Finite Group Databasebeta

← C2×#22573045 #31735622

Subgroups — C2×#22573045 #31735622

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864124C211yesmaximal, characteristic, complemented
2#22573045C2116yesmaximal, direct product factor
3C2×#16863764C211yesmaximal, characteristic, complemented
4C2×#16863755C211yesmaximal, characteristic
5C2×#16863750C211yesmaximal, characteristic
6C2×#16863703C211yesmaximal, characteristic, complemented
7C2×#16863691C211yesmaximal, characteristic, complemented
8C2×#16863696C211yesmaximal, characteristic
9C2×#16863615C211yesmaximal, characteristic
10C2×#16863615C211yesmaximal, characteristic
11C2×#16863603C211yesmaximal, characteristic, complemented
12C2×#16863527C211yesmaximal, characteristic, complemented
13C2×#16863501C211yesmaximal, characteristic, complemented
14C2×#16863496C211yesmaximal, characteristic
15C2×C4×#11761618C211yesmaximal, characteristic, complemented
16C2×#556×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761616C2211yescharacteristic
20#16864124—24no—
21#16864124C2218yescomplemented
22C2×#14524043C2211yescharacteristic
23C2×#14524041—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524035C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524033—21no—
28C2×C4×Dic134C2211yescharacteristic
29C2×C4×Dic134C2211yescharacteristic
30C2×C4×Dic134C2211yescharacteristic
31C2×#14524008—21no—
32#16863764C2218yescomplemented
33#16863755C2218yes—
34#16863750C2218yes—
35#16863703C2218yescomplemented
36#16863696C2218yes—
37#16863691C2218yescomplemented
38#16863615C2218yes—
39#16863615C2218yes—
40#16863603C2218yescomplemented
41#16863527C2218yescomplemented
42#16863501C2218yescomplemented
43#16863496C2218yes—
44C4×#11761618C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49C2×C4⋊(C67⋊C8)C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×#14523967C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#556×C67—24no—
65#556×C67C2218yes—
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#126×C67—21no—
68C2×#126×C67—21no—
69C2×#124×C67C2211yescharacteristic
70C2×#124×C67C2211yescharacteristic
71C2×C22⋊Q8×C67—21no—
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×D4×C67C2211yescharacteristic
76C2×#117×C67—21no—
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C2×#11761618—24no—
80C2×#11761618—24no—
81C2×#11761618C2314yes—
82C2×#11761618C2314yes—
83C2×#11761616—24no—
84C2×#11761616C2314yes—
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89#14524043—22no—
90#14524043C2314yes—
91#14524041—28no—
92#14524035—22no—
93#14524035—22no—
94#14524035C2314yes—
95#14524035C2314yes—
96#14524033—28no—
97#14524033—28no—
98C4×Dic134—22no—
99C4×Dic134—22no—
100C4×Dic134—22no—
101C4×Dic134C2314yes—
102C4×Dic134C2314yes—
103C4×Dic134C2314yes—
104#14524008—28no—
105C2×C4⋊Dic67—21no—
106C2×C4⋊Dic67C2311yescharacteristic
107C2×C4⋊Dic67C2311yescharacteristic
108C2×C4⋊Dic67C2311yescharacteristic
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C2×Dic67⋊C4—21no—
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×Dic67⋊C4—21no—
115C2×Dic67⋊C4—21no—
116C2×C4×Dic67—21no—
117C2×C4×Dic67—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523974C2314yes—
122C4⋊(C67⋊C8)C2314yes—
123C4⋊(C67⋊C8)C2314yes—
124C4⋊(C67⋊C8)C2314yes—
125#14523967C2314yes—
126#14523967C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523966C2314yes—
132#14523964C2314yes—
133#14523964C2314yes—
134#14523964C2314yes—
135#14523954C2314yes—
136#14523954C2314yes—
137C4×C67⋊C8C2314yes—
138C22×Q8×C67D411yescharacteristic
139C22×Q8×C67C2311yescharacteristic
140C22×Q8×C67C2311yescharacteristic
141C22×D4×C67C2311yescharacteristic
142C23×C4×C67—21no—
143C4⋊Q8×C67—22no—
144C4⋊Q8×C67C2314yes—
145#126×C67—28no—
146#126×C67—28no—
147#124×C67—22no—
148#124×C67—22no—
149#124×C67C2314yes—
150#124×C67C2314yes—
151C22⋊Q8×C67—28no—
152C4×Q8×C67—22no—
153C4×Q8×C67—22no—
154C4×Q8×C67D414yes—
155C4×Q8×C67C2314yes—
156C4×Q8×C67C2314yes—
157C4×Q8×C67C2314yes—
158C4×D4×C67—22no—
159C4×D4×C67C2314yes—
160#117×C67—28no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C22⋊C4×C67—21no—
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C42×C67—21no—
175C2×C42×C67—21no—
176C2×C42×C67C2311yescharacteristic
177C2×C42×C67C2311yescharacteristic
178C2×C42×C67C2311yescharacteristic
179C2×Dic134—21no—
180C2×Dic134—22no—
181C2×Dic134—24no—
182C2×Dic134—44no—
183C2×Dic134#4114yes—
184C2×Dic134C2412yes—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C22×Dic67—21no—
189#11761618—28no—
190#11761618—28no—
191#11761616—28no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8—22no—
194C2×C67⋊C8—22no—
195C2×C67⋊C8—22no—
196C2×C67⋊C8C2412yes—
197C2×C67⋊C8C2412yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C4⋊Dic67—24no—
201C4⋊Dic67—21no—
202C4⋊Dic67—21no—
203C4⋊Dic67—21no—
204C4⋊Dic67C2412yes—
205C4⋊Dic67C2412yes—
206C4⋊Dic67C2412yes—
207Dic67⋊C4—24no—
208Dic67⋊C4—24no—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212Dic67⋊C4—24no—
213Dic67⋊C4—24no—
214C4×Dic67—24no—
215C4×Dic67—24no—
216C4×Dic67—24no—
217C24×C67—21no—
218C2×Q8×C67—21no—
219C2×Q8×C67—21no—
220C2×Q8×C67—22no—
221C2×Q8×C67—22no—
222C2×Q8×C67—22no—
223C2×Q8×C67—22no—
224C2×Q8×C67—42no—
225C2×Q8×C67C2×D414yes—
226C2×Q8×C67C2412yes—
227C2×Q8×C67C2412yes—
228C2×D4×C67—21no—
229C2×D4×C67—22no—
230C2×D4×C67—22no—
231C2×D4×C67C2412yes—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—24no—
236C22×C4×C67—44no—
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2411yescharacteristic
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—24no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67C2×D414yes—
250C4⋊C4×C67C2×D414yes—
251C4⋊C4×C67C2×D414yes—
252C4⋊C4×C67C2412yes—
253C22⋊C4×C67—24no—
254C22⋊C4×C67—24no—
255C22⋊C4×C67—24no—
256C22⋊C4×C67—24no—
257C22⋊C4×C67—24no—
258C42×C67—24no—
259C42×C67—24no—
260C42×C67C2×D412yes—
261C42×C67C2×D412yes—
262C42×C67C2×D412yes—
263C42×C67C2412yes—
264C42×C67C2412yes—
265C42×C67C2412yes—
266C23×C67—22no—
267C23×C67—42no—
268C23×C67—42no—
269C23×C67—42no—
270C23×C67C22×D411yescharacteristic
271Q8×C67—22no—
272Q8×C67—22no—
273Q8×C67—22no—
274Q8×C67—22no—
275Q8×C67—44no—
276Q8×C67—42no—
277Q8×C67—42no—
278D4×C67—22no—
279D4×C67—22no—
280D4×C67—42no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
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—48no—
291C2×C4×C67—42no—
292C2×C4×C67—42no—
293C2×C4×C67—42no—
294C2×C4×C67C22×D412yes—
295C2×C4×C67C22×D412yes—
296C2×C4×C67C22×D412yes—
297C2×C4×C67C22×D412yes—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D412yes—
300C2×C4×C67C22×D411yescharacteristic
301C2×C4×C67C2×#4112yes—
302C2×C4×C672−1+412yes—
303C2×C4×C67C2511yescharacteristic
304C2×Dic67—24no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—42no—
310C2×Dic67—42no—
311C2×Dic67—42no—
312Dic134—24no—
313Dic134—22no—
314Dic134—48no—
315Dic134C2×#4114yes—
316C67⋊C8—22no—
317C67⋊C8—22no—
318C67⋊C8—22no—
319C67⋊C8—22no—
320C22×C67—42no—
321C22×C67—42no—
322C22×C67—42no—
323C22×C67—84no—
324C22×C67#54812yes—
325C22×C67#57512yes—
326C22×C67#57812yes—
327C22×C67C23×D411yescharacteristic
328C4×C67—22no—
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#54812yes—
338C4×C67C22×#4111yescharacteristic
339C4×C67C2×2−1+411yescharacteristic
340Dic67—24no—
341Dic67—42no—
342Dic67—42no—
343Dic67—42no—
344C2×#3377—671nomaximal, Sylow
345C2×C67—82no—
346C2×C67#337714yescomplemented
347C2×C67C2×#54811yescharacteristic
348C2×C67C2×#57511yescharacteristic
349C2×C67C2×#57811yescharacteristic
350C2×#557—671no—
351C2×#556D6711yescharacteristic
352#3377—6716no—
353C2×#491—671no—
354C2×#489—671no—
355C2×#488—671no—
356C2×#479—671no—
357C2×#477—671no—
358C2×#478—671no—
359C2×#464—671no—
360C2×#464—671no—
361C2×#462—671no—
362C2×#446—671no—
363C2×#441—671no—
364C2×#440—671no—
365C2×C4×Q16—671no—
366C67C2×#337711yescharacteristic, complemented, Sylow
367C22×Q16—671no—
368C22×Q16—671no—
369C22×SD16—671no—
370#557—678no—
371#557—1344no—
372#556—24no—
373#556C2×D6718yes—
374C2×C4⋊Q8—671no—
375C2×C4⋊Q8—1341no—
376C2×C4⋊Q8C2×D6711yescharacteristic
377C2×#126—21no—
378C2×#126—21no—
379C2×#125—671no—
380C2×#125—671no—
381C2×#125—1341no—
382C2×#125—1341no—
383C2×#124C2×D6711yescharacteristic
384C2×#124C2×D6711yescharacteristic
385C2×C22⋊Q8—21no—
386C2×C4×Q8—671no—
387C2×C4×Q8—671no—
388C2×C4×Q8—671no—
389C2×C4×Q8—1341no—
390C2×C4×Q8C2×D6711yescharacteristic
391C2×C4×Q8C2×D6711yescharacteristic
392C2×C4×Q8C2×D6711yescharacteristic
393C2×C4×D4C2×D6711yescharacteristic
394C2×#117—21no—
395#491—678no—
396#489—678no—
397#488—678no—
398#479—678no—
399#478—678no—
400#477—678no—
401#464—678no—
402#464—678no—
403#462—678no—
404#446—678no—
405#441—678no—
406#440—678no—
407C4×Q16—678no—
408C2×#107—671no—
409C2×#107—671no—
410C2×#106—671no—
411C2×C4⋊C8—671no—
412C2×C4⋊C8—671no—
413C2×C4⋊C8—671no—
414C2×#103—671no—
415C2×#103—671no—
416C2×#103—671no—
417C2×#103—671no—
418C2×#103—671no—
419C2×#103—671no—
420C2×#103—671no—
421C2×#102—671no—
422C2×#102—671no—
423C2×#102—671no—
424C2×#97—671no—
425C2×#97—671no—
426C2×C4×C8—671no—
427C22×Q8—671no—
428C22×Q8—1341no—
429C22×Q8C22⋊D6711yescharacteristic
430C22×Q8C22×D6711yescharacteristic
431C22×Q8C22×D6711yescharacteristic
432C22×D4C22×D6711yescharacteristic
433C23×C4—21no—
434C2×Q16—674no—
435C2×Q16—674no—
436C2×Q16—1344no—
437C2×Q16—1344no—
438C2×SD16—674no—
439C2×SD16—1344no—
440C22×C8—671no—
441C22×C8—671no—
442C22×C8—671no—
443C22×C8—671no—
444C4⋊Q8—22no—
445C4⋊Q8—674no—
446C4⋊Q8—1348no—
447C4⋊Q8—1342no—
448C4⋊Q8C22×D6714yes—
449#126—28no—
450#126—28no—
451#125—674no—
452#125—674no—
453#125—1348no—
454#125—1348no—
455#125—1342no—
456#125—1342no—
457#124—22no—
458#124—22no—
459#124C22×D6714yes—
460#124C22×D6714yes—
461C22⋊Q8—28no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—674no—
465C4×Q8—674no—
466C4×Q8—674no—
467C4×Q8—1348no—
468C4×Q8—1342no—
469C4×Q8—1342no—
470C4×Q8—1342no—
471C4×Q8C22⋊D6714yes—
472C4×Q8C22×D6714yes—
473C4×Q8C22×D6714yes—
474C4×Q8C22×D6714yes—
475C4×D4—22no—
476C4×D4C22×D6714yes—
477#117—28no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—671no—
483C2×C4⋊C4—671no—
484C2×C4⋊C4—671no—
485C2×C4⋊C4—1341no—
486C2×C4⋊C4—1341no—
487C2×C4⋊C4—1341no—
488C2×C4⋊C4—1341no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1341no—
491C2×C4⋊C4—1341no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4C22⋊D6711yescharacteristic
494C2×C4⋊C4C22⋊D6711yescharacteristic
495C2×C4⋊C4C22⋊D6711yescharacteristic
496C2×C4⋊C4C22×D6711yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—1341no—
505C2×C42—1341no—
506C2×C42—1341no—
507C2×C42C22×D6711yescharacteristic
508C2×C42C22×D6711yescharacteristic
509C2×C42C22×D6711yescharacteristic
510#107—674no—
511#107—674no—
512#106—674no—
513C4⋊C8—674no—
514C4⋊C8—674no—
515C4⋊C8—674no—
516#103—674no—
517#103—674no—
518#103—674no—
519#103—674no—
520#103—674no—
521#103—674no—
522#103—674no—
523#102—674no—
524#102—674no—
525#102—674no—
526#97—674no—
527#97—674no—
528C4×C8—674no—
529C24—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—42no—
537C2×Q8—2684no—
538C2×Q8—674no—
539C2×Q8—672no—
540C2×Q8—1344no—
541C2×Q8—1341no—
542C2×Q8—1342no—
543C2×Q8C2×C22⋊D6714yes—
544C2×Q8C23×D6712yes—
545C2×Q8C23×D6712yes—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4C23×D6712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—44no—
555C22×C4—1341no—
556C22×C4—1341no—
557C22×C4—1341no—
558C22×C4—1341no—
559C22×C4C2×C22⋊D6711yescharacteristic
560C22×C4C2×C22⋊D6711yescharacteristic
561C22×C4C2×C22⋊D6711yescharacteristic
562C22×C4C2×C22⋊D6711yescharacteristic
563C22×C4C2×C22⋊D6711yescharacteristic
564C22×C4C2×C22⋊D6711yescharacteristic
565C22×C4C23×D6711yescharacteristic
566Q16—1348no—
567Q16—1348no—
568SD16—1348no—
569C2×C8—672no—
570C2×C8—672no—
571C2×C8—672no—
572C2×C8—672no—
573C2×C8—1342no—
574C2×C8—1342no—
575C2×C8—1342no—
576C2×C8—1342no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—21no—
582C4⋊C4—672no—
583C4⋊C4—672no—
584C4⋊C4—672no—
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⋊C4—1344no—
595C4⋊C4—1344no—
596C4⋊C4C2×C22⋊D6714yes—
597C4⋊C4C2×C22⋊D6714yes—
598C4⋊C4C2×C22⋊D6714yes—
599C4⋊C4C23×D6712yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C42—24no—
606C42—24no—
607C42—1344no—
608C42—1344no—
609C42—1344no—
610C42C2×C22⋊D6712yes—
611C42C2×C22⋊D6712yes—
612C42C2×C22⋊D6712yes—
613C42C23×D6712yes—
614C42C23×D6712yes—
615C42C23×D6712yes—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C22×C22⋊D6711yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—44no—
626Q8—42no—
627Q8—42no—
628Q8—2688no—
629Q8—674no—
630Q8—1344no—
631Q8—1342no—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—48no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—2682no—
649C2×C4—2682no—
650C2×C4—2682no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1344no—
655C2×C4—1342no—
656C2×C4C22×C22⋊D6712yes—
657C2×C4C22×C22⋊D6712yes—
658C2×C4C22×C22⋊D6712yes—
659C2×C4C22×C22⋊D6712yes—
660C2×C4C22×C22⋊D6712yes—
661C2×C4C22×C22⋊D6712yes—
662C2×C4C22×C22⋊D6711yescharacteristic
663C2×C4#41×D6712yes—
664C2×C4#1452409012yes—
665C2×C4C24×D6711yescharacteristic
666C8—1342no—
667C8—1342no—
668C8—1342no—
669C8—1342no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1686405312yes—
675C22#1686419412yes—
676C22#1686421112yes—
677C22C23×C22⋊D6711yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—2682no—
688C4—2682no—
689C4—2682no—
690C4—1344no—
691C4#1686405312yes—
692C4C2×#41×D6711yescharacteristic
693C4C2×#1452409011yescharacteristic
694C2—82no—
695C2#2257304514yesdirect product factor
696C2C2×#1686405311yescharacteristic
697C2C2×#1686419411yescharacteristic
698C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#556×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67C23
hypercenterC2×#556D67
hypocenterC67C2×#3377
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16864124C2semidirect
2. #22573045C2direct (N × H)
3. C2×#16863764C2semidirect
6. C2×#16863703C2semidirect
7. C2×#16863691C2semidirect
11. C2×#16863603C2semidirect
12. C2×#16863527C2semidirect
13. C2×#16863501C2semidirect
15. C2×C4×#11761618C2semidirect
21. #16864124C22semidirect
32. #16863764C22semidirect
35. #16863703C22semidirect
37. #16863691C22semidirect
40. #16863603C22semidirect
41. #16863527C22semidirect
42. #16863501C22semidirect
44. C4×#11761618C22semidirect
346. C2×C67#3377semidirect
366. C67C2×#3377semidirect
695. C2#22573045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641242
#225730452
C2×#168637642
C2×#168637552
C2×#168637502
C2×#168637032
C2×#168636912
C2×#168636962
C2×#168636152
C2×#168636032
C2×#168635272
C2×#168635012
C2×#168634962
C2×C4×#117616182
C2×#556×C672
C2×#337767