2×#16863994C2semidirect
15. C2×#16863971C2semidirect
16. C2×#16863946C2semidirect
17. C2×#16863930C2semidirect
18. C2×#533×C67C2semidirect
22. #16864142C22semidirect
23. #16864131C22semidirect
24. #16864131C22semidirect
25. #16864124C22semidirect
26. #16864106C22semidirect
27. #16864068C22semidirect
28. Q8×D268C22semidirect
29. #16864056C22semidirect
30. #16864048C22semidirect
31. #16864020C22semidirect
32. #16864017C22semidirect
33. #16864001C22semidirect
34. #16863994C22semidirect
35. #16863971C22semidirect
36. #16863946C22semidirect
42. #16863930C22semidirect
89. #533×C67C22semidirect
436. C2×C67#3554semidirect
457. C2×#533D67semidirect
460. C67C2×#3554semidirect
478. #533C2×D67semidirect
879. C2#22574680direct (N × H)

Maximal subgroups

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

subgroupindex
#225746802
C2×#168641422
C2×#168641312
C2×#168641242
C2×#168641062
C2×#168640682
C2×Q8×D2682
C2×#168640562
C2×#168640482
C2×#168640202
C2×#168640172
C2×#168640012
C2×#168639942
C2×#168639712
C2×#168639462
C2×#168639302
C2×#533×C672
C2×#355467