Finite Group Databasebeta

← C2×#22572320 #31732421

Subgroups — C2×#22572320 #31732421

Order 17152.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864103C211yesmaximal, characteristic, complemented
2#22572320C2116yesmaximal, direct product factor
3C2×#16863755C211yesmaximal, characteristic, complemented
4C2×#16863712C211yesmaximal, characteristic, complemented
5C2×#16863724C211yesmaximal, characteristic, complemented
6C2×#16863681C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863623C211yesmaximal, characteristic, complemented
9C2×#16863615C211yesmaximal, characteristic, complemented
10C2×#16863558C211yesmaximal, characteristic, complemented
11C2×#16863552C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863397C211yesmaximal, characteristic, complemented
15C22×#14523967C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761616C2211yescharacteristic
20C22×#11761612C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22#16864103—24no—
23#16864103C2218yescomplemented
24C2×#14524043C2211yescharacteristic
25C2×#14524034—21no—
26C2×#14524022C2211yescharacteristic
27C2×#14524022C2211yescharacteristic
28C2×#14524020—21no—
29C2×#14524020—21no—
30C2×C4×Dic134C2211yescharacteristic
31C2×D4×Dic67—21no—
32C22×C4⋊Dic67C2211yescharacteristic
33C22×C4⋊Dic67C2211yescharacteristic
34#16863755C2218yescomplemented
35#16863724C2218yescomplemented
36#16863712C2218yescomplemented
37#16863681C2218yescomplemented
38#16863652C2218yescomplemented
39#16863623C2218yescomplemented
40#16863615C2218yescomplemented
41#16863558C2218yescomplemented
42#16863552C2218yescomplemented
43#16863501C2218yescomplemented
44#16863468C2218yescomplemented
45C2×#14523974C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49#16863397C2218yescomplemented
50C2×#14523967C2211yescharacteristic
51C2×#14523967C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2218yescomplemented
57C2×#14523966C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64C22×#41×C67C2211yescharacteristic
65C23×Q8×C67C2211yescharacteristic
66#548×C67—24no—
67#548×C67C2218yes—
68C2×#124×C67—21no—
69C2×#124×C67C2211yescharacteristic
70C2×C22⋊Q8×C67—21no—
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×#121×C67—21no—
73C2×#121×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×D4×C67—21no—
76C2×C4×D4×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C23×Dic67—21no—
80C23×Dic67—21no—
81C2×#11761618—24no—
82C2×#11761618—42no—
83C2×#11761618C2314yes—
84C2×#11761618C2314yes—
85C2×#11761616—42no—
86C2×#11761616C2314yes—
87C2×#11761612—42no—
88C2×#11761612C2314yes—
89C22×C67⋊C8—42no—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2314yes—
95#14524043—22no—
96#14524043C2314yes—
97#14524034—28no—
98#14524022—22no—
99#14524022—22no—
100#14524022C2314yes—
101#14524022C2314yes—
102#14524020—28no—
103#14524020—28no—
104C4×Dic134—22no—
105C4×Dic134C2314yes—
106D4×Dic67—28no—
107C2×C4⋊Dic67—22no—
108C2×C4⋊Dic67—22no—
109C2×C4⋊Dic67—21no—
110C2×C4⋊Dic67—21no—
111C2×C4⋊Dic67—21no—
112C2×C4⋊Dic67C2311yescharacteristic
113C2×C4⋊Dic67C2314yes—
114C2×C4⋊Dic67C2314yes—
115C2×C4⋊Dic67C2311yescharacteristic
116C2×C4⋊Dic67C2311yescharacteristic
117C2×Dic67⋊C4—21no—
118C2×Dic67⋊C4—21no—
119C2×Dic67⋊C4—21no—
120C2×C22⋊Dic67—21no—
121C2×C22⋊Dic67—21no—
122C2×C4×Dic67—21no—
123#14523974C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523967C2314yes—
133#14523966C2314yes—
134#14523964C2314yes—
135#14523964C2314yes—
136#14523964C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139#14523954C2314yes—
140C2×#41×C67—22no—
141C2×#41×C67—24no—
142C2×#41×C67—42no—
143C2×#41×C67C2314yes—
144C22×Q8×C67—21no—
145C22×Q8×C67—22no—
146C22×Q8×C67—24no—
147C22×Q8×C67—42no—
148C22×Q8×C67C2311yescharacteristic
149C22×Q8×C67C2314yes—
150C22×Q8×C67C2311yescharacteristic
151C22×D4×C67—21no—
152C22×D4×C67—21no—
153C22×D4×C67D411yescharacteristic
154C22×D4×C67C2311yescharacteristic
155C23×C4×C67—21no—
156C23×C4×C67—21no—
157C23×C4×C67C2311yescharacteristic
158C23×C4×C67C2311yescharacteristic
159#124×C67—28no—
160#124×C67—22no—
161#124×C67C2314yes—
162C22⋊Q8×C67—22no—
163C22⋊Q8×C67—28no—
164C22⋊Q8×C67C2314yes—
165#121×C67—28no—
166#121×C67—22no—
167#121×C67C2314yes—
168C4×Q8×C67—22no—
169C4×Q8×C67C2314yes—
170C4×D4×C67—28no—
171C4×D4×C67D414yes—
172C4×D4×C67C2314yes—
173C2×C4⋊C4×C67—21no—
174C2×C4⋊C4×C67—21no—
175C2×C4⋊C4×C67D411yescharacteristic
176C2×C4⋊C4×C67C2311yescharacteristic
177C2×C22⋊C4×C67—21no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—21no—
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C22⋊C4×C67D411yescharacteristic
183C2×C42×C67—21no—
184C2×C42×C67C2311yescharacteristic
185C2×Dic134—22no—
186C2×Dic134—22no—
187C2×Dic134—21no—
188C2×Dic134—24no—
189C2×Dic134—82no—
190C2×Dic134C2412yes—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—24no—
196C22×Dic67—24no—
197C22×Dic67—82no—
198C22×Dic67—82no—
199#11761618—28no—
200#11761618—44no—
201#11761616—44no—
202#11761612—44no—
203C2×C67⋊C8—22no—
204C2×C67⋊C8—22no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8—22no—
207C2×C67⋊C8—44no—
208C2×C67⋊C8C2412yes—
209C2×C67⋊C8C2412yes—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C4⋊Dic67—21no—
213C4⋊Dic67—24no—
214C4⋊Dic67—24no—
215C4⋊Dic67—21no—
216C4⋊Dic67—21no—
217C4⋊Dic67—24no—
218C4⋊Dic67C2412yes—
219C4⋊Dic67C2412yes—
220C4⋊Dic67C2412yes—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224C22⋊Dic67—24no—
225C22⋊Dic67—24no—
226C4×Dic67—24no—
227C24×C67—21no—
228C24×C67C2×D411yescharacteristic
229C24×C67C2×D411yescharacteristic
230#41×C67—28no—
231#41×C67—44no—
232#41×C67—48no—
233C2×Q8×C67—21no—
234C2×Q8×C67—24no—
235C2×Q8×C67—21no—
236C2×Q8×C67—22no—
237C2×Q8×C67—28no—
238C2×Q8×C67—22no—
239C2×Q8×C67—22no—
240C2×Q8×C67—44no—
241C2×Q8×C67—44no—
242C2×Q8×C67—48no—
243C2×Q8×C67#4114yes—
244C2×Q8×C67C2412yes—
245C2×Q8×C67C2412yes—
246C2×D4×C67—24no—
247C2×D4×C67—24no—
248C2×D4×C67—24no—
249C2×D4×C67—21no—
250C2×D4×C67—22no—
251C2×D4×C67—22no—
252C2×D4×C67—44no—
253C2×D4×C67—44no—
254C2×D4×C67C2×D414yes—
255C2×D4×C67C2412yes—
256C22×C4×C67—21no—
257C22×C4×C67—22no—
258C22×C4×C67—22no—
259C22×C4×C67—22no—
260C22×C4×C67—22no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—24no—
264C22×C4×C67—24no—
265C22×C4×C67—44no—
266C22×C4×C67—44no—
267C22×C4×C67C2×D411yescharacteristic
268C22×C4×C67C2×D411yescharacteristic
269C22×C4×C67C2×D411yescharacteristic
270C22×C4×C67C2×D411yescharacteristic
271C22×C4×C67C2×D412yes—
272C22×C4×C67C2×D412yes—
273C22×C4×C67C2412yes—
274C22×C4×C67C2412yes—
275C22×C4×C67C2411yescharacteristic
276C4⋊C4×C67—24no—
277C4⋊C4×C67—24no—
278C4⋊C4×C67—21no—
279C4⋊C4×C67C2×D414yes—
280C4⋊C4×C67C2412yes—
281C22⋊C4×C67—24no—
282C22⋊C4×C67—24no—
283C22⋊C4×C67—24no—
284C22⋊C4×C67—24no—
285C22⋊C4×C67C2×D414yes—
286C22⋊C4×C67C2×D414yes—
287C42×C67—24no—
288C42×C67C2×D412yes—
289C42×C67C2412yes—
290C23×C67—22no—
291C23×C67—22no—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67—22no—
296C23×C67—42no—
297C23×C67—42no—
298C23×C67—42no—
299C23×C67#13714yes—
300C23×C67C22×D412yes—
301C23×C67C22×D412yes—
302C23×C67C22×D411yescharacteristic
303Q8×C67—24no—
304Q8×C67—22no—
305Q8×C67—22no—
306Q8×C67—22no—
307Q8×C67—48no—
308Q8×C67—42no—
309Q8×C67C2×#4114yes—
310D4×C67—28no—
311D4×C67—22no—
312D4×C67—22no—
313D4×C67—48no—
314D4×C67—48no—
315D4×C67—42no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—24no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—24no—
323C2×C4×C67—24no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—48no—
331C2×C4×C67—48no—
332C2×C4×C67—42no—
333C2×C4×C67—42no—
334C2×C4×C67C22×D412yes—
335C2×C4×C67C22×D412yes—
336C2×C4×C67C22×D412yes—
337C2×C4×C67C22×D412yes—
338C2×C4×C67C22×D411yescharacteristic
339C2×C4×C67C2×#4112yes—
340C2×C4×C67H(5,𝔽2)12yes—
341C2×C4×C67C2511yescharacteristic
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—42no—
347C2×Dic67—42no—
348C2×Dic67—42no—
349C2×Dic67—42no—
350C2×Dic67—84no—
351C2×Dic67—84no—
352Dic134—22no—
353Dic134—22no—
354Dic134—42no—
355Dic134—84no—
356C67⋊C8—22no—
357C67⋊C8—22no—
358C67⋊C8—22no—
359C67⋊C8—22no—
360C22×C67—22no—
361C22×C67—28no—
362C22×C67—22no—
363C22×C67—22no—
364C22×C67—22no—
365C22×C67—22no—
366C22×C67—44no—
367C22×C67—42no—
368C22×C67—42no—
369C22×C67—42no—
370C22×C67—84no—
371C22×C67#54612yes—
372C22×C67C2×#13714yes—
373C22×C67C2×#13712yes—
374C22×C67#57712yes—
375C22×C67C23×D411yescharacteristic
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—24no—
379C4×C67—22no—
380C4×C67—22no—
381C4×C67—42no—
382C4×C67—42no—
383C4×C67#54612yes—
384C4×C67C22×#4111yescharacteristic
385C4×C67C2×H(5,𝔽2)11yescharacteristic
386Dic67—42no—
387Dic67—42no—
388Dic67—42no—
389Dic67—42no—
390C2×#3316—671nomaximal, Sylow
391C2×C67—24no—
392C2×C67—42no—
393C2×C67—82no—
394C2×C67#331614yescomplemented
395C2×C67C2×#54611yescharacteristic
396C2×C67C22×#13711yescharacteristic
397C2×C67C2×#57711yescharacteristic
398C2×#554—671no—
399C2×#548D6711yescharacteristic
400#3316—6716no—
401C2×#489—671no—
402C2×#481—671no—
403C2×#483—671no—
404C2×#475—671no—
405C2×#470—671no—
406C2×#465—671no—
407C2×#464—671no—
408C2×#452—671no—
409C2×#451—671no—
410C2×#441—671no—
411C2×#435—671no—
412C2×#417—671no—
413C22×#103—671no—
414C67C2×#331611yescharacteristic, complemented, Sylow
415C22×#41C2×D6711yescharacteristic
416C23×Q8C2×D6711yescharacteristic
417C22×Q16—671no—
418C22×Q16—671no—
419C22×SD16—671no—
420C22×M16—671no—
421C23×C8—671no—
422#554—678no—
423#554—1344no—
424#548—24no—
425#548C2×D6718yes—
426C2×C4⋊Q8—671no—
427C2×#125—1341no—
428C2×#124—21no—
429C2×#124C2×D6711yescharacteristic
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—671no—
432C2×C22⋊Q8—671no—
433C2×C22⋊Q8—1341no—
434C2×C22⋊Q8—1341no—
435C2×C22⋊Q8C2×D6711yescharacteristic
436C2×#121—21no—
437C2×#121C2×D6711yescharacteristic
438C2×C4×Q8—671no—
439C2×C4×Q8C2×D6711yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4—1341no—
442C2×C4×D4C2×D6711yescharacteristic
443C22×C4⋊C4—671no—
444C22×C4⋊C4—671no—
445#489—678no—
446#483—678no—
447#481—678no—
448#475—678no—
449#470—678no—
450#465—678no—
451#464—678no—
452#452—678no—
453#451—678no—
454#441—678no—
455#435—678no—
456C2×#106—671no—
457C2×#106—671no—
458C2×#106—671no—
459C2×C4⋊C8—671no—
460#417—678no—
461C2×#103—671no—
462C2×#103—671no—
463C2×#103—671no—
464C2×#103—671no—
465C2×#103—671no—
466C2×#103—671no—
467C2×#103—678no—
468C2×#103—671no—
469C2×#102—671no—
470C2×#102—671no—
471C2×#102—671no—
472C2×C22⋊C8—671no—
473C2×C22⋊C8—671no—
474C2×#97—671no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D6714yes—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—671no—
484C22×Q8—1341no—
485C22×Q8C22×D6711yescharacteristic
486C22×Q8C22×D6714yes—
487C22×Q8C22×D6711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D6711yescharacteristic
491C22×D4C22×D6711yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1341no—
495C23×C4—1341no—
496C23×C4C22×D6711yescharacteristic
497C23×C4C22×D6711yescharacteristic
498C2×Q16—2682no—
499C2×Q16—674no—
500C2×Q16—674no—
501C2×Q16—1344no—
502C2×SD16—2682no—
503C2×SD16—674no—
504C2×M16—2682no—
505C2×M16—674no—
506C22×C8—2682no—
507C22×C8—674no—
508C22×C8—671no—
509C22×C8—671no—
510C22×C8—671no—
511C22×C8—671no—
512C4⋊Q8—674no—
513C4⋊Q8—1342no—
514#125—1348no—
515#124—28no—
516#124—22no—
517#124C22×D6714yes—
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—674no—
521C22⋊Q8—674no—
522C22⋊Q8—1342no—
523C22⋊Q8—1342no—
524C22⋊Q8—1348no—
525C22⋊Q8—1348no—
526C22⋊Q8C22×D6714yes—
527#121—28no—
528#121—22no—
529#121C22×D6714yes—
530C4×Q8—22no—
531C4×Q8—674no—
532C4×Q8—1342no—
533C4×Q8C22×D6714yes—
534C4×D4—28no—
535C4×D4—1348no—
536C4×D4C22⋊D6714yes—
537C4×D4C22×D6714yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—671no—
541C2×C4⋊C4—671no—
542C2×C4⋊C4—671no—
543C2×C4⋊C4—674no—
544C2×C4⋊C4—674no—
545C2×C4⋊C4—1341no—
546C2×C4⋊C4—1341no—
547C2×C4⋊C4—1342no—
548C2×C4⋊C4—1342no—
549C2×C4⋊C4—1341no—
550C2×C4⋊C4—1341no—
551C2×C4⋊C4—1341no—
552C2×C4⋊C4—1341no—
553C2×C4⋊C4C22⋊D6711yescharacteristic
554C2×C4⋊C4C22×D6711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1341no—
560C2×C22⋊C4—1341no—
561C2×C22⋊C4C22⋊D6711yescharacteristic
562C2×C22⋊C4C22⋊D6711yescharacteristic
563C2×C42—21no—
564C2×C42—1341no—
565C2×C42C22×D6711yescharacteristic
566#106—674no—
567#106—674no—
568#106—674no—
569C4⋊C8—674no—
570#103—674no—
571#103—674no—
572#103—674no—
573#103—674no—
574#103—674no—
575#103—674no—
576#103—674no—
577#102—674no—
578#102—674no—
579#102—674no—
580C22⋊C8—674no—
581C22⋊C8—674no—
582#97—674no—
583C24—21no—
584C24C2×C22⋊D6711yescharacteristic
585C24C2×C22⋊D6711yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8—5362no—
600C2×Q8—672no—
601C2×Q8—1342no—
602C2×Q8—1342no—
603C2×Q8—1341no—
604C2×Q8—1344no—
605C2×Q8#1176162714yes—
606C2×Q8C23×D6712yes—
607C2×Q8C23×D6712yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4C2×C22⋊D6714yes—
617C2×D4C23×D6712yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—5362no—
630C22×C4—5362no—
631C22×C4—1341no—
632C22×C4—1341no—
633C22×C4—1341no—
634C22×C4—1341no—
635C22×C4—1344no—
636C22×C4—1344no—
637C22×C4C2×C22⋊D6712yes—
638C22×C4C2×C22⋊D6712yes—
639C22×C4C2×C22⋊D6711yescharacteristic
640C22×C4C2×C22⋊D6711yescharacteristic
641C22×C4C2×C22⋊D6711yescharacteristic
642C22×C4C2×C22⋊D6711yescharacteristic
643C22×C4C23×D6712yes—
644C22×C4C23×D6712yes—
645C22×C4C23×D6711yescharacteristic
646Q16—2684no—
647Q16—1348no—
648SD16—2684no—
649M16—2684no—
650C2×C8—2684no—
651C2×C8—672no—
652C2×C8—672no—
653C2×C8—672no—
654C2×C8—672no—
655C2×C8—1342no—
656C2×C8—1342no—
657C2×C8—1342no—
658C2×C8—1342no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—672no—
663C4⋊C4—672no—
664C4⋊C4—672no—
665C4⋊C4—1341no—
666C4⋊C4—1344no—
667C4⋊C4—1344no—
668C4⋊C4—1341no—
669C4⋊C4—1341no—
670C4⋊C4—1344no—
671C4⋊C4—1344no—
672C4⋊C4—1344no—
673C4⋊C4—1344no—
674C4⋊C4C2×C22⋊D6714yes—
675C4⋊C4C23×D6712yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1344no—
681C22⋊C4—1344no—
682C22⋊C4C2×C22⋊D6714yes—
683C22⋊C4C2×C22⋊D6714yes—
684C42—24no—
685C42—1344no—
686C42C2×C22⋊D6712yes—
687C42C23×D6712yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1452407314yes—
698C23C22×C22⋊D6712yes—
699C23C22×C22⋊D6712yes—
700C23C22×C22⋊D6711yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—2682no—
708Q8—5364no—
709Q8—1342no—
710Q8—1342no—
711Q8C2×#1176162714yes—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—48no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—2682no—
737C2×C4—2682no—
738C2×C4—2682no—
739C2×C4—2682no—
740C2×C4—5364no—
741C2×C4—5364no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1342no—
746C2×C4C22×C22⋊D6712yes—
747C2×C4C22×C22⋊D6712yes—
748C2×C4C22×C22⋊D6712yes—
749C2×C4C22×C22⋊D6712yes—
750C2×C4C22×C22⋊D6711yescharacteristic
751C2×C4C2×#1176162712yes—
752C2×C4#1452408812yes—
753C2×C4C24×D6711yescharacteristic
754C8—1342no—
755C8—1342no—
756C8—1342no—
757C8—1342no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1686404012yes—
770C22C2×#1452407314yes—
771C22C2×#1452407312yes—
772C22#1686420412yes—
773C22C23×C22⋊D6711yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—2682no—
782C4—2682no—
783C4—2682no—
784C4—2682no—
785C4#1686404012yes—
786C4C22×#1176162711yescharacteristic
787C4C2×#1452408811yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#2257232014yesdirect product factor
792C2C2×#1686404011yescharacteristic
793C2C22×#1452407311yescharacteristic
794C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#548×C67C2
socleC23×C67C22×D4
hypercenterC2×#548D67
hypocenterC67C2×#3316
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16864103C2semidirect
2. #22572320C2direct (N × H)
3. C2×#16863755C2semidirect
4. C2×#16863712C2semidirect
5. C2×#16863724C2semidirect
6. C2×#16863681C2semidirect
7. C2×#16863652C2semidirect
8. C2×#16863623C2semidirect
9. C2×#16863615C2semidirect
10. C2×#16863558C2semidirect
11. C2×#16863552C2semidirect
12. C2×#16863501C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863397C2semidirect
15. C22×#14523967C2semidirect
23. #16864103C22semidirect
34. #16863755C22semidirect
35. #16863724C22semidirect
36. #16863712C22semidirect
37. #16863681C22semidirect
38. #16863652C22semidirect
39. #16863623C22semidirect
40. #16863615C22semidirect
41. #16863558C22semidirect
42. #16863552C22semidirect
43. #16863501C22semidirect
44. #16863468C22semidirect
49. #16863397C22semidirect
56. C2×#14523967C22semidirect
394. C2×C67#3316semidirect
414. C67C2×#3316semidirect
791. C2#22572320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641032
#225723202
C2×#168637552
C2×#168637122
C2×#168637242
C2×#168636812
C2×#168636522
C2×#168636232
C2×#168636152
C2×#168635582
C2×#168635522
C2×#168635012
C2×#168634682
C2×#168633972
C22×#145239672
C2×#548×C672
C2×#331667