Finite Group Databasebeta

← C67×#14045 #30693296

Subgroups — C67×#14045 #30693296

Order 17152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C67C211yesmaximal, characteristic
2C2×#389×C67C211yesmaximal, characteristic
3C2×#389×C67C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C67C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C67C211yesmaximal, characteristic
6C67×#1444C212yesmaximal
7C67×#1441C212yesmaximal
8C67×#1436C212yesmaximal
9C67×C4⋊#95C211yesmaximal, characteristic
10C67×C4⋊#95C212yesmaximal
11C67×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C67C2211yescharacteristic
13C22×C4⋊C4×C67C2211yescharacteristic
14C22×C4⋊C4×C67C2212yes—
15C22×C4⋊C4×C67C2211yescharacteristic
16C22×C4⋊C4×C67C2211yescharacteristic
17C22×C4⋊C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2212yes—
19C22×C4⋊C4×C67C2212yes—
20C22×C4⋊C4×C67C2211yescharacteristic
21C22×C42×C67C2211yescharacteristic
22C22×C42×C67C2212yes—
23C22×C42×C67C2211yescharacteristic
24C22×C42×C67C2211yescharacteristic
25#389×C67—24no—
26#389×C67—24no—
27#389×C67C418yescomplemented
28C4×C4⋊C4×C67—24no—
29C4×C4⋊C4×C67—24no—
30C2×#95×C67C2211yescharacteristic
31C2×#95×C67C2211yescharacteristic
32C2×#95×C67C2212yes—
33C2×#95×C67C2212yes—
34C2×#95×C67C2212yes—
35C2×#95×C67C2212yes—
36C2×#95×C67C2212yes—
37C2×#95×C67C2212yes—
38C2×#95×C67C2212yes—
39C2×#95×C67C2212yes—
40C23×C4×C67C2312yes—
41C23×C4×C67C2311yescharacteristic
42C23×C4×C67C2312yes—
43C23×C4×C67C2311yescharacteristic
44C23×C4×C67C2311yescharacteristic
45C23×C4×C67C2312yes—
46C23×C4×C67C2311yescharacteristic
47C23×C4×C67C2312yes—
48C23×C4×C67C2311yescharacteristic
49C23×C4×C67C2311yescharacteristic
50C23×C4×C67C2311yescharacteristic
51C2×C4⋊C4×C67—22no—
52C2×C4⋊C4×C67—22no—
53C2×C4⋊C4×C67—22no—
54C2×C4⋊C4×C67—22no—
55C2×C4⋊C4×C67—22no—
56C2×C4⋊C4×C67—22no—
57C2×C4⋊C4×C67—22no—
58C2×C4⋊C4×C67—22no—
59C2×C4⋊C4×C67—22no—
60C2×C4⋊C4×C67—24no—
61C2×C4⋊C4×C67—24no—
62C2×C4⋊C4×C67—22no—
63C2×C4⋊C4×C67—22no—
64C2×C4⋊C4×C67—24no—
65C2×C4⋊C4×C67—22no—
66C2×C4⋊C4×C67—42no—
67C2×C4⋊C4×C67—42no—
68C2×C4⋊C4×C67—42no—
69C2×C4⋊C4×C67—42no—
70C2×C4⋊C4×C67—42no—
71C2×C4⋊C4×C67C2×C414yes—
72C2×C4⋊C4×C67C2×C418yes—
73C2×C4⋊C4×C67C2×C414yes—
74C2×C4⋊C4×C67D414yes—
75C2×C4⋊C4×C67Q814yes—
76C2×C4⋊C4×C67Q814yes—
77C2×C4⋊C4×C67Q814yes—
78C2×C42×C67—22no—
79C2×C42×C67—22no—
80C2×C42×C67—22no—
81C2×C42×C67—22no—
82C2×C42×C67—24no—
83C2×C42×C67—22no—
84C2×C42×C67—22no—
85C2×C42×C67—24no—
86C2×C42×C67—22no—
87C2×C42×C67—42no—
88C2×C42×C67C2×C414yes—
89C2×C42×C67D414yes—
90#95×C67—22no—
91#95×C67—24no—
92#95×C67—22no—
93#95×C67—24no—
94#95×C67—24no—
95#95×C67—24no—
96#95×C67—42no—
97#95×C67—42no—
98#95×C67—42no—
99#95×C67C2×C418yes—
100C24×C67C2411yescharacteristic
101C22×C4×C67—21no—
102C22×C4×C67—21no—
103C22×C4×C67—21no—
104C22×C4×C67—22no—
105C22×C4×C67—21no—
106C22×C4×C67—21no—
107C22×C4×C67—21no—
108C22×C4×C67—22no—
109C22×C4×C67—21no—
110C22×C4×C67—22no—
111C22×C4×C67—22no—
112C22×C4×C67—21no—
113C22×C4×C67—21no—
114C22×C4×C67—21no—
115C22×C4×C67—22no—
116C22×C4×C67—21no—
117C22×C4×C67—21no—
118C22×C4×C67—21no—
119C22×C4×C67—21no—
120C22×C4×C67—22no—
121C22×C4×C67—21no—
122C22×C4×C67—21no—
123C22×C4×C67—21no—
124C22×C4×C67—21no—
125C22×C4×C67—22no—
126C22×C4×C67—22no—
127C22×C4×C67—22no—
128C22×C4×C67—21no—
129C22×C4×C67—21no—
130C22×C4×C67—21no—
131C22×C4×C67—21no—
132C22×C4×C67—22no—
133C22×C4×C67—22no—
134C22×C4×C67—21no—
135C22×C4×C67—21no—
136C22×C4×C67—22no—
137C22×C4×C67—21no—
138C22×C4×C67—21no—
139C22×C4×C67—21no—
140C22×C4×C67—22no—
141C22×C4×C67—22no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—22no—
146C22×C4×C67—21no—
147C22×C4×C67—22no—
148C22×C4×C67—21no—
149C22×C4×C67—22no—
150C22×C4×C67—22no—
151C22×C4×C67—22no—
152C22×C4×C67—22no—
153C22×C4×C67—22no—
154C22×C4×C67—22no—
155C22×C4×C67—22no—
156C22×C4×C67C22×C412yes—
157C22×C4×C67C22×C414yes—
158C22×C4×C67C22×C414yes—
159C22×C4×C67C22×C412yes—
160C22×C4×C67C22×C412yes—
161C22×C4×C67C2×D412yes—
162C22×C4×C67C2×D414yes—
163C22×C4×C67C2×D412yes—
164C22×C4×C67C2×D412yes—
165C22×C4×C67C2×D412yes—
166C22×C4×C67C2×Q812yes—
167C22×C4×C67C2×Q814yes—
168C22×C4×C67C2×Q814yes—
169C22×C4×C67C2×Q812yes—
170C22×C4×C67C2×Q812yes—
171C22×C4×C67C2×Q812yes—
172C22×C4×C67C2×Q812yes—
173C22×C4×C67#4112yes—
174C22×C4×C67#4112yes—
175C22×C4×C67#4112yes—
176C22×C4×C67#4112yes—
177C22×C4×C67#4112yes—
178C4⋊C4×C67—28no—
179C4⋊C4×C67—28no—
180C4⋊C4×C67—28no—
181C4⋊C4×C67—28no—
182C4⋊C4×C67—48no—
183C4⋊C4×C67—48no—
184C4⋊C4×C67—48no—
185C4⋊C4×C67—44no—
186C4⋊C4×C67C4⋊C4116yescomplemented
187C42×C67—28no—
188C42×C67—28no—
189C42×C67—48no—
190C42×C67—44no—
191C23×C67C23×C411yescharacteristic
192C23×C67C22×D411yescharacteristic
193C23×C67C22×D411yescharacteristic
194C23×C67C22×Q811yescharacteristic
195C23×C67C22×Q811yescharacteristic
196C23×C67C22×Q811yescharacteristic
197C23×C67C2×#4111yescharacteristic
198C23×C67C2×#4111yescharacteristic
199C23×C67C2×#4111yescharacteristic
200C23×C67C2×#4111yescharacteristic
201C23×C67C2×#4111yescharacteristic
202C23×C67H(5,𝔽2)11yescharacteristic
203C23×C67H(5,𝔽2)11yescharacteristic
204C23×C67H(5,𝔽2)11yescharacteristic
205C23×C672−1+411yescharacteristic
206C2×C4×C67—22no—
207C2×C4×C67—24no—
208C2×C4×C67—22no—
209C2×C4×C67—24no—
210C2×C4×C67—22no—
211C2×C4×C67—22no—
212C2×C4×C67—22no—
213C2×C4×C67—22no—
214C2×C4×C67—22no—
215C2×C4×C67—22no—
216C2×C4×C67—22no—
217C2×C4×C67—24no—
218C2×C4×C67—24no—
219C2×C4×C67—22no—
220C2×C4×C67—22no—
221C2×C4×C67—24no—
222C2×C4×C67—24no—
223C2×C4×C67—22no—
224C2×C4×C67—22no—
225C2×C4×C67—24no—
226C2×C4×C67—22no—
227C2×C4×C67—24no—
228C2×C4×C67—24no—
229C2×C4×C67—22no—
230C2×C4×C67—22no—
231C2×C4×C67—22no—
232C2×C4×C67—24no—
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—24no—
241C2×C4×C67—24no—
242C2×C4×C67—41no—
243C2×C4×C67—41no—
244C2×C4×C67—42no—
245C2×C4×C67—42no—
246C2×C4×C67—41no—
247C2×C4×C67—41no—
248C2×C4×C67—41no—
249C2×C4×C67—42no—
250C2×C4×C67—41no—
251C2×C4×C67—41no—
252C2×C4×C67—42no—
253C2×C4×C67—42no—
254C2×C4×C67—41no—
255C2×C4×C67—42no—
256C2×C4×C67—42no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—42no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
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×C67C2×C4⋊C418yes—
274C2×C4×C67C2×C4⋊C414yes—
275C2×C4×C67C4×D414yes—
276C2×C4×C67C4×Q814yes—
277C2×C4×C67C4×Q814yes—
278C2×C4×C67#12114yes—
279C2×C4×C67C22⋊Q814yes—
280C2×C4×C67C22⋊Q814yes—
281C2×C4×C67#12514yes—
282C2×C4×C67C4⋊Q814yes—
283C22×C67C22×C4⋊C411yescharacteristic
284C22×C67C2×C4×D411yescharacteristic
285C22×C67C2×C4×Q811yescharacteristic
286C22×C67C2×C4×Q811yescharacteristic
287C22×C67C4×#4111yescharacteristic
288C22×C67#51811yescharacteristic
289C22×C67#52011yescharacteristic
290C22×C67C2×#12111yescharacteristic
291C22×C67C2×C22⋊Q811yescharacteristic
292C22×C67C2×C22⋊Q811yescharacteristic
293C22×C67#52511yescharacteristic
294C22×C67C2×#12511yescharacteristic
295C22×C67#52911yescharacteristic
296C22×C67C2×C4⋊Q811yescharacteristic
297C22×C67#53311yescharacteristic
298C22×C67#53511yescharacteristic
299C22×C67#53711yescharacteristic
300C22×C67#54011yescharacteristic
301C22×C67#54211yescharacteristic
302C22×C67#54611yescharacteristic
303C22×C67#54611yescharacteristic
304C22×C67D4×Q811yescharacteristic
305C22×C67#55011yescharacteristic
306C22×C67#55211yescharacteristic
307C22×C67#55311yescharacteristic
308C22×C67#55411yescharacteristic
309C22×C67#55411yescharacteristic
310C22×C67#55411yescharacteristic
311C22×C67#55411yescharacteristic
312C22×C67#55411yescharacteristic
313C22×C67#55511yescharacteristic
314C22×C67#55711yescharacteristic
315C22×C67#55711yescharacteristic
316C22×C67Q8211yescharacteristic
317C22×C67Q8211yescharacteristic
318C4×C67—28no—
319C4×C67—24no—
320C4×C67—24no—
321C4×C67—42no—
322C4×C67—44no—
323C4×C67—42no—
324C4×C67—42no—
325C4×C67—42no—
326C4×C67—44no—
327C4×C67—82no—
328C4×C67#38918yes—
329#14045C6711yesmaximal, characteristic, direct product factor, Sylow
330C2×C67C2×#38911yescharacteristic
331C2×C67C4×C22⋊Q811yescharacteristic
332C2×C67#232411yescharacteristic
333C2×C67#234911yescharacteristic
334C2×C67Q8×C4⋊C411yescharacteristic
335C2×C67#236911yescharacteristic
336C2×C67#237011yescharacteristic
337C2×C67#241411yescharacteristic
338C2×C67#241711yescharacteristic
339C2×C67#245111yescharacteristic
340C2×C67#245411yescharacteristic
341C2×C67#250711yescharacteristic
342C2×C67#250811yescharacteristic
343C2×C67#256711yescharacteristic
344C2×C67#258411yescharacteristic
345C2×#389C2×C6711yescharacteristic
346C2×#389C2×C6711yescharacteristic
347C2×#389C2×C6711yescharacteristic
348C2×C4×C4⋊C4C2×C6711yescharacteristic
349C2×C4×C4⋊C4C2×C6711yescharacteristic
350#1444C2×C6712yes—
351#1441C2×C6712yes—
352#1436C2×C6712yes—
353C4⋊#95C2×C6711yescharacteristic
354C4⋊#95C2×C6712yes—
355C4⋊#95C2×C6711yescharacteristic
356C67#1404511yescharacteristic, direct product factor, Sylow
357C22×C4⋊C4C22×C6711yescharacteristic
358C22×C4⋊C4C22×C6711yescharacteristic
359C22×C4⋊C4C22×C6712yes—
360C22×C4⋊C4C22×C6711yescharacteristic
361C22×C4⋊C4C22×C6711yescharacteristic
362C22×C4⋊C4C22×C6711yescharacteristic
363C22×C4⋊C4C22×C6712yes—
364C22×C4⋊C4C22×C6712yes—
365C22×C4⋊C4C22×C6711yescharacteristic
366C22×C42C22×C6711yescharacteristic
367C22×C42C22×C6712yes—
368C22×C42C22×C6711yescharacteristic
369C22×C42C22×C6711yescharacteristic
370#389—24no—
371#389—24no—
372#389C4×C6718yescomplemented
373C4×C4⋊C4—24no—
374C4×C4⋊C4—24no—
375C2×#95C22×C6711yescharacteristic
376C2×#95C22×C6712yes—
377C2×#95C22×C6712yes—
378C2×#95C22×C6712yes—
379C2×#95C22×C6711yescharacteristic
380C2×#95C22×C6712yes—
381C2×#95C22×C6712yes—
382C2×#95C22×C6712yes—
383C2×#95C22×C6712yes—
384C2×#95C22×C6712yes—
385C23×C4C23×C6712yes—
386C23×C4C23×C6712yes—
387C23×C4C23×C6711yescharacteristic
388C23×C4C23×C6711yescharacteristic
389C23×C4C23×C6711yescharacteristic
390C23×C4C23×C6712yes—
391C23×C4C23×C6711yescharacteristic
392C23×C4C23×C6712yes—
393C23×C4C23×C6711yescharacteristic
394C23×C4C23×C6711yescharacteristic
395C23×C4C23×C6711yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4C2×C4×C6714yes—
417C2×C4⋊C4C2×C4×C6718yes—
418C2×C4⋊C4C2×C4×C6714yes—
419C2×C4⋊C4D4×C6714yes—
420C2×C4⋊C4Q8×C6714yes—
421C2×C4⋊C4Q8×C6714yes—
422C2×C4⋊C4Q8×C6714yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—42no—
433C2×C42C2×C4×C6714yes—
434C2×C42D4×C6714yes—
435#95—22no—
436#95—24no—
437#95—22no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95C2×C4×C6718yes—
445C24C24×C6711yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4C22×C4×C6714yes—
502C22×C4C22×C4×C6712yes—
503C22×C4C22×C4×C6714yes—
504C22×C4C22×C4×C6712yes—
505C22×C4C22×C4×C6712yes—
506C22×C4C2×D4×C6712yes—
507C22×C4C2×D4×C6714yes—
508C22×C4C2×D4×C6712yes—
509C22×C4C2×D4×C6712yes—
510C22×C4C2×D4×C6712yes—
511C22×C4C2×Q8×C6712yes—
512C22×C4C2×Q8×C6714yes—
513C22×C4C2×Q8×C6714yes—
514C22×C4C2×Q8×C6712yes—
515C22×C4C2×Q8×C6712yes—
516C22×C4C2×Q8×C6712yes—
517C22×C4C2×Q8×C6712yes—
518C22×C4#41×C6712yes—
519C22×C4#41×C6712yes—
520C22×C4#41×C6712yes—
521C22×C4#41×C6712yes—
522C22×C4#41×C6712yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—44no—
531C4⋊C4C4⋊C4×C67116yescomplemented
532C42—28no—
533C42—28no—
534C42—48no—
535C42—44no—
536C23C23×C4×C6711yescharacteristic
537C23C22×D4×C6711yescharacteristic
538C23C22×D4×C6711yescharacteristic
539C23C22×Q8×C6711yescharacteristic
540C23C22×Q8×C6711yescharacteristic
541C23C22×Q8×C6711yescharacteristic
542C23C2×#41×C6711yescharacteristic
543C23C2×#41×C6711yescharacteristic
544C23C2×#41×C6711yescharacteristic
545C23C2×#41×C6711yescharacteristic
546C23C2×#41×C6711yescharacteristic
547C23H(5,𝔽2)×C6711yescharacteristic
548C23H(5,𝔽2)×C6711yescharacteristic
549C23H(5,𝔽2)×C6711yescharacteristic
550C232−1+4×C6711yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×C4⋊C4×C6718yes—
619C2×C4C2×C4⋊C4×C6714yes—
620C2×C4C4×D4×C6714yes—
621C2×C4C4×Q8×C6714yes—
622C2×C4C4×Q8×C6714yes—
623C2×C4#121×C6714yes—
624C2×C4C22⋊Q8×C6714yes—
625C2×C4C22⋊Q8×C6714yes—
626C2×C4#125×C6714yes—
627C2×C4C4⋊Q8×C6714yes—
628C22C22×C4⋊C4×C6711yescharacteristic
629C22C2×C4×D4×C6711yescharacteristic
630C22C2×C4×Q8×C6711yescharacteristic
631C22C2×C4×Q8×C6711yescharacteristic
632C22C4×#41×C6711yescharacteristic
633C22#518×C6711yescharacteristic
634C22#520×C6711yescharacteristic
635C22C2×#121×C6711yescharacteristic
636C22C2×C22⋊Q8×C6711yescharacteristic
637C22C2×C22⋊Q8×C6711yescharacteristic
638C22#525×C6711yescharacteristic
639C22C2×#125×C6711yescharacteristic
640C22#529×C6711yescharacteristic
641C22C2×C4⋊Q8×C6711yescharacteristic
642C22#533×C6711yescharacteristic
643C22#535×C6711yescharacteristic
644C22#537×C6711yescharacteristic
645C22#540×C6711yescharacteristic
646C22#542×C6711yescharacteristic
647C22#546×C6711yescharacteristic
648C22#546×C6711yescharacteristic
649C22D4×Q8×C6711yescharacteristic
650C22#550×C6711yescharacteristic
651C22#552×C6711yescharacteristic
652C22#553×C6711yescharacteristic
653C22#554×C6711yescharacteristic
654C22#554×C6711yescharacteristic
655C22#554×C6711yescharacteristic
656C22#554×C6711yescharacteristic
657C22#554×C6711yescharacteristic
658C22#555×C6711yescharacteristic
659C22#557×C6711yescharacteristic
660C22#557×C6711yescharacteristic
661C22Q82×C6711yescharacteristic
662C22Q82×C6711yescharacteristic
663C4—24no—
664C4—28no—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—82no—
673C4#389×C6718yes—
674C2C2×#389×C6711yescharacteristic
675C2C4×C22⋊Q8×C6711yescharacteristic
676C2C67×#232411yescharacteristic
677C2C67×#234911yescharacteristic
678C2Q8×C4⋊C4×C6711yescharacteristic
679C2C67×#236911yescharacteristic
680C2C67×#237011yescharacteristic
681C2C67×#241411yescharacteristic
682C2C67×#241711yescharacteristic
683C2C67×#245111yescharacteristic
684C2C67×#245411yescharacteristic
685C2C67×#250711yescharacteristic
686C2C67×#250811yescharacteristic
687C2C67×#256711yescharacteristic
688C2C67×#258411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
27. #389×C67C4semidirect
186. C4⋊C4×C67C4⋊C4semidirect
329. #14045C67direct (N × H)
356. C67#14045direct (N × H)
372. #389C4×C67semidirect
531. C4⋊C4C4⋊C4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C672
C2×C4×C4⋊C4×C672
C67×#14442
C67×#14412
C67×#14362
C67×C4⋊#952
#1404567