Finite Group Databasebeta

← C2×#22563908 #31023656

Subgroups — C2×#22563908 #31023656

Order 17152.

3550 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
1C22×#14524041C211yesmaximal, characteristic, complemented
2C22×#14524020C211yesmaximal, characteristic
3C23×Dic67⋊C4C211yesmaximal, characteristic
4#22563908C2116yesmaximal, direct product factor
5C2×#16863327C211yesmaximal, characteristic, complemented
6C2×#16863326C211yesmaximal, characteristic, complemented
7C2×#16863316C211yesmaximal, characteristic, complemented
8C2×#16863315C211yesmaximal, characteristic, complemented
9C2×#16863291C211yesmaximal, characteristic, complemented
10C2×#16863291C211yesmaximal, characteristic, complemented
11C2×#16863269C211yesmaximal, characteristic
12C2×#16863268C211yesmaximal, characteristic
13C2×#16863265C211yesmaximal, characteristic, complemented
14C2×#16863254C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C22×C22⋊Q8×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C2×#14524041—28no—
21C2×#14524041C2218yescomplemented
22C2×#14524020—28no—
23C2×#14524020C2218yes—
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4—28no—
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2218yes—
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×Dic67⋊C4C2211yescharacteristic
36C22×Dic67⋊C4C2211yescharacteristic
37C22×Dic67⋊C4C2211yescharacteristic
38C22×Dic67⋊C4C2211yescharacteristic
39C22×C22⋊Dic67C2211yescharacteristic
40C22×C22⋊Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43#16863327C2218yescomplemented
44#16863326C2218yescomplemented
45#16863316C2218yescomplemented
46#16863315C2218yescomplemented
47#16863291C2218yescomplemented
48#16863291C2218yescomplemented
49#16863269C2218yes—
50#16863268C2218yes—
51#16863265C2218yescomplemented
52#16863254C2218yes—
53C22⋊C4×Dic67C2218yes—
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C23×Q8×C67C2211yescharacteristic
63C24×C4×C67C2211yescharacteristic
64C2×C22⋊Q8×C67—28no—
65C2×C22⋊Q8×C67C2218yes—
66C22×C4⋊C4×C67C2211yescharacteristic
67C22×C4⋊C4×C67C2211yescharacteristic
68C22×C4⋊C4×C67C2211yescharacteristic
69C22×C22⋊C4×C67C2211yescharacteristic
70C22×C22⋊C4×C67C2211yescharacteristic
71C22×Dic134—24no—
72C22×Dic134—24no—
73C22×Dic134—42no—
74C22×Dic134C2314yes—
75C23×Dic67—24no—
76C23×Dic67—24no—
77C23×Dic67—24no—
78C23×Dic67—24no—
79C23×Dic67—42no—
80C23×Dic67Q818yescomplemented
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2314yes—
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2311yescharacteristic
88C23×Dic67C2311yescharacteristic
89C23×Dic67C2314yes—
90C23×Dic67C2311yescharacteristic
91#14524041—232no—
92#14524020—232no—
93C2×C4⋊Dic67—24no—
94C2×C4⋊Dic67C2314yes—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—24no—
98C2×Dic67⋊C4—24no—
99C2×Dic67⋊C4—24no—
100C2×Dic67⋊C4—232no—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4—24no—
104C2×Dic67⋊C4—24no—
105C2×Dic67⋊C4—42no—
106C2×Dic67⋊C4—42no—
107C2×Dic67⋊C4D418yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×Dic67⋊C4C2314yes—
112C2×Dic67⋊C4C2314yes—
113C2×Dic67⋊C4C2314yes—
114C2×Dic67⋊C4C2314yes—
115C2×Dic67⋊C4C2314yes—
116C2×Dic67⋊C4C2314yes—
117C2×Dic67⋊C4C2314yes—
118C2×Dic67⋊C4C2314yes—
119C2×Dic67⋊C4C2314yes—
120C2×C22⋊Dic67—24no—
121C2×C22⋊Dic67Q818yescomplemented
122C2×C22⋊Dic67C2314yes—
123C2×C22⋊Dic67C2314yes—
124C2×C4×Dic67—24no—
125C2×C4×Dic67—24no—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C25×C67C2311yescharacteristic
137C22×Q8×C67—24no—
138C22×Q8×C67—24no—
139C22×Q8×C67—42no—
140C22×Q8×C67C2314yes—
141C23×C4×C67—24no—
142C23×C4×C67—24no—
143C23×C4×C67—42no—
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2314yes—
148C23×C4×C67C2311yescharacteristic
149C23×C4×C67C2311yescharacteristic
150C23×C4×C67C2311yescharacteristic
151C22⋊Q8×C67—232no—
152C2×C4⋊C4×C67—24no—
153C2×C4⋊C4×C67—24no—
154C2×C4⋊C4×C67—24no—
155C2×C4⋊C4×C67C2314yes—
156C2×C4⋊C4×C67C2314yes—
157C2×C4⋊C4×C67C2314yes—
158C2×C22⋊C4×C67—24no—
159C2×C22⋊C4×C67D418yes—
160C2×C22⋊C4×C67C2314yes—
161C2×C22⋊C4×C67C2314yes—
162C2×Dic134—28no—
163C2×Dic134—28no—
164C2×Dic134—44no—
165C2×Dic134—416no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—232no—
175C22×Dic67—28no—
176C22×Dic67—28no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—28no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—28no—
188C22×Dic67—44no—
189C22×Dic67—416no—
190C22×Dic67C2×D414yes—
191C22×Dic67C2×D414yes—
192C22×Dic67C2×Q814yes—
193C22×Dic67C2×Q814yes—
194C22×Dic67C2×Q814yes—
195C22×Dic67C2×Q814yes—
196C22×Dic67C2×Q8116yescomplemented
197C22×Dic67#4114yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C22×Dic67C2412yes—
203C22×Dic67C2412yes—
204C22×Dic67C2412yes—
205C22×Dic67C2412yes—
206C4⋊Dic67—28no—
207Dic67⋊C4—28no—
208Dic67⋊C4—28no—
209Dic67⋊C4—28no—
210Dic67⋊C4—28no—
211Dic67⋊C4—28no—
212Dic67⋊C4—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4—28no—
215Dic67⋊C4—28no—
216Dic67⋊C4—44no—
217Dic67⋊C4—44no—
218Dic67⋊C4C2×D4116yes—
219C22⋊Dic67—28no—
220C22⋊Dic67C2×Q8116yescomplemented
221C4×Dic67—28no—
222C4×Dic67—28no—
223C24×C67—22no—
224C24×C67—22no—
225C24×C67—22no—
226C24×C67—22no—
227C24×C67C2×D414yes—
228C24×C67C2×Q814yes—
229C24×C67C2×Q814yes—
230C24×C67C2412yes—
231C24×C67C2411yescharacteristic
232C2×Q8×C67—28no—
233C2×Q8×C67—28no—
234C2×Q8×C67—44no—
235C2×Q8×C67—416no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—28no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67—22no—
250C22×C4×C67—22no—
251C22×C4×C67—22no—
252C22×C4×C67—28no—
253C22×C4×C67—44no—
254C22×C4×C67—416no—
255C22×C4×C67C2×D414yes—
256C22×C4×C67C2×D414yes—
257C22×C4×C67C2×D414yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C22×C4×C67C2412yes—
263C22×C4×C67C2412yes—
264C4⋊C4×C67—28no—
265C4⋊C4×C67—28no—
266C4⋊C4×C67—28no—
267C22⋊C4×C67—28no—
268C22⋊C4×C67C2×D4116yes—
269C23×C67—28no—
270C23×C67—28no—
271C23×C67—28no—
272C23×C67—28no—
273C23×C67—28no—
274C23×C67—28no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67C4⋊Q8116yescomplemented
280C23×C67C22×D412yes—
281C23×C67C22×D414yes—
282C23×C67C22×D412yes—
283C23×C67C22×Q814yes—
284C23×C67C22×Q814yes—
285C23×C67C22×Q812yes—
286C23×C67C22×Q812yes—
287C23×C67C2×#4112yes—
288C23×C67H(5,𝔽2)12yes—
289C23×C672−1+412yes—
290C23×C67C2511yescharacteristic
291Q8×C67—416no—
292C2×C4×C67—28no—
293C2×C4×C67—28no—
294C2×C4×C67—28no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—416no—
311C2×C4×C67—44no—
312C2×C4×C67—44no—
313C2×C4×C67—44no—
314C2×C4×C67C22×D414yes—
315C2×C4×C67C22×D414yes—
316C2×C4×C67C22×D414yes—
317C2×Dic67—28no—
318C2×Dic67—28no—
319C2×Dic67—28no—
320C2×Dic67—28no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—232no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—416no—
340C2×Dic67—44no—
341C2×Dic67—44no—
342C2×Dic67—44no—
343C2×Dic67C22⋊Q8116yescomplemented
344C2×Dic67C22×D414yes—
345C2×Dic67C22×D414yes—
346C2×Dic67C22×Q814yes—
347C2×Dic67C22×Q814yes—
348C2×Dic67C22×Q814yes—
349C2×Dic67C22×Q814yes—
350C2×Dic67C2×#4114yes—
351Dic134—416no—
352C22×C67—24no—
353C22×C67—24no—
354C22×C67—24no—
355C22×C67—232no—
356C22×C67—24no—
357C22×C67—24no—
358C22×C67—24no—
359C22×C67C2×C22⋊Q814yes—
360C22×C67C2×C4⋊Q814yes—
361C22×C67C2×C4⋊Q818yescomplemented
362C22×C67#54414yes—
363C22×C67D4214yes—
364C22×C67#54714yes—
365C22×C67D4×Q814yes—
366C22×C67#55414yes—
367C22×C67C23×D411yescharacteristic
368C22×C67C23×D411yescharacteristic
369C22×C67C23×Q811yescharacteristic
370C22×C67C23×Q811yescharacteristic
371C22×C67C22×#4111yescharacteristic
372C22×C67C2×H(5,𝔽2)11yescharacteristic
373C22×C67C2×2−1+411yescharacteristic
374C4×C67—24no—
375C4×C67—24no—
376C4×C67—24no—
377C4×C67—42no—
378C4×C67—42no—
379C4×C67—42no—
380Dic67—24no—
381Dic67—24no—
382Dic67—24no—
383Dic67—24no—
384Dic67—42no—
385Dic67—42no—
386Dic67—42no—
387Dic67C2×C22⋊Q818yescomplemented
388C2×#2440—671nomaximal, Sylow
389C2×C67—28no—
390C2×C67#244018yescomplemented
391C2×C67C22×C22⋊Q811yescharacteristic
392C2×C67C22×C4⋊Q811yescharacteristic
393C2×C67C2×#54411yescharacteristic
394C2×C67C2×D4211yescharacteristic
395C2×C67C2×#54711yescharacteristic
396C2×C67C2×D4×Q811yescharacteristic
397C2×C67C2×#55411yescharacteristic
398C22×C4⋊Q8—671no—
399C22×C22⋊Q8—671no—
400C22×C22⋊Q8D6711yescharacteristic
401C23×C4⋊C4—671no—
402#2440—6716no—
403C2×#398—671no—
404C2×#398—671no—
405C2×#395—671no—
406C2×#395—671no—
407C2×#389—671no—
408C2×#389—671no—
409C2×#385—671no—
410C2×#385—671no—
411C2×#384—671no—
412C2×#380—671no—
413C2×C4×C22⋊C4—671no—
414C67C2×#244011yescharacteristic, complemented, Sylow
415C23×Q8—671no—
416C23×Q8C2×D6711yescharacteristic
417C24×C4—671no—
418C24×C4—671no—
419C24×C4C2×D6711yescharacteristic
420C2×C4⋊Q8—678no—
421C2×C4⋊Q8—1348no—
422C2×C22⋊Q8—28no—
423C2×C22⋊Q8—678no—
424C2×C22⋊Q8—1348no—
425C2×C22⋊Q8C2×D6718yes—
426C22×C4⋊C4—671no—
427C22×C4⋊C4—671no—
428C22×C4⋊C4—671no—
429C22×C4⋊C4—671no—
430C22×C4⋊C4—671no—
431C22×C4⋊C4—671no—
432C22×C4⋊C4—671no—
433C22×C4⋊C4—671no—
434C22×C4⋊C4—671no—
435C22×C4⋊C4—671no—
436C22×C4⋊C4—678no—
437C22×C4⋊C4—671no—
438C22×C4⋊C4—671no—
439C22×C4⋊C4—671no—
440C22×C4⋊C4—1348no—
441C22×C4⋊C4C2×D6711yescharacteristic
442C22×C4⋊C4C2×D6711yescharacteristic
443C22×C4⋊C4C2×D6711yescharacteristic
444C22×C22⋊C4—671no—
445C22×C22⋊C4—671no—
446C22×C22⋊C4C2×D6711yescharacteristic
447C22×C22⋊C4C2×D6711yescharacteristic
448C22×C42—671no—
449C22×C42—671no—
450#398—678no—
451#398—678no—
452#395—678no—
453#395—678no—
454#389—678no—
455#389—678no—
456#385—678no—
457#385—678no—
458#384—678no—
459#380—678no—
460C4×C22⋊C4—678no—
461C2×#95—671no—
462C2×#95—671no—
463C2×#95—671no—
464C2×#95—671no—
465C2×#95—671no—
466C2×#95—671no—
467C2×#95—671no—
468C2×#95—671no—
469C25C22×D6711yescharacteristic
470C22×Q8—24no—
471C22×Q8—24no—
472C22×Q8—42no—
473C22×Q8—2682no—
474C22×Q8—674no—
475C22×Q8—1344no—
476C22×Q8—1344no—
477C22×Q8C22×D6714yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—2682no—
482C23×C4—674no—
483C23×C4—671no—
484C23×C4—678no—
485C23×C4—674no—
486C23×C4—671no—
487C23×C4—671no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—671no—
492C23×C4—671no—
493C23×C4—1344no—
494C23×C4—1344no—
495C23×C4—1344no—
496C23×C4—1344no—
497C23×C4C22×D6711yescharacteristic
498C23×C4C22×D6711yescharacteristic
499C23×C4C22×D6711yescharacteristic
500C23×C4C22×D6714yes—
501C23×C4C22×D6711yescharacteristic
502C23×C4C22×D6711yescharacteristic
503C23×C4C22×D6711yescharacteristic
504C4⋊Q8—13432no—
505C22⋊Q8—232no—
506C22⋊Q8—13432no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—2682no—
511C2×C4⋊C4—2682no—
512C2×C4⋊C4—674no—
513C2×C4⋊C4—674no—
514C2×C4⋊C4—678no—
515C2×C4⋊C4—674no—
516C2×C4⋊C4—674no—
517C2×C4⋊C4—674no—
518C2×C4⋊C4—674no—
519C2×C4⋊C4—674no—
520C2×C4⋊C4—674no—
521C2×C4⋊C4—674no—
522C2×C4⋊C4—674no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—13432no—
527C2×C4⋊C4—1344no—
528C2×C4⋊C4—1344no—
529C2×C4⋊C4—1344no—
530C2×C4⋊C4—1344no—
531C2×C4⋊C4—1344no—
532C2×C4⋊C4—1344no—
533C2×C4⋊C4—1344no—
534C2×C4⋊C4—1344no—
535C2×C4⋊C4—1344no—
536C2×C4⋊C4—1344no—
537C2×C4⋊C4C22×D6714yes—
538C2×C4⋊C4C22×D6714yes—
539C2×C4⋊C4C22×D6714yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—678no—
542C2×C22⋊C4—674no—
543C2×C22⋊C4—674no—
544C2×C22⋊C4—1344no—
545C2×C22⋊C4C22⋊D6718yes—
546C2×C22⋊C4C22×D6714yes—
547C2×C22⋊C4C22×D6714yes—
548C2×C42—674no—
549C2×C42—674no—
550C2×C42—1344no—
551C2×C42—1344no—
552#95—674no—
553#95—674no—
554#95—674no—
555#95—674no—
556#95—674no—
557#95—674no—
558#95—674no—
559#95—674no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×C22⋊D6714yes—
565C24Q8×D6714yes—
566C24Q8×D6714yes—
567C24C23×D6712yes—
568C24C23×D6711yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—26816no—
574C2×Q8—2684no—
575C2×Q8—1348no—
576C2×Q8—1348no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—26816no—
597C22×C4—2684no—
598C22×C4—674no—
599C22×C4—674no—
600C22×C4—674no—
601C22×C4—672no—
602C22×C4—674no—
603C22×C4—674no—
604C22×C4—674no—
605C22×C4—674no—
606C22×C4—6716no—
607C22×C4—672no—
608C22×C4—672no—
609C22×C4—672no—
610C22×C4—672no—
611C22×C4—672no—
612C22×C4—672no—
613C22×C4—672no—
614C22×C4—1348no—
615C22×C4—1342no—
616C22×C4—1342no—
617C22×C4—1342no—
618C22×C4—1342no—
619C22×C4—1342no—
620C22×C4—1348no—
621C22×C4—1342no—
622C22×C4—1342no—
623C22×C4—1342no—
624C22×C4—1342no—
625C22×C4—1348no—
626C22×C4—13432no—
627C22×C4—1348no—
628C22×C4—1342no—
629C22×C4—1342no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4—1342no—
633C22×C4—1342no—
634C22×C4—1342no—
635C22×C4—1342no—
636C22×C4D4×D6714yes—
637C22×C4C2×C22⋊D6714yes—
638C22×C4C2×C22⋊D6714yes—
639C22×C4C23×D6712yes—
640C22×C4C23×D6712yes—
641C22×C4C23×D6712yes—
642C22×C4C23×D6712yes—
643C22×C4C23×D6712yes—
644C22×C4C23×D6712yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—2684no—
649C4⋊C4—2684no—
650C4⋊C4—6716no—
651C4⋊C4—1348no—
652C4⋊C4—1348no—
653C4⋊C4—1348no—
654C4⋊C4—1348no—
655C4⋊C4—1348no—
656C4⋊C4—1348no—
657C4⋊C4—1348no—
658C4⋊C4—1348no—
659C4⋊C4—1348no—
660C4⋊C4—1348no—
661C22⋊C4—28no—
662C22⋊C4—6716no—
663C22⋊C4—1348no—
664C22⋊C4C2×C22⋊D67116yes—
665C42—1348no—
666C42—1348no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23#14524041116yescomplemented
678C23C2×D4×D6712yes—
679C23C22×C22⋊D6714yes—
680C23C22×C22⋊D6712yes—
681C23C2×Q8×D6714yes—
682C23C2×Q8×D6714yes—
683C23C2×Q8×D6712yes—
684C23C2×Q8×D6712yes—
685C23#41×D6712yes—
686C23#1452408812yes—
687C23#1452409012yes—
688C23C24×D6711yescharacteristic
689Q8—416no—
690Q8—26816no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—2684no—
714C2×C4—2684no—
715C2×C4—2684no—
716C2×C4—26816no—
717C2×C4—6716no—
718C2×C4—674no—
719C2×C4—674no—
720C2×C4—674no—
721C2×C4—674no—
722C2×C4—674no—
723C2×C4—674no—
724C2×C4—674no—
725C2×C4—1342no—
726C2×C4—1342no—
727C2×C4—1342no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1342no—
733C2×C4—1342no—
734C2×C4—13432no—
735C2×C4—1348no—
736C2×C4—1348no—
737C2×C4—1348no—
738C2×C4—1348no—
739C2×C4—1342no—
740C2×C4—1342no—
741C2×C4—1342no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1342no—
746C2×C4—1342no—
747C2×C4C2×D4×D6714yes—
748C2×C4C22×C22⋊D6714yes—
749C2×C4C22×C22⋊D6714yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D6714yes—
758C22C2×#1452404114yes—
759C22C2×#1452404118yescomplemented
760C22#1686402514yes—
761C22D4×C22⋊D6714yes—
762C22#1686404514yes—
763C22#1686405914yes—
764C22#1686410014yes—
765C22C22×D4×D6711yescharacteristic
766C22C23×C22⋊D6711yescharacteristic
767C22C22×Q8×D6711yescharacteristic
768C22C22×Q8×D6711yescharacteristic
769C22C2×#41×D6711yescharacteristic
770C22C2×#1452408811yescharacteristic
771C22C2×#1452409011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—2682no—
779C4—2682no—
780C4—2682no—
781C4—678no—
782C4—1344no—
783C4—1344no—
784C4—1344no—
785C4—1344no—
786C2—28no—
787C2#2256390818yesdirect product factor
788C2C2×C22⋊Q8×D6711yescharacteristic
789C2C22×#1452404111yescharacteristic
790C2C2×#1686402511yescharacteristic
791C2C2×D4×C22⋊D6711yescharacteristic
792C2C2×#1686404511yescharacteristic
793C2C2×#1686405911yescharacteristic
794C2C2×#1686410011yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×C22⋊Q8×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC22×C22⋊Q8D67
hypocenterC67C2×#2440
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14524041C2semidirect
4. #22563908C2direct (N × H)
5. C2×#16863327C2semidirect
6. C2×#16863326C2semidirect
7. C2×#16863316C2semidirect
8. C2×#16863315C2semidirect
9. C2×#16863291C2semidirect
10. C2×#16863291C2semidirect
13. C2×#16863265C2semidirect
21. C2×#14524041C22semidirect
43. #16863327C22semidirect
44. #16863326C22semidirect
45. #16863316C22semidirect
46. #16863315C22semidirect
47. #16863291C22semidirect
48. #16863291C22semidirect
51. #16863265C22semidirect
80. C23×Dic67Q8semidirect
121. C2×C22⋊Dic67Q8semidirect
196. C22×Dic67C2×Q8semidirect
220. C22⋊Dic67C2×Q8semidirect
279. C23×C67C4⋊Q8semidirect
343. C2×Dic67C22⋊Q8semidirect
361. C22×C67C2×C4⋊Q8semidirect
387. Dic67C2×C22⋊Q8semidirect
390. C2×C67#2440semidirect
414. C67C2×#2440semidirect
677. C23#14524041semidirect
759. C22C2×#14524041semidirect
787. C2#22563908direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240412
C22×#145240202
C23×Dic67⋊C42
#225639082
C2×#168633272
C2×#168633262
C2×#168633162
C2×#168633152
C2×#168632912
C2×#168632692
C2×#168632682
C2×#168632652
C2×#168632542
C2×C22⋊C4×Dic672
C22×C22⋊Q8×C672
C2×#244067