Finite Group Databasebeta

← C2×#22572977 #31735612

Subgroups — C2×#22572977 #31735612

Order 17152.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864131C211yesmaximal, characteristic
2#22572977C2116yesmaximal, direct product factor
3C2×#16863762C211yesmaximal, characteristic
4C2×#16863758C211yesmaximal, characteristic, complemented
5C2×#16863753C211yesmaximal, characteristic, complemented
6C2×#16863700C211yesmaximal, characteristic, complemented
7C2×#16863693C211yesmaximal, characteristic, complemented
8C2×#16863683C211yesmaximal, characteristic, complemented
9C2×#16863618C211yesmaximal, characteristic, complemented
10C2×#16863618C211yesmaximal, characteristic, complemented
11C2×#16863596C211yesmaximal, characteristic
12C2×#16863527C211yesmaximal, characteristic, complemented
13C2×#16863501C211yesmaximal, characteristic, complemented
14C2×#16863494C211yesmaximal, characteristic, complemented
15C2×C4×#11761615C211yesmaximal, characteristic, complemented
16C2×#557×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C22×#11761615C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20#16864131—24no—
21#16864131C2218yes—
22C2×#14524040C2211yescharacteristic
23C2×#14524032—21no—
24C2×#14524031C2211yescharacteristic
25C2×#14524031C2211yescharacteristic
26C2×#14524028—21no—
27C2×#14524028—21no—
28C2×C4×Dic134C2211yescharacteristic
29C2×C4×D268C2211yescharacteristic
30C2×C4×D268C2211yescharacteristic
31C2×#14524005—21no—
32#16863762C2218yes—
33#16863758C2218yescomplemented
34#16863753C2218yescomplemented
35#16863700C2218yescomplemented
36#16863693C2218yescomplemented
37#16863683C2218yescomplemented
38#16863618C2218yescomplemented
39#16863618C2218yescomplemented
40#16863596C2218yes—
41#16863527C2218yescomplemented
42#16863501C2218yescomplemented
43#16863494C2218yescomplemented
44C4×#11761615C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49C2×C4⋊(C67⋊C8)C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×#14523967C2211yescharacteristic
52C2×#14523966C2211yescharacteristic
53C2×#14523966C2211yescharacteristic
54C2×#14523966C2211yescharacteristic
55C2×#14523963C2211yescharacteristic
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#557×C67—24no—
65#557×C67C2218yescomplemented
66C2×C4⋊Q8×C67—21no—
67C2×C4⋊Q8×C67C2211yescharacteristic
68C2×#125×C67—21no—
69C2×#125×C67—21no—
70C2×#125×C67C2211yescharacteristic
71C2×#125×C67C2211yescharacteristic
72C2×C4×Q8×C67—21no—
73C2×C4×Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×Q8×C67C2211yescharacteristic
76C2×C4×Q8×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C22×D268—21no—
79C22×D268—21no—
80C22×D268C2311yescharacteristic
81C22×D268C2311yescharacteristic
82C22×C4×D67—21no—
83C22×C4×D67—21no—
84C2×#11761618—24no—
85C2×#11761618C2314yes—
86C2×#11761615—24no—
87C2×#11761615—24no—
88C2×#11761615C2314yes—
89C2×#11761615C2314yes—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94#14524040—22no—
95#14524040C2314yes—
96#14524032—28no—
97#14524031—22no—
98#14524031—22no—
99#14524031C2314yes—
100#14524031C2314yes—
101#14524028—28no—
102#14524028—28no—
103C4×Dic134—22no—
104C4×Dic134C2314yes—
105C4×D268—22no—
106C4×D268—22no—
107C4×D268C2314yes—
108C4×D268C2314yes—
109#14524005—28no—
110C2×C4⋊Dic67C2311yescharacteristic
111C2×Dic67⋊C4—21no—
112C2×(C2×D67)⋊C4—21no—
113C2×(C2×D67)⋊C4—21no—
114C2×(C2×D67)⋊C4—21no—
115C2×(C2×D67)⋊C4—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523974C2314yes—
121#14523974C2314yes—
122C4⋊(C67⋊C8)C2314yes—
123C4⋊(C67⋊C8)C2314yes—
124C4⋊(C67⋊C8)C2314yes—
125#14523967C2314yes—
126#14523966C2314yes—
127#14523966C2314yes—
128#14523966C2314yes—
129#14523963C2314yes—
130#14523963C2314yes—
131#14523963C2314yes—
132#14523963C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135#14523954C2314yes—
136#14523954C2314yes—
137C4×C67⋊C8C2314yes—
138C22×Q8×C67—21no—
139C22×Q8×C67D411yescharacteristic
140C22×Q8×C67C2311yescharacteristic
141C4⋊Q8×C67—28no—
142C4⋊Q8×C67—22no—
143C4⋊Q8×C67C2314yes—
144#125×C67—28no—
145#125×C67—28no—
146#125×C67—22no—
147#125×C67—22no—
148#125×C67C2314yes—
149#125×C67C2314yes—
150C4×Q8×C67—28no—
151C4×Q8×C67—22no—
152C4×Q8×C67—22no—
153C4×Q8×C67—22no—
154C4×Q8×C67D414yes—
155C4×Q8×C67C2314yes—
156C4×Q8×C67C2314yes—
157C4×Q8×C67C2314yes—
158C4×Q8×C67C2314yes—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C42×C67—21no—
174C2×C42×C67—21no—
175C2×C42×C67—21no—
176C2×C42×C67C2311yescharacteristic
177C2×C42×C67C2311yescharacteristic
178C2×C42×C67C2311yescharacteristic
179C23×D67—21no—
180C23×D67—21no—
181C2×Dic134—22no—
182C2×Dic134—22no—
183C2×Dic134—21no—
184C2×Dic134C2412yes—
185C2×D268—22no—
186C2×D268—22no—
187C2×D268—22no—
188C2×D268—22no—
189C2×D268—24no—
190C2×D268—21no—
191C2×D268—21no—
192C2×D268—24no—
193C2×D268—44no—
194C2×D268—82no—
195C2×D268C2412yes—
196C2×D268C2412yes—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C2×C4×D67—24no—
200C2×C4×D67—24no—
201C2×C4×D67—82no—
202C2×C4×D67—82no—
203#11761618—28no—
204#11761615—28no—
205#11761615—28no—
206C2×C67⋊C8—22no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—22no—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C2×C67⋊C8C2412yes—
213C2×C67⋊C8C2412yes—
214C4⋊Dic67—21no—
215C4⋊Dic67C2412yes—
216Dic67⋊C4—24no—
217(C2×D67)⋊C4—24no—
218(C2×D67)⋊C4—24no—
219(C2×D67)⋊C4—24no—
220(C2×D67)⋊C4—24no—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223C4×Dic67—24no—
224C2×Q8×C67—21no—
225C2×Q8×C67—24no—
226C2×Q8×C67—22no—
227C2×Q8×C67—42no—
228C2×Q8×C67—44no—
229C2×Q8×C67C2×D414yes—
230C2×Q8×C67#4114yes—
231C2×Q8×C67C2412yes—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67C2×D411yescharacteristic
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2411yescharacteristic
243C4⋊C4×C67—24no—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—24no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67C2×D414yes—
255C4⋊C4×C67C2×D414yes—
256C4⋊C4×C67C2×D414yes—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
259C4⋊C4×C67C2412yes—
260C42×C67—24no—
261C42×C67—24no—
262C42×C67—24no—
263C42×C67C2×D412yes—
264C42×C67C2×D412yes—
265C42×C67C2×D412yes—
266C42×C67C2412yes—
267C42×C67C2412yes—
268C42×C67C2412yes—
269C23×C67C22×D411yescharacteristic
270C22×D67—22no—
271C22×D67—22no—
272C22×D67—42no—
273C22×D67—42no—
274C22×D67—42no—
275C22×D67—42no—
276C22×D67—42no—
277C22×D67—42no—
278Q8×C67—24no—
279Q8×C67—22no—
280Q8×C67—44no—
281Q8×C67—48no—
282Q8×C67C2×#4114yes—
283C2×C4×C67—24no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—42no—
295C2×C4×C67—42no—
296C2×C4×C67—42no—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D412yes—
300C2×C4×C67C22×D412yes—
301C2×C4×C67C22×D412yes—
302C2×C4×C67C22×D412yes—
303C2×C4×C67C22×D411yescharacteristic
304C2×C4×C67C2×#4112yes—
305C2×C4×C672−1+412yes—
306C2×C4×C67C2511yescharacteristic
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311D268—22no—
312D268—22no—
313D268—22no—
314D268—22no—
315D268—48no—
316D268—42no—
317D268—42no—
318D268—84no—
319C4×D67—84no—
320C4×D67—84no—
321Dic134—22no—
322Dic134—22no—
323Dic134—42no—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C67⋊C8—22no—
327C67⋊C8—22no—
328C22×C67#54812yes—
329C22×C67#57512yes—
330C22×C67#57712yes—
331C22×C67C23×D411yescharacteristic
332C2×D67—42no—
333C2×D67—42no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—42no—
338C2×D67—84no—
339C2×D67—84no—
340C4×C67—24no—
341C4×C67—22no—
342C4×C67—22no—
343C4×C67—22no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67—22no—
347C4×C67—42no—
348C4×C67—42no—
349C4×C67—42no—
350C4×C67#54812yes—
351C4×C67C22×#4111yescharacteristic
352C4×C67C2×2−1+411yescharacteristic
353Dic67—42no—
354Dic67—42no—
355C2×#3371—671nomaximal, Sylow
356C2×C67#337114yescomplemented
357C2×C67C2×#54811yescharacteristic
358C2×C67C2×#57511yescharacteristic
359C2×C67C2×#57711yescharacteristic
360D67—82no—
361D67—82no—
362C2×#559—671no—
363C2×#557D6711yescharacteristic, complemented
364#3371—6716no—
365C2×#490—671no—
366C2×#489—671no—
367C2×#488—671no—
368C2×#479—671no—
369C2×#478—671no—
370C2×#476—671no—
371C2×#464—671no—
372C2×#464—671no—
373C2×#460—671no—
374C2×#446—671no—
375C2×#441—671no—
376C2×#440—671no—
377C2×C4×SD16—671no—
378C67C2×#337111yescharacteristic, complemented, Sylow
379C22×Q16—671no—
380C22×SD16—671no—
381C22×SD16—671no—
382#559—678no—
383#559—1344no—
384#557—24no—
385#557C2×D6718yescomplemented
386C2×C4⋊Q8—21no—
387C2×C4⋊Q8C2×D6711yescharacteristic
388C2×#127—671no—
389C2×#125—21no—
390C2×#125—21no—
391C2×#125C2×D6711yescharacteristic
392C2×#125C2×D6711yescharacteristic
393C2×#124—671no—
394C2×#124—671no—
395C2×#124—1341no—
396C2×#123—1341no—
397C2×#123—1341no—
398C2×C4×Q8—21no—
399C2×C4×Q8—671no—
400C2×C4×Q8C2×D6711yescharacteristic
401C2×C4×Q8C2×D6711yescharacteristic
402C2×C4×Q8C2×D6711yescharacteristic
403C2×C4×Q8C2×D6711yescharacteristic
404C2×C4×D4—671no—
405C2×C4×D4—671no—
406C2×C4×D4—1341no—
407#490—678no—
408#489—678no—
409#488—678no—
410#479—678no—
411#478—678no—
412#476—678no—
413#464—678no—
414#464—678no—
415#460—678no—
416#446—678no—
417#441—678no—
418#440—678no—
419C4×SD16—678no—
420C2×#107—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×C4⋊C8—671no—
424C2×C4⋊C8—671no—
425C2×C4⋊C8—671no—
426C2×#103—671no—
427C2×#103—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×#102—671no—
431C2×#102—671no—
432C2×#102—671no—
433C2×#102—671no—
434C2×#102—671no—
435C2×#102—671no—
436C2×#97—671no—
437C2×#97—671no—
438C2×C4×C8—671no—
439C22×Q8—21no—
440C22×Q8—671no—
441C22×Q8C22⋊D6711yescharacteristic
442C22×Q8C22×D6711yescharacteristic
443C22×D4—671no—
444C22×D4—671no—
445C22×D4—1341no—
446C22×D4—1341no—
447C23×C4—1341no—
448C23×C4—1341no—
449C2×Q16—674no—
450C2×Q16—1344no—
451C2×SD16—674no—
452C2×SD16—674no—
453C2×SD16—1344no—
454C2×SD16—1344no—
455C22×C8—671no—
456C22×C8—671no—
457C22×C8—671no—
458C22×C8—671no—
459C4⋊Q8—28no—
460C4⋊Q8—22no—
461C4⋊Q8C22×D6714yes—
462#127—674no—
463#127—1342no—
464#125—28no—
465#125—28no—
466#125—22no—
467#125—22no—
468#125C22×D6714yes—
469#125C22×D6714yes—
470#124—674no—
471#124—674no—
472#124—1348no—
473#124—1342no—
474#124—1342no—
475#123—1348no—
476#123—1348no—
477C4×Q8—28no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—674no—
482C4×Q8—1342no—
483C4×Q8C22⋊D6714yes—
484C4×Q8C22×D6714yes—
485C4×Q8C22×D6714yes—
486C4×Q8C22×D6714yes—
487C4×Q8C22×D6714yes—
488C4×D4—674no—
489C4×D4—674no—
490C4×D4—1348no—
491C4×D4—1342no—
492C4×D4—1342no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—671no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4C22⋊D6711yescharacteristic
504C2×C4⋊C4C22⋊D6711yescharacteristic
505C2×C4⋊C4C22⋊D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C4⋊C4C22×D6711yescharacteristic
508C2×C4⋊C4C22×D6711yescharacteristic
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4—1341no—
513C2×C22⋊C4—1341no—
514C2×C22⋊C4—1341no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1341no—
519C2×C42C22×D6711yescharacteristic
520C2×C42C22×D6711yescharacteristic
521C2×C42C22×D6711yescharacteristic
522#107—674no—
523#106—674no—
524#106—674no—
525C4⋊C8—674no—
526C4⋊C8—674no—
527C4⋊C8—674no—
528#103—674no—
529#103—674no—
530#103—674no—
531#103—674no—
532#102—674no—
533#102—674no—
534#102—674no—
535#102—674no—
536#102—674no—
537#102—674no—
538#97—674no—
539#97—674no—
540C4×C8—674no—
541C24—1341no—
542C24—1341no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—672no—
549C2×Q8—1342no—
550C2×Q8—1342no—
551C2×Q8—1341no—
552C2×Q8C2×C22⋊D6714yes—
553C2×Q8#1176162914yes—
554C2×Q8C23×D6712yes—
555C2×D4—2684no—
556C2×D4—5362no—
557C2×D4—672no—
558C2×D4—672no—
559C2×D4—1344no—
560C2×D4—1341no—
561C2×D4—1341no—
562C2×D4—1344no—
563C2×D4—1342no—
564C2×D4—1342no—
565C2×D4—1342no—
566C2×D4—1342no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—5362no—
572C22×C4—5362no—
573C22×C4—1341no—
574C22×C4—1341no—
575C22×C4—1344no—
576C22×C4—1344no—
577C22×C4C2×C22⋊D6711yescharacteristic
578C22×C4C2×C22⋊D6711yescharacteristic
579C22×C4C2×C22⋊D6711yescharacteristic
580C22×C4C2×C22⋊D6711yescharacteristic
581C22×C4C2×C22⋊D6711yescharacteristic
582C22×C4C2×C22⋊D6711yescharacteristic
583C22×C4C23×D6711yescharacteristic
584Q16—1348no—
585SD16—1348no—
586SD16—1348no—
587C2×C8—672no—
588C2×C8—672no—
589C2×C8—672no—
590C2×C8—672no—
591C2×C8—1342no—
592C2×C8—1342no—
593C2×C8—1342no—
594C2×C8—1342no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—672no—
607C4⋊C4—1341no—
608C4⋊C4—1344no—
609C4⋊C4C2×C22⋊D6714yes—
610C4⋊C4C2×C22⋊D6714yes—
611C4⋊C4C2×C22⋊D6714yes—
612C4⋊C4C23×D6712yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C22⋊C4—1344no—
616C22⋊C4—1344no—
617C22⋊C4—1344no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4—1344no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—1344no—
625C42C2×C22⋊D6712yes—
626C42C2×C22⋊D6712yes—
627C42C2×C22⋊D6712yes—
628C42C23×D6712yes—
629C42C23×D6712yes—
630C42C23×D6712yes—
631C23—2682no—
632C23—2682no—
633C23—2682no—
634C23—2682no—
635C23—2682no—
636C23—2682no—
637C23—1342no—
638C23—1342no—
639C23C22×C22⋊D6711yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—2682no—
645Q8—1342no—
646Q8—1342no—
647Q8C2×#1176162914yes—
648D4—2688no—
649D4—2682no—
650D4—2682no—
651D4—5364no—
652D4—1342no—
653D4—1342no—
654D4—1342no—
655D4—1342no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—2682no—
671C2×C4—2682no—
672C2×C4—5364no—
673C2×C4—5364no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4C22×C22⋊D6712yes—
677C2×C4C22×C22⋊D6712yes—
678C2×C4C22×C22⋊D6712yes—
679C2×C4C22×C22⋊D6712yes—
680C2×C4C22×C22⋊D6712yes—
681C2×C4C22×C22⋊D6712yes—
682C2×C4C22×C22⋊D6711yescharacteristic
683C2×C4C2×#1176162912yes—
684C2×C4#1452409112yes—
685C2×C4C24×D6711yescharacteristic
686C8—1342no—
687C8—1342no—
688C8—1342no—
689C8—1342no—
690C22—2682no—
691C22—2682no—
692C22—2682no—
693C22—2682no—
694C22—2682no—
695C22—2682no—
696C22—5364no—
697C22—5364no—
698C22#1686405712yes—
699C22#1686419412yes—
700C22#1686420412yes—
701C22C23×C22⋊D6711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—2682no—
713C4—2682no—
714C4#1686405712yes—
715C4C22×#1176162911yescharacteristic
716C4C2×#1452409111yescharacteristic
717C2—5362no—
718C2—5362no—
719C2#2257297714yesdirect product factor
720C2C2×#1686405711yescharacteristic
721C2C2×#1686419411yescharacteristic
722C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#557×C67C2
socleC23×C67C22×D4
prime radicalC2×#14524040C22
hypercenterC2×#557D67
hypocenterC67C2×#3371
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #22572977C2direct (N × H)
4. C2×#16863758C2semidirect
5. C2×#16863753C2semidirect
6. C2×#16863700C2semidirect
7. C2×#16863693C2semidirect
8. C2×#16863683C2semidirect
9. C2×#16863618C2semidirect
10. C2×#16863618C2semidirect
12. C2×#16863527C2semidirect
13. C2×#16863501C2semidirect
14. C2×#16863494C2semidirect
15. C2×C4×#11761615C2semidirect
16. C2×#557×C67C2semidirect
33. #16863758C22semidirect
34. #16863753C22semidirect
35. #16863700C22semidirect
36. #16863693C22semidirect
37. #16863683C22semidirect
38. #16863618C22semidirect
39. #16863618C22semidirect
41. #16863527C22semidirect
42. #16863501C22semidirect
43. #16863494C22semidirect
44. C4×#11761615C22semidirect
65. #557×C67C22semidirect
356. C2×C67#3371semidirect
363. C2×#557D67semidirect
378. C67C2×#3371semidirect
385. #557C2×D67semidirect
719. C2#22572977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641312
#225729772
C2×#168637622
C2×#168637582
C2×#168637532
C2×#168637002
C2×#168636932
C2×#168636832
C2×#168636182
C2×#168635962
C2×#168635272
C2×#168635012
C2×#168634942
C2×C4×#117616152
C2×#557×C672
C2×#337167