Finite Group Databasebeta

← C2×#22571462 #31728020

Subgroups — C2×#22571462 #31728020

Order 17152.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864001C211yesmaximal, characteristic
2#22571462C2116yesmaximal, direct product factor
3C2×#16863802C211yesmaximal, characteristic, complemented
4C2×#16863795C211yesmaximal, characteristic, complemented
5C2×#16863762C211yesmaximal, characteristic, complemented
6C2×#16863744C211yesmaximal, characteristic, complemented
7C2×#16863714C211yesmaximal, characteristic, complemented
8C2×#16863720C211yesmaximal, characteristic, complemented
9C2×#16863720C211yesmaximal, characteristic, complemented
10C2×#16863709C211yesmaximal, characteristic, complemented
11C2×#16863693C211yesmaximal, characteristic, complemented
12C2×#16863693C211yesmaximal, characteristic, complemented
13C2×#16863683C211yesmaximal, characteristic, complemented
14C2×#16863673C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#544×C67C211yesmaximal, characteristic, complemented
17#16864001—24no—
18#16864001C2218yes—
19C2×#14524040C2211yescharacteristic
20C2×#14524035C2211yescharacteristic
21C2×#14524028—21no—
22C2×#14524028—21no—
23C2×#14524017C2211yescharacteristic
24C2×#14524017C2211yescharacteristic
25C2×#14524016—21no—
26C2×#14524016—21no—
27C2×C4×D268C2211yescharacteristic
28C2×C4×D268C2211yescharacteristic
29#16863802C2218yescomplemented
30#16863795C2218yescomplemented
31#16863762C2218yescomplemented
32#16863744C2218yescomplemented
33#16863720C2218yescomplemented
34#16863720C2218yescomplemented
35#16863714C2218yescomplemented
36#16863709C2218yescomplemented
37#16863693C2218yescomplemented
38#16863693C2218yescomplemented
39#16863683C2218yescomplemented
40#16863673C2218yescomplemented
41#16863457C2218yescomplemented
42C2×#14523976C2211yescharacteristic
43C2×#14523976C2211yescharacteristic
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523963C2211yescharacteristic
53C2×#14523963C2211yescharacteristic
54C2×#14523963C2211yescharacteristic
55C2×#14523963C2211yescharacteristic
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#544×C67—24no—
65#544×C67C2218yescomplemented
66C2×C4⋊Q8×C67—21no—
67C2×C4⋊Q8×C67C2211yescharacteristic
68C2×C4⋊Q8×C67C2211yescharacteristic
69C2×#125×C67—21no—
70C2×#125×C67C2211yescharacteristic
71C2×#125×C67C2211yescharacteristic
72C2×C22⋊Q8×C67—21no—
73C2×C22⋊Q8×C67—21no—
74C2×#117×C67C2211yescharacteristic
75C2×#117×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×D268—21no—
78C22×D268—21no—
79C22×D268C2311yescharacteristic
80C22×D268C2311yescharacteristic
81C22×C22⋊D67—21no—
82C22×C22⋊D67—21no—
83C22×C4×D67—21no—
84C22×C4×D67—21no—
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89#14524040—22no—
90#14524040C2314yes—
91#14524035—22no—
92#14524035C2314yes—
93#14524028—28no—
94#14524028—28no—
95#14524017—22no—
96#14524017—22no—
97#14524017C2314yes—
98#14524017C2314yes—
99#14524016—28no—
100#14524016—28no—
101C4×D268—22no—
102C4×D268—22no—
103C4×D268C2314yes—
104C4×D268C2314yes—
105C2×C4⋊Dic67C2311yescharacteristic
106C2×C4⋊Dic67C2311yescharacteristic
107C2×Dic67⋊C4—21no—
108C2×Dic67⋊C4—21no—
109C2×(C2×D67)⋊C4—21no—
110C2×(C2×D67)⋊C4—21no—
111C2×(C2×D67)⋊C4—21no—
112C2×(C2×D67)⋊C4—21no—
113#14523976C2314yes—
114#14523976C2314yes—
115#14523976C2314yes—
116#14523976C2314yes—
117#14523974C2314yes—
118#14523974C2314yes—
119#14523974C2314yes—
120#14523974C2314yes—
121C4⋊(C67⋊C8)C2314yes—
122C4⋊(C67⋊C8)C2314yes—
123#14523963C2314yes—
124#14523963C2314yes—
125#14523963C2314yes—
126#14523963C2314yes—
127#14523963C2314yes—
128#14523963C2314yes—
129#14523963C2314yes—
130#14523963C2314yes—
131C22⋊(C67⋊C8)C2314yes—
132C22⋊(C67⋊C8)C2314yes—
133#14523954C2314yes—
134C4×C67⋊C8C2314yes—
135C22×Q8×C67—21no—
136C22×Q8×C67—21no—
137C23×C4×C67—21no—
138C23×C4×C67C2311yescharacteristic
139C4⋊Q8×C67—28no—
140C4⋊Q8×C67—22no—
141C4⋊Q8×C67—22no—
142C4⋊Q8×C67C2314yes—
143C4⋊Q8×C67C2314yes—
144#125×C67—28no—
145#125×C67—22no—
146#125×C67—22no—
147#125×C67C2314yes—
148#125×C67C2314yes—
149C22⋊Q8×C67—28no—
150C22⋊Q8×C67—28no—
151#117×C67—22no—
152#117×C67D414yes—
153#117×C67C2314yes—
154#117×C67C2314yes—
155C2×C4⋊C4×C67—21no—
156C2×C4⋊C4×C67—22no—
157C2×C4⋊C4×C67—21no—
158C2×C4⋊C4×C67—21no—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67D411yescharacteristic
164C2×C4⋊C4×C67D411yescharacteristic
165C2×C4⋊C4×C67C2311yescharacteristic
166C2×C4⋊C4×C67C2311yescharacteristic
167C2×C4⋊C4×C67C2314yes—
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C42×C67—21no—
174C2×C42×C67C2311yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C23×D67—21no—
177C23×D67—21no—
178C2×D268—22no—
179C2×D268—22no—
180C2×D268—22no—
181C2×D268—22no—
182C2×D268—21no—
183C2×D268—21no—
184C2×D268—24no—
185C2×D268—24no—
186C2×D268—82no—
187C2×D268—82no—
188C2×D268C2412yes—
189C2×D268C2412yes—
190C2×C22⋊D67—24no—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—82no—
193C2×C22⋊D67—82no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C2×C4×D67—24no—
197C2×C4×D67—24no—
198C2×C4×D67—82no—
199C2×C4×D67—82no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8—22no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—22no—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C2×C67⋊C8C2412yes—
207C2×C67⋊C8C2412yes—
208C4⋊Dic67—21no—
209C4⋊Dic67—21no—
210C4⋊Dic67C2412yes—
211C4⋊Dic67C2412yes—
212Dic67⋊C4—24no—
213Dic67⋊C4—24no—
214(C2×D67)⋊C4—24no—
215(C2×D67)⋊C4—24no—
216(C2×D67)⋊C4—24no—
217(C2×D67)⋊C4—24no—
218C24×C67C2×D411yescharacteristic
219C2×Q8×C67—24no—
220C2×Q8×C67—24no—
221C2×Q8×C67—82no—
222C2×Q8×C67—82no—
223C22×C4×C67—22no—
224C22×C4×C67—22no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—24no—
230C22×C4×C67—82no—
231C22×C4×C67C2×D411yescharacteristic
232C22×C4×C67C2×D411yescharacteristic
233C22×C4×C67C2×D411yescharacteristic
234C22×C4×C67C2×D411yescharacteristic
235C22×C4×C67C2×D411yescharacteristic
236C22×C4×C67C2×D412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2411yescharacteristic
239C4⋊C4×C67—24no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—24no—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—24no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67C2×D414yes—
251C4⋊C4×C67C2×D414yes—
252C4⋊C4×C67C2412yes—
253C4⋊C4×C67C2412yes—
254C4⋊C4×C67C2412yes—
255C4⋊C4×C67C2412yes—
256C22⋊C4×C67—24no—
257C22⋊C4×C67C2×D414yes—
258C22⋊C4×C67C2×D414yes—
259C42×C67—24no—
260C42×C67C2×D412yes—
261C42×C67C2×D412yes—
262C42×C67C2412yes—
263C42×C67C2412yes—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67C22×D412yes—
268C23×C67C22×D411yescharacteristic
269C22×D67—22no—
270C22×D67—22no—
271C22×D67—42no—
272C22×D67—42no—
273C22×D67—42no—
274C22×D67—42no—
275C22×D67—42no—
276C22×D67—42no—
277Q8×C67—84no—
278Q8×C67—84no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—24no—
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—42no—
292C2×C4×C67—42no—
293C2×C4×C67—42no—
294C2×C4×C67—42no—
295C2×C4×C67—84no—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D412yes—
300C2×C4×C67C22×D412yes—
301C2×C4×C67C22×D411yescharacteristic
302C2×C4×C672−1+412yes—
303C2×C4×C672−1+412yes—
304C2×C4×C67C2511yescharacteristic
305C22⋊D67—84no—
306C22⋊D67—84no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311D268—22no—
312D268—22no—
313D268—22no—
314D268—22no—
315D268—42no—
316D268—42no—
317D268—84no—
318D268—84no—
319C4×D67—84no—
320C4×D67—84no—
321C67⋊C8—22no—
322C67⋊C8—22no—
323C67⋊C8—22no—
324C67⋊C8—22no—
325C22×C67—22no—
326C22×C67—22no—
327C22×C67—22no—
328C22×C67—44no—
329C22×C67#53612yes—
330C22×C67#57612yes—
331C22×C67#57712yes—
332C22×C67C23×D411yescharacteristic
333C2×D67—42no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—42no—
338C2×D67—42no—
339C2×D67—84no—
340C2×D67—84no—
341C4×C67—22no—
342C4×C67—22no—
343C4×C67—22no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67—42no—
347C4×C67—42no—
348C4×C67—42no—
349C4×C67—42no—
350C4×C67#53612yes—
351C4×C67C2×2−1+411yescharacteristic
352C4×C67C2×2−1+411yescharacteristic
353Dic67—42no—
354Dic67—42no—
355C2×#3241—671nomaximal, Sylow
356C2×C67—42no—
357C2×C67#324114yescomplemented
358C2×C67C2×#53611yescharacteristic
359C2×C67C2×#57611yescharacteristic
360C2×C67C2×#57711yescharacteristic
361D67—82no—
362D67—82no—
363C2×#544D6711yescharacteristic, complemented
364C2×#540—671no—
365#3241—6716no—
366C2×#501—671no—
367C2×#499—671no—
368C2×#490—671no—
369C2×#486—671no—
370C2×#481—671no—
371C2×#482—671no—
372C2×#482—671no—
373C2×#480—671no—
374C2×#478—671no—
375C2×#478—671no—
376C2×#476—671no—
377C2×#474—671no—
378C2×#433—671no—
379C67C2×#324111yescharacteristic, complemented, Sylow
380#544—24no—
381#544C2×D6718yescomplemented
382#540—678no—
383#540—1344no—
384C2×C4⋊Q8—21no—
385C2×C4⋊Q8C2×D6711yescharacteristic
386C2×C4⋊Q8C2×D6711yescharacteristic
387C2×#127—671no—
388C2×#125—21no—
389C2×#125—671no—
390C2×#125C2×D6711yescharacteristic
391C2×#125C2×D6711yescharacteristic
392C2×#123—1341no—
393C2×#123—1341no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×#121—671no—
397C2×#121—671no—
398C2×#121—1341no—
399C2×#121—1341no—
400C2×C4×D4—671no—
401C2×C4×D4—671no—
402C2×#117C2×D6711yescharacteristic
403C2×#117C2×D6711yescharacteristic
404C22×C4⋊C4C2×D6711yescharacteristic
405#501—678no—
406#499—678no—
407#490—678no—
408#486—678no—
409#482—678no—
410#482—678no—
411#481—678no—
412#480—678no—
413#478—678no—
414#478—678no—
415#476—678no—
416#474—678no—
417#433—678no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#107—671no—
421C2×#107—671no—
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—671no—
425C2×#106—671no—
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×#102—671no—
429C2×#102—671no—
430C2×#102—671no—
431C2×#102—671no—
432C2×#102—671no—
433C2×#102—671no—
434C2×#102—671no—
435C2×#102—671no—
436C2×C22⋊C8—671no—
437C2×C22⋊C8—671no—
438C2×#97—671no—
439C2×C4×C8—671no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×D4—671no—
443C22×D4—671no—
444C22×D4—1341no—
445C22×D4—1341no—
446C22×D4—1341no—
447C22×D4—1341no—
448C23×C4—21no—
449C23×C4—1341no—
450C23×C4—1341no—
451C23×C4C22×D6711yescharacteristic
452C22×C8—671no—
453C22×C8—671no—
454C22×C8—671no—
455C22×C8—671no—
456C4⋊Q8—28no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C22×D6714yes—
460C4⋊Q8C22×D6714yes—
461#127—674no—
462#127—1342no—
463#125—28no—
464#125—22no—
465#125—22no—
466#125—674no—
467#125—1342no—
468#125C22×D6714yes—
469#125C22×D6714yes—
470#123—1348no—
471#123—1348no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—674no—
475#121—674no—
476#121—1342no—
477#121—1342no—
478#121—1348no—
479#121—1348no—
480C4×D4—674no—
481C4×D4—674no—
482C4×D4—1342no—
483C4×D4—1342no—
484#117—22no—
485#117C22⋊D6714yes—
486#117C22×D6714yes—
487#117C22×D6714yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4C22⋊D6711yescharacteristic
501C2×C4⋊C4C22⋊D6711yescharacteristic
502C2×C4⋊C4C22×D6711yescharacteristic
503C2×C4⋊C4C22×D6711yescharacteristic
504C2×C4⋊C4C22×D6714yes—
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1341no—
509C2×C22⋊C4—1341no—
510C2×C22⋊C4—1341no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4C22⋊D6711yescharacteristic
513C2×C22⋊C4C22⋊D6711yescharacteristic
514C2×C42—21no—
515C2×C42C22×D6711yescharacteristic
516C2×C42C22×D6711yescharacteristic
517#107—674no—
518#107—674no—
519#107—674no—
520#107—674no—
521#106—674no—
522#106—674no—
523#106—674no—
524#106—674no—
525C4⋊C8—674no—
526C4⋊C8—674no—
527#102—674no—
528#102—674no—
529#102—674no—
530#102—674no—
531#102—674no—
532#102—674no—
533#102—674no—
534#102—674no—
535C22⋊C8—674no—
536C22⋊C8—674no—
537#97—674no—
538C4×C8—674no—
539C24—1341no—
540C24—1341no—
541C24C2×C22⋊D6711yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—5362no—
547C2×D4—5362no—
548C2×D4—5362no—
549C2×D4—5362no—
550C2×D4—672no—
551C2×D4—672no—
552C2×D4—1344no—
553C2×D4—1344no—
554C2×D4—1341no—
555C2×D4—1341no—
556C2×D4—1344no—
557C2×D4—1344no—
558C2×D4—1342no—
559C2×D4—1342no—
560C2×D4—1342no—
561C2×D4—1342no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—5362no—
571C22×C4—5362no—
572C22×C4—1341no—
573C22×C4—1341no—
574C22×C4—1344no—
575C22×C4—1344no—
576C22×C4C2×C22⋊D6712yes—
577C22×C4C2×C22⋊D6711yescharacteristic
578C22×C4C2×C22⋊D6711yescharacteristic
579C22×C4C2×C22⋊D6711yescharacteristic
580C22×C4C2×C22⋊D6711yescharacteristic
581C22×C4C2×C22⋊D6711yescharacteristic
582C22×C4C23×D6712yes—
583C22×C4C23×D6711yescharacteristic
584C2×C8—672no—
585C2×C8—672no—
586C2×C8—672no—
587C2×C8—672no—
588C2×C8—1342no—
589C2×C8—1342no—
590C2×C8—1342no—
591C2×C8—1342no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—672no—
604C4⋊C4—672no—
605C4⋊C4—1341no—
606C4⋊C4—1341no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4C2×C22⋊D6714yes—
610C4⋊C4C2×C22⋊D6714yes—
611C4⋊C4C23×D6712yes—
612C4⋊C4C23×D6712yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C22⋊C4—24no—
616C22⋊C4—1344no—
617C22⋊C4—1344no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4C2×C22⋊D6714yes—
621C22⋊C4C2×C22⋊D6714yes—
622C42—24no—
623C42C2×C22⋊D6712yes—
624C42C2×C22⋊D6712yes—
625C42C23×D6712yes—
626C42C23×D6712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—2682no—
631C23—2682no—
632C23—2682no—
633C23—2682no—
634C23—2682no—
635C23—2682no—
636C23—1342no—
637C23—1342no—
638C23C22×C22⋊D6712yes—
639C23C22×C22⋊D6711yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—2682no—
643D4—2682no—
644D4—5364no—
645D4—5364no—
646D4—5364no—
647D4—5364no—
648D4—1342no—
649D4—1342no—
650D4—1342no—
651D4—1342no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—2682no—
670C2×C4—2682no—
671C2×C4—5364no—
672C2×C4—5364no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4C22×C22⋊D6712yes—
676C2×C4C22×C22⋊D6712yes—
677C2×C4C22×C22⋊D6712yes—
678C2×C4C22×C22⋊D6712yes—
679C2×C4C22×C22⋊D6712yes—
680C2×C4C22×C22⋊D6711yescharacteristic
681C2×C4#1452409112yes—
682C2×C4#1452409112yes—
683C2×C4C24×D6711yescharacteristic
684C8—1342no—
685C8—1342no—
686C8—1342no—
687C8—1342no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—2682no—
693C22—2682no—
694C22—2682no—
695C22—2682no—
696C22—2682no—
697C22—2682no—
698C22—5364no—
699C22—5364no—
700C22#1686397012yes—
701C22#1686419912yes—
702C22#1686420412yes—
703C22C23×C22⋊D6711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—2682no—
714C4—2682no—
715C4#1686397012yes—
716C4C2×#1452409111yescharacteristic
717C4C2×#1452409111yescharacteristic
718C2—42no—
719C2—5362no—
720C2—5362no—
721C2#2257146214yesdirect product factor
722C2C2×#1686397011yescharacteristic
723C2C2×#1686419911yescharacteristic
724C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#544×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864001C2
hypercenterC2×#544D67
hypocenterC67C2×#3241
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22571462C2direct (N × H)
3. C2×#16863802C2semidirect
4. C2×#16863795C2semidirect
5. C2×#16863762C2semidirect
6. C2×#16863744C2semidirect
7. C2×#16863714C2semidirect
8. C2×#16863720C2semidirect
9. C2×#16863720C2semidirect
10. C2×#16863709C2semidirect
11. C2×#16863693C2semidirect
12. C2×#16863693C2semidirect
13. C2×#16863683C2semidirect
14. C2×#16863673C2semidirect
15. C2×#16863457C2semidirect
16. C2×#544×C67C2semidirect
29. #16863802C22semidirect
30. #16863795C22semidirect
31. #16863762C22semidirect
32. #16863744C22semidirect
33. #16863720C22semidirect
34. #16863720C22semidirect
35. #16863714C22semidirect
36. #16863709C22semidirect
37. #16863693C22semidirect
38. #16863693C22semidirect
39. #16863683C22semidirect
40. #16863673C22semidirect
41. #16863457C22semidirect
65. #544×C67C22semidirect
357. C2×C67#3241semidirect
363. C2×#544D67semidirect
379. C67C2×#3241semidirect
381. #544C2×D67semidirect
721. C2#22571462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640012
#225714622
C2×#168638022
C2×#168637952
C2×#168637622
C2×#168637442
C2×#168637142
C2×#168637202
C2×#168637092
C2×#168636932
C2×#168636832
C2×#168636732
C2×#168634572
C2×#544×C672
C2×#324167