Finite Group Databasebeta

← C67×#22712 #30701963

Subgroups — C67×#22712 #30701963

Order 17152.

898 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C67C211yesmaximal, characteristic
2C67×#2354C211yesmaximal, characteristic
3C67×#2352C211yesmaximal, characteristic
4C67×#1949C211yesmaximal, characteristic, complemented
5C67×#1947C211yesmaximal, characteristic, complemented
6C67×#1854C211yesmaximal, characteristic, complemented
7C67×#1854C211yesmaximal, characteristic, complemented
8C67×#1854C211yesmaximal, characteristic, complemented
9C67×#1852C211yesmaximal, characteristic, complemented
10C67×#1836C211yesmaximal, characteristic, complemented
11C67×#1809C211yesmaximal, characteristic, complemented
12C67×#1808C211yesmaximal, characteristic, complemented
13C67×#1776C211yesmaximal, characteristic, complemented
14C67×#1736C211yesmaximal, characteristic, complemented
15C67×#1735C211yesmaximal, characteristic, complemented
16C22×M16×C67C2211yescharacteristic
17C23×C8×C67C2211yescharacteristic
18C2×C4×D4×C67C2211yescharacteristic
19C2×#117×C67C2211yescharacteristic
20C2×#117×C67C2211yescharacteristic
21C2×#117×C67C2211yescharacteristic
22C22×C4⋊C4×C67C2211yescharacteristic
23#435×C67C418yescomplemented
24C2×#107×C67C2211yescharacteristic
25C2×#107×C67C2211yescharacteristic
26C2×#107×C67C2211yescharacteristic
27C2×#107×C67C2211yescharacteristic
28C2×#106×C67C2211yescharacteristic
29C2×#106×C67C2211yescharacteristic
30C2×C4⋊C8×C67C2211yescharacteristic
31C2×C22⋊C8×C67C2211yescharacteristic
32C2×C22⋊C8×C67C2211yescharacteristic
33C2×#97×C67C2211yescharacteristic
34#390×C67—21no—
35#388×C67—21no—
36#388×C67—21no—
37#388×C67—21no—
38#387×C67—21no—
39#386×C67—21no—
40#384×C67C2211yescharacteristic
41#382×C67C2211yescharacteristic
42#380×C67C2211yescharacteristic
43#380×C67C2211yescharacteristic
44#380×C67C2211yescharacteristic
45#380×C67C2211yescharacteristic
46C4×C4⋊C4×C67—21no—
47C4×C4⋊C4×C67C2211yescharacteristic
48C4×C4⋊C4×C67C2211yescharacteristic
49C4×C22⋊C4×C67—21no—
50#340×C67C2211yescharacteristic
51#340×C67C2211yescharacteristic
52#340×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60C22×D4×C67D411yescharacteristic
61C23×C4×C67—21no—
62C23×C4×C67C2311yescharacteristic
63C23×C4×C67C2311yescharacteristic
64C2×M16×C67—41no—
65C2×M16×C67—41no—
66C2×M16×C67C2×C414yes—
67C22×C8×C67—41no—
68C22×C8×C67—41no—
69C22×C8×C67C2×C414yescomplemented
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22×C8×C67C2311yescharacteristic
73C22×C8×C67C2311yescharacteristic
74C4×D4×C67C2×C414yes—
75C4×D4×C67Q814yes—
76#117×C67—22no—
77#117×C67—22no—
78#117×C67—22no—
79#117×C67—41no—
80#117×C67—41no—
81#117×C67—41no—
82C2×C4⋊C4×C67—22no—
83C2×C4⋊C4×C67—21no—
84C2×C4⋊C4×C67—21no—
85C2×C4⋊C4×C67—21no—
86C2×C4⋊C4×C67—41no—
87C2×C4⋊C4×C67D411yescharacteristic
88C2×C4⋊C4×C67C2311yescharacteristic
89C2×C4⋊C4×C67C2311yescharacteristic
90C2×C4⋊C4×C67C2311yescharacteristic
91C2×C4⋊C4×C67C2311yescharacteristic
92C2×C4⋊C4×C67C2311yescharacteristic
93C2×C4⋊C4×C67C2311yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C22⋊C4×C67—21no—
97C2×C22⋊C4×C67—21no—
98C2×C22⋊C4×C67—21no—
99C2×C22⋊C4×C67—21no—
100C2×C22⋊C4×C67—21no—
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67D411yescharacteristic
104C2×C22⋊C4×C67D411yescharacteristic
105C2×C42×C67—21no—
106C2×C42×C67—21no—
107C2×C42×C67—21no—
108C2×C42×C67—21no—
109C2×C42×C67—21no—
110C2×C42×C67C2311yescharacteristic
111#107×C67—22no—
112#107×C67—41no—
113#107×C67—41no—
114#107×C67—41no—
115#106×C67—22no—
116#106×C67—41no—
117C4⋊C8×C67C2×C414yescomplemented
118C22⋊C8×C67C2×C414yes—
119C22⋊C8×C67C2×C414yescomplemented
120#97×C67C2×C414yescomplemented
121#95×C67—21no—
122#95×C67—21no—
123#95×C67—21no—
124#95×C67—21no—
125#95×C67—21no—
126#95×C67—21no—
127#95×C67—21no—
128#95×C67—21no—
129C24×C67C2×D411yescharacteristic
130C24×C67C2×D411yescharacteristic
131C2×D4×C67—41no—
132C2×D4×C67—41no—
133C2×D4×C67C4⋊C414yes—
134C22×C4×C67—21no—
135C22×C4×C67—21no—
136C22×C4×C67—21no—
137C22×C4×C67—21no—
138C22×C4×C67—21no—
139C22×C4×C67—21no—
140C22×C4×C67—21no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—42no—
151C22×C4×C67—42no—
152C22×C4×C67—81no—
153C22×C4×C67C22×C412yes—
154C22×C4×C67C22×C412yes—
155C22×C4×C67C2×D411yescharacteristic
156C22×C4×C67C2×D411yescharacteristic
157C22×C4×C67C2×D411yescharacteristic
158C22×C4×C67C2×D411yescharacteristic
159C22×C4×C67C2×Q812yes—
160C22×C4×C67C2×Q812yes—
161C22×C4×C67C2411yescharacteristic
162M16×C67—44no—
163C2×C8×C67—21no—
164C2×C8×C67—21no—
165C2×C8×C67—21no—
166C2×C8×C67—21no—
167C2×C8×C67—21no—
168C2×C8×C67—21no—
169C2×C8×C67—21no—
170C2×C8×C67—21no—
171C2×C8×C67—44no—
172C2×C8×C67C22×C412yes—
173C2×C8×C67C22×C412yes—
174C2×C8×C67C22×C412yes—
175C2×C8×C67C22×C412yes—
176C4⋊C4×C67—21no—
177C4⋊C4×C67—21no—
178C4⋊C4×C67—21no—
179C4⋊C4×C67—21no—
180C4⋊C4×C67—21no—
181C4⋊C4×C67—21no—
182C4⋊C4×C67—21no—
183C4⋊C4×C67—21no—
184C4⋊C4×C67—21no—
185C4⋊C4×C67—21no—
186C4⋊C4×C67—21no—
187C4⋊C4×C67—21no—
188C4⋊C4×C67—21no—
189C4⋊C4×C67—21no—
190C4⋊C4×C67—42no—
191C4⋊C4×C67—42no—
192C4⋊C4×C67—81no—
193C4⋊C4×C67C4⋊C414yes—
194C4⋊C4×C67#4112yes—
195C4⋊C4×C67#4112yes—
196C22⋊C4×C67—42no—
197C22⋊C4×C67—42no—
198C22⋊C4×C67—42no—
199C22⋊C4×C67—42no—
200C22⋊C4×C67—81no—
201C22⋊C4×C67—81no—
202C22⋊C4×C67—81no—
203C22⋊C4×C67C4⋊C414yes—
204C22⋊C4×C67C4⋊C414yes—
205C42×C67—42no—
206C42×C67—42no—
207C42×C67—42no—
208C42×C67—42no—
209C42×C67—81no—
210C42×C67C22×C412yes—
211C42×C67C2×Q812yes—
212C23×C67—21no—
213C23×C67—21no—
214C23×C67—21no—
215C23×C67—21no—
216C23×C67—21no—
217C23×C67—21no—
218C23×C67—21no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67C2×C4⋊C412yes—
225C23×C67C2×C4⋊C412yes—
226C23×C67C22×D411yescharacteristic
227D4×C67—44no—
228C2×C4×C67—21no—
229C2×C4×C67—21no—
230C2×C4×C67—21no—
231C2×C4×C67—21no—
232C2×C4×C67—21no—
233C2×C4×C67—21no—
234C2×C4×C67—21no—
235C2×C4×C67—21no—
236C2×C4×C67—22no—
237C2×C4×C67—22no—
238C2×C4×C67—22no—
239C2×C4×C67—22no—
240C2×C4×C67—22no—
241C2×C4×C67—22no—
242C2×C4×C67—22no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—22no—
246C2×C4×C67—41no—
247C2×C4×C67—41no—
248C2×C4×C67—41no—
249C2×C4×C67—41no—
250C2×C4×C67—41no—
251C2×C4×C67—41no—
252C2×C4×C67—41no—
253C2×C4×C67—41no—
254C2×C4×C67—41no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—84no—
269C2×C4×C67C2×C4⋊C412yes—
270C2×C4×C67C2×C4⋊C412yes—
271C2×C4×C67C2×C4⋊C412yes—
272C2×C4×C67C2×C4⋊C412yes—
273C2×C4×C67C23×C411yescharacteristic
274C2×C4×C67C22×Q811yescharacteristic
275C2×C4×C67C2×#4111yescharacteristic
276C2×C4×C67C2×#4111yescharacteristic
277C2×C4×C67H(5,𝔽2)11yescharacteristic
278C2×C4×C67H(5,𝔽2)11yescharacteristic
279C8×C67—22no—
280C8×C67—22no—
281C8×C67—22no—
282C8×C67—22no—
283C22×C67—22no—
284C22×C67—22no—
285C22×C67—22no—
286C22×C67—22no—
287C22×C67—22no—
288C22×C67—22no—
289C22×C67—41no—
290C22×C67—41no—
291C22×C67—41no—
292C22×C67—41no—
293C22×C67—41no—
294C22×C67—41no—
295C22×C67—41no—
296C22×C67—41no—
297C22×C67C22×C4⋊C411yescharacteristic
298C22×C67#54611yescharacteristic
299C22×C67#54611yescharacteristic
300C22×C67#57511yescharacteristic
301C22×C67#57511yescharacteristic
302C22×C67#57611yescharacteristic
303C22×C67#57811yescharacteristic
304C4×C67—22no—
305C4×C67—22no—
306C4×C67—22no—
307C4×C67—22no—
308C4×C67—42no—
309C4×C67—42no—
310C4×C67—81no—
311C4×C67—81no—
312C4×C67—81no—
313C4×C67—81no—
314C4×C67—81no—
315C4×C67—81no—
316C4×C67C4×#4111yescharacteristic
317C4×C67#51811yescharacteristic
318C4×C67#55411yescharacteristic
319C4×C67#55411yescharacteristic
320#22712C6711yesmaximal, characteristic, direct product factor, Sylow
321C2×C67—42no—
322C2×C67—42no—
323C2×C67#234911yescharacteristic
324C2×C67#291111yescharacteristic
325C2×C67#291311yescharacteristic
326C2×C67#330911yescharacteristic
327C2×C67#331311yescharacteristic
328C2×C67#331511yescharacteristic
329C2×C67#331911yescharacteristic
330C2×#435C2×C6711yescharacteristic
331#2354C2×C6711yescharacteristic
332#2352C2×C6711yescharacteristic
333#1949C2×C6711yescharacteristic, complemented
334#1947C2×C6711yescharacteristic, complemented
335#1854C2×C6711yescharacteristic, complemented
336#1854C2×C6711yescharacteristic, complemented
337#1854C2×C6711yescharacteristic, complemented
338#1852C2×C6711yescharacteristic, complemented
339#1836C2×C6711yescharacteristic, complemented
340#1809C2×C6711yescharacteristic, complemented
341#1808C2×C6711yescharacteristic, complemented
342#1776C2×C6711yescharacteristic, complemented
343#1736C2×C6711yescharacteristic, complemented
344#1735C2×C6711yescharacteristic, complemented
345C67#2271211yescharacteristic, direct product factor, Sylow
346C22×M16C22×C6711yescharacteristic
347C23×C8C22×C6711yescharacteristic
348C2×C4×D4C22×C6711yescharacteristic
349C2×#117C22×C6711yescharacteristic
350C2×#117C22×C6711yescharacteristic
351C2×#117C22×C6711yescharacteristic
352C22×C4⋊C4C22×C6711yescharacteristic
353#435C4×C6718yescomplemented
354C2×#107C22×C6711yescharacteristic
355C2×#107C22×C6711yescharacteristic
356C2×#107C22×C6711yescharacteristic
357C2×#107C22×C6711yescharacteristic
358C2×#106C22×C6711yescharacteristic
359C2×#106C22×C6711yescharacteristic
360C2×C4⋊C8C22×C6711yescharacteristic
361C2×C22⋊C8C22×C6711yescharacteristic
362C2×C22⋊C8C22×C6711yescharacteristic
363C2×#97C22×C6711yescharacteristic
364#390—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#387—21no—
369#386—21no—
370#384C22×C6711yescharacteristic
371#382C22×C6711yescharacteristic
372#380C22×C6711yescharacteristic
373#380C22×C6711yescharacteristic
374#380C22×C6711yescharacteristic
375#380C22×C6711yescharacteristic
376C4×C4⋊C4—21no—
377C4×C4⋊C4C22×C6711yescharacteristic
378C4×C4⋊C4C22×C6711yescharacteristic
379C4×C22⋊C4—21no—
380#340C22×C6711yescharacteristic
381#340C22×C6711yescharacteristic
382#340C22×C6711yescharacteristic
383#340C22×C6711yescharacteristic
384#340C22×C6711yescharacteristic
385#340C22×C6711yescharacteristic
386#340C22×C6711yescharacteristic
387#340C22×C6711yescharacteristic
388#340C22×C6711yescharacteristic
389#340C22×C6711yescharacteristic
390C22×D4D4×C6711yescharacteristic
391C23×C4—21no—
392C23×C4C23×C6711yescharacteristic
393C23×C4C23×C6711yescharacteristic
394C2×M16—41no—
395C2×M16—41no—
396C2×M16C2×C4×C6714yes—
397C22×C8—41no—
398C22×C8—41no—
399C22×C8C2×C4×C6714yescomplemented
400C22×C8C23×C6711yescharacteristic
401C22×C8C23×C6711yescharacteristic
402C22×C8C23×C6711yescharacteristic
403C22×C8C23×C6711yescharacteristic
404C4×D4C2×C4×C6714yes—
405C4×D4Q8×C6714yes—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—41no—
410#117—41no—
411#117—41no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4D4×C6711yescharacteristic
418C2×C4⋊C4C23×C6711yescharacteristic
419C2×C4⋊C4C23×C6711yescharacteristic
420C2×C4⋊C4C23×C6711yescharacteristic
421C2×C4⋊C4C23×C6711yescharacteristic
422C2×C4⋊C4C23×C6711yescharacteristic
423C2×C4⋊C4C23×C6711yescharacteristic
424C2×C4⋊C4C23×C6711yescharacteristic
425C2×C4⋊C4C23×C6711yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4D4×C6711yescharacteristic
434C2×C22⋊C4D4×C6711yescharacteristic
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42C23×C6711yescharacteristic
441#107—22no—
442#107—41no—
443#107—41no—
444#107—41no—
445#106—22no—
446#106—41no—
447C4⋊C8C2×C4×C6714yescomplemented
448C22⋊C8C2×C4×C6714yes—
449C22⋊C8C2×C4×C6714yescomplemented
450#97C2×C4×C6714yescomplemented
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459C24C2×D4×C6711yescharacteristic
460C24C2×D4×C6711yescharacteristic
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C4⋊C4×C6714yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4C22×C4×C6712yes—
484C22×C4C22×C4×C6712yes—
485C22×C4C2×D4×C6711yescharacteristic
486C22×C4C2×D4×C6711yescharacteristic
487C22×C4C2×D4×C6711yescharacteristic
488C22×C4C2×D4×C6711yescharacteristic
489C22×C4C2×Q8×C6712yes—
490C22×C4C2×Q8×C6712yes—
491C22×C4C24×C6711yescharacteristic
492M16—44no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—44no—
502C2×C8C22×C4×C6712yes—
503C2×C8C22×C4×C6712yes—
504C2×C8C22×C4×C6712yes—
505C2×C8C22×C4×C6712yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4C4⋊C4×C6714yes—
524C4⋊C4#41×C6712yes—
525C4⋊C4#41×C6712yes—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C22⋊C4—81no—
533C22⋊C4C4⋊C4×C6714yes—
534C22⋊C4C4⋊C4×C6714yes—
535C42—42no—
536C42—42no—
537C42—42no—
538C42—42no—
539C42—81no—
540C42C22×C4×C6712yes—
541C42C2×Q8×C6712yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23C2×C4⋊C4×C6712yes—
555C23C2×C4⋊C4×C6712yes—
556C23C22×D4×C6711yescharacteristic
557D4—44no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4C2×C4⋊C4×C6712yes—
600C2×C4C2×C4⋊C4×C6712yes—
601C2×C4C2×C4⋊C4×C6712yes—
602C2×C4C2×C4⋊C4×C6712yes—
603C2×C4C23×C4×C6711yescharacteristic
604C2×C4C22×Q8×C6711yescharacteristic
605C2×C4C2×#41×C6711yescharacteristic
606C2×C4C2×#41×C6711yescharacteristic
607C2×C4H(5,𝔽2)×C6711yescharacteristic
608C2×C4H(5,𝔽2)×C6711yescharacteristic
609C8—22no—
610C8—22no—
611C8—22no—
612C8—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22C22×C4⋊C4×C6711yescharacteristic
628C22#546×C6711yescharacteristic
629C22#546×C6711yescharacteristic
630C22#575×C6711yescharacteristic
631C22#575×C6711yescharacteristic
632C22#576×C6711yescharacteristic
633C22#578×C6711yescharacteristic
634C4—22no—
635C4—22no—
636C4—22no—
637C4—22no—
638C4—42no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4C4×#41×C6711yescharacteristic
647C4#518×C6711yescharacteristic
648C4#554×C6711yescharacteristic
649C4#554×C6711yescharacteristic
650C2—42no—
651C2—42no—
652C2C67×#234911yescharacteristic
653C2C67×#291111yescharacteristic
654C2C67×#291311yescharacteristic
655C2C67×#330911yescharacteristic
656C2C67×#331311yescharacteristic
657C2C67×#331511yescharacteristic
658C2C67×#331911yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC22×D4×C67D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
4. C67×#1949C2semidirect
5. C67×#1947C2semidirect
6. C67×#1854C2semidirect
7. C67×#1854C2semidirect
8. C67×#1854C2semidirect
9. C67×#1852C2semidirect
10. C67×#1836C2semidirect
11. C67×#1809C2semidirect
12. C67×#1808C2semidirect
13. C67×#1776C2semidirect
14. C67×#1736C2semidirect
15. C67×#1735C2semidirect
23. #435×C67C4semidirect
69. C22×C8×C67C2×C4semidirect
117. C4⋊C8×C67C2×C4semidirect
119. C22⋊C8×C67C2×C4semidirect
120. #97×C67C2×C4semidirect
320. #22712C67direct (N × H)
333. #1949C2×C67semidirect
334. #1947C2×C67semidirect
335. #1854C2×C67semidirect
336. #1854C2×C67semidirect
337. #1854C2×C67semidirect
338. #1852C2×C67semidirect
339. #1836C2×C67semidirect
340. #1809C2×C67semidirect
341. #1808C2×C67semidirect
342. #1776C2×C67semidirect
343. #1736C2×C67semidirect
344. #1735C2×C67semidirect
345. C67#22712direct (N × H)
353. #435C4×C67semidirect
399. C22×C8C2×C4×C67semidirect
447. C4⋊C8C2×C4×C67semidirect
449. C22⋊C8C2×C4×C67semidirect
450. #97C2×C4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C672
C67×#23542
C67×#23522
C67×#19492
C67×#19472
C67×#18542
C67×#18522
C67×#18362
C67×#18092
C67×#18082
C67×#17762
C67×#17362
C67×#17352
#2271267