Finite Group Databasebeta

← C2×#22574683 #31763461

Subgroups — C2×#22574683 #31763461

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#22574683C2132yesmaximal, direct product factor
2C2×#16864144C214yesmaximal, complemented
3C2×#16864131C212yesmaximal, complemented
4C2×#16864131C211yesmaximal, characteristic, complemented
5C2×#16864102C212yesmaximal, complemented
6C2×#16864068C211yesmaximal, characteristic, complemented
7C2×#16864061C211yesmaximal, characteristic, complemented
8C2×#16864058C212yesmaximal, complemented
9C2×#16864049C212yesmaximal, complemented
10C2×#16864018C212yesmaximal, complemented
11C2×#16864018C212yesmaximal, complemented
12C2×#16864002C212yesmaximal, complemented
13C2×#16863994C214yesmaximal, complemented
14C2×#16863971C212yesmaximal, complemented
15C2×#16863950C211yesmaximal, characteristic, complemented
16C2×#16863947C211yesmaximal, characteristic, complemented
17C2×#16863933C211yesmaximal, characteristic, complemented
18C2×#557×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2212yes—
20C22×#11761629C2212yes—
21C22×Q8×D67C2212yes—
22#16864144C22164yescomplemented
23#16864131C22132yescomplemented
24#16864131C22116yescomplemented
25#16864102C22132yescomplemented
26#16864068C22116yescomplemented
27#16864061C22116yescomplemented
28#16864058C22132yescomplemented
29#16864049C22132yescomplemented
30#16864018C22132yescomplemented
31#16864018C22132yescomplemented
32#16864002C22132yescomplemented
33#16863994C22164yescomplemented
34#16863971C22132yescomplemented
35#16863950C22116yescomplemented
36#16863947C22116yescomplemented
37C2×#14524042C2211yescharacteristic
38C2×#14524042C2212yes—
39C2×#14524041C2211yescharacteristic
40C2×#14524040C2212yes—
41C2×#14524040C2211yescharacteristic
42#16863933C22116yescomplemented
43C2×#14524038C2212yes—
44C2×#14524037C2214yes—
45C2×#14524034C2211yescharacteristic
46C2×#14524033C2212yes—
47C2×#14524032C2212yes—
48C2×#14524032C2212yes—
49C2×#14524032C2211yescharacteristic
50C2×#14524031C2214yes—
51C2×#14524031C2214yes—
52C2×#14524031C2212yes—
53C2×#14524028C2212yes—
54C2×#14524028C2214yes—
55C2×#14524028C2214yes—
56C2×#14524028C2214yes—
57C2×#14524028C2214yes—
58C2×#14524028C2214yes—
59C2×#14524028C2214yes—
60C2×#14524023C2211yescharacteristic
61C2×#14524023C2214yes—
62C2×#14524021C2212yes—
63C2×#14524021C2214yes—
64C2×#14524021C2214yes—
65C2×#14524021C2214yes—
66C2×#14524021C2214yes—
67C2×#14524019C2211yescharacteristic
68C2×#14524019C2212yes—
69C2×#14524019C2211yescharacteristic
70C2×#14524018C2212yes—
71C2×#14524018C2214yes—
72C2×#14524018C2214yes—
73C2×#14524018C2214yes—
74C2×#14524018C2211yescharacteristic
75C2×#14524018C2212yes—
76C2×#14524018C2212yes—
77C2×C4×Dic134C2211yescharacteristic
78C2×C4×Dic134C2212yes—
79C2×C4×D268C2212yes—
80C2×C4×D268C2212yes—
81C2×C4×D268C2212yes—
82C2×C4×D268C2214yes—
83C2×C4×D268C2211yescharacteristic
84C2×#14524005C2212yes—
85C2×#14524005C2212yes—
86C2×#14524005C2212yes—
87C2×#14524005C2212yes—
88C2×#14524000C2212yes—
89C2×#14524000C2212yes—
90C2×C4⋊C4×D67C2214yes—
91C2×C42×D67C2211yescharacteristic
92#557×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2212yes—
94C2×C4⋊Q8×C67C2211yescharacteristic
95C2×#125×C67C2214yes—
96C2×#125×C67C2212yes—
97C2×C4×Q8×C67C2212yes—
98C2×C4×Q8×C67C2212yes—
99C2×C4×Q8×C67C2211yescharacteristic
100C2×C4×Q8×C67C2211yescharacteristic
101C2×#11761629—48no—
102C2×#11761629—48no—
103C2×#11761629C23116yes—
104C2×#11761629C23116yes—
105C22×Dic134C2311yescharacteristic
106C22×Dic134C2312yes—
107C22×Dic134C2314yes—
108C2×Q8×D67—48no—
109C2×Q8×D67C23116yes—
110C22×D268C2311yescharacteristic
111C22×D268C2312yes—
112C22×D268C2312yes—
113C22×D268C2312yes—
114C22×D268C2312yes—
115C22×D268C2314yes—
116C22×D268C2314yes—
117C22×D268C2314yes—
118C22×C4×D67C2311yescharacteristic
119C22×C4×D67C2311yescharacteristic
120C22×C4×D67C2312yes—
121C22×C4×D67C2311yescharacteristic
122C22×C4×D67C2314yes—
123C22×C4×D67C2314yes—
124C22×C4×D67C2314yes—
125C22×C4×D67C2314yes—
126#14524042C2318yes—
127#14524042C23116yes—
128#14524041C2318yes—
129#14524040C23116yes—
130#14524040C2318yes—
131#14524038C23116yes—
132#14524037C23132yes—
133#14524034C2318yes—
134#14524033C23116yes—
135#14524032C23116yes—
136#14524032C23116yes—
137#14524032C2318yes—
138#14524031C23132yes—
139#14524031C23132yes—
140#14524031C23116yes—
141#14524028C23132yes—
142#14524028C23132yes—
143#14524028C23132yes—
144#14524028C23132yes—
145#14524028C23132yes—
146#14524028C23132yes—
147#14524028C23116yes—
148#14524023C2318yes—
149#14524023C23132yes—
150#14524021C23132yes—
151#14524021C23132yes—
152#14524021C23132yes—
153#14524021C23132yes—
154#14524021C23116yes—
155#14524019C2318yes—
156#14524019C23116yes—
157#14524019C2318yes—
158#14524018C2318yes—
159#14524018C23116yes—
160#14524018C23132yes—
161#14524018C23132yes—
162#14524018C23116yes—
163#14524018C23132yes—
164#14524018C23116yes—
165C4×Dic134C2318yes—
166C4×Dic134C23116yes—
167C4×D268C23116yes—
168C4×D268C23116yes—
169C4×D268C23116yes—
170C4×D268C23132yes—
171C4×D268C2318yes—
172#14524005C23116yes—
173#14524005C23116yes—
174#14524005C23116yes—
175#14524005C23116yes—
176#14524000C23116yes—
177#14524000C23116yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2311yescharacteristic
180C2×C4⋊Dic67C2311yescharacteristic
181C2×C4⋊Dic67C2312yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C2×Dic67⋊C4C2312yes—
189C2×Dic67⋊C4C2312yes—
190C4⋊C4×D67C23132yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2312yes—
200C2×(C2×D67)⋊C4C2312yes—
201C2×(C2×D67)⋊C4C2314yes—
202C2×(C2×D67)⋊C4C2312yes—
203C2×(C2×D67)⋊C4C2314yes—
204C2×(C2×D67)⋊C4C2314yes—
205C2×C4×Dic67C2311yescharacteristic
206C2×C4×Dic67C2311yescharacteristic
207C2×C4×Dic67C2311yescharacteristic
208C2×C4×Dic67C2312yes—
209C42×D67C2318yes—
210C22×Q8×C67C2311yescharacteristic
211C22×Q8×C67C2312yes—
212C22×Q8×C67C2311yescharacteristic
213C4⋊Q8×C67C23116yes—
214C4⋊Q8×C67C2318yes—
215#125×C67C23116yes—
216#125×C67C23132yes—
217C4×Q8×C67C23116yes—
218C4×Q8×C67C23116yes—
219C4×Q8×C67C2318yes—
220C4×Q8×C67C2318yes—
221C2×C4⋊C4×C67C2311yescharacteristic
222C2×C4⋊C4×C67C2311yescharacteristic
223C2×C4⋊C4×C67C2312yes—
224C2×C4⋊C4×C67C2314yes—
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C2314yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C4⋊C4×C67C2312yes—
230C2×C42×C67C2312yes—
231C2×C42×C67C2314yes—
232C2×C42×C67C2311yescharacteristic
233C2×C42×C67C2312yes—
234C23×D67C2412yes—
235C23×D67C2411yescharacteristic
236C23×D67C2414yes—
237#11761629—432no—
238#11761629—432no—
239C2×Dic134—24no—
240C2×Dic134—48no—
241C2×Dic134—44no—
242C2×Dic134C2414yes—
243C2×Dic134C2418yes—
244C2×Dic134C24116yes—
245Q8×D67—432no—
246C2×D268—28no—
247C2×D268—24no—
248C2×D268—28no—
249C2×D268—44no—
250C2×D268—44no—
251C2×D268—48no—
252C2×D268—48no—
253C2×D268—48no—
254C2×D268C2414yes—
255C2×D268C2418yes—
256C2×D268C2418yes—
257C2×D268C2418yes—
258C2×D268C2418yes—
259C2×D268C24116yes—
260C2×D268C24116yes—
261C2×D268C24116yes—
262C22×Dic67C2411yescharacteristic
263C22×Dic67C2411yescharacteristic
264C22×Dic67C2411yescharacteristic
265C22×Dic67C2412yes—
266C22×Dic67C2412yes—
267C22×Dic67C2412yes—
268C2×C4×D67—28no—
269C2×C4×D67—24no—
270C2×C4×D67—24no—
271C2×C4×D67—48no—
272C2×C4×D67—42no—
273C2×C4×D67—48no—
274C2×C4×D67—48no—
275C2×C4×D67—48no—
276C2×C4×D67C2414yes—
277C2×C4×D67C2414yes—
278C2×C4×D67C2418yes—
279C2×C4×D67C2414yes—
280C2×C4×D67C24116yes—
281C2×C4×D67C24116yes—
282C2×C4×D67C24116yes—
283C2×C4×D67C24116yes—
284C4⋊Dic67C2418yes—
285C4⋊Dic67C2414yes—
286C4⋊Dic67C2414yes—
287C4⋊Dic67C2418yes—
288Dic67⋊C4C2418yes—
289Dic67⋊C4C24116yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C2418yes—
292Dic67⋊C4C2418yes—
293Dic67⋊C4C2418yes—
294Dic67⋊C4C2418yes—
295Dic67⋊C4C2418yes—
296(C2×D67)⋊C4C2418yes—
297(C2×D67)⋊C4C2418yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C24116yes—
303(C2×D67)⋊C4C24116yes—
304(C2×D67)⋊C4C2418yes—
305(C2×D67)⋊C4C2418yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C2418yes—
308(C2×D67)⋊C4C24116yes—
309(C2×D67)⋊C4C24116yes—
310C4×Dic67C2414yes—
311C4×Dic67C2414yes—
312C4×Dic67C2414yes—
313C4×Dic67C2418yes—
314C2×Q8×C67—28no—
315C2×Q8×C67—24no—
316C2×Q8×C67—24no—
317C2×Q8×C67C2414yes—
318C2×Q8×C67C2418yes—
319C2×Q8×C67C2414yes—
320C22×C4×C67C2412yes—
321C22×C4×C67C2412yes—
322C22×C4×C67C2411yescharacteristic
323C22×C4×C67C2412yes—
324C22×C4×C67C2414yes—
325C22×C4×C67C2412yes—
326C22×C4×C67C2411yescharacteristic
327C22×C4×C67C2411yescharacteristic
328C4⋊C4×C67C2414yes—
329C4⋊C4×C67C2414yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C24116yes—
332C4⋊C4×C67C2418yes—
333C4⋊C4×C67C2418yes—
334C4⋊C4×C67C24116yes—
335C4⋊C4×C67C24116yes—
336C4⋊C4×C67C2418yes—
337C42×C67C2418yes—
338C42×C67C24116yes—
339C42×C67C2414yes—
340C42×C67C2418yes—
341C23×C67C2511yescharacteristic
342C22×D67—24no—
343C22×D67—22no—
344C22×D67—28no—
345C22×D67—22no—
346C22×D67—24no—
347C22×D67—28no—
348C22×D67—22no—
349C22×D67—28no—
350C22×D67—24no—
351C22×D67C2514yes—
352C22×D67C2512yes—
353C22×D67C2518yes—
354Q8×C67—216no—
355Q8×C67—28no—
356Q8×C67—28no—
357C2×C4×C67—24no—
358C2×C4×C67—28no—
359C2×C4×C67—24no—
360C2×C4×C67—24no—
361C2×C4×C67—22no—
362C2×C4×C67—24no—
363C2×C4×C67H(5,𝔽2)14yes—
364C2×C4×C672−1+414yes—
365C2×C4×C67C2514yes—
366C2×C4×C67C2514yes—
367C2×C4×C67C2512yes—
368C2×C4×C67C2514yes—
369C2×C4×C67C2518yes—
370C2×C4×C67C2514yes—
371C2×C4×C67C2512yes—
372C2×C4×C67C2512yes—
373C2×Dic67—22no—
374C2×Dic67—24no—
375C2×Dic67—24no—
376C2×Dic67—22no—
377C2×Dic67—24no—
378C2×Dic67—22no—
379C2×Dic67C2512yes—
380C2×Dic67C2512yes—
381C2×Dic67C2512yes—
382C2×Dic67C2514yes—
383C2×Dic67C2514yes—
384C2×Dic67C2514yes—
385D268—216no—
386D268—28no—
387D268—216no—
388D268—416no—
389D268—48no—
390D268—48no—
391D268—416no—
392D268—416no—
393C4×D67—216no—
394C4×D67—28no—
395C4×D67—28no—
396C4×D67—44no—
397C4×D67—416no—
398C4×D67—416no—
399C4×D67—416no—
400C4×D67—416no—
401Dic134—28no—
402Dic134—416no—
403Dic134—48no—
404C22×C67C2×H(5,𝔽2)12yes—
405C22×C67C2×2−1+412yes—
406C22×C67#58512yes—
407C22×C67C2611yescharacteristic
408C2×D67—24no—
409C2×D67—22no—
410C2×D67—28no—
411C2×D67—22no—
412C2×D67—24no—
413C2×D67—28no—
414C2×D67—22no—
415C2×D67—28no—
416C2×D67—24no—
417C2×D67—48no—
418C2×D67—44no—
419C2×D67—416no—
420C4×C67—28no—
421C4×C67—24no—
422C4×C67—24no—
423C4×C67—24no—
424C4×C67—24no—
425C4×C67—22no—
426C4×C67C2×H(5,𝔽2)14yes—
427C4×C67C2×2−1+414yes—
428Dic67—24no—
429Dic67—24no—
430Dic67—22no—
431Dic67—22no—
432Dic67—22no—
433Dic67—24no—
434C2×#3554—671nomaximal, Sylow
435C2×C67#355414yescomplemented
436C2×C67C22×H(5,𝔽2)11yescharacteristic
437C2×C67C22×2−1+411yescharacteristic
438C2×C67C2×#58511yescharacteristic
439D67—44no—
440D67—42no—
441D67—48no—
442#3554—6732no—
443C2×#562—674no—
444C2×#559—672no—
445C2×#559—671no—
446C2×#557D6711yescharacteristic, complemented
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×#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#557C2×D67116yescomplemented
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—671no—
481C2×C4⋊Q8—671no—
482C2×C4⋊Q8—672no—
483C2×C4⋊Q8C2×D6711yescharacteristic
484C2×C4⋊Q8C2×D6712yes—
485C2×#127—671no—
486C2×#127—672no—
487#529—6716no—
488C2×#126—672no—
489C2×#126—674no—
490C2×#125—671no—
491C2×#125—672no—
492C2×#125C2×D6714yes—
493C2×#125C2×D6712yes—
494C2×#124—671no—
495C2×#124—672no—
496C2×#124—672no—
497C2×#124—672no—
498C2×#124—674no—
499C2×#124—674no—
500C2×#123—672no—
501C2×#123—674no—
502C2×#123—674no—
503C2×#123—674no—
504C2×#123—674no—
505C2×#123—674no—
506C2×#123—674no—
507C2×C22⋊Q8—671no—
508C2×C22⋊Q8—671no—
509C2×C22⋊Q8—672no—
510C2×C22⋊Q8—671no—
511C2×C22⋊Q8—672no—
512C2×C22⋊Q8—674no—
513C2×C22⋊Q8—674no—
514C2×C22⋊Q8—674no—
515C2×C22⋊Q8—674no—
516C2×C22⋊Q8—674no—
517C2×#121—671no—
518C2×#121—672no—
519C2×#121—672no—
520C2×#121—674no—
521C2×#121—674no—
522C2×#121—674no—
523C2×#121—672no—
524C2×C4×Q8—671no—
525C2×C4×Q8—672no—
526C2×C4×Q8C2×D6711yescharacteristic
527C2×C4×Q8C2×D6711yescharacteristic
528C2×C4×Q8C2×D6712yes—
529C2×C4×Q8C2×D6712yes—
530C2×C4×D4—672no—
531C2×C4×D4—672no—
532C2×C4×D4—672no—
533C2×C4×D4—672no—
534C2×C4×D4—672no—
535C2×C4×D4—671no—
536C2×C4×D4—674no—
537C2×C4×D4—672no—
538C2×C4×D4—672no—
539C2×#117—672no—
540C2×#117—672no—
541C22×C4⋊C4—674no—
542C22×C42—671no—
543C2×#41—2688no—
544C2×#41—2688no—
545C2×#41—6716no—
546C2×#41—6716no—
547C22×Q8—2688no—
548C22×Q8—6716no—
549C22×Q8—672no—
550C22×Q8—674no—
551C22×Q8—671no—
552C22×Q8C22×D6711yescharacteristic
553C22×Q8C22×D6712yes—
554C22×Q8C22×D6711yescharacteristic
555C22×D4—672no—
556C22×D4—672no—
557C22×D4—674no—
558C22×D4—674no—
559C22×D4—674no—
560C22×D4—672no—
561C22×D4—671no—
562C22×D4—672no—
563C23×C4—674no—
564C23×C4—674no—
565C23×C4—674no—
566C23×C4—674no—
567C23×C4—671no—
568C23×C4—671no—
569C23×C4—672no—
570C23×C4—671no—
571C4⋊Q8—678no—
572C4⋊Q8—678no—
573C4⋊Q8—6716no—
574C4⋊Q8C22×D6718yes—
575C4⋊Q8C22×D67116yes—
576#127—678no—
577#127—6716no—
578#126—6716no—
579#126—6732no—
580#125—678no—
581#125—6716no—
582#125C22×D67132yes—
583#125C22×D67116yes—
584#124—678no—
585#124—6716no—
586#124—6716no—
587#124—6716no—
588#124—6732no—
589#124—6732no—
590#123—6716no—
591#123—6732no—
592#123—6732no—
593#123—6732no—
594#123—6732no—
595#123—6732no—
596#123—6732no—
597C22⋊Q8—678no—
598C22⋊Q8—678no—
599C22⋊Q8—6716no—
600C22⋊Q8—678no—
601C22⋊Q8—6716no—
602C22⋊Q8—6732no—
603C22⋊Q8—6732no—
604C22⋊Q8—6732no—
605C22⋊Q8—6732no—
606C22⋊Q8—6732no—
607#121—678no—
608#121—6716no—
609#121—6716no—
610#121—6732no—
611#121—6732no—
612#121—6732no—
613#121—6716no—
614C4×Q8—678no—
615C4×Q8—6716no—
616C4×Q8C22×D6718yes—
617C4×Q8C22×D6718yes—
618C4×Q8C22×D67116yes—
619C4×Q8C22×D67116yes—
620C4×D4—6716no—
621C4×D4—6716no—
622C4×D4—6716no—
623C4×D4—6716no—
624C4×D4—6716no—
625C4×D4—678no—
626C4×D4—6732no—
627C4×D4—6716no—
628C4×D4—6716no—
629#117—6716no—
630#117—6716no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—672no—
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—672no—
643C2×C4⋊C4—6732no—
644C2×C4⋊C4C22×D6714yes—
645C2×C4⋊C4C22×D6711yescharacteristic
646C2×C4⋊C4C22×D6712yes—
647C2×C4⋊C4C22×D6712yes—
648C2×C4⋊C4C22×D6711yescharacteristic
649C2×C4⋊C4C22×D6712yes—
650C2×C4⋊C4C22×D6714yes—
651C2×C4⋊C4C22×D6714yes—
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—672no—
659C2×C22⋊C4—674no—
660C2×C22⋊C4—674no—
661C2×C22⋊C4—674no—
662C2×C22⋊C4—674no—
663C2×C22⋊C4—674no—
664C2×C22⋊C4—672no—
665C2×C22⋊C4—674no—
666C2×C22⋊C4—674no—
667C2×C42—671no—
668C2×C42—672no—
669C2×C42—671no—
670C2×C42—671no—
671C2×C42—678no—
672C2×C42C22×D6712yes—
673C2×C42C22×D6712yes—
674C2×C42C22×D6711yescharacteristic
675C2×C42C22×D6714yes—
676C24—672no—
677C24—674no—
678C24—671no—
679#41—26832no—
680#41—26832no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—2688no—
685C2×Q8—2684no—
686C2×Q8—26832no—
687C2×Q8—678no—
688C2×Q8—6716no—
689C2×Q8—674no—
690C2×Q8—1344no—
691C2×Q8C23×D6714yes—
692C2×Q8C23×D6718yes—
693C2×Q8C23×D6714yes—
694C2×D4—2688no—
695C2×D4—2688no—
696C2×D4—2684no—
697C2×D4—2684no—
698C2×D4—2688no—
699C2×D4—678no—
700C2×D4—678no—
701C2×D4—6716no—
702C2×D4—6716no—
703C2×D4—6716no—
704C2×D4—678no—
705C2×D4—674no—
706C2×D4—678no—
707C2×D4—1348no—
708C2×D4—1348no—
709C2×D4—1344no—
710C22×C4—2688no—
711C22×C4—2688no—
712C22×C4—2688no—
713C22×C4—2688no—
714C22×C4—2682no—
715C22×C4—674no—
716C22×C4—6716no—
717C22×C4—6716no—
718C22×C4—6716no—
719C22×C4—6716no—
720C22×C4—671no—
721C22×C4—671no—
722C22×C4—671no—
723C22×C4—672no—
724C22×C4—672no—
725C22×C4—672no—
726C22×C4—674no—
727C22×C4—674no—
728C22×C4—678no—
729C22×C4—1348no—
730C22×C4—1344no—
731C22×C4—1344no—
732C22×C4C23×D6711yescharacteristic
733C22×C4C23×D6712yes—
734C22×C4C23×D6712yes—
735C22×C4C23×D6712yes—
736C22×C4C23×D6714yes—
737C22×C4C23×D6712yes—
738C22×C4C23×D6711yescharacteristic
739C22×C4C23×D6711yescharacteristic
740C4⋊C4—678no—
741C4⋊C4—678no—
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—678no—
752C4⋊C4C23×D67116yes—
753C4⋊C4C23×D6714yes—
754C4⋊C4C23×D6718yes—
755C4⋊C4C23×D6718yes—
756C4⋊C4C23×D6714yes—
757C4⋊C4C23×D6718yes—
758C4⋊C4C23×D67116yes—
759C4⋊C4C23×D67116yes—
760C4⋊C4C23×D6718yes—
761C22⋊C4—678no—
762C22⋊C4—678no—
763C22⋊C4—678no—
764C22⋊C4—678no—
765C22⋊C4—678no—
766C22⋊C4—678no—
767C22⋊C4—6716no—
768C22⋊C4—6716no—
769C22⋊C4—6716no—
770C22⋊C4—6716no—
771C22⋊C4—6716no—
772C22⋊C4—678no—
773C22⋊C4—6716no—
774C22⋊C4—6716no—
775C42—674no—
776C42—674no—
777C42—674no—
778C42—678no—
779C42C23×D6714yes—
780C42C23×D6718yes—
781C42C23×D6718yes—
782C42C23×D67116yes—
783C23—674no—
784C23—678no—
785C23—672no—
786C23—1344no—
787C23—1348no—
788C23—1342no—
789C23—1342no—
790C23—1344no—
791C23—1348no—
792C23—1348no—
793C23—1342no—
794C23—1344no—
795C23C24×D6711yescharacteristic
796Q8—216no—
797Q8—28no—
798Q8—28no—
799Q8—26816no—
800Q8—2688no—
801Q8—1348no—
802D4—26816no—
803D4—26816no—
804D4—2688no—
805D4—2688no—
806D4—26816no—
807D4—13416no—
808D4—13416no—
809D4—1348no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—26816no—
817C2×C4—26816no—
818C2×C4—26816no—
819C2×C4—26816no—
820C2×C4—2684no—
821C2×C4—672no—
822C2×C4—672no—
823C2×C4—672no—
824C2×C4—674no—
825C2×C4—674no—
826C2×C4—674no—
827C2×C4—1342no—
828C2×C4—1344no—
829C2×C4—1344no—
830C2×C4—1342no—
831C2×C4—1344no—
832C2×C4—1342no—
833C2×C4—13416no—
834C2×C4—1348no—
835C2×C4—1348no—
836C2×C4#1452408914yes—
837C2×C4#1452409114yes—
838C2×C4C24×D6712yes—
839C2×C4C24×D6714yes—
840C2×C4C24×D6714yes—
841C2×C4C24×D6714yes—
842C2×C4C24×D6718yes—
843C2×C4C24×D6714yes—
844C2×C4C24×D6712yes—
845C2×C4C24×D6712yes—
846C22—2688no—
847C22—26816no—
848C22—2684no—
849C22—1344no—
850C22—1348no—
851C22—1342no—
852C22—1342no—
853C22—1344no—
854C22—1348no—
855C22—1348no—
856C22—1342no—
857C22—1344no—
858C22C2×#1452408912yes—
859C22C2×#1452409112yes—
860C22#1686423312yes—
861C22C25×D6711yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—1342no—
869C4—1344no—
870C4—1344no—
871C4—1342no—
872C4—1344no—
873C4—1342no—
874C4C2×#1452408914yes—
875C4C2×#1452409114yes—
876C2—2684no—
877C2—2688no—
878C2—2682no—
879C2#2257468314yesdirect product factor
880C2C22×#1452408911yescharacteristic
881C2C22×#1452409111yescharacteristic
882C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#557×C67C2
socleC23×C67C25
hypercenterC2×#557D67
hypocenterC67C2×#3554
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22574683C2direct (N × H)
2. C2×#16864144C2semidirect
3. C2×#16864131C2semidirect
4. C2×#16864131C2semidirect
5. C2×#16864102C2semidirect
6. C2×#16864068C2semidirect
7. C2×#16864061C2semidirect
8. C2×#16864058C2semidirect
9. C2×#16864049C2semidirect
10. C2×#16864018C2semidirect
11. C2×#16864018C2semidirect
12. C2×#16864002C2semidirect
13. C2×#16863994C2semidirect
14. C2×#16863971C2semidirect
15. C2×#16863950C2semidirect
16. C2×#16863947C2semidirect
17. C2×#16863933C2semidirect
18. C2×#557×C67C2semidirect
22. #16864144C22semidirect
23. #16864131C22semidirect
24. #16864131C22semidirect
25. #16864102C22semidirect
26. #16864068C22semidirect
27. #16864061C22semidirect
28. #16864058C22semidirect
29. #16864049C22semidirect
30. #16864018C22semidirect
31. #16864018C22semidirect
32. #16864002C22semidirect
33. #16863994C22semidirect
34. #16863971C22semidirect
35. #16863950C22semidirect
36. #16863947C22semidirect
42. #16863933C22semidirect
92. #557×C67C22semidirect
435. C2×C67#3554semidirect
446. C2×#557D67semidirect
460. C67C2×#3554semidirect
467. #557C2×D67semidirect
879. C2#22574683direct (N × H)

Maximal subgroups

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

subgroupindex
#225746832
C2×#168641442
C2×#168641312
C2×#168641022
C2×#168640682
C2×#168640612
C2×#168640582
C2×#168640492
C2×#168640182
C2×#168640022
C2×#168639942
C2×#168639712
C2×#168639502
C2×#168639472
C2×#168639332
C2×#557×C672
C2×#355467