Finite Group Databasebeta

← C2×#22571501 #31728062

Subgroups — C2×#22571501 #31728062

Order 17152.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864024C211yesmaximal, characteristic, complemented
2#22571501C2116yesmaximal, direct product factor
3C2×#16863802C211yesmaximal, characteristic, complemented
4C2×#16863792C211yesmaximal, characteristic, complemented
5C2×#16863755C211yesmaximal, characteristic, complemented
6C2×#16863750C211yesmaximal, characteristic, complemented
7C2×#16863712C211yesmaximal, characteristic
8C2×#16863734C211yesmaximal, characteristic, complemented
9C2×#16863717C211yesmaximal, characteristic
10C2×#16863724C211yesmaximal, characteristic, complemented
11C2×#16863703C211yesmaximal, characteristic, complemented
12C2×#16863681C211yesmaximal, characteristic, complemented
13C2×#16863696C211yesmaximal, characteristic, complemented
14C2×#16863686C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#542×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#16863802C2218yescomplemented
30#16863792C2218yescomplemented
31#16863755C2218yescomplemented
32#16863750C2218yescomplemented
33#16863734C2218yescomplemented
34#16863724C2218yescomplemented
35#16863717C2218yes—
36#16863712C2218yes—
37#16863703C2218yescomplemented
38#16863696C2218yescomplemented
39#16863686C2218yescomplemented
40#16863681C2218yescomplemented
41#16863457C2218yescomplemented
42C2×#14523976C2211yescharacteristic
43C2×#14523976C2211yescharacteristic
44C2×#14523974C2211yescharacteristic
45C2×#14523974C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
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#542×C67—24no—
65#542×C67C2218yes—
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#126×C67—21no—
68C2×#124×C67—21no—
69C2×#124×C67C2211yescharacteristic
70C2×#123×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×#121×C67C2211yescharacteristic
74C2×C4×Q8×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#14523974C2314yes—
116#14523974C2314yes—
117#14523974C2314yes—
118#14523974C2314yes—
119#14523974C2314yes—
120#14523974C2314yes—
121C4⋊(C67⋊C8)C2314yes—
122C4⋊(C67⋊C8)C2314yes—
123#14523967C2314yes—
124#14523967C2314yes—
125#14523967C2314yes—
126#14523967C2314yes—
127#14523964C2314yes—
128#14523964C2314yes—
129#14523964C2314yes—
130#14523964C2314yes—
131C22⋊(C67⋊C8)C2314yes—
132C22⋊(C67⋊C8)C2314yes—
133#14523954C2314yes—
134C4×C67⋊C8C2314yes—
135C22×Q8×C67—21no—
136C22×Q8×C67C2311yescharacteristic
137C22×D4×C67—21no—
138C22×D4×C67C2311yescharacteristic
139C23×C4×C67—21no—
140C23×C4×C67C2311yescharacteristic
141C4⋊Q8×C67—22no—
142C4⋊Q8×C67C2314yes—
143#126×C67—28no—
144#124×C67—28no—
145#124×C67—22no—
146#124×C67C2314yes—
147#123×C67—28no—
148C22⋊Q8×C67—22no—
149C22⋊Q8×C67—28no—
150C22⋊Q8×C67C2314yes—
151#121×C67—22no—
152#121×C67C2314yes—
153C4×Q8×C67—22no—
154C4×Q8×C67C2314yes—
155C4×D4×C67—22no—
156C4×D4×C67C2314yes—
157#117×C67D414yes—
158#117×C67C2314yes—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67D411yescharacteristic
163C2×C4⋊C4×C67D411yescharacteristic
164C2×C4⋊C4×C67C2311yescharacteristic
165C2×C4⋊C4×C67C2311yescharacteristic
166C2×C22⋊C4×C67—21no—
167C2×C22⋊C4×C67—21no—
168C2×C22⋊C4×C67—21no—
169C2×C22⋊C4×C67—21no—
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67D411yescharacteristic
172C2×C22⋊C4×C67D411yescharacteristic
173C2×C42×C67—21no—
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×C67C2×D411yescharacteristic
213C2×Q8×C67—21no—
214C2×Q8×C67—24no—
215C2×Q8×C67—22no—
216C2×Q8×C67—22no—
217C2×Q8×C67—82no—
218C2×Q8×C67C2412yes—
219C2×D4×C67—24no—
220C2×D4×C67—21no—
221C2×D4×C67—22no—
222C2×D4×C67—22no—
223C2×D4×C67—82no—
224C2×D4×C67C2412yes—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—24no—
231C22×C4×C67—82no—
232C22×C4×C67C2×D411yescharacteristic
233C22×C4×C67C2×D411yescharacteristic
234C22×C4×C67C2×D411yescharacteristic
235C22×C4×C67C2×D411yescharacteristic
236C22×C4×C67C2×D411yescharacteristic
237C22×C4×C67C2×D412yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2411yescharacteristic
240C4⋊C4×C67—24no—
241C4⋊C4×C67—24no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67C2×D414yes—
246C4⋊C4×C67C2×D414yes—
247C4⋊C4×C67C2412yes—
248C4⋊C4×C67C2412yes—
249C22⋊C4×C67—24no—
250C22⋊C4×C67—24no—
251C22⋊C4×C67—24no—
252C22⋊C4×C67—24no—
253C22⋊C4×C67—24no—
254C22⋊C4×C67C2×D414yes—
255C22⋊C4×C67C2×D414yes—
256C42×C67—24no—
257C42×C67C2×D412yes—
258C42×C67C2×D412yes—
259C42×C67C2412yes—
260C42×C67C2412yes—
261C23×C67—22no—
262C23×C67—22no—
263C23×C67—22no—
264C23×C67—22no—
265C23×C67—42no—
266C23×C67—42no—
267C23×C67—42no—
268C23×C67C22×D412yes—
269C23×C67C22×D411yescharacteristic
270Q8×C67—22no—
271Q8×C67—22no—
272Q8×C67—42no—
273Q8×C67—84no—
274D4×C67—22no—
275D4×C67—22no—
276D4×C67—42no—
277D4×C67—84no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
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—42no—
290C2×C4×C67—42no—
291C2×C4×C67—42no—
292C2×C4×C67—84no—
293C2×C4×C67C22×D412yes—
294C2×C4×C67C22×D412yes—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D411yescharacteristic
299C2×C4×C672−1+412yes—
300C2×C4×C672−1+412yes—
301C2×C4×C67C2511yescharacteristic
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309C2×Dic67—42no—
310C2×Dic67—84no—
311Dic134—84no—
312Dic134—84no—
313C67⋊C8—22no—
314C67⋊C8—22no—
315C67⋊C8—22no—
316C67⋊C8—22no—
317C22×C67—22no—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—44no—
321C22×C67—42no—
322C22×C67—42no—
323C22×C67—42no—
324C22×C67—84no—
325C22×C67#53612yes—
326C22×C67#57712yes—
327C22×C67#57712yes—
328C22×C67C23×D411yescharacteristic
329C4×C67—22no—
330C4×C67—22no—
331C4×C67—22no—
332C4×C67—22no—
333C4×C67—22no—
334C4×C67—42no—
335C4×C67—42no—
336C4×C67—42no—
337C4×C67#53612yes—
338C4×C67C2×2−1+411yescharacteristic
339C4×C67C2×2−1+411yescharacteristic
340Dic67—42no—
341Dic67—42no—
342Dic67—42no—
343Dic67—42no—
344C2×#3244—671nomaximal, Sylow
345C2×C67—42no—
346C2×C67—82no—
347C2×C67#324414yescomplemented
348C2×C67C2×#53611yescharacteristic
349C2×C67C2×#57711yescharacteristic
350C2×C67C2×#57711yescharacteristic
351C2×#544—671no—
352C2×#542D6711yescharacteristic
353#3244—6716no—
354C2×#501—671no—
355C2×#498—671no—
356C2×#489—671no—
357C2×#488—671no—
358C2×#481—671no—
359C2×#485—671no—
360C2×#482—671no—
361C2×#483—671no—
362C2×#479—671no—
363C2×#475—671no—
364C2×#478—671no—
365C2×#476—671no—
366C2×#433—671no—
367C67C2×#324411yescharacteristic, complemented, Sylow
368#544—678no—
369#544—1344no—
370#542—24no—
371#542C2×D6718yes—
372C2×C4⋊Q8—671no—
373C2×C4⋊Q8—671no—
374C2×C4⋊Q8—1341no—
375C2×C4⋊Q8C2×D6711yescharacteristic
376C2×#126—21no—
377C2×#125—671no—
378C2×#125—671no—
379C2×#125—1341no—
380C2×#124—21no—
381C2×#124C2×D6711yescharacteristic
382C2×#123—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—1341no—
385C2×C22⋊Q8—1341no—
386C2×C22⋊Q8C2×D6711yescharacteristic
387C2×#121C2×D6711yescharacteristic
388C2×C4×Q8C2×D6711yescharacteristic
389C2×C4×D4C2×D6711yescharacteristic
390C2×#117—671no—
391C2×#117C2×D6711yescharacteristic
392C22×C4⋊C4—671no—
393#501—678no—
394#498—678no—
395#489—678no—
396#488—678no—
397#485—678no—
398#483—678no—
399#482—678no—
400#481—678no—
401#479—678no—
402#478—678no—
403#476—678no—
404#475—678no—
405#433—678no—
406C2×#107—671no—
407C2×#107—671no—
408C2×#106—671no—
409C2×#106—671no—
410C2×#106—671no—
411C2×#106—671no—
412C2×#106—671no—
413C2×#106—671no—
414C2×C4⋊C8—671no—
415C2×C4⋊C8—671no—
416C2×#103—671no—
417C2×#103—671no—
418C2×#103—671no—
419C2×#103—671no—
420C2×#102—671no—
421C2×#102—671no—
422C2×#102—671no—
423C2×#102—671no—
424C2×C22⋊C8—671no—
425C2×C22⋊C8—671no—
426C2×#97—671no—
427C2×C4×C8—671no—
428C22×Q8—21no—
429C22×Q8—1341no—
430C22×Q8—1341no—
431C22×Q8C22×D6711yescharacteristic
432C22×D4—21no—
433C22×D4C22×D6711yescharacteristic
434C23×C4—21no—
435C23×C4—1341no—
436C23×C4C22×D6711yescharacteristic
437C22×C8—671no—
438C22×C8—671no—
439C22×C8—671no—
440C22×C8—671no—
441C4⋊Q8—22no—
442C4⋊Q8—674no—
443C4⋊Q8—674no—
444C4⋊Q8—1348no—
445C4⋊Q8—1342no—
446C4⋊Q8—1342no—
447C4⋊Q8C22×D6714yes—
448#126—28no—
449#125—674no—
450#125—674no—
451#125—1348no—
452#125—1342no—
453#125—1342no—
454#124—28no—
455#124—22no—
456#124C22×D6714yes—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—1348no—
461C22⋊Q8—1348no—
462C22⋊Q8C22×D6714yes—
463#121—22no—
464#121C22×D6714yes—
465C4×Q8—22no—
466C4×Q8C22×D6714yes—
467C4×D4—22no—
468C4×D4C22×D6714yes—
469#117—674no—
470#117—1342no—
471#117C22⋊D6714yes—
472#117C22×D6714yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—671no—
477C2×C4⋊C4—671no—
478C2×C4⋊C4—674no—
479C2×C4⋊C4—671no—
480C2×C4⋊C4—671no—
481C2×C4⋊C4—1341no—
482C2×C4⋊C4—1342no—
483C2×C4⋊C4—1341no—
484C2×C4⋊C4—1341no—
485C2×C4⋊C4—1341no—
486C2×C4⋊C4—1341no—
487C2×C4⋊C4—1341no—
488C2×C4⋊C4—1341no—
489C2×C4⋊C4C22⋊D6711yescharacteristic
490C2×C4⋊C4C22⋊D6711yescharacteristic
491C2×C4⋊C4C22×D6711yescharacteristic
492C2×C4⋊C4C22×D6711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1341no—
499C2×C22⋊C4C22⋊D6711yescharacteristic
500C2×C22⋊C4C22⋊D6711yescharacteristic
501C2×C42—21no—
502C2×C42—1341no—
503C2×C42C22×D6711yescharacteristic
504C2×C42C22×D6711yescharacteristic
505#107—674no—
506#107—674no—
507#106—674no—
508#106—674no—
509#106—674no—
510#106—674no—
511#106—674no—
512#106—674no—
513C4⋊C8—674no—
514C4⋊C8—674no—
515#103—674no—
516#103—674no—
517#103—674no—
518#103—674no—
519#102—674no—
520#102—674no—
521#102—674no—
522#102—674no—
523C22⋊C8—674no—
524C22⋊C8—674no—
525#97—674no—
526C4×C8—674no—
527C24—21no—
528C24C2×C22⋊D6711yescharacteristic
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—5362no—
535C2×Q8—5362no—
536C2×Q8—1344no—
537C2×Q8—1344no—
538C2×Q8C23×D6712yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—82no—
544C2×D4C23×D6712yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—5362no—
553C22×C4—1341no—
554C22×C4—1341no—
555C22×C4—1341no—
556C22×C4—1341no—
557C22×C4—1344no—
558C22×C4C2×C22⋊D6712yes—
559C22×C4C2×C22⋊D6711yescharacteristic
560C22×C4C2×C22⋊D6711yescharacteristic
561C22×C4C2×C22⋊D6711yescharacteristic
562C22×C4C2×C22⋊D6711yescharacteristic
563C22×C4C2×C22⋊D6711yescharacteristic
564C22×C4C23×D6712yes—
565C22×C4C23×D6711yescharacteristic
566C2×C8—672no—
567C2×C8—672no—
568C2×C8—672no—
569C2×C8—672no—
570C2×C8—1342no—
571C2×C8—1342no—
572C2×C8—1342no—
573C2×C8—1342no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—672no—
580C4⋊C4—672no—
581C4⋊C4—672no—
582C4⋊C4—672no—
583C4⋊C4—1344no—
584C4⋊C4—1341no—
585C4⋊C4—1341no—
586C4⋊C4—1341no—
587C4⋊C4—1341no—
588C4⋊C4—1344no—
589C4⋊C4—1344no—
590C4⋊C4—1344no—
591C4⋊C4—1344no—
592C4⋊C4—1344no—
593C4⋊C4—1344no—
594C4⋊C4C2×C22⋊D6714yes—
595C4⋊C4C2×C22⋊D6714yes—
596C4⋊C4C23×D6712yes—
597C4⋊C4C23×D6712yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—1344no—
604C22⋊C4C2×C22⋊D6714yes—
605C22⋊C4C2×C22⋊D6714yes—
606C42—24no—
607C42—1344no—
608C42C2×C22⋊D6712yes—
609C42C2×C22⋊D6712yes—
610C42C23×D6712yes—
611C42C23×D6712yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D6712yes—
620C23C22×C22⋊D6711yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—5364no—
626Q8—5364no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—84no—
646C2×C4—2682no—
647C2×C4—2682no—
648C2×C4—2682no—
649C2×C4—2682no—
650C2×C4—5364no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4C22×C22⋊D6712yes—
656C2×C4C22×C22⋊D6712yes—
657C2×C4C22×C22⋊D6712yes—
658C2×C4C22×C22⋊D6712yes—
659C2×C4C22×C22⋊D6712yes—
660C2×C4C22×C22⋊D6711yescharacteristic
661C2×C4#1452409012yes—
662C2×C4#1452409012yes—
663C2×C4C24×D6711yescharacteristic
664C8—1342no—
665C8—1342no—
666C8—1342no—
667C8—1342no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1686396712yes—
677C22#1686420412yes—
678C22#1686420712yes—
679C22C23×C22⋊D6711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2682no—
689C4—2682no—
690C4—2682no—
691C4—2682no—
692C4#1686396712yes—
693C4C2×#1452409011yescharacteristic
694C4C2×#1452409011yescharacteristic
695C2—42no—
696C2—82no—
697C2#2257150114yesdirect product factor
698C2C2×#1686396711yescharacteristic
699C2C2×#1686420411yescharacteristic
700C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#542×C67C2
socleC23×C67C22×D4
prime radicalC2×#121×C67C22
hypercenterC2×#542D67
hypocenterC67C2×#3244
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16864024C2semidirect
2. #22571501C2direct (N × H)
3. C2×#16863802C2semidirect
4. C2×#16863792C2semidirect
5. C2×#16863755C2semidirect
6. C2×#16863750C2semidirect
8. C2×#16863734C2semidirect
10. C2×#16863724C2semidirect
11. C2×#16863703C2semidirect
12. C2×#16863681C2semidirect
13. C2×#16863696C2semidirect
14. C2×#16863686C2semidirect
15. C2×#16863457C2semidirect
18. #16864024C22semidirect
29. #16863802C22semidirect
30. #16863792C22semidirect
31. #16863755C22semidirect
32. #16863750C22semidirect
33. #16863734C22semidirect
34. #16863724C22semidirect
37. #16863703C22semidirect
38. #16863696C22semidirect
39. #16863686C22semidirect
40. #16863681C22semidirect
41. #16863457C22semidirect
347. C2×C67#3244semidirect
367. C67C2×#3244semidirect
697. C2#22571501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640242
#225715012
C2×#168638022
C2×#168637922
C2×#168637552
C2×#168637502
C2×#168637122
C2×#168637342
C2×#168637172
C2×#168637242
C2×#168637032
C2×#168636812
C2×#168636962
C2×#168636862
C2×#168634572
C2×#542×C672
C2×#324467