Finite Group Databasebeta

← C2×#22571456 #31728014

Subgroups — C2×#22571456 #31728014

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×#16864024C211yesmaximal, characteristic, complemented
2#22571456C2116yesmaximal, direct product factor
3C2×#16863806C211yesmaximal, characteristic, complemented
4C2×#16863795C211yesmaximal, characteristic, complemented
5C2×#16863760C211yesmaximal, characteristic, complemented
6C2×#16863742C211yesmaximal, characteristic, complemented
7C2×#16863712C211yesmaximal, characteristic, complemented
8C2×#16863717C211yesmaximal, characteristic, complemented
9C2×#16863717C211yesmaximal, characteristic, complemented
10C2×#16863707C211yesmaximal, characteristic, complemented
11C2×#16863696C211yesmaximal, characteristic, complemented
12C2×#16863696C211yesmaximal, characteristic, complemented
13C2×#16863686C211yesmaximal, characteristic, complemented
14C2×#16863676C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#540×C67C211yesmaximal, characteristic
17#16864024—24no—
18#16864024C2218yescomplemented
19C2×#14524043C2211yescharacteristic
20C2×#14524043C2211yescharacteristic
21C2×#14524042—21no—
22C2×#14524035C2211yescharacteristic
23C2×#14524035C2211yescharacteristic
24C2×#14524034—21no—
25C2×#14524020—21no—
26C2×#14524020—21no—
27C2×#14524002C2211yescharacteristic
28C22×C4⋊Dic67C2211yescharacteristic
29#16863806C2218yescomplemented
30#16863795C2218yescomplemented
31#16863760C2218yescomplemented
32#16863742C2218yescomplemented
33#16863717C2218yescomplemented
34#16863717C2218yescomplemented
35#16863712C2218yescomplemented
36#16863707C2218yescomplemented
37#16863696C2218yescomplemented
38#16863696C2218yescomplemented
39#16863686C2218yescomplemented
40#16863676C2218yescomplemented
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×#14523964C2211yescharacteristic
53C2×#14523964C2211yescharacteristic
54C2×#14523964C2211yescharacteristic
55C2×#14523964C2211yescharacteristic
56C2×#14523964C2211yescharacteristic
57C2×#14523964C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#540×C67—24no—
65#540×C67C2218yes—
66C2×#127×C67C2211yescharacteristic
67C2×#125×C67C2211yescharacteristic
68C2×#123×C67—21no—
69C2×#123×C67—21no—
70C2×#121×C67—21no—
71C2×#121×C67—21no—
72C2×#121×C67C2211yescharacteristic
73C2×#121×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C2×C4×D4×C67C2211yescharacteristic
76C2×#117×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134—21no—
79C23×Dic67—21no—
80C22×C67⋊C8C2311yescharacteristic
81C22×C67⋊C8C2311yescharacteristic
82C22×C67⋊C8C2311yescharacteristic
83C22×C67⋊C8C2311yescharacteristic
84#14524043—22no—
85#14524043—22no—
86#14524043C2314yes—
87#14524043C2314yes—
88#14524042—28no—
89#14524035—22no—
90#14524035—22no—
91#14524035C2314yes—
92#14524035C2314yes—
93#14524034—28no—
94#14524020—28no—
95#14524020—28no—
96#14524002—22no—
97#14524002C2314yes—
98C2×C4⋊Dic67—22no—
99C2×C4⋊Dic67—21no—
100C2×C4⋊Dic67—21no—
101C2×C4⋊Dic67—21no—
102C2×C4⋊Dic67C2314yes—
103C2×C4⋊Dic67C2311yescharacteristic
104C2×C4⋊Dic67C2311yescharacteristic
105C2×C4⋊Dic67C2311yescharacteristic
106C2×C4⋊Dic67C2311yescharacteristic
107C2×Dic67⋊C4—21no—
108C2×Dic67⋊C4—21no—
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C2×C22⋊Dic67—21no—
112C2×C4×Dic67—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#14523964C2314yes—
124#14523964C2314yes—
125#14523964C2314yes—
126#14523964C2314yes—
127#14523964C2314yes—
128#14523964C2314yes—
129#14523964C2314yes—
130#14523964C2314yes—
131C22⋊(C67⋊C8)C2314yes—
132C22⋊(C67⋊C8)C2314yes—
133#14523954C2314yes—
134C4×C67⋊C8C2314yes—
135C22×D4×C67—21no—
136C22×D4×C67—21no—
137C22×D4×C67—21no—
138C22×D4×C67—21no—
139C22×D4×C67C2311yescharacteristic
140C22×D4×C67C2311yescharacteristic
141C23×C4×C67—21no—
142C23×C4×C67—21no—
143C23×C4×C67C2311yescharacteristic
144#127×C67—22no—
145#127×C67C2314yes—
146#125×C67—22no—
147#125×C67C2314yes—
148#123×C67—28no—
149#123×C67—28no—
150#121×C67—22no—
151#121×C67—22no—
152#121×C67—28no—
153#121×C67—28no—
154#121×C67C2314yes—
155#121×C67C2314yes—
156C4×D4×C67—22no—
157C4×D4×C67—22no—
158C4×D4×C67C2314yes—
159C4×D4×C67C2314yes—
160#117×C67D414yes—
161#117×C67C2314yes—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67D411yescharacteristic
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C4⋊C4×C67C2311yescharacteristic
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C22⋊C4×C67—21no—
169C2×C22⋊C4×C67—21no—
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C22⋊C4×C67D411yescharacteristic
174C2×C42×C67C2311yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C2×Dic134—24no—
177C2×Dic134—24no—
178C2×Dic134—82no—
179C2×Dic134—82no—
180C22×Dic67—21no—
181C22×Dic67—21no—
182C22×Dic67—21no—
183C22×Dic67—21no—
184C22×Dic67—24no—
185C22×Dic67—82no—
186C2×C67⋊C8—22no—
187C2×C67⋊C8—22no—
188C2×C67⋊C8—22no—
189C2×C67⋊C8—22no—
190C2×C67⋊C8C2412yes—
191C2×C67⋊C8C2412yes—
192C2×C67⋊C8C2412yes—
193C2×C67⋊C8C2412yes—
194C4⋊Dic67—24no—
195C4⋊Dic67—21no—
196C4⋊Dic67—21no—
197C4⋊Dic67—24no—
198C4⋊Dic67—24no—
199C4⋊Dic67—21no—
200C4⋊Dic67—21no—
201C4⋊Dic67C2412yes—
202C4⋊Dic67C2412yes—
203C4⋊Dic67C2412yes—
204C4⋊Dic67C2412yes—
205Dic67⋊C4—24no—
206Dic67⋊C4—24no—
207Dic67⋊C4—24no—
208Dic67⋊C4—24no—
209C22⋊Dic67—24no—
210C4×Dic67—24no—
211C24×C67—21no—
212C24×C67—21no—
213C24×C67C2×D411yescharacteristic
214C2×D4×C67—24no—
215C2×D4×C67—24no—
216C2×D4×C67—21no—
217C2×D4×C67—21no—
218C2×D4×C67—24no—
219C2×D4×C67—24no—
220C2×D4×C67—22no—
221C2×D4×C67—22no—
222C2×D4×C67—22no—
223C2×D4×C67—22no—
224C2×D4×C67—82no—
225C2×D4×C67—82no—
226C2×D4×C67—82no—
227C2×D4×C67—82no—
228C2×D4×C67C2412yes—
229C2×D4×C67C2412yes—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—24no—
235C22×C4×C67—24no—
236C22×C4×C67—82no—
237C22×C4×C67—82no—
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D412yes—
244C22×C4×C67C2412yes—
245C22×C4×C67C2411yescharacteristic
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—
254C22⋊C4×C67—24no—
255C22⋊C4×C67—24no—
256C22⋊C4×C67—24no—
257C22⋊C4×C67—24no—
258C22⋊C4×C67C2×D414yes—
259C22⋊C4×C67C2×D414yes—
260C42×C67C2×D412yes—
261C42×C67C2×D412yes—
262C42×C67C2412yes—
263C42×C67C2412yes—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—42no—
270C23×C67—42no—
271C23×C67—42no—
272C23×C67—42no—
273C23×C67—42no—
274C23×C67—42no—
275C23×C67C22×D412yes—
276C23×C67C22×D411yescharacteristic
277D4×C67—22no—
278D4×C67—22no—
279D4×C67—22no—
280D4×C67—22no—
281D4×C67—42no—
282D4×C67—42no—
283D4×C67—84no—
284D4×C67—84no—
285D4×C67—84no—
286D4×C67—84no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—24no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—42no—
298C2×C4×C67—42no—
299C2×C4×C67—84no—
300C2×C4×C67—84no—
301C2×C4×C67C22×D412yes—
302C2×C4×C67C22×D412yes—
303C2×C4×C67C22×D412yes—
304C2×C4×C67C22×D412yes—
305C2×C4×C67C22×D412yes—
306C2×C4×C67C22×D411yescharacteristic
307C2×C4×C672−1+412yes—
308C2×C4×C672−1+412yes—
309C2×C4×C67C2511yescharacteristic
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—42no—
315C2×Dic67—42no—
316C2×Dic67—42no—
317C2×Dic67—42no—
318C2×Dic67—84no—
319Dic134—84no—
320Dic134—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—42no—
330C22×C67—42no—
331C22×C67—42no—
332C22×C67—42no—
333C22×C67—42no—
334C22×C67—42no—
335C22×C67—84no—
336C22×C67—84no—
337C22×C67#53612yes—
338C22×C67#57612yes—
339C22×C67#57712yes—
340C22×C67C23×D411yescharacteristic
341C4×C67—22no—
342C4×C67—22no—
343C4×C67—22no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67—42no—
347C4×C67—42no—
348C4×C67#53612yes—
349C4×C67C2×2−1+411yescharacteristic
350C4×C67C2×2−1+411yescharacteristic
351Dic67—42no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355C2×#3241—671nomaximal, Sylow
356C2×C67—42no—
357C2×C67—82no—
358C2×C67—82no—
359C2×C67#324114yescomplemented
360C2×C67C2×#53611yescharacteristic
361C2×C67C2×#57611yescharacteristic
362C2×C67C2×#57711yescharacteristic
363C2×#544—671no—
364C2×#540D6711yescharacteristic
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—678no—
381#544—1344no—
382#540—24no—
383#540C2×D6718yes—
384C2×C4⋊Q8—671no—
385C2×C4⋊Q8—671no—
386C2×C4⋊Q8—1341no—
387C2×#127C2×D6711yescharacteristic
388C2×#125—671no—
389C2×#125—671no—
390C2×#125—1341no—
391C2×#125C2×D6711yescharacteristic
392C2×#123—21no—
393C2×#123—21no—
394C2×C22⋊Q8—1341no—
395C2×C22⋊Q8—1341no—
396C2×#121—21no—
397C2×#121—21no—
398C2×#121C2×D6711yescharacteristic
399C2×#121C2×D6711yescharacteristic
400C2×C4×D4C2×D6711yescharacteristic
401C2×C4×D4C2×D6711yescharacteristic
402C2×#117—671no—
403C2×#117C2×D6711yescharacteristic
404C22×C4⋊C4—671no—
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—1341no—
441C22×Q8—1341no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C22×D6711yescharacteristic
447C22×D4C22×D6711yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—1341no—
451C23×C4C22×D6711yescharacteristic
452C22×C8—671no—
453C22×C8—671no—
454C22×C8—671no—
455C22×C8—671no—
456C4⋊Q8—674no—
457C4⋊Q8—674no—
458C4⋊Q8—1348no—
459C4⋊Q8—1342no—
460C4⋊Q8—1342no—
461#127—22no—
462#127C22×D6714yes—
463#125—22no—
464#125—674no—
465#125—674no—
466#125—1348no—
467#125—1342no—
468#125—1342no—
469#125C22×D6714yes—
470#123—28no—
471#123—28no—
472C22⋊Q8—1348no—
473C22⋊Q8—1348no—
474#121—22no—
475#121—22no—
476#121—28no—
477#121—28no—
478#121C22×D6714yes—
479#121C22×D6714yes—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4C22×D6714yes—
483C4×D4C22×D6714yes—
484#117—674no—
485#117—1342no—
486#117C22⋊D6714yes—
487#117C22×D6714yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—671no—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—674no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1342no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4C22⋊D6711yescharacteristic
504C2×C4⋊C4C22⋊D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4C22⋊D6711yescharacteristic
513C2×C22⋊C4C22⋊D6711yescharacteristic
514C2×C42—1341no—
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—21no—
540C24—21no—
541C24C2×C22⋊D6711yescharacteristic
542C2×Q8—5362no—
543C2×Q8—5362no—
544C2×Q8—1344no—
545C2×Q8—1344no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C23×D6712yes—
561C2×D4C23×D6712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—5362no—
571C22×C4—1341no—
572C22×C4—1341no—
573C22×C4—1341no—
574C22×C4—1341no—
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—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—672no—
597C4⋊C4—672no—
598C4⋊C4—672no—
599C4⋊C4—672no—
600C4⋊C4—1344no—
601C4⋊C4—1341no—
602C4⋊C4—1341no—
603C4⋊C4—1341no—
604C4⋊C4—1341no—
605C4⋊C4—1344no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4C2×C22⋊D6714yes—
612C4⋊C4C2×C22⋊D6714yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—1344no—
620C22⋊C4C2×C22⋊D6714yes—
621C22⋊C4C2×C22⋊D6714yes—
622C42—1344no—
623C42C2×C22⋊D6712yes—
624C42C2×C22⋊D6712yes—
625C42C23×D6712yes—
626C42C23×D6712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D6712yes—
639C23C22×C22⋊D6711yescharacteristic
640Q8—5364no—
641Q8—5364no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
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—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—2682no—
667C2×C4—2682no—
668C2×C4—2682no—
669C2×C4—2682no—
670C2×C4—5364no—
671C2×C4—1342no—
672C2×C4—1342no—
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#1452409012yes—
682C2×C4#1452409012yes—
683C2×C4C24×D6711yescharacteristic
684C8—1342no—
685C8—1342no—
686C8—1342no—
687C8—1342no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1686396712yes—
701C22#1686419912yes—
702C22#1686420712yes—
703C22C23×C22⋊D6711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—2682no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4#1686396712yes—
716C4C2×#1452409011yescharacteristic
717C4C2×#1452409011yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#2257145614yesdirect product factor
722C2C2×#1686396711yescharacteristic
723C2C2×#1686419911yescharacteristic
724C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#540×C67C2
socleC23×C67C22×D4
hypercenterC2×#540D67
hypocenterC67C2×#3241
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#16864024C2semidirect
2. #22571456C2direct (N × H)
3. C2×#16863806C2semidirect
4. C2×#16863795C2semidirect
5. C2×#16863760C2semidirect
6. C2×#16863742C2semidirect
7. C2×#16863712C2semidirect
8. C2×#16863717C2semidirect
9. C2×#16863717C2semidirect
10. C2×#16863707C2semidirect
11. C2×#16863696C2semidirect
12. C2×#16863696C2semidirect
13. C2×#16863686C2semidirect
14. C2×#16863676C2semidirect
15. C2×#16863457C2semidirect
18. #16864024C22semidirect
29. #16863806C22semidirect
30. #16863795C22semidirect
31. #16863760C22semidirect
32. #16863742C22semidirect
33. #16863717C22semidirect
34. #16863717C22semidirect
35. #16863712C22semidirect
36. #16863707C22semidirect
37. #16863696C22semidirect
38. #16863696C22semidirect
39. #16863686C22semidirect
40. #16863676C22semidirect
41. #16863457C22semidirect
359. C2×C67#3241semidirect
379. C67C2×#3241semidirect
721. C2#22571456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640242
#225714562
C2×#168638062
C2×#168637952
C2×#168637602
C2×#168637422
C2×#168637122
C2×#168637172
C2×#168637072
C2×#168636962
C2×#168636862
C2×#168636762
C2×#168634572
C2×#540×C672
C2×#324167