Finite Group Databasebeta

← C67×#13882 #30693133

Subgroups — C67×#13882 #30693133

Order 17152.

2222 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C67C211yesmaximal, characteristic
2C2×#387×C67C212yesmaximal, complemented
3C2×#380×C67C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
5C67×#1445C212yesmaximal, complemented
6C67×#1441C212yesmaximal, complemented
7C67×#1436C212yesmaximal, complemented
8C67×C22⋊#95C211yesmaximal, characteristic
9C67×C22⋊#95C211yesmaximal, characteristic
10C67×C22⋊#95C211yesmaximal, characteristic
11C67×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C67C2211yescharacteristic
13C24×C4×C67C2211yescharacteristic
14C24×C4×C67C2211yescharacteristic
15C22×C4⋊C4×C67—28no—
16C22×C4⋊C4×C67C418yescomplemented
17C22×C4⋊C4×C67C2212yes—
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C4⋊C4×C67C2211yescharacteristic
20C22×C4⋊C4×C67C2211yescharacteristic
21C22×C4⋊C4×C67C2211yescharacteristic
22C22×C22⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C42×C67C2212yes—
27#387×C67—28no—
28#380×C67—24no—
29C4×C22⋊C4×C67—24no—
30C2×#95×C67C2212yes—
31C2×#95×C67C2212yes—
32C2×#95×C67C2212yes—
33C2×#95×C67C2212yes—
34C2×#95×C67C2212yes—
35C2×#95×C67C2212yes—
36C2×#95×C67C2212yes—
37C2×#95×C67C2212yes—
38C2×#95×C67C2212yes—
39C2×#95×C67C2212yes—
40C25×C67C2311yescharacteristic
41C23×C4×C67—22no—
42C23×C4×C67—22no—
43C23×C4×C67—24no—
44C23×C4×C67—24no—
45C23×C4×C67—22no—
46C23×C4×C67—22no—
47C23×C4×C67—22no—
48C23×C4×C67—22no—
49C23×C4×C67—24no—
50C23×C4×C67—24no—
51C23×C4×C67—42no—
52C23×C4×C67—42no—
53C23×C4×C67C2×C414yes—
54C23×C4×C67C2×C414yes—
55C23×C4×C67C2×C414yes—
56C23×C4×C67C2312yes—
57C23×C4×C67C2312yes—
58C23×C4×C67C2311yescharacteristic
59C23×C4×C67C2311yescharacteristic
60C23×C4×C67C2312yes—
61C23×C4×C67C2312yes—
62C23×C4×C67C2311yescharacteristic
63C23×C4×C67C2311yescharacteristic
64C23×C4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C2×C4⋊C4×C67—24no—
67C2×C4⋊C4×C67—24no—
68C2×C4⋊C4×C67—24no—
69C2×C4⋊C4×C67—232no—
70C2×C4⋊C4×C67—24no—
71C2×C4⋊C4×C67—24no—
72C2×C4⋊C4×C67—42no—
73C2×C4⋊C4×C67C2×C414yes—
74C2×C4⋊C4×C67C2×C414yes—
75C2×C4⋊C4×C67C2×C414yes—
76C2×C4⋊C4×C67C2×C414yes—
77C2×C4⋊C4×C67D418yes—
78C2×C22⋊C4×C67—22no—
79C2×C22⋊C4×C67—22no—
80C2×C22⋊C4×C67—22no—
81C2×C22⋊C4×C67—22no—
82C2×C22⋊C4×C67—22no—
83C2×C22⋊C4×C67—22no—
84C2×C22⋊C4×C67—22no—
85C2×C22⋊C4×C67—22no—
86C2×C22⋊C4×C67—22no—
87C2×C22⋊C4×C67—22no—
88C2×C22⋊C4×C67D414yes—
89C2×C22⋊C4×C67Q814yes—
90C2×C42×C67—24no—
91C2×C42×C67—24no—
92C2×C42×C67—42no—
93#95×C67—24no—
94#95×C67—24no—
95#95×C67—24no—
96#95×C67—24no—
97#95×C67—24no—
98#95×C67—24no—
99#95×C67—24no—
100#95×C67—24no—
101#95×C67—42no—
102#95×C67—42no—
103C24×C67—22no—
104C24×C67—22no—
105C24×C67—22no—
106C24×C67—22no—
107C24×C67C22×C412yes—
108C24×C67C2×D412yes—
109C24×C67C2×Q812yes—
110C24×C67#4112yes—
111C24×C67#4112yes—
112C24×C67#4112yes—
113C24×C67#4112yes—
114C24×C67C2411yescharacteristic
115C22×C4×C67—216no—
116C22×C4×C67—216no—
117C22×C4×C67—28no—
118C22×C4×C67—21no—
119C22×C4×C67—22no—
120C22×C4×C67—21no—
121C22×C4×C67—21no—
122C22×C4×C67—21no—
123C22×C4×C67—22no—
124C22×C4×C67—21no—
125C22×C4×C67—21no—
126C22×C4×C67—21no—
127C22×C4×C67—21no—
128C22×C4×C67—22no—
129C22×C4×C67—22no—
130C22×C4×C67—28no—
131C22×C4×C67—28no—
132C22×C4×C67—28no—
133C22×C4×C67—28no—
134C22×C4×C67—22no—
135C22×C4×C67—22no—
136C22×C4×C67—22no—
137C22×C4×C67—22no—
138C22×C4×C67—22no—
139C22×C4×C67—21no—
140C22×C4×C67—21no—
141C22×C4×C67—22no—
142C22×C4×C67—22no—
143C22×C4×C67—22no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—22no—
147C22×C4×C67—22no—
148C22×C4×C67—22no—
149C22×C4×C67—22no—
150C22×C4×C67—22no—
151C22×C4×C67—22no—
152C22×C4×C67—22no—
153C22×C4×C67—22no—
154C22×C4×C67—28no—
155C22×C4×C67—28no—
156C22×C4×C67—22no—
157C22×C4×C67—22no—
158C22×C4×C67—22no—
159C22×C4×C67—22no—
160C22×C4×C67—22no—
161C22×C4×C67—22no—
162C22×C4×C67—22no—
163C22×C4×C67—22no—
164C22×C4×C67—22no—
165C22×C4×C67—22no—
166C22×C4×C67—22no—
167C22×C4×C67—22no—
168C22×C4×C67—22no—
169C22×C4×C67—22no—
170C22×C4×C67—44no—
171C22×C4×C67—44no—
172C22×C4×C67—48no—
173C22×C4×C67—48no—
174C22×C4×C67—48no—
175C22×C4×C67—48no—
176C22×C4×C67C22×C412yes—
177C22×C4×C67C22×C412yes—
178C22×C4×C67C22×C412yes—
179C22×C4×C67C22×C412yes—
180C22×C4×C67C22×C412yes—
181C22×C4×C67C22×C412yes—
182C22×C4×C67C2×D414yes—
183C22×C4×C67C2×D414yes—
184C22×C4×C67C2×D414yes—
185C22×C4×C67C2×D414yes—
186C22×C4×C67C2×Q814yes—
187C22×C4×C67#4114yes—
188C4⋊C4×C67—28no—
189C4⋊C4×C67—28no—
190C4⋊C4×C67—28no—
191C4⋊C4×C67—48no—
192C4⋊C4×C67C22⋊C4116yescomplemented
193C22⋊C4×C67—28no—
194C22⋊C4×C67—28no—
195C22⋊C4×C67—44no—
196C22⋊C4×C67—44no—
197C42×C67—48no—
198C23×C67—22no—
199C23×C67—22no—
200C23×C67—22no—
201C23×C67—22no—
202C23×C67—24no—
203C23×C67—24no—
204C23×C67—24no—
205C23×C67—24no—
206C23×C67—24no—
207C23×C67—24no—
208C23×C67—24no—
209C23×C67—24no—
210C23×C67—24no—
211C23×C67—24no—
212C23×C67—24no—
213C23×C67—24no—
214C23×C67#11714yes—
215C23×C67C4×D414yes—
216C23×C67C4×Q814yes—
217C23×C67C22⋊Q814yes—
218C23×C67#12314yes—
219C23×C67#12514yes—
220C23×C67#12614yes—
221C23×C67C23×C411yescharacteristic
222C23×C67C22×D412yes—
223C23×C67C22×D411yescharacteristic
224C23×C67C22×Q811yescharacteristic
225C23×C67C2×#4111yescharacteristic
226C23×C67C2×#4111yescharacteristic
227C23×C67C2×#4112yes—
228C23×C67C2×#4111yescharacteristic
229C23×C67C2×#4111yescharacteristic
230C23×C67H(5,𝔽2)12yes—
231C23×C672−1+412yes—
232C2×C4×C67—232no—
233C2×C4×C67—22no—
234C2×C4×C67—22no—
235C2×C4×C67—22no—
236C2×C4×C67—22no—
237C2×C4×C67—22no—
238C2×C4×C67—22no—
239C2×C4×C67—22no—
240C2×C4×C67—22no—
241C2×C4×C67—24no—
242C2×C4×C67—24no—
243C2×C4×C67—24no—
244C2×C4×C67—24no—
245C2×C4×C67—24no—
246C2×C4×C67—24no—
247C2×C4×C67—24no—
248C2×C4×C67—24no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67—24no—
256C2×C4×C67—24no—
257C2×C4×C67—24no—
258C2×C4×C67—24no—
259C2×C4×C67—24no—
260C2×C4×C67—24no—
261C2×C4×C67—416no—
262C2×C4×C67—416no—
263C2×C4×C67—42no—
264C2×C4×C67—42no—
265C2×C4×C67—42no—
266C2×C4×C67—42no—
267C2×C4×C67—42no—
268C2×C4×C67—42no—
269C2×C4×C67—42no—
270C2×C4×C67—42no—
271C2×C4×C67—42no—
272C2×C4×C67—42no—
273C2×C4×C67—42no—
274C2×C4×C67—42no—
275C2×C4×C67—42no—
276C2×C4×C67—42no—
277C2×C4×C67—42no—
278C2×C4×C67—42no—
279C2×C4×C67—42no—
280C2×C4×C67—42no—
281C2×C4×C67—42no—
282C2×C4×C67—42no—
283C2×C4×C67—42no—
284C2×C4×C67—42no—
285C2×C4×C67—42no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67—42no—
289C2×C4×C67C2×C22⋊C414yes—
290C2×C4×C67C2×C22⋊C414yes—
291C2×C4×C67C2×C22⋊C414yes—
292C2×C4×C67#11714yes—
293C22×C67—24no—
294C22×C67—24no—
295C22×C67—24no—
296C22×C67—24no—
297C22×C67—24no—
298C22×C67—28no—
299C22×C67—28no—
300C22×C67—28no—
301C22×C67—28no—
302C22×C67—24no—
303C22×C67#38718yescomplemented
304C22×C67C22×C22⋊C411yescharacteristic
305C22×C67C2×#11711yescharacteristic
306C22×C67C2×#11711yescharacteristic
307C22×C67C2×C4×D411yescharacteristic
308C22×C67C2×C4×Q811yescharacteristic
309C22×C67#51811yescharacteristic
310C22×C67#51911yescharacteristic
311C22×C67C2×C22⋊Q811yescharacteristic
312C22×C67C2×#12311yescharacteristic
313C22×C67#52512yes—
314C22×C67#52512yes—
315C22×C67C2×#12511yescharacteristic
316C22×C67C2×#12611yescharacteristic
317C22×C67#53912yes—
318C22×C67#53912yes—
319C22×C67D4212yes—
320C22×C67#54612yes—
321C22×C67#54712yes—
322C22×C67#54812yes—
323C22×C67D4×Q812yes—
324C22×C67#55212yes—
325C22×C67#55312yes—
326C22×C67#55412yes—
327C4×C67—24no—
328C4×C67—24no—
329C4×C67—24no—
330C4×C67—24no—
331C4×C67—42no—
332C4×C67—42no—
333C4×C67—44no—
334C4×C67—44no—
335C4×C67—82no—
336C4×C67—82no—
337#13882C6711yesmaximal, characteristic, direct product factor, Sylow
338C2×C67—28no—
339C2×C67#228011yescharacteristic
340C2×C67C2×#38711yescharacteristic
341C2×C67#231311yescharacteristic
342C2×C67D4×C22⋊C411yescharacteristic
343C2×C67Q8×C22⋊C411yescharacteristic
344C2×C67#234411yescharacteristic
345C2×C67#234511yescharacteristic
346C2×C67#244312yes—
347C2×C67#244912yes—
348C2×C67#247312yes—
349C2×C67#248112yes—
350C23×C4⋊C4C2×C6711yescharacteristic
351C2×#387C2×C6712yescomplemented
352C2×#380C2×C6711yescharacteristic
353C2×C4×C22⋊C4C2×C6711yescharacteristic
354#1445C2×C6712yescomplemented
355#1441C2×C6712yescomplemented
356#1436C2×C6712yescomplemented
357C22⋊#95C2×C6711yescharacteristic
358C22⋊#95C2×C6711yescharacteristic
359C22⋊#95C2×C6711yescharacteristic
360C22⋊#95C2×C6711yescharacteristic
361C67#1388211yescharacteristic, direct product factor, Sylow
362C24×C4C22×C6711yescharacteristic
363C24×C4C22×C6711yescharacteristic
364C24×C4C22×C6711yescharacteristic
365C22×C4⋊C4—28no—
366C22×C4⋊C4C4×C6718yescomplemented
367C22×C4⋊C4C22×C6712yes—
368C22×C4⋊C4C22×C6711yescharacteristic
369C22×C4⋊C4C22×C6711yescharacteristic
370C22×C4⋊C4C22×C6711yescharacteristic
371C22×C4⋊C4C22×C6711yescharacteristic
372C22×C22⋊C4C22×C6711yescharacteristic
373C22×C22⋊C4C22×C6711yescharacteristic
374C22×C22⋊C4C22×C6711yescharacteristic
375C22×C22⋊C4C22×C6711yescharacteristic
376C22×C42C22×C6712yes—
377#387—28no—
378#380—24no—
379C4×C22⋊C4—24no—
380C2×#95C22×C6712yes—
381C2×#95C22×C6712yes—
382C2×#95C22×C6712yes—
383C2×#95C22×C6712yes—
384C2×#95C22×C6712yes—
385C2×#95C22×C6712yes—
386C2×#95C22×C6712yes—
387C2×#95C22×C6712yes—
388C2×#95C22×C6712yes—
389C2×#95C22×C6712yes—
390C25C23×C6711yescharacteristic
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4C2×C4×C6714yes—
404C23×C4C2×C4×C6714yes—
405C23×C4C2×C4×C6714yes—
406C23×C4C23×C6712yes—
407C23×C4C23×C6712yes—
408C23×C4C23×C6711yescharacteristic
409C23×C4C23×C6711yescharacteristic
410C23×C4C23×C6712yes—
411C23×C4C23×C6712yes—
412C23×C4C23×C6711yescharacteristic
413C23×C4C23×C6711yescharacteristic
414C23×C4C23×C6711yescharacteristic
415C23×C4C23×C6711yescharacteristic
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—232no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×C4×C6714yes—
424C2×C4⋊C4C2×C4×C6714yes—
425C2×C4⋊C4C2×C4×C6714yes—
426C2×C4⋊C4C2×C4×C6714yes—
427C2×C4⋊C4D4×C6718yes—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4D4×C6714yes—
439C2×C22⋊C4Q8×C6714yes—
440C2×C42—24no—
441C2×C42—24no—
442C2×C42—42no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—42no—
452#95—42no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22×C4×C6712yes—
458C24C2×D4×C6712yes—
459C24C2×Q8×C6712yes—
460C24#41×C6712yes—
461C24#41×C6712yes—
462C24#41×C6712yes—
463C24#41×C6712yes—
464C24C24×C6711yescharacteristic
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4C22×C4×C6712yes—
527C22×C4C22×C4×C6712yes—
528C22×C4C22×C4×C6712yes—
529C22×C4C22×C4×C6712yes—
530C22×C4C22×C4×C6712yes—
531C22×C4C22×C4×C6712yes—
532C22×C4C2×D4×C6714yes—
533C22×C4C2×D4×C6714yes—
534C22×C4C2×D4×C6714yes—
535C22×C4C2×D4×C6714yes—
536C22×C4C2×Q8×C6714yes—
537C22×C4#41×C6714yes—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—48no—
542C4⋊C4C22⋊C4×C67116yescomplemented
543C22⋊C4—28no—
544C22⋊C4—28no—
545C22⋊C4—44no—
546C22⋊C4—44no—
547C42—48no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23#117×C6714yes—
565C23C4×D4×C6714yes—
566C23C4×Q8×C6714yes—
567C23C22⋊Q8×C6714yes—
568C23#123×C6714yes—
569C23#125×C6714yes—
570C23#126×C6714yes—
571C23C23×C4×C6711yescharacteristic
572C23C22×D4×C6712yes—
573C23C22×D4×C6711yescharacteristic
574C23C22×Q8×C6711yescharacteristic
575C23C2×#41×C6711yescharacteristic
576C23C2×#41×C6711yescharacteristic
577C23C2×#41×C6712yes—
578C23C2×#41×C6711yescharacteristic
579C23C2×#41×C6711yescharacteristic
580C23H(5,𝔽2)×C6712yes—
581C232−1+4×C6712yes—
582C2×C4—232no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—416no—
612C2×C4—416no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4C2×C22⋊C4×C6714yes—
640C2×C4C2×C22⋊C4×C6714yes—
641C2×C4C2×C22⋊C4×C6714yes—
642C2×C4#117×C6714yes—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—24no—
649C22—28no—
650C22—28no—
651C22—28no—
652C22—28no—
653C22#387×C6718yescomplemented
654C22C22×C22⋊C4×C6711yescharacteristic
655C22C2×#117×C6711yescharacteristic
656C22C2×#117×C6711yescharacteristic
657C22C2×C4×D4×C6711yescharacteristic
658C22C2×C4×Q8×C6711yescharacteristic
659C22#518×C6711yescharacteristic
660C22#519×C6711yescharacteristic
661C22C2×C22⋊Q8×C6711yescharacteristic
662C22C2×#123×C6711yescharacteristic
663C22#525×C6712yes—
664C22#525×C6712yes—
665C22C2×#125×C6711yescharacteristic
666C22C2×#126×C6711yescharacteristic
667C22#539×C6712yes—
668C22#539×C6712yes—
669C22D42×C6712yes—
670C22#546×C6712yes—
671C22#547×C6712yes—
672C22#548×C6712yes—
673C22D4×Q8×C6712yes—
674C22#552×C6712yes—
675C22#553×C6712yes—
676C22#554×C6712yes—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—24no—
681C4—42no—
682C4—42no—
683C4—44no—
684C4—44no—
685C4—82no—
686C4—82no—
687C2—28no—
688C2C67×#228011yescharacteristic
689C2C2×#387×C6711yescharacteristic
690C2C67×#231311yescharacteristic
691C2D4×C22⋊C4×C6711yescharacteristic
692C2Q8×C22⋊C4×C6711yescharacteristic
693C2C67×#234411yescharacteristic
694C2C67×#234511yescharacteristic
695C2C67×#244312yes—
696C2C67×#244912yes—
697C2C67×#247312yes—
698C2C67×#248112yes—
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC25×C67C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#387×C67C2semidirect
5. C67×#1445C2semidirect
6. C67×#1441C2semidirect
7. C67×#1436C2semidirect
16. C22×C4⋊C4×C67C4semidirect
192. C4⋊C4×C67C22⋊C4semidirect
303. C22×C67#387semidirect
337. #13882C67direct (N × H)
351. C2×#387C2×C67semidirect
354. #1445C2×C67semidirect
355. #1441C2×C67semidirect
356. #1436C2×C67semidirect
361. C67#13882direct (N × H)
366. C22×C4⋊C4C4×C67semidirect
542. C4⋊C4C22⋊C4×C67semidirect
653. C22#387×C67semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C672
C2×#387×C672
C2×#380×C672
C2×C4×C22⋊C4×C672
C67×#14452
C67×#14412
C67×#14362
C67×C22⋊#952
#1388267