Finite Group Databasebeta

← C2×#22573163 #31736368

Subgroups — C2×#22573163 #31736368

Order 17152.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864106C211yesmaximal, characteristic, complemented
2#22573163C2116yesmaximal, direct product factor
3C2×#16863806C211yesmaximal, characteristic, complemented
4C2×#16863802C211yesmaximal, characteristic, complemented
5C2×#16863795C211yesmaximal, characteristic, complemented
6C2×#16863696C211yesmaximal, characteristic, complemented
7C2×#16863696C211yesmaximal, characteristic, complemented
8C2×#16863693C211yesmaximal, characteristic, complemented
9C2×#16863693C211yesmaximal, characteristic, complemented
10C2×#16863676C211yesmaximal, characteristic, complemented
11C2×#16863673C211yesmaximal, characteristic, complemented
12C2×#16863527C211yesmaximal, characteristic, complemented
13C2×#16863506C211yesmaximal, characteristic
14C2×#16863506C211yesmaximal, characteristic
15C2×C4×#11761613C211yesmaximal, characteristic
16C2×#554×C67C211yesmaximal, characteristic, complemented
17C22×#11761613C2211yescharacteristic
18#16864106—24no—
19#16864106C2218yescomplemented
20C2×#14524043C2211yescharacteristic
21C2×#14524035C2211yescharacteristic
22C2×#14524035C2211yescharacteristic
23C2×#14524021—21no—
24C2×#14524021—21no—
25C2×#14524019—21no—
26C2×C4×D268C2211yescharacteristic
27C2×C4×D268C2211yescharacteristic
28C2×C4×D268C2211yescharacteristic
29C2×C4⋊C4×D67—21no—
30#16863806C2218yescomplemented
31#16863802C2218yescomplemented
32#16863795C2218yescomplemented
33#16863696C2218yescomplemented
34#16863696C2218yescomplemented
35#16863693C2218yescomplemented
36#16863693C2218yescomplemented
37#16863676C2218yescomplemented
38#16863673C2218yescomplemented
39#16863527C2218yescomplemented
40#16863506C2218yes—
41#16863506C2218yes—
42C4×#11761613C2218yes—
43C2×#14523976C2211yescharacteristic
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×C4⋊(C67⋊C8)C2211yescharacteristic
53C2×C4⋊(C67⋊C8)C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523964C2211yescharacteristic
56C2×#14523964C2211yescharacteristic
57C2×#14523964C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#554×C67—24no—
65#554×C67C2218yescomplemented
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#125×C67C2211yescharacteristic
68C2×#125×C67C2211yescharacteristic
69C2×C22⋊Q8×C67—21no—
70C2×C22⋊Q8×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C2×C4×D4×C67C2211yescharacteristic
76C22×C4⋊C4×C67—21no—
77C22×Dic134—21no—
78C22×D268C2311yescharacteristic
79C22×C4×D67—21no—
80C22×C4×D67—21no—
81C22×C4×D67—21no—
82C2×#11761613Q818yescomplemented
83C2×#11761613C2314yes—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88#14524043—22no—
89#14524043C2314yes—
90#14524035—22no—
91#14524035—22no—
92#14524035C2314yes—
93#14524035C2314yes—
94#14524021—28no—
95#14524021—28no—
96#14524019—28no—
97C4×D268—22no—
98C4×D268—22no—
99C4×D268—22no—
100C4×D268C2314yes—
101C4×D268C2314yes—
102C4×D268C2314yes—
103C2×C4⋊Dic67—21no—
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—
111C4⋊C4×D67—28no—
112C2×(C2×D67)⋊C4—21no—
113C2×(C2×D67)⋊C4—21no—
114C2×(C2×D67)⋊C4—21no—
115#14523976C2314yes—
116#14523976C2314yes—
117#14523976C2314yes—
118#14523976C2314yes—
119#14523976C2314yes—
120#14523974C2314yes—
121#14523974C2314yes—
122#14523974C2314yes—
123#14523974C2314yes—
124C4⋊(C67⋊C8)C2314yes—
125C4⋊(C67⋊C8)C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523964C2314yes—
128#14523964C2314yes—
129#14523964C2314yes—
130#14523963C2314yes—
131#14523963C2314yes—
132#14523963C2314yes—
133#14523954C2314yes—
134#14523954C2314yes—
135C4×C67⋊C8C2314yes—
136C22×Q8×C67—21no—
137C22×Q8×C67D411yescharacteristic
138C22×D4×C67C2311yescharacteristic
139C23×C4×C67—21no—
140C23×C4×C67—21no—
141C23×C4×C67—21no—
142C4⋊Q8×C67—22no—
143C4⋊Q8×C67C2314yes—
144#125×C67—22no—
145#125×C67—22no—
146#125×C67C2314yes—
147#125×C67C2314yes—
148C22⋊Q8×C67—28no—
149C22⋊Q8×C67—28no—
150C22⋊Q8×C67—28no—
151C4×Q8×C67D414yes—
152C4×Q8×C67C2314yes—
153C4×D4×C67—22no—
154C4×D4×C67—22no—
155C4×D4×C67—22no—
156C4×D4×C67C2314yes—
157C4×D4×C67C2314yes—
158C4×D4×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—28no—
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C42×C67C2311yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C2×C42×C67C2311yescharacteristic
177C23×D67—21no—
178C2×Dic134—24no—
179C2×Dic134—82no—
180C2×D268—21no—
181C2×D268—22no—
182C2×D268C2×Q814yes—
183C2×D268C2412yes—
184C22×Dic67—21no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C2×C4×D67—24no—
188C2×C4×D67—24no—
189C2×C4×D67—24no—
190C2×C4×D67—44no—
191C2×C4×D67—82no—
192C2×C4×D67—82no—
193#11761613C2×Q8116yescomplemented
194C2×C67⋊C8—22no—
195C2×C67⋊C8—22no—
196C2×C67⋊C8—22no—
197C2×C67⋊C8C2×Q814yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C2×C67⋊C8C2412yes—
201C2×C67⋊C8C2412yes—
202C4⋊Dic67—24no—
203C4⋊Dic67—21no—
204C4⋊Dic67—21no—
205C4⋊Dic67—21no—
206C4⋊Dic67C2412yes—
207C4⋊Dic67C2412yes—
208C4⋊Dic67C2412yes—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212Dic67⋊C4—24no—
213(C2×D67)⋊C4—24no—
214(C2×D67)⋊C4—24no—
215(C2×D67)⋊C4—24no—
216C24×C67—21no—
217C2×Q8×C67—24no—
218C2×Q8×C67—42no—
219C2×Q8×C67—82no—
220C2×Q8×C67C2×D414yes—
221C2×D4×C67—21no—
222C2×D4×C67—22no—
223C2×D4×C67C2×Q814yes—
224C2×D4×C67C2412yes—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67—24no—
229C22×C4×C67—24no—
230C22×C4×C67—24no—
231C22×C4×C67—44no—
232C22×C4×C67—82no—
233C22×C4×C67—82no—
234C22×C4×C67C2×D411yescharacteristic
235C22×C4×C67C2×D411yescharacteristic
236C22×C4×C67C2×D411yescharacteristic
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2411yescharacteristic
241C4⋊C4×C67—24no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—24no—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67C2×D414yes—
250C4⋊C4×C67C2×D414yes—
251C4⋊C4×C67C2×D414yes—
252C4⋊C4×C67C2412yes—
253C4⋊C4×C67C2412yes—
254C4⋊C4×C67C2412yes—
255C22⋊C4×C67—24no—
256C22⋊C4×C67—24no—
257C22⋊C4×C67—24no—
258C42×C67C2×D412yes—
259C42×C67C2×D412yes—
260C42×C67C2×D412yes—
261C42×C67C2412yes—
262C42×C67C2412yes—
263C42×C67C2412yes—
264C23×C67—24no—
265C23×C67—22no—
266C23×C67—42no—
267C23×C67—42no—
268C23×C67C22×D411yescharacteristic
269C22×D67—24no—
270C22×D67—22no—
271C22×D67—42no—
272C22×D67—42no—
273Q8×C67—44no—
274Q8×C67—84no—
275D4×C67—24no—
276D4×C67—22no—
277D4×C67C22×Q814yes—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
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—48no—
288C2×C4×C67—42no—
289C2×C4×C67—42no—
290C2×C4×C67—42no—
291C2×C4×C67—84no—
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×D412yes—
299C2×C4×C67C22×D411yescharacteristic
300C2×C4×C67C22×Q812yes—
301C2×C4×C672−1+412yes—
302C2×C4×C67C2511yescharacteristic
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67—42no—
309D268—24no—
310D268—22no—
311D268C22×Q814yes—
312C4×D67—48no—
313C4×D67—84no—
314C4×D67—84no—
315Dic134—84no—
316C67⋊C8—22no—
317C67⋊C8—22no—
318C67⋊C8—22no—
319C67⋊C8C22×Q814yes—
320C22×C67—24no—
321C22×C67—48no—
322C22×C67—42no—
323C22×C67—42no—
324C22×C67D4×Q812yes—
325C22×C67#57512yes—
326C22×C67#57612yes—
327C22×C67C23×D411yescharacteristic
328C2×D67—24no—
329C2×D67—48no—
330C2×D67—42no—
331C2×D67—42no—
332C4×C67—22no—
333C4×C67—22no—
334C4×C67—22no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—22no—
338C4×C67—42no—
339C4×C67—42no—
340C4×C67—42no—
341C4×C67D4×Q812yes—
342C4×C67C23×Q811yescharacteristic
343C4×C67C2×2−1+411yescharacteristic
344Dic67—42no—
345Dic67—42no—
346Dic67—42no—
347C2×#3389—671nomaximal, Sylow
348C2×C67—44no—
349C2×C67#338914yescomplemented
350C2×C67C2×D4×Q811yescharacteristic
351C2×C67C2×#57511yescharacteristic
352C2×C67C2×#57611yescharacteristic
353D67—44no—
354C2×#554—671no—
355C2×#554D6711yescharacteristic, complemented
356#3389—6716no—
357C2×#501—671no—
358C2×#501—671no—
359C2×#499—671no—
360C2×#478—671no—
361C2×#478—671no—
362C2×#478—671no—
363C2×#478—671no—
364C2×#474—671no—
365C2×#474—671no—
366C2×#446—671no—
367C2×#442—671no—
368C2×#442—671no—
369C2×C4×D8—671no—
370C67C2×#338911yescharacteristic, complemented, Sylow
371C22×D8—671no—
372#554—24no—
373#554—678no—
374#554—1344no—
375#554C2×D6718yescomplemented
376C2×C4⋊Q8—671no—
377C2×C4⋊Q8C2×D6711yescharacteristic
378C2×#125—671no—
379C2×#125—671no—
380C2×#125C2×D6711yescharacteristic
381C2×#125C2×D6711yescharacteristic
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—1341no—
386C2×C22⋊Q8—1341no—
387C2×C22⋊Q8—1341no—
388C2×C4×Q8C2×D6711yescharacteristic
389C2×C4×D4—671no—
390C2×C4×D4—671no—
391C2×C4×D4—671no—
392C2×C4×D4C2×D6711yescharacteristic
393C2×C4×D4C2×D6711yescharacteristic
394C2×C4×D4C2×D6711yescharacteristic
395C22×C4⋊C4—21no—
396C22×C4⋊C4—1341no—
397#501—678no—
398#501—678no—
399#499—678no—
400#478—678no—
401#478—678no—
402#478—678no—
403#478—678no—
404#474—678no—
405#474—678no—
406#446—678no—
407#442—678no—
408#442—678no—
409C4×D8—678no—
410C2×#107—671no—
411C2×#107—671no—
412C2×#107—671no—
413C2×#107—671no—
414C2×#107—671no—
415C2×#106—671no—
416C2×#106—671no—
417C2×#106—671no—
418C2×#106—671no—
419C2×C4⋊C8—671no—
420C2×C4⋊C8—671no—
421C2×C4⋊C8—671no—
422C2×#102—671no—
423C2×#102—671no—
424C2×#102—671no—
425C2×#102—671no—
426C2×#102—671no—
427C2×#102—671no—
428C2×#97—671no—
429C2×#97—671no—
430C2×C4×C8—671no—
431C22×Q8—21no—
432C22×Q8—1341no—
433C22×Q8C22⋊D6711yescharacteristic
434C22×D4—671no—
435C22×D4C22×D6711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—1341no—
440C23×C4—1341no—
441C23×C4—1341no—
442C2×D8—678no—
443C2×D8—674no—
444C22×C8—671no—
445C22×C8—671no—
446C22×C8—671no—
447C22×C8—671no—
448C4⋊Q8—22no—
449C4⋊Q8—674no—
450C4⋊Q8—1342no—
451C4⋊Q8C22×D6714yes—
452#125—22no—
453#125—22no—
454#125—674no—
455#125—674no—
456#125—1342no—
457#125—1342no—
458#125C22×D6714yes—
459#125C22×D6714yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—1348no—
464C22⋊Q8—1348no—
465C22⋊Q8—1348no—
466C4×Q8C22⋊D6714yes—
467C4×Q8C22×D6714yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—674no—
472C4×D4—674no—
473C4×D4—674no—
474C4×D4—1342no—
475C4×D4—1342no—
476C4×D4—1342no—
477C4×D4C22×D6714yes—
478C4×D4C22×D6714yes—
479C4×D4C22×D6714yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—671no—
487C2×C4⋊C4—671no—
488C2×C4⋊C4—671no—
489C2×C4⋊C4—1341no—
490C2×C4⋊C4—1341no—
491C2×C4⋊C4—1341no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1348no—
495C2×C4⋊C4C22⋊D6711yescharacteristic
496C2×C4⋊C4C22⋊D6711yescharacteristic
497C2×C4⋊C4C22⋊D6711yescharacteristic
498C2×C4⋊C4C22×D6711yescharacteristic
499C2×C4⋊C4C22×D6711yescharacteristic
500C2×C4⋊C4C22×D6711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1341no—
505C2×C22⋊C4—1341no—
506C2×C22⋊C4—1341no—
507C2×C42C22×D6711yescharacteristic
508C2×C42C22×D6711yescharacteristic
509C2×C42C22×D6711yescharacteristic
510#107—674no—
511#107—674no—
512#107—674no—
513#107—674no—
514#107—674no—
515#106—674no—
516#106—674no—
517#106—674no—
518#106—674no—
519C4⋊C8—674no—
520C4⋊C8—674no—
521C4⋊C8—674no—
522#102—674no—
523#102—674no—
524#102—674no—
525#102—674no—
526#102—674no—
527#102—674no—
528#97—674no—
529#97—674no—
530C4×C8—674no—
531C24—21no—
532C24—1341no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—5362no—
537C2×Q8—1344no—
538C2×Q8C2×C22⋊D6714yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—674no—
542C2×D4—672no—
543C2×D4—1341no—
544C2×D4—1342no—
545C2×D4Q8×D6714yes—
546C2×D4C23×D6712yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—2684no—
557C22×C4—5362no—
558C22×C4—5362no—
559C22×C4—1341no—
560C22×C4—1341no—
561C22×C4—1341no—
562C22×C4—1344no—
563C22×C4—1344no—
564C22×C4—1344no—
565C22×C4C2×C22⋊D6711yescharacteristic
566C22×C4C2×C22⋊D6711yescharacteristic
567C22×C4C2×C22⋊D6711yescharacteristic
568C22×C4C2×C22⋊D6711yescharacteristic
569C22×C4C2×C22⋊D6711yescharacteristic
570C22×C4C2×C22⋊D6711yescharacteristic
571C22×C4C23×D6711yescharacteristic
572D8—6716no—
573C2×C8—674no—
574C2×C8—672no—
575C2×C8—672no—
576C2×C8—672no—
577C2×C8—672no—
578C2×C8—1342no—
579C2×C8—1342no—
580C2×C8—1342no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—672no—
590C4⋊C4—672no—
591C4⋊C4—672no—
592C4⋊C4—1341no—
593C4⋊C4—1341no—
594C4⋊C4—1341no—
595C4⋊C4—1344no—
596C4⋊C4—1344no—
597C4⋊C4—1344no—
598C4⋊C4—1344no—
599C4⋊C4—1344no—
600C4⋊C4C2×C22⋊D6714yes—
601C4⋊C4C2×C22⋊D6714yes—
602C4⋊C4C2×C22⋊D6714yes—
603C4⋊C4C23×D6712yes—
604C4⋊C4C23×D6712yes—
605C4⋊C4C23×D6712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1344no—
610C22⋊C4—1344no—
611C22⋊C4—1344no—
612C42C2×C22⋊D6712yes—
613C42C2×C22⋊D6712yes—
614C42C2×C22⋊D6712yes—
615C42C23×D6712yes—
616C42C23×D6712yes—
617C42C23×D6712yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—2682no—
623C23—2682no—
624C23—1344no—
625C23—1342no—
626C23C22×C22⋊D6711yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—5364no—
630D4—24no—
631D4—22no—
632D4—674no—
633D4—1344no—
634D4—1342no—
635D4C2×Q8×D6714yes—
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—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—2688no—
652C2×C4—2682no—
653C2×C4—2682no—
654C2×C4—2682no—
655C2×C4—5364no—
656C2×C4—5364no—
657C2×C4—1342no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4C22×C22⋊D6712yes—
661C2×C4C22×C22⋊D6712yes—
662C2×C4C22×C22⋊D6712yes—
663C2×C4C22×C22⋊D6712yes—
664C2×C4C22×C22⋊D6712yes—
665C2×C4C22×C22⋊D6712yes—
666C2×C4C22×C22⋊D6711yescharacteristic
667C2×C4C2×Q8×D6712yes—
668C2×C4#1452409112yes—
669C2×C4C24×D6711yescharacteristic
670C8—674no—
671C8—1342no—
672C8—1342no—
673C8—1342no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—2682no—
679C22—2688no—
680C22—2682no—
681C22—1344no—
682C22Q8×C22⋊D6712yes—
683C22#1686419412yes—
684C22#1686419912yes—
685C22C23×C22⋊D6711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2682no—
696C4—2682no—
697C4—2682no—
698C4Q8×C22⋊D6712yes—
699C4C22×Q8×D6711yescharacteristic
700C4C2×#1452409111yescharacteristic
701C2—44no—
702C2—2684no—
703C2#2257316314yesdirect product factor
704C2C2×Q8×C22⋊D6711yescharacteristic
705C2C2×#1686419411yescharacteristic
706C2C2×#1686419911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC22×#11761613C22
hypercenterC2×#554D67
hypocenterC67C2×#3389
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16864106C2semidirect
2. #22573163C2direct (N × H)
3. C2×#16863806C2semidirect
4. C2×#16863802C2semidirect
5. C2×#16863795C2semidirect
6. C2×#16863696C2semidirect
7. C2×#16863696C2semidirect
8. C2×#16863693C2semidirect
9. C2×#16863693C2semidirect
10. C2×#16863676C2semidirect
11. C2×#16863673C2semidirect
12. C2×#16863527C2semidirect
16. C2×#554×C67C2semidirect
19. #16864106C22semidirect
30. #16863806C22semidirect
31. #16863802C22semidirect
32. #16863795C22semidirect
33. #16863696C22semidirect
34. #16863696C22semidirect
35. #16863693C22semidirect
36. #16863693C22semidirect
37. #16863676C22semidirect
38. #16863673C22semidirect
39. #16863527C22semidirect
65. #554×C67C22semidirect
82. C2×#11761613Q8semidirect
193. #11761613C2×Q8semidirect
349. C2×C67#3389semidirect
355. C2×#554D67semidirect
370. C67C2×#3389semidirect
375. #554C2×D67semidirect
703. C2#22573163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641062
#225731632
C2×#168638062
C2×#168638022
C2×#168637952
C2×#168636962
C2×#168636932
C2×#168636762
C2×#168636732
C2×#168635272
C2×#168635062
C2×C4×#117616132
C2×#554×C672
C2×#338967