Finite Group Databasebeta

← C2×#22574682 #31763452

Subgroups — C2×#22574682 #31763452

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#22574682C2132yesmaximal, direct product factor
2C2×#16864143C214yesmaximal, complemented
3C2×#16864131C211yesmaximal, characteristic, complemented
4C2×#16864128C212yesmaximal, complemented
5C2×#16864125C211yesmaximal, characteristic, complemented
6C2×#16864102C212yesmaximal, complemented
7C2×#16864067C211yesmaximal, characteristic, complemented
8C2×D4×Dic134C211yesmaximal, characteristic, complemented
9C2×#16864055C212yesmaximal, complemented
10C2×#16864051C212yesmaximal, complemented
11C2×#16864019C212yesmaximal, complemented
12C2×#16864017C212yesmaximal, complemented
13C2×#16863999C212yesmaximal, complemented
14C2×#16863987C214yesmaximal, complemented
15C2×#16863972C212yesmaximal, complemented
16C2×#16863953C211yesmaximal, characteristic, complemented
17C2×#16863946C211yesmaximal, characteristic, complemented
18C2×#529×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2212yes—
20C22×#11761628C2212yes—
21C23×Dic134C2212yes—
22#16864143C22164yescomplemented
23#16864131C22116yescomplemented
24#16864128C22132yescomplemented
25#16864125C22116yescomplemented
26#16864102C22132yescomplemented
27#16864067C22116yescomplemented
28D4×Dic134C22116yescomplemented
29#16864055C22132yescomplemented
30#16864051C22132yescomplemented
31#16864019C22132yescomplemented
32#16864017C22132yescomplemented
33#16863999C22132yescomplemented
34#16863987C22164yescomplemented
35#16863972C22132yescomplemented
36#16863953C22116yescomplemented
37#16863946C22116yescomplemented
38C2×#14524043C2211yescharacteristic
39C2×#14524043C2212yes—
40C2×#14524043C2211yescharacteristic
41C2×#14524043C2211yescharacteristic
42C2×#14524042C2212yes—
43C2×#14524040C2211yescharacteristic
44C2×#14524039C2212yes—
45C2×#14524038C2214yes—
46C2×#14524035C2212yes—
47C2×#14524034C2212yes—
48C2×#14524034C2214yes—
49C2×#14524032C2212yes—
50C2×#14524031C2212yes—
51C2×#14524031C2212yes—
52C2×#14524029C2214yes—
53C2×#14524029C2214yes—
54C2×#14524028C2214yes—
55C2×#14524027C2214yes—
56C2×#14524027C2214yes—
57C2×#14524025C2214yes—
58C2×#14524025C2214yes—
59C2×#14524025C2214yes—
60C2×#14524023C2214yes—
61C2×#14524023C2214yes—
62C2×#14524022C2212yes—
63C2×#14524022C2211yescharacteristic
64C2×#14524022C2211yescharacteristic
65C2×#14524022C2212yes—
66C2×#14524021C2214yes—
67C2×#14524021C2214yes—
68C2×#14524020C2214yes—
69C2×#14524017C2212yes—
70C2×#14524017C2212yes—
71C2×#14524017C2212yes—
72C2×#14524016C2214yes—
73C2×#14524015C2214yes—
74C2×#14524014C2214yes—
75C2×Q8×Dic67C2212yes—
76C2×C4×Dic134C2212yes—
77C2×C4×Dic134C2211yescharacteristic
78C2×C4×Dic134C2211yescharacteristic
79C2×C4×Dic134C2212yes—
80C2×C4×D268C2212yes—
81C2×C4×D268C2212yes—
82C2×C4×D268C2212yes—
83C2×D4×Dic67C2212yes—
84C2×#14524005C2212yes—
85C2×#14524005C2212yes—
86C2×(C22⋊D67)⋊C4C2214yes—
87C2×#14524002C2212yes—
88C2×C4⋊C4×D67C2214yes—
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×C67C2212yes—
98C2×C4×D4×C67C2211yescharacteristic
99C2×#117×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C2×#11761628—48no—
102C2×#11761628—48no—
103C2×#11761628C23116yes—
104C2×#11761628C23116yes—
105C22×Dic134—48no—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2312yes—
108C22×Dic134C2311yescharacteristic
109C22×Dic134C23116yes—
110C22×Dic134C2312yes—
111C22×Dic134C2314yes—
112C22×D268C2312yes—
113C22×D268C2312yes—
114C22×D268C2312yes—
115C22×C22⋊D67C2314yes—
116C22×C22⋊D67C2314yes—
117C22×C22⋊D67C2314yes—
118C23×Dic67C2314yes—
119C22×C4×D67C2314yes—
120C22×C4×D67C2314yes—
121C22×C4×D67C2314yes—
122#14524043C2318yes—
123#14524043C23116yes—
124#14524043C2318yes—
125#14524043C2318yes—
126#14524042C23116yes—
127#14524040C2318yes—
128#14524039C23116yes—
129#14524038C23132yes—
130#14524035C23116yes—
131#14524034C23116yes—
132#14524034C23132yes—
133#14524032C23116yes—
134#14524031C23116yes—
135#14524031C23116yes—
136#14524029C23132yes—
137#14524029C23132yes—
138#14524028C23132yes—
139#14524027C23132yes—
140#14524027C23132yes—
141#14524025C23132yes—
142#14524025C23132yes—
143#14524025C23132yes—
144#14524023C23132yes—
145#14524023C23132yes—
146#14524022C23116yes—
147#14524022C2318yes—
148#14524022C2318yes—
149#14524022C23116yes—
150#14524021C23132yes—
151#14524021C23132yes—
152#14524020C23132yes—
153#14524017C23116yes—
154#14524017C23116yes—
155#14524017C23116yes—
156#14524016C23132yes—
157#14524015C23132yes—
158#14524014C23132yes—
159Q8×Dic67C23116yes—
160C4×Dic134C23116yes—
161C4×Dic134C2318yes—
162C4×Dic134C2318yes—
163C4×Dic134C23116yes—
164C4×D268C23116yes—
165C4×D268C23116yes—
166C4×D268C23116yes—
167D4×Dic67C23116yes—
168#14524005C23116yes—
169#14524005C23116yes—
170(C22⋊D67)⋊C4C23132yes—
171#14524002C23116yes—
172C2×C4⋊Dic67C2314yes—
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2312yes—
175C2×C4⋊Dic67C2312yes—
176C2×C4⋊Dic67C2311yescharacteristic
177C2×C4⋊Dic67C2312yes—
178C2×C4⋊Dic67C2311yescharacteristic
179C2×C4⋊Dic67C2312yes—
180C2×C4⋊Dic67C2314yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C4⋊C4×D67C23132yes—
188C2×C22⋊Dic67C2312yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2314yes—
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×C4×Dic67C2312yes—
198C2×C4×Dic67C2312yes—
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×C67C23116yes—
215C4×D4×C67C2318yes—
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×D67C2414yes—
235#11761628—432no—
236#11761628—432no—
237C2×Dic134—24no—
238C2×Dic134—28no—
239C2×Dic134—24no—
240C2×Dic134—432no—
241C2×Dic134—48no—
242C2×Dic134—44no—
243C2×Dic134C2414yes—
244C2×Dic134C2418yes—
245C2×Dic134C2414yes—
246C2×Dic134C2418yes—
247C2×Dic134C24116yes—
248C2×D268—28no—
249C2×D268—28no—
250C2×D268—44no—
251C2×D268C2418yes—
252C2×D268C2418yes—
253C2×D268C2418yes—
254C2×C22⋊D67—48no—
255C2×C22⋊D67—48no—
256C2×C22⋊D67—48no—
257C2×C22⋊D67C24116yes—
258C2×C22⋊D67C24116yes—
259C2×C22⋊D67C24116yes—
260C22×Dic67—48no—
261C22×Dic67C2412yes—
262C22×Dic67C2412yes—
263C22×Dic67C2412yes—
264C22×Dic67C2414yes—
265C22×Dic67C2412yes—
266C22×Dic67C24116yes—
267C2×C4×D67—48no—
268C2×C4×D67—48no—
269C2×C4×D67—48no—
270C2×C4×D67C24116yes—
271C2×C4×D67C24116yes—
272C2×C4×D67C24116yes—
273C4⋊Dic67C24116yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C2418yes—
276C4⋊Dic67C2418yes—
277C4⋊Dic67C2414yes—
278C4⋊Dic67C2418yes—
279C4⋊Dic67C2414yes—
280C4⋊Dic67C2418yes—
281C4⋊Dic67C24116yes—
282Dic67⋊C4C2418yes—
283Dic67⋊C4C24116yes—
284Dic67⋊C4C2418yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C2418yes—
287Dic67⋊C4C2418yes—
288C22⋊Dic67C2418yes—
289C22⋊Dic67C2418yes—
290C22⋊Dic67C24116yes—
291(C2×D67)⋊C4C24116yes—
292(C2×D67)⋊C4C24116yes—
293(C2×D67)⋊C4C24116yes—
294(C2×D67)⋊C4C24116yes—
295(C2×D67)⋊C4C24116yes—
296(C2×D67)⋊C4C24116yes—
297C4×Dic67C2418yes—
298C4×Dic67C2418yes—
299C4×Dic67C24116yes—
300C24×C67C2412yes—
301C24×C67C2411yescharacteristic
302C2×Q8×C67—24no—
303C2×Q8×C67C2414yes—
304C2×D4×C67—24no—
305C2×D4×C67—44no—
306C2×D4×C67C2414yes—
307C2×D4×C67C2418yes—
308C22×C4×C67—28no—
309C22×C4×C67—24no—
310C22×C4×C67—24no—
311C22×C4×C67—42no—
312C22×C4×C67C2411yescharacteristic
313C22×C4×C67C2411yescharacteristic
314C22×C4×C67C2411yescharacteristic
315C22×C4×C67C2411yescharacteristic
316C22×C4×C67C2414yes—
317C22×C4×C67C2414yes—
318C22×C4×C67C2412yes—
319C22×C4×C67C2412yes—
320C22×C4×C67C2412yes—
321C22×C4×C67C2418yes—
322C22×C4×C67C2414yes—
323C22×C4×C67C2411yescharacteristic
324C22×C4×C67C2411yescharacteristic
325C4⋊C4×C67C2418yes—
326C4⋊C4×C67C2418yes—
327C4⋊C4×C67C2414yes—
328C4⋊C4×C67C2418yes—
329C4⋊C4×C67C2414yes—
330C4⋊C4×C67C2418yes—
331C22⋊C4×C67C2418yes—
332C22⋊C4×C67C2418yes—
333C22⋊C4×C67C2418yes—
334C22⋊C4×C67C2418yes—
335C22⋊C4×C67C2418yes—
336C42×C67C2414yes—
337C42×C67C2414yes—
338C42×C67C2414yes—
339C42×C67C2414yes—
340C42×C67C2418yes—
341C23×C67—24no—
342C23×C67—22no—
343C23×C67—22no—
344C23×C67—24no—
345C23×C67—22no—
346C23×C67—24no—
347C23×C67C2514yes—
348C23×C67C2512yes—
349C23×C67C2511yescharacteristic
350C22×D67—28no—
351C22×D67—28no—
352C22×D67—28no—
353C22×D67C2518yes—
354Q8×C67—28no—
355D4×C67—28no—
356D4×C67—48no—
357C2×C4×C67—22no—
358C2×C4×C67—24no—
359C2×C4×C67—22no—
360C2×C4×C67—24no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—24no—
364C2×C4×C67—216no—
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×C67C2512yes—
378C2×C4×C67C2512yes—
379C22⋊D67—416no—
380C22⋊D67—416no—
381C22⋊D67—416no—
382C2×Dic67—24no—
383C2×Dic67—28no—
384C2×Dic67—24no—
385C2×Dic67—24no—
386C2×Dic67—24no—
387C2×Dic67—416no—
388C2×Dic67C2514yes—
389C2×Dic67C2514yes—
390C2×Dic67C2514yes—
391C2×Dic67C2518yes—
392C2×Dic67C2514yes—
393D268—216no—
394D268—216no—
395D268—48no—
396C4×D67—416no—
397C4×D67—416no—
398C4×D67—416no—
399Dic134—28no—
400Dic134—216no—
401Dic134—28no—
402Dic134—416no—
403Dic134—48no—
404C22×C67—24no—
405C22×C67—22no—
406C22×C67—22no—
407C22×C67—24no—
408C22×C67—24no—
409C22×C67—22no—
410C22×C67—48no—
411C22×C67—44no—
412C22×C67C2×H(5,𝔽2)12yes—
413C22×C67C2×2−1+412yes—
414C22×C67#58512yes—
415C22×C67C2611yescharacteristic
416C2×D67—28no—
417C2×D67—28no—
418C2×D67—28no—
419C2×D67—416no—
420C4×C67—24no—
421C4×C67—22no—
422C4×C67—22no—
423C4×C67—24no—
424C4×C67—22no—
425C4×C67—24no—
426C4×C67—22no—
427C4×C67C2×H(5,𝔽2)14yes—
428C4×C67C2×2−1+414yes—
429Dic67—24no—
430Dic67—28no—
431Dic67—24no—
432Dic67—24no—
433Dic67—24no—
434C2×#3554—671nomaximal, Sylow
435C2×C67—44no—
436C2×C67—42no—
437C2×C67#355414yescomplemented
438C2×C67C22×H(5,𝔽2)11yescharacteristic
439C2×C67C22×2−1+411yescharacteristic
440C2×C67C2×#58511yescharacteristic
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×#533—671no—
458C2×#532—671no—
459C2×#529D6711yescharacteristic, complemented
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#533—6716no—
479#532—6716no—
480C2×C4⋊Q8—672no—
481C2×C4⋊Q8—671no—
482C2×C4⋊Q8—671no—
483C2×C4⋊Q8—671no—
484C2×C4⋊Q8—672no—
485C2×#127—672no—
486C2×#127—671no—
487#529C2×D67116yescomplemented
488C2×#126—674no—
489C2×#126C2×D6712yes—
490C2×#125—674no—
491C2×#125—672no—
492C2×#125—672no—
493C2×#125C2×D6711yescharacteristic
494C2×#124—672no—
495C2×#124—674no—
496C2×#124—674no—
497C2×#124—672no—
498C2×#124—672no—
499C2×#124C2×D6711yescharacteristic
500C2×#123—674no—
501C2×#123—674no—
502C2×#123—674no—
503C2×#123—674no—
504C2×#123—674no—
505C2×#123—674no—
506C2×#123C2×D6712yes—
507C2×C22⋊Q8—671no—
508C2×C22⋊Q8—671no—
509C2×C22⋊Q8—672no—
510C2×C22⋊Q8—672no—
511C2×C22⋊Q8—674no—
512C2×C22⋊Q8—674no—
513C2×C22⋊Q8—674no—
514C2×C22⋊Q8—674no—
515C2×C22⋊Q8—674no—
516C2×C22⋊Q8C2×D6711yescharacteristic
517C2×#121—674no—
518C2×#121—674no—
519C2×#121—672no—
520C2×#121—672no—
521C2×#121—672no—
522C2×#121—674no—
523C2×#121C2×D6711yescharacteristic
524C2×C4×Q8—672no—
525C2×C4×Q8—671no—
526C2×C4×Q8—671no—
527C2×C4×Q8—672no—
528C2×C4×Q8—672no—
529C2×C4×Q8C2×D6711yescharacteristic
530C2×C4×D4—672no—
531C2×C4×D4—672no—
532C2×C4×D4—672no—
533C2×C4×D4—674no—
534C2×C4×D4—672no—
535C2×C4×D4—672no—
536C2×C4×D4—672no—
537C2×C4×D4C2×D6712yes—
538C2×C4×D4C2×D6711yescharacteristic
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—672no—
549C22×Q8—674no—
550C22×Q8—6716no—
551C22×Q8—671no—
552C22×Q8—672no—
553C22×Q8—671no—
554C22×Q8C22×D6711yescharacteristic
555C22×D4—674no—
556C22×D4—674no—
557C22×D4—674no—
558C22×D4—672no—
559C22×D4—672no—
560C22×D4—672no—
561C22×D4C22×D6711yescharacteristic
562C22×D4C22×D6712yes—
563C23×C4—674no—
564C23×C4—674no—
565C23×C4—674no—
566C23×C4—674no—
567C23×C4C22×D6711yescharacteristic
568C23×C4C22×D6712yes—
569C23×C4C22×D6711yescharacteristic
570C23×C4C22×D6711yescharacteristic
571C4⋊Q8—6716no—
572C4⋊Q8—678no—
573C4⋊Q8—678no—
574C4⋊Q8—678no—
575C4⋊Q8—6716no—
576#127—6716no—
577#127—678no—
578#126—6732no—
579#126C22×D67116yes—
580#125—6732no—
581#125—6716no—
582#125—6716no—
583#125C22×D6718yes—
584#124—6716no—
585#124—6732no—
586#124—6732no—
587#124—6716no—
588#124—6716no—
589#124C22×D6718yes—
590#123—6732no—
591#123—6732no—
592#123—6732no—
593#123—6732no—
594#123—6732no—
595#123—6732no—
596#123C22×D67116yes—
597C22⋊Q8—678no—
598C22⋊Q8—678no—
599C22⋊Q8—6716no—
600C22⋊Q8—6716no—
601C22⋊Q8—6732no—
602C22⋊Q8—6732no—
603C22⋊Q8—6732no—
604C22⋊Q8—6732no—
605C22⋊Q8—6732no—
606C22⋊Q8C22×D6718yes—
607#121—6732no—
608#121—6732no—
609#121—6716no—
610#121—6716no—
611#121—6716no—
612#121—6732no—
613#121C22×D6718yes—
614C4×Q8—6716no—
615C4×Q8—678no—
616C4×Q8—678no—
617C4×Q8—6716no—
618C4×Q8—6716no—
619C4×Q8C22×D6718yes—
620C4×D4—6716no—
621C4×D4—6716no—
622C4×D4—6716no—
623C4×D4—6732no—
624C4×D4—6716no—
625C4×D4—6716no—
626C4×D4—6716no—
627C4×D4C22×D67116yes—
628C4×D4C22×D6718yes—
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—672no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—671no—
639C2×C4⋊C4—672no—
640C2×C4⋊C4—671no—
641C2×C4⋊C4—672no—
642C2×C4⋊C4—674no—
643C2×C4⋊C4—672no—
644C2×C4⋊C4—672no—
645C2×C4⋊C4—674no—
646C2×C4⋊C4—6732no—
647C2×C4⋊C4C22×D6712yes—
648C2×C4⋊C4C22×D6712yes—
649C2×C4⋊C4C22×D6712yes—
650C2×C4⋊C4C22×D6711yescharacteristic
651C2×C4⋊C4C22×D6711yescharacteristic
652C2×C4⋊C4C22×D6712yes—
653C2×C22⋊C4—672no—
654C2×C22⋊C4—672no—
655C2×C22⋊C4—674no—
656C2×C22⋊C4—674no—
657C2×C22⋊C4—674no—
658C2×C22⋊C4—674no—
659C2×C22⋊C4—674no—
660C2×C22⋊C4—674no—
661C2×C22⋊C4—674no—
662C2×C22⋊C4C22×D6712yes—
663C2×C22⋊C4C22×D6712yes—
664C2×C22⋊C4C22×D6712yes—
665C2×C22⋊C4C22×D6712yes—
666C2×C22⋊C4C22×D6712yes—
667C2×C42—672no—
668C2×C42—672no—
669C2×C42—674no—
670C2×C42C22×D6711yescharacteristic
671C2×C42C22×D6712yes—
672C2×C42C22×D6711yescharacteristic
673C2×C42C22×D6711yescharacteristic
674C2×C42C22×D6711yescharacteristic
675C2×C42C22×D6718yes—
676C24—674no—
677C24C23×D6711yescharacteristic
678C24C23×D6712yes—
679#41—26832no—
680#41—26832no—
681C2×Q8—24no—
682C2×Q8—26832no—
683C2×Q8—2688no—
684C2×Q8—2684no—
685C2×Q8—678no—
686C2×Q8—6716no—
687C2×Q8—674no—
688C2×Q8—678no—
689C2×Q8—674no—
690C2×Q8—1344no—
691C2×Q8—1348no—
692C2×Q8—1344no—
693C2×Q8C23×D6714yes—
694C2×D4—24no—
695C2×D4—44no—
696C2×D4—2684no—
697C2×D4—2688no—
698C2×D4—2688no—
699C2×D4—2688no—
700C2×D4—6716no—
701C2×D4—6716no—
702C2×D4—6716no—
703C2×D4—678no—
704C2×D4—678no—
705C2×D4—678no—
706C2×D4—1348no—
707C2×D4—1348no—
708C2×D4C23×D6714yes—
709C2×D4C23×D6718yes—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—42no—
714C22×C4—2688no—
715C22×C4—2688no—
716C22×C4—2688no—
717C22×C4—2688no—
718C22×C4—6716no—
719C22×C4—6716no—
720C22×C4—6716no—
721C22×C4—6716no—
722C22×C4—672no—
723C22×C4—672no—
724C22×C4—672no—
725C22×C4—674no—
726C22×C4—672no—
727C22×C4C23×D6714yes—
728C22×C4C23×D6714yes—
729C22×C4C23×D6718yes—
730C22×C4C23×D6712yes—
731C22×C4C23×D6711yescharacteristic
732C22×C4C23×D6711yescharacteristic
733C22×C4C23×D6711yescharacteristic
734C22×C4C23×D6711yescharacteristic
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—678no—
746C4⋊C4—678no—
747C4⋊C4—674no—
748C4⋊C4—678no—
749C4⋊C4—674no—
750C4⋊C4—678no—
751C4⋊C4—6716no—
752C4⋊C4—678no—
753C4⋊C4—678no—
754C4⋊C4—6716no—
755C4⋊C4C23×D6718yes—
756C4⋊C4C23×D6718yes—
757C4⋊C4C23×D6718yes—
758C4⋊C4C23×D6714yes—
759C4⋊C4C23×D6714yes—
760C4⋊C4C23×D6718yes—
761C22⋊C4—678no—
762C22⋊C4—678no—
763C22⋊C4—6716no—
764C22⋊C4—6716no—
765C22⋊C4—6716no—
766C22⋊C4—6716no—
767C22⋊C4—6716no—
768C22⋊C4—6716no—
769C22⋊C4—6716no—
770C22⋊C4C23×D6718yes—
771C22⋊C4C23×D6718yes—
772C22⋊C4C23×D6718yes—
773C22⋊C4C23×D6718yes—
774C22⋊C4C23×D6718yes—
775C42—678no—
776C42—678no—
777C42—6716no—
778C42C23×D6714yes—
779C42C23×D6714yes—
780C42C23×D6714yes—
781C42C23×D6714yes—
782C42C23×D6718yes—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—24no—
789C23—678no—
790C23—1348no—
791C23—1348no—
792C23—1348no—
793C23C24×D6712yes—
794C23C24×D6714yes—
795C23C24×D6711yescharacteristic
796Q8—28no—
797Q8—26816no—
798Q8—2688no—
799Q8—1348no—
800Q8—13416no—
801Q8—1348no—
802D4—28no—
803D4—48no—
804D4—2688no—
805D4—26816no—
806D4—26816no—
807D4—26816no—
808D4—13416no—
809D4—13416no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—216no—
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—674no—
828C2×C4—678no—
829C2×C4—674no—
830C2×C4—1344no—
831C2×C4—1348no—
832C2×C4—1344no—
833C2×C4—1344no—
834C2×C4—1344no—
835C2×C4#1452408914yes—
836C2×C4#1452409014yes—
837C2×C4C24×D6714yes—
838C2×C4C24×D6712yes—
839C2×C4C24×D6712yes—
840C2×C4C24×D6712yes—
841C2×C4C24×D6712yes—
842C2×C4C24×D6714yes—
843C2×C4C24×D6714yes—
844C2×C4C24×D6712yes—
845C2×C4C24×D6712yes—
846C22—24no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—24no—
852C22—48no—
853C22—44no—
854C22—26816no—
855C22—1348no—
856C22—1348no—
857C22—1348no—
858C22C2×#1452408912yes—
859C22C2×#1452409012yes—
860C22#1686423212yes—
861C22C25×D6711yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—1344no—
870C4—1348no—
871C4—1344no—
872C4—1344no—
873C4—1344no—
874C4C2×#1452408914yes—
875C4C2×#1452409014yes—
876C2—44no—
877C2—42no—
878C2—2688no—
879C2#2257468214yesdirect product factor
880C2C22×#1452408911yescharacteristic
881C2C22×#1452409011yescharacteristic
882C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
hypercenterC2×#529D67
hypocenterC67C2×#3554
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574682C2direct (N × H)
2. C2×#16864143C2semidirect
3. C2×#16864131C2semidirect
4. C2×#16864128C2semidirect
5. C2×#16864125C2semidirect
6. C2×#16864102C2semidirect
7. C2×#16864067C2semidirect
8. C2×D4×Dic134C2semidirect
9. C2×#16864055C2semidirect
10. C2×#16864051C2semidirect
11. C2×#16864019C2semidirect
12. C2×#16864017C2semidirect
13. C2×#16863999C2semidirect
14. C2×#16863987C2semidirect
15. C2×#16863972C2semidirect
16. C2×#16863953C2semidirect
17. C2×#16863946C2semidirect
18. C2×#529×C67C2semidirect
22. #16864143C22semidirect
23. #16864131C22semidirect
24. #16864128C22semidirect
25. #16864125C22semidirect
26. #16864102C22semidirect
27. #16864067C22semidirect
28. D4×Dic134C22semidirect
29. #16864055C22semidirect
30. #16864051C22semidirect
31. #16864019C22semidirect
32. #16864017C22semidirect
33. #16863999C22semidirect
34. #16863987C22semidirect
35. #16863972C22semidirect
36. #16863953C22semidirect
37. #16863946C22semidirect
89. #529×C67C22semidirect
437. C2×C67#3554semidirect
459. C2×#529D67semidirect
460. C67C2×#3554semidirect
487. #529C2×D67semidirect
879. C2#22574682direct (N × H)

Maximal subgroups

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

subgroupindex
#225746822
C2×#168641432
C2×#168641312
C2×#168641282
C2×#168641252
C2×#168641022
C2×#168640672
C2×D4×Dic1342
C2×#168640552
C2×#168640512
C2×#168640192
C2×#168640172
C2×#168639992
C2×#168639872
C2×#168639722
C2×#168639532
C2×#168639462
C2×#529×C672
C2×#355467