Finite Group Databasebeta

← C2×#22563906 #31023659

Subgroups — C2×#22563906 #31023659

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×#14524042C211yesmaximal, characteristic, complemented
2C22×#14524023C211yesmaximal, characteristic
3C22×#14524021C211yesmaximal, characteristic
4C22×C4⋊C4×D67C211yesmaximal, characteristic
5#22563906C2116yesmaximal, direct product factor
6C2×#16863328C211yesmaximal, characteristic, complemented
7C2×#16863317C211yesmaximal, characteristic, complemented
8C2×#16863316C211yesmaximal, characteristic, complemented
9C2×#16863293C211yesmaximal, characteristic, complemented
10C2×#16863291C211yesmaximal, characteristic, complemented
11C2×#16863270C211yesmaximal, characteristic
12C2×#16863267C211yesmaximal, characteristic
13C2×#16863265C211yesmaximal, characteristic, complemented
14C2×#16863255C211yesmaximal, characteristic
15C2×#16863243C211yesmaximal, characteristic
16C2×#398×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×Dic134C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C2×#14524042—28no—
23C2×#14524042C2218yescomplemented
24C2×#14524023—28no—
25C2×#14524023C2218yes—
26C2×#14524021—28no—
27C2×#14524021C2218yes—
28C22×C4⋊Dic67C2211yescharacteristic
29C22×C4⋊Dic67C2211yescharacteristic
30C22×C4⋊Dic67C2211yescharacteristic
31C22×C4⋊Dic67C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×Dic67⋊C4C2211yescharacteristic
36C22×Dic67⋊C4C2211yescharacteristic
37C22×Dic67⋊C4C2211yescharacteristic
38C22×Dic67⋊C4C2211yescharacteristic
39C22×Dic67⋊C4C2211yescharacteristic
40C2×C4⋊C4×D67—28no—
41C2×C4⋊C4×D67C2218yes—
42C22×(C2×D67)⋊C4C2211yescharacteristic
43C22×(C2×D67)⋊C4C2211yescharacteristic
44C22×(C2×D67)⋊C4C2211yescharacteristic
45C22×(C2×D67)⋊C4C2211yescharacteristic
46C22×C4×Dic67C2211yescharacteristic
47C22×C4×Dic67C2211yescharacteristic
48#16863328C2218yescomplemented
49#16863317C2218yescomplemented
50#16863316C2218yescomplemented
51#16863293C2218yescomplemented
52#16863291C2218yescomplemented
53#16863270C2218yes—
54#16863267C2218yes—
55#16863265C2218yescomplemented
56#16863255C2218yes—
57#16863243C2218yes—
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C2×C67⋊#95C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65C22×C4⋊C4×C67C2211yescharacteristic
66C22×C4⋊C4×C67C2211yescharacteristic
67#398×C67C2218yescomplemented
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C2×#95×C67C2211yescharacteristic
71C24×D67C2311yescharacteristic
72C22×Dic134—24no—
73C22×Dic134—24no—
74C22×Dic134—24no—
75C22×Dic134—24no—
76C22×Dic134—42no—
77C22×Dic134—42no—
78C22×Dic134C2314yes—
79C22×Dic134C2314yes—
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—24no—
90C22×C4×D67—24no—
91C22×C4×D67—24no—
92C22×C4×D67—24no—
93C22×C4×D67—42no—
94C22×C4×D67—42no—
95C22×C4×D67Q818yescomplemented
96C22×C4×D67C2314yes—
97C22×C4×D67C2314yes—
98C22×C4×D67C2314yes—
99#14524042—232no—
100#14524023—232no—
101#14524021—232no—
102C2×C4⋊Dic67—24no—
103C2×C4⋊Dic67—24no—
104C2×C4⋊Dic67—24no—
105C2×C4⋊Dic67—24no—
106C2×C4⋊Dic67C2314yes—
107C2×C4⋊Dic67C2314yes—
108C2×C4⋊Dic67C2314yes—
109C2×C4⋊Dic67C2314yes—
110C2×Dic67⋊C4—24no—
111C2×Dic67⋊C4—24no—
112C2×Dic67⋊C4—24no—
113C2×Dic67⋊C4—24no—
114C2×Dic67⋊C4—24no—
115C2×Dic67⋊C4—42no—
116C2×Dic67⋊C4—42no—
117C2×Dic67⋊C4D418yes—
118C2×Dic67⋊C4C2314yes—
119C2×Dic67⋊C4C2314yes—
120C2×Dic67⋊C4C2314yes—
121C2×Dic67⋊C4C2314yes—
122C2×Dic67⋊C4C2314yes—
123C2×Dic67⋊C4C2314yes—
124C2×Dic67⋊C4C2314yes—
125C2×Dic67⋊C4C2314yes—
126C4⋊C4×D67—232no—
127C2×(C2×D67)⋊C4—24no—
128C2×(C2×D67)⋊C4—24no—
129C2×(C2×D67)⋊C4D418yes—
130C2×(C2×D67)⋊C4Q818yescomplemented
131C2×(C2×D67)⋊C4C2314yes—
132C2×(C2×D67)⋊C4C2314yes—
133C2×(C2×D67)⋊C4C2314yes—
134C2×(C2×D67)⋊C4C2314yes—
135C2×C4×Dic67—24no—
136C2×C4×Dic67—24no—
137C2×C4×Dic67C2314yes—
138C2×C4×Dic67C2314yes—
139C67⋊#95C2314yes—
140C67⋊#95C2314yes—
141C67⋊#95C2314yes—
142C67⋊#95C2314yes—
143C67⋊#95C2314yes—
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2311yescharacteristic
148C23×C4×C67C2311yescharacteristic
149C23×C4×C67C2311yescharacteristic
150C23×C4×C67C2311yescharacteristic
151C2×C4⋊C4×C67—24no—
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×C4⋊C4×C67C2314yes—
159#95×C67C2314yes—
160#95×C67C2314yes—
161#95×C67C2314yes—
162C23×D67—22no—
163C23×D67—22no—
164C23×D67—22no—
165C23×D67—22no—
166C23×D67C2×D414yes—
167C23×D67C2×Q814yes—
168C23×D67C2×Q814yes—
169C23×D67C2412yes—
170C2×Dic134—28no—
171C2×Dic134—28no—
172C2×Dic134—28no—
173C2×Dic134—28no—
174C2×Dic134—44no—
175C2×Dic134—44no—
176C2×Dic134—416no—
177C2×Dic134—416no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—22no—
188C22×Dic67—22no—
189C22×Dic67—22no—
190C22×Dic67—22no—
191C22×Dic67—22no—
192C22×Dic67—22no—
193C22×Dic67C2×D414yes—
194C22×Dic67C2×D414yes—
195C22×Dic67C2×D414yes—
196C22×Dic67C2×Q814yes—
197C22×Dic67C2×Q814yes—
198C22×Dic67#4114yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C22×Dic67C2412yes—
203C22×Dic67C2412yes—
204C22×Dic67C2412yes—
205C22×Dic67C2412yes—
206C2×C4×D67—232no—
207C2×C4×D67—28no—
208C2×C4×D67—28no—
209C2×C4×D67—28no—
210C2×C4×D67—28no—
211C2×C4×D67—28no—
212C2×C4×D67—28no—
213C2×C4×D67—44no—
214C2×C4×D67—44no—
215C2×C4×D67—416no—
216C2×C4×D67—416no—
217C2×C4×D67C2×Q8116yescomplemented
218C4⋊Dic67—28no—
219C4⋊Dic67—28no—
220C4⋊Dic67—28no—
221C4⋊Dic67—28no—
222Dic67⋊C4—28no—
223Dic67⋊C4—28no—
224Dic67⋊C4—28no—
225Dic67⋊C4—28no—
226Dic67⋊C4—28no—
227Dic67⋊C4—44no—
228Dic67⋊C4—44no—
229Dic67⋊C4C2×D4116yes—
230(C2×D67)⋊C4—28no—
231(C2×D67)⋊C4—28no—
232(C2×D67)⋊C4C2×D4116yes—
233(C2×D67)⋊C4C2×Q8116yescomplemented
234C4×Dic67—28no—
235C4×Dic67—28no—
236C24×C67C2411yescharacteristic
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—22no—
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—22no—
253C22×C4×C67—22no—
254C22×C4×C67C2×D414yes—
255C22×C4×C67C2×D414yes—
256C22×C4×C67C2×Q814yes—
257C22×C4×C67C2×Q814yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C22×C4×C67C2412yes—
263C22×C4×C67C2412yes—
264C22×C4×C67C2412yes—
265C4⋊C4×C67—28no—
266C4⋊C4×C67—28no—
267C4⋊C4×C67—28no—
268C4⋊C4×C67—28no—
269C23×C67C22×D412yes—
270C23×C67C22×D412yes—
271C23×C67C22×Q812yes—
272C23×C67C22×Q812yes—
273C23×C67C2×#4112yes—
274C23×C67H(5,𝔽2)12yes—
275C23×C672−1+412yes—
276C23×C67C2511yescharacteristic
277C22×D67—28no—
278C22×D67—28no—
279C22×D67—28no—
280C22×D67—28no—
281C22×D67—28no—
282C22×D67—28no—
283C22×D67—22no—
284C22×D67—22no—
285C22×D67—22no—
286C22×D67—22no—
287C22×D67C4⋊Q8116yescomplemented
288C22×D67C22×D414yes—
289C22×D67C22×Q814yes—
290C22×D67C22×Q814yes—
291C2×C4×C67—28no—
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—22no—
311C2×C4×C67—22no—
312C2×C4×C67—44no—
313C2×C4×C67—44no—
314C2×C4×C67—44no—
315C2×C4×C67C22×D414yes—
316C2×C4×C67C22×D414yes—
317C2×C4×C67C22×Q814yes—
318C2×C4×C67C22×Q814yes—
319C2×Dic67—28no—
320C2×Dic67—28no—
321C2×Dic67—28no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—44no—
338C2×Dic67—44no—
339C2×Dic67—44no—
340C2×Dic67C22⋊Q8116yescomplemented
341C2×Dic67C22×D414yes—
342C2×Dic67C22×D414yes—
343C2×Dic67C22×D414yes—
344C2×Dic67C22×Q814yes—
345C2×Dic67C22×Q814yes—
346C2×Dic67C2×#4114yes—
347C4×D67—232no—
348C4×D67—416no—
349C4×D67—416no—
350Dic134—416no—
351Dic134—416no—
352C22×C67C2×C22⋊Q814yes—
353C22×C67C2×C4⋊Q814yes—
354C22×C67#54414yes—
355C22×C67D4214yes—
356C22×C67#54714yes—
357C22×C67D4×Q814yes—
358C22×C67#55414yes—
359C22×C67C23×D411yescharacteristic
360C22×C67C23×D411yescharacteristic
361C22×C67C23×Q811yescharacteristic
362C22×C67C23×Q811yescharacteristic
363C22×C67C22×#4111yescharacteristic
364C22×C67C2×H(5,𝔽2)11yescharacteristic
365C22×C67C2×2−1+411yescharacteristic
366C2×D67—24no—
367C2×D67—24no—
368C2×D67—24no—
369C2×D67—232no—
370C2×D67—24no—
371C2×D67—24no—
372C2×D67—24no—
373C2×D67C2×C4⋊Q818yescomplemented
374C4×C67—24no—
375C4×C67—24no—
376C4×C67—24no—
377C4×C67—24no—
378C4×C67—42no—
379C4×C67—42no—
380C4×C67—42no—
381Dic67—24no—
382Dic67—24no—
383Dic67—24no—
384Dic67—42no—
385Dic67—42no—
386Dic67—42no—
387Dic67C2×C22⋊Q818yescomplemented
388C2×#2440—671nomaximal, Sylow
389C2×C67#244018yescomplemented
390C2×C67C22×C22⋊Q811yescharacteristic
391C2×C67C22×C4⋊Q811yescharacteristic
392C2×C67C2×#54411yescharacteristic
393C2×C67C2×D4211yescharacteristic
394C2×C67C2×#54711yescharacteristic
395C2×C67C2×D4×Q811yescharacteristic
396C2×C67C2×#55411yescharacteristic
397D67—28no—
398C22×C4⋊Q8—671no—
399C22×C22⋊Q8—671no—
400C22×C22⋊Q8—671no—
401C23×C4⋊C4—671no—
402#2440—6716no—
403C2×#398—671no—
404C2×#398D6711yescharacteristic, complemented
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×Q8—671no—
417C24×C4—671no—
418C24×C4—671no—
419C24×C4—671no—
420C2×C4⋊Q8—678no—
421C2×C4⋊Q8—1348no—
422C2×C22⋊Q8—678no—
423C2×C22⋊Q8—678no—
424C2×C22⋊Q8—1348no—
425C2×C22⋊Q8—1348no—
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—671no—
437C22×C4⋊C4—671no—
438C22×C4⋊C4—678no—
439C22×C4⋊C4—1348no—
440C22×C4⋊C4C2×D6711yescharacteristic
441C22×C4⋊C4C2×D6711yescharacteristic
442C22×C4⋊C4C2×D6711yescharacteristic
443C22×C4⋊C4C2×D6711yescharacteristic
444C22×C22⋊C4—671no—
445C22×C22⋊C4—671no—
446C22×C22⋊C4—671no—
447C22×C22⋊C4—671no—
448C22×C42—671no—
449C22×C42—671no—
450#398—678no—
451#398C2×D6718yescomplemented
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×#95C2×D6711yescharacteristic
467C2×#95C2×D6711yescharacteristic
468C2×#95C2×D6711yescharacteristic
469C25—671no—
470C22×Q8—2682no—
471C22×Q8—2682no—
472C22×Q8—674no—
473C22×Q8—674no—
474C22×Q8—1344no—
475C22×Q8—1344no—
476C22×Q8—1344no—
477C22×Q8—1344no—
478C23×C4—2682no—
479C23×C4—2682no—
480C23×C4—674no—
481C23×C4—674no—
482C23×C4—671no—
483C23×C4—671no—
484C23×C4—671no—
485C23×C4—671no—
486C23×C4—678no—
487C23×C4—674no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—1344no—
492C23×C4—1344no—
493C23×C4—1344no—
494C23×C4—1344no—
495C23×C4—1344no—
496C23×C4—1344no—
497C23×C4C22×D6711yescharacteristic
498C23×C4C22×D6711yescharacteristic
499C23×C4C22×D6711yescharacteristic
500C23×C4C22×D6711yescharacteristic
501C23×C4C22×D6711yescharacteristic
502C23×C4C22×D6711yescharacteristic
503C23×C4C22×D6711yescharacteristic
504C4⋊Q8—13432no—
505C22⋊Q8—13432no—
506C22⋊Q8—13432no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—2682no—
512C2×C4⋊C4—2682no—
513C2×C4⋊C4—674no—
514C2×C4⋊C4—674no—
515C2×C4⋊C4—678no—
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⋊C4C22×D6714yes—
537C2×C4⋊C4C22×D6714yes—
538C2×C4⋊C4C22×D6714yes—
539C2×C4⋊C4C22×D6714yes—
540C2×C22⋊C4—678no—
541C2×C22⋊C4—678no—
542C2×C22⋊C4—674no—
543C2×C22⋊C4—674no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—674no—
546C2×C22⋊C4—1344no—
547C2×C22⋊C4—1344no—
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#95C22×D6714yes—
558#95C22×D6714yes—
559#95C22×D6714yes—
560C24—674no—
561C24—674no—
562C24—674no—
563C24—672no—
564C24—1342no—
565C24—1342no—
566C24—1342no—
567C24—1342no—
568C24C23×D6711yescharacteristic
569C2×Q8—26816no—
570C2×Q8—2684no—
571C2×Q8—2684no—
572C2×Q8—26816no—
573C2×Q8—1348no—
574C2×Q8—1348no—
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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—26816no—
595C22×C4—2684no—
596C22×C4—2684no—
597C22×C4—26816no—
598C22×C4—674no—
599C22×C4—674no—
600C22×C4—674no—
601C22×C4—672no—
602C22×C4—674no—
603C22×C4—674no—
604C22×C4—674no—
605C22×C4—672no—
606C22×C4—672no—
607C22×C4—672no—
608C22×C4—6716no—
609C22×C4—672no—
610C22×C4—672no—
611C22×C4—672no—
612C22×C4—1348no—
613C22×C4—1348no—
614C22×C4—1348no—
615C22×C4—1348no—
616C22×C4—13432no—
617C22×C4—1348no—
618C22×C4—1342no—
619C22×C4—1342no—
620C22×C4—1342no—
621C22×C4—1342no—
622C22×C4—1342no—
623C22×C4—1342no—
624C22×C4—1342no—
625C22×C4—1342no—
626C22×C4—1342no—
627C22×C4—1348no—
628C22×C4—1342no—
629C22×C4—1342no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4—1342no—
633C22×C4—1342no—
634C22×C4D4×D6714yes—
635C22×C4D4×D6714yes—
636C22×C4Q8×D6714yes—
637C22×C4Q8×D6714yes—
638C22×C4C23×D6712yes—
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—28no—
649C4⋊C4—2684no—
650C4⋊C4—2684no—
651C4⋊C4—6716no—
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—6716no—
662C22⋊C4—6716no—
663C22⋊C4—1348no—
664C22⋊C4—1348no—
665C42—1348no—
666C42—1348no—
667C23—6716no—
668C23—674no—
669C23—674no—
670C23—674no—
671C23—1348no—
672C23—1348no—
673C23—1348no—
674C23—1348no—
675C23—1348no—
676C23—1348no—
677C23—1342no—
678C23—1342no—
679C23—1342no—
680C23—1342no—
681C23C2×D4×D6712yes—
682C23C2×D4×D6712yes—
683C23C2×Q8×D6712yes—
684C23C2×Q8×D6712yes—
685C23#41×D6712yes—
686C23#1452408912yes—
687C23#1452409012yes—
688C23C24×D6711yescharacteristic
689Q8—26816no—
690Q8—26816no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
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—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—26816no—
716C2×C4—26816no—
717C2×C4—2684no—
718C2×C4—2684no—
719C2×C4—2684no—
720C2×C4—6716no—
721C2×C4—674no—
722C2×C4—674no—
723C2×C4—674no—
724C2×C4—674no—
725C2×C4—674no—
726C2×C4—674no—
727C2×C4—13432no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1342no—
733C2×C4—1342no—
734C2×C4—1342no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1348no—
738C2×C4—1348no—
739C2×C4—1348no—
740C2×C4—1342no—
741C2×C4—1342no—
742C2×C4—1342no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—1342no—
746C2×C4C2×D4×D6714yes—
747C2×C4C2×D4×D6714yes—
748C2×C4C2×Q8×D6714yes—
749C2×C4C2×Q8×D6714yes—
750C22—678no—
751C22—1344no—
752C22—13432no—
753C22—1344no—
754C22—1344no—
755C22—1344no—
756C22—1344no—
757C22—1344no—
758C22C22⋊Q8×D6714yes—
759C22C4⋊Q8×D6714yes—
760C22#1686402614yes—
761C22#1686403014yes—
762C22#1686404414yes—
763C22#1686405914yes—
764C22#1686410214yes—
765C22C22×D4×D6711yescharacteristic
766C22C22×D4×D6711yescharacteristic
767C22C22×Q8×D6711yescharacteristic
768C22C22×Q8×D6711yescharacteristic
769C22C2×#41×D6711yescharacteristic
770C22C2×#1452408911yescharacteristic
771C22C2×#1452409011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2682no—
780C4—2682no—
781C4—2682no—
782C4—678no—
783C4—1344no—
784C4—1344no—
785C4—1344no—
786C2—1348no—
787C2#2256390618yesdirect product factor
788C2C2×C22⋊Q8×D6711yescharacteristic
789C2C2×C4⋊Q8×D6711yescharacteristic
790C2C2×#1686402611yescharacteristic
791C2C2×#1686403011yescharacteristic
792C2C2×#1686404411yescharacteristic
793C2C2×#1686405911yescharacteristic
794C2C2×#1686410211yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#398×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×#398D67
hypocenterC67C2×#2440
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14524042C2semidirect
5. #22563906C2direct (N × H)
6. C2×#16863328C2semidirect
7. C2×#16863317C2semidirect
8. C2×#16863316C2semidirect
9. C2×#16863293C2semidirect
10. C2×#16863291C2semidirect
13. C2×#16863265C2semidirect
16. C2×#398×C67C2semidirect
23. C2×#14524042C22semidirect
48. #16863328C22semidirect
49. #16863317C22semidirect
50. #16863316C22semidirect
51. #16863293C22semidirect
52. #16863291C22semidirect
55. #16863265C22semidirect
67. #398×C67C22semidirect
95. C22×C4×D67Q8semidirect
130. C2×(C2×D67)⋊C4Q8semidirect
217. C2×C4×D67C2×Q8semidirect
233. (C2×D67)⋊C4C2×Q8semidirect
287. C22×D67C4⋊Q8semidirect
340. C2×Dic67C22⋊Q8semidirect
373. C2×D67C2×C4⋊Q8semidirect
387. Dic67C2×C22⋊Q8semidirect
389. C2×C67#2440semidirect
404. C2×#398D67semidirect
414. C67C2×#2440semidirect
451. #398C2×D67semidirect
787. C2#22563906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240422
C22×#145240232
C22×#145240212
C22×C4⋊C4×D672
#225639062
C2×#168633282
C2×#168633172
C2×#168633162
C2×#168632932
C2×#168632912
C2×#168632702
C2×#168632672
C2×#168632652
C2×#168632552
C2×#168632432
C2×#398×C672
C2×#244067