Finite Group Databasebeta

← C2×#387×D67 #31014146

Subgroups — C2×#387×D67 #31014146

Order 17152.

4286 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D67C211yesmaximal, characteristic
2C22×C4⋊C4×D67C211yesmaximal, characteristic
3C22×C42×D67C211yesmaximal, characteristic
4C2×#16863283C211yesmaximal, characteristic, complemented
5C2×#16863282C211yesmaximal, characteristic, complemented
6C2×#16863281C211yesmaximal, characteristic, complemented
7C2×#16863280C211yesmaximal, characteristic, complemented
8C2×#16863279C211yesmaximal, characteristic, complemented
9C2×#16863278C211yesmaximal, characteristic, complemented
10C2×#16863277C211yesmaximal, characteristic, complemented
11#387×D67C2116yesmaximal, direct product factor
12C2×#95×D67C211yesmaximal, characteristic
13C2×#95×D67C211yesmaximal, characteristic
14C2×#95×D67C211yesmaximal, characteristic
15C2×#95×D67C211yesmaximal, characteristic
16C2×#387×C67C211yesmaximal, characteristic, complemented
17C23×C4×D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C23×C4×D67C2211yescharacteristic
23C23×C4×D67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×C4⋊Dic67C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C2×C4⋊C4×D67—28no—
31C2×C4⋊C4×D67C4116yescomplemented
32C2×C4⋊C4×D67C2218yes—
33C2×C4⋊C4×D67C2218yes—
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37C2×C42×D67—28no—
38C2×C42×D67C2218yes—
39#16863283C2218yescomplemented
40#16863282C2218yescomplemented
41#16863281C2218yescomplemented
42#16863280C2218yescomplemented
43#16863279C2218yescomplemented
44#16863278C2218yescomplemented
45#16863277C2218yescomplemented
46C2×C67⋊#95C2211yescharacteristic
47C2×C67⋊#95C2211yescharacteristic
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58#95×D67C2218yes—
59#95×D67C2218yes—
60#95×D67C2218yes—
61#95×D67C2218yes—
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C42×C67C2211yescharacteristic
65#387×C67C2218yescomplemented
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C24×D67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C22×C4×D67—24no—
79C22×C4×D67—24no—
80C22×C4×D67—24no—
81C22×C4×D67—24no—
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—24no—
85C22×C4×D67—24no—
86C22×C4×D67—24no—
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—24no—
94C22×C4×D67C2×C418yes—
95C22×C4×D67C2×C418yes—
96C22×C4×D67C2×C418yes—
97C22×C4×D67D418yes—
98C22×C4×D67Q818yes—
99C22×C4×D67C2314yes—
100C22×C4×D67C2314yes—
101C22×C4×D67C2314yes—
102C22×C4×D67C2314yes—
103C22×C4×D67C2314yes—
104C22×C4×D67C2314yes—
105C22×C4×D67C2314yes—
106C2×C4⋊Dic67—24no—
107C2×C4⋊Dic67C2×C418yescomplemented
108C2×C4⋊Dic67C2314yes—
109C2×C4⋊Dic67C2314yes—
110C2×Dic67⋊C4—24no—
111C2×Dic67⋊C4—24no—
112C2×Dic67⋊C4C2×C418yescomplemented
113C2×Dic67⋊C4C2×C418yescomplemented
114C2×Dic67⋊C4C2314yes—
115C2×Dic67⋊C4C2314yes—
116C2×Dic67⋊C4C2314yes—
117C2×Dic67⋊C4C2314yes—
118C4⋊C4×D67—232no—
119C4⋊C4×D67C2×C4164yescomplemented
120C2×C4×Dic67—24no—
121C2×C4×Dic67—24no—
122C2×C4×Dic67—24no—
123C2×C4×Dic67C2314yes—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C42×D67—232no—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C67⋊#95C2314yes—
137C67⋊#95C2314yes—
138C67⋊#95C2314yes—
139C23×C4×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C2×C4⋊C4×C67—24no—
147C2×C4⋊C4×C67C2×C418yescomplemented
148C2×C4⋊C4×C67C2314yes—
149C2×C4⋊C4×C67C2314yes—
150C2×C42×C67—24no—
151C2×C42×C67C2314yes—
152#95×C67C2314yes—
153#95×C67C2314yes—
154#95×C67C2314yes—
155#95×C67C2314yes—
156C23×D67C22×C414yes—
157C23×D67C2×D414yes—
158C23×D67C2×Q814yes—
159C23×D67#4114yes—
160C23×D67#4114yes—
161C23×D67#4114yes—
162C23×D67#4114yes—
163C23×D67C2412yes—
164C22×Dic67—22no—
165C22×Dic67—22no—
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—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67C22×C414yes—
181C22×Dic67C22×C414yes—
182C22×Dic67C22×C414yes—
183C22×Dic67C2×D414yes—
184C22×Dic67C2×Q814yes—
185C22×Dic67C2412yes—
186C22×Dic67C2412yes—
187C22×Dic67C2412yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C2×C4×D67—232no—
193C2×C4×D67—232no—
194C2×C4×D67—232no—
195C2×C4×D67—232no—
196C2×C4×D67—232no—
197C2×C4×D67—28no—
198C2×C4×D67—28no—
199C2×C4×D67—28no—
200C2×C4×D67—28no—
201C2×C4×D67—28no—
202C2×C4×D67—28no—
203C2×C4×D67—28no—
204C2×C4×D67—28no—
205C2×C4×D67—28no—
206C2×C4×D67—28no—
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—416no—
214C2×C4×D67—416no—
215C2×C4×D67C22×C4116yes—
216C2×C4×D67C22×C4116yes—
217C2×C4×D67C22×C4116yes—
218C2×C4×D67C2×D4116yes—
219C2×C4×D67C2×Q8116yes—
220C4⋊Dic67—28no—
221C4⋊Dic67C22×C4116yescomplemented
222Dic67⋊C4—28no—
223Dic67⋊C4—28no—
224Dic67⋊C4C22×C4116yescomplemented
225Dic67⋊C4C22×C4116yescomplemented
226C4×Dic67—28no—
227C4×Dic67—28no—
228C4×Dic67—28no—
229C24×C67C2411yescharacteristic
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
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—22no—
246C22×C4×C67C22×C414yes—
247C22×C4×C67C22×C414yes—
248C22×C4×C67C22×C414yes—
249C22×C4×C67C2×D414yes—
250C22×C4×C67C2×Q814yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2412yes—
253C22×C4×C67C2412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2412yes—
258C4⋊C4×C67—28no—
259C4⋊C4×C67C22×C4116yescomplemented
260C42×C67—28no—
261C23×C67C23×C412yes—
262C23×C67C22×D412yes—
263C23×C67C22×Q812yes—
264C23×C67C2×#4112yes—
265C23×C67C2×#4112yes—
266C23×C67C2×#4112yes—
267C23×C67C2×#4112yes—
268C23×C67C2511yescharacteristic
269C22×D67#117116yes—
270C22×D67C4×D4116yes—
271C22×D67C4×Q8116yes—
272C22×D67C22⋊Q8116yes—
273C22×D67#123116yes—
274C22×D67#125116yes—
275C22×D67#126116yes—
276C22×D67C23×C414yes—
277C22×D67C22×D414yes—
278C22×D67C22×Q814yes—
279C22×D67C2×#4114yes—
280C22×D67C2×#4114yes—
281C22×D67C2×#4114yes—
282C22×D67C2×#4114yes—
283C2×C4×C67—28no—
284C2×C4×C67—28no—
285C2×C4×C67—28no—
286C2×C4×C67—28no—
287C2×C4×C67—28no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
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—44no—
305C2×C4×C67—44no—
306C2×C4×C67C23×C414yes—
307C2×C4×C67C23×C414yes—
308C2×C4×C67C23×C414yes—
309C2×C4×C67C22×D414yes—
310C2×C4×C67C22×Q814yes—
311C2×Dic67—28no—
312C2×Dic67—28no—
313C2×Dic67—28no—
314C2×Dic67—28no—
315C2×Dic67—28no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—22no—
320C2×Dic67—22no—
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—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—44no—
333C2×Dic67—44no—
334C2×Dic67C23×C414yes—
335C2×Dic67C23×C414yes—
336C2×Dic67C23×C414yes—
337C2×Dic67C22×D414yes—
338C2×Dic67C22×Q814yes—
339C4×D67—232no—
340C4×D67—232no—
341C4×D67—232no—
342C4×D67—232no—
343C4×D67—232no—
344C4×D67—416no—
345C4×D67—416no—
346C22×C67C2×#11714yes—
347C22×C67C2×C4×D414yes—
348C22×C67C2×C4×Q814yes—
349C22×C67C2×C22⋊Q814yes—
350C22×C67C2×#12314yes—
351C22×C67C2×#12514yes—
352C22×C67C2×#12614yes—
353C22×C67C24×C411yescharacteristic
354C22×C67C23×D411yescharacteristic
355C22×C67C23×Q811yescharacteristic
356C22×C67C22×#4111yescharacteristic
357C22×C67C22×#4111yescharacteristic
358C22×C67C22×#4111yescharacteristic
359C22×C67C22×#4111yescharacteristic
360C2×D67#387164yesdirect product factor
361C2×D67C2×#11718yes—
362C2×D67C2×C4×D418yes—
363C2×D67C2×C4×Q818yes—
364C2×D67C2×C22⋊Q818yes—
365C2×D67C2×#12318yes—
366C2×D67C2×#12518yes—
367C2×D67C2×#12618yes—
368C4×C67—24no—
369C4×C67—24no—
370C4×C67—24no—
371C4×C67—24no—
372C4×C67—24no—
373C4×C67—42no—
374C4×C67—42no—
375Dic67—24no—
376Dic67—24no—
377Dic67—24no—
378Dic67—24no—
379Dic67—24no—
380Dic67—42no—
381Dic67—42no—
382C22×#387—671nomaximal, Sylow
383C2×C67C2×#38718yescomplemented
384C2×C67C22×#11711yescharacteristic
385C2×C67C22×C4×D411yescharacteristic
386C2×C67C22×C4×Q811yescharacteristic
387C2×C67C22×C22⋊Q811yescharacteristic
388C2×C67C22×#12311yescharacteristic
389C2×C67C22×#12511yescharacteristic
390C2×C67C22×#12611yescharacteristic
391D67C2×#387116yesdirect product factor
392C23×C4⋊C4—671no—
393C23×C4⋊C4—671no—
394C23×C42—671no—
395C2×#387—671no—
396C2×#387—6716no—
397C2×#387—671no—
398C2×#387—671no—
399C2×#387—671no—
400C2×#387—671no—
401C2×#387—671no—
402C2×#387—671no—
403C2×#387D6711yescharacteristic, direct product factor
404C22×#95—671no—
405C22×#95—671no—
406C22×#95—671no—
407C22×#95—671no—
408C67C22×#38711yescharacteristic, complemented, Sylow
409C24×C4—671no—
410C24×C4—671no—
411C24×C4—671no—
412C24×C4—671no—
413C24×C4—671no—
414C24×C4—671no—
415C24×C4—671no—
416C22×C4⋊C4—671no—
417C22×C4⋊C4—671no—
418C22×C4⋊C4—671no—
419C22×C4⋊C4—6716no—
420C22×C4⋊C4—678no—
421C22×C4⋊C4—671no—
422C22×C4⋊C4—671no—
423C22×C4⋊C4—671no—
424C22×C4⋊C4—678no—
425C22×C4⋊C4—1348no—
426C22×C4⋊C4C2×D6711yescharacteristic
427C22×C4⋊C4C2×D6711yescharacteristic
428C22×C42—671no—
429C22×C42—671no—
430C22×C42—671no—
431C22×C42—678no—
432C22×C42—1348no—
433C22×C42C2×D6711yescharacteristic
434#387—678no—
435#387—678no—
436#387—678no—
437#387—678no—
438#387—678no—
439#387—678no—
440#387—678no—
441#387C2×D6718yesdirect product factor
442C2×#95—671no—
443C2×#95—671no—
444C2×#95—671no—
445C2×#95—671no—
446C2×#95—671no—
447C2×#95—671no—
448C2×#95—671no—
449C2×#95—671no—
450C2×#95—671no—
451C2×#95—671no—
452C2×#95—671no—
453C2×#95—671no—
454C2×#95—678no—
455C2×#95—678no—
456C2×#95—678no—
457C2×#95—678no—
458C2×#95C2×D6711yescharacteristic
459C2×#95C2×D6711yescharacteristic
460C2×#95C2×D6711yescharacteristic
461C2×#95C2×D6711yescharacteristic
462C25—671no—
463C23×C4—671no—
464C23×C4—671no—
465C23×C4—671no—
466C23×C4—671no—
467C23×C4—671no—
468C23×C4—678no—
469C23×C4—678no—
470C23×C4—678no—
471C23×C4—678no—
472C23×C4—678no—
473C23×C4—674no—
474C23×C4—674no—
475C23×C4—674no—
476C23×C4—674no—
477C23×C4—674no—
478C23×C4—671no—
479C23×C4—671no—
480C23×C4—674no—
481C23×C4—674no—
482C23×C4—1344no—
483C23×C4—1344no—
484C23×C4—1344no—
485C23×C4—1344no—
486C23×C4—1344no—
487C23×C4—1344no—
488C23×C4—1344no—
489C23×C4—1344no—
490C23×C4—1344no—
491C23×C4—1344no—
492C23×C4—1344no—
493C23×C4—1344no—
494C23×C4—1344no—
495C23×C4—1344no—
496C23×C4—1344no—
497C23×C4—1344no—
498C23×C4C22×D6711yescharacteristic
499C23×C4C22×D6711yescharacteristic
500C23×C4C22×D6711yescharacteristic
501C23×C4C22×D6711yescharacteristic
502C23×C4C22×D6711yescharacteristic
503C23×C4C22×D6711yescharacteristic
504C23×C4C22×D6711yescharacteristic
505C2×C4⋊C4—24no—
506C2×C4⋊C4—678no—
507C2×C4⋊C4—678no—
508C2×C4⋊C4—678no—
509C2×C4⋊C4—674no—
510C2×C4⋊C4—674no—
511C2×C4⋊C4—674no—
512C2×C4⋊C4—6764no—
513C2×C4⋊C4—674no—
514C2×C4⋊C4—674no—
515C2×C4⋊C4—674no—
516C2×C4⋊C4—13432no—
517C2×C4⋊C4—1344no—
518C2×C4⋊C4—1344no—
519C2×C4⋊C4—1344no—
520C2×C4⋊C4C4×D6718yescomplemented
521C2×C4⋊C4C22×D6714yes—
522C2×C4⋊C4C22×D6714yes—
523C2×C42—24no—
524C2×C42—674no—
525C2×C42—674no—
526C2×C42—674no—
527C2×C42—13432no—
528C2×C42—1344no—
529C2×C42—1344no—
530C2×C42—1344no—
531C2×C42C22×D6714yes—
532#95—674no—
533#95—674no—
534#95—674no—
535#95—674no—
536#95—674no—
537#95—674no—
538#95—674no—
539#95—674no—
540#95—674no—
541#95—674no—
542#95—674no—
543#95—674no—
544#95C22×D6714yes—
545#95C22×D6714yes—
546#95C22×D6714yes—
547#95C22×D6714yes—
548C24—674no—
549C24—674no—
550C24—674no—
551C24—674no—
552C24—674no—
553C24—674no—
554C24—674no—
555C24—672no—
556C24C23×D6711yescharacteristic
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—26816no—
574C22×C4—26816no—
575C22×C4—674no—
576C22×C4—674no—
577C22×C4—674no—
578C22×C4—674no—
579C22×C4—674no—
580C22×C4—672no—
581C22×C4—672no—
582C22×C4—672no—
583C22×C4—672no—
584C22×C4—672no—
585C22×C4—6716no—
586C22×C4—6716no—
587C22×C4—6716no—
588C22×C4—6716no—
589C22×C4—6716no—
590C22×C4—672no—
591C22×C4—672no—
592C22×C4—1348no—
593C22×C4—1348no—
594C22×C4—1348no—
595C22×C4—1348no—
596C22×C4—1348no—
597C22×C4—1348no—
598C22×C4—1348no—
599C22×C4—1348no—
600C22×C4—1348no—
601C22×C4—13432no—
602C22×C4—13432no—
603C22×C4—13432no—
604C22×C4—13432no—
605C22×C4—13432no—
606C22×C4—1348no—
607C22×C4—1348no—
608C22×C4—1348no—
609C22×C4—1348no—
610C22×C4—1348no—
611C22×C4—1348no—
612C22×C4—1348no—
613C22×C4—1342no—
614C22×C4—1342no—
615C22×C4—1342no—
616C22×C4—1342no—
617C22×C4—1342no—
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—1342no—
628C22×C4—1342no—
629C22×C4C2×C4×D6714yes—
630C22×C4C2×C4×D6714yes—
631C22×C4C2×C4×D6714yes—
632C22×C4D4×D6714yes—
633C22×C4Q8×D6714yes—
634C22×C4C23×D6712yes—
635C22×C4C23×D6712yes—
636C22×C4C23×D6712yes—
637C22×C4C23×D6712yes—
638C22×C4C23×D6712yes—
639C22×C4C23×D6712yes—
640C22×C4C23×D6712yes—
641C4⋊C4—28no—
642C4⋊C4—6716no—
643C4⋊C4—6716no—
644C4⋊C4—6716no—
645C4⋊C4—1348no—
646C4⋊C4—1348no—
647C4⋊C4—1348no—
648C4⋊C4C2×C4×D67116yescomplemented
649C42—28no—
650C42—1348no—
651C42—1348no—
652C42—1348no—
653C23—6716no—
654C23—6716no—
655C23—6716no—
656C23—6716no—
657C23—6716no—
658C23—6716no—
659C23—6716no—
660C23—674no—
661C23—674no—
662C23—674no—
663C23—674no—
664C23—674no—
665C23—674no—
666C23—674no—
667C23C22×C4×D6712yes—
668C23C2×D4×D6712yes—
669C23C2×Q8×D6712yes—
670C23#41×D6712yes—
671C23#41×D6712yes—
672C23#41×D6712yes—
673C23#41×D6712yes—
674C23C24×D6711yescharacteristic
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—26816no—
699C2×C4—26816no—
700C2×C4—2684no—
701C2×C4—2684no—
702C2×C4—674no—
703C2×C4—674no—
704C2×C4—674no—
705C2×C4—674no—
706C2×C4—674no—
707C2×C4—13432no—
708C2×C4—13432no—
709C2×C4—13432no—
710C2×C4—13432no—
711C2×C4—13432no—
712C2×C4—1342no—
713C2×C4—1342no—
714C2×C4—1342no—
715C2×C4—1342no—
716C2×C4—1342no—
717C2×C4—1342no—
718C2×C4—1348no—
719C2×C4—1348no—
720C2×C4—1348no—
721C2×C4—1348no—
722C2×C4—1348no—
723C2×C4—1342no—
724C2×C4—1342no—
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×C4C22×C4×D6714yes—
734C2×C4C22×C4×D6714yes—
735C2×C4C22×C4×D6714yes—
736C2×C4C2×D4×D6714yes—
737C2×C4C2×Q8×D6714yes—
738C22—678no—
739C22—678no—
740C22—6764no—
741C22—678no—
742C22—678no—
743C22—678no—
744C22—678no—
745C22—678no—
746C22#117×D6714yes—
747C22C4×D4×D6714yes—
748C22C4×Q8×D6714yes—
749C22C22⋊Q8×D6714yes—
750C22#123×D6714yes—
751C22#125×D6714yes—
752C22#126×D6714yes—
753C22C23×C4×D6711yescharacteristic
754C22C22×D4×D6711yescharacteristic
755C22C22×Q8×D6711yescharacteristic
756C22C2×#41×D6711yescharacteristic
757C22C2×#41×D6711yescharacteristic
758C22C2×#41×D6711yescharacteristic
759C22C2×#41×D6711yescharacteristic
760C4—24no—
761C4—24no—
762C4—24no—
763C4—24no—
764C4—24no—
765C4—42no—
766C4—42no—
767C4—2682no—
768C4—2682no—
769C4—1344no—
770C4—1344no—
771C4—1344no—
772C4—1344no—
773C4—1344no—
774C2—6716no—
775C2#387×D6718yesdirect product factor
776C2C2×#117×D6711yescharacteristic
777C2C2×C4×D4×D6711yescharacteristic
778C2C2×C4×Q8×D6711yescharacteristic
779C2C2×C22⋊Q8×D6711yescharacteristic
780C2C2×#123×D6711yescharacteristic
781C2C2×#125×D6711yescharacteristic
782C2C2×#126×D6711yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#387×C67C2
socleC24×C67C24
prime radicalC24×D67C23
cosocleC23×C67C25
hypercenterC2×#387D67
hypocenterC67C22×#387
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. C2×#16863283C2semidirect
5. C2×#16863282C2semidirect
6. C2×#16863281C2semidirect
7. C2×#16863280C2semidirect
8. C2×#16863279C2semidirect
9. C2×#16863278C2semidirect
10. C2×#16863277C2semidirect
11. #387×D67C2direct (N × H)
16. C2×#387×C67C2semidirect
31. C2×C4⋊C4×D67C4semidirect
39. #16863283C22semidirect
40. #16863282C22semidirect
41. #16863281C22semidirect
42. #16863280C22semidirect
43. #16863279C22semidirect
44. #16863278C22semidirect
45. #16863277C22semidirect
65. #387×C67C22semidirect
107. C2×C4⋊Dic67C2×C4semidirect
112. C2×Dic67⋊C4C2×C4semidirect
113. C2×Dic67⋊C4C2×C4semidirect
119. C4⋊C4×D67C2×C4semidirect
147. C2×C4⋊C4×C67C2×C4semidirect
221. C4⋊Dic67C22×C4semidirect
224. Dic67⋊C4C22×C4semidirect
225. Dic67⋊C4C22×C4semidirect
259. C4⋊C4×C67C22×C4semidirect
360. C2×D67#387direct (N × H)
383. C2×C67C2×#387semidirect
391. D67C2×#387direct (N × H)
403. C2×#387D67direct (N × H)
408. C67C22×#387semidirect
441. #387C2×D67direct (N × H)
520. C2×C4⋊C4C4×D67semidirect
648. C4⋊C4C2×C4×D67semidirect
775. C2#387×D67direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D672
C22×C42×D672
C2×#168632832
C2×#168632822
C2×#168632812
C2×#168632802
C2×#168632792
C2×#168632782
C2×#168632772
#387×D672
C2×#95×D672
C2×#387×C672
C22×#38767