Finite Group Databasebeta

← C67×#25916 #30705167

Subgroups — C67×#25916 #30705167

Order 17152.

1052 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C67C211yesmaximal, characteristic, complemented
2C2×#489×C67C211yesmaximal, characteristic, complemented
3C2×#488×C67C211yesmaximal, characteristic, complemented
4C67×#2620C211yesmaximal, characteristic
5C67×#2026C211yesmaximal, characteristic, complemented
6C67×#2025C211yesmaximal, characteristic, complemented
7C67×#2024C211yesmaximal, characteristic, complemented
8C67×#2023C211yesmaximal, characteristic, complemented
9C67×#1992C211yesmaximal, characteristic, complemented
10C67×#1990C211yesmaximal, characteristic, complemented
11C67×#1875C211yesmaximal, characteristic
12C67×#1874C211yesmaximal, characteristic
13C67×#1873C211yesmaximal, characteristic, complemented
14C67×#1872C211yesmaximal, characteristic, complemented
15C67×#1750C211yesmaximal, characteristic, complemented
16#544×C67—24no—
17#544×C67—24no—
18C2×C4⋊Q8×C67—21no—
19C2×C4⋊Q8×C67C2211yescharacteristic
20C2×C4⋊Q8×C67C2211yescharacteristic
21C2×#125×C67—21no—
22C2×#125×C67C2211yescharacteristic
23C2×#125×C67C2211yescharacteristic
24C2×#124×C67C2211yescharacteristic
25C2×C22⋊Q8×C67—21no—
26C2×C22⋊Q8×C67—21no—
27C2×C22⋊Q8×C67C2211yescharacteristic
28C2×#121×C67C2211yescharacteristic
29C2×#117×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31C22×C4⋊C4×C67C2211yescharacteristic
32#489×C67—24no—
33#488×C67—24no—
34C2×#103×C67C2211yescharacteristic
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#103×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×C22⋊C8×C67C2211yescharacteristic
43C2×C22⋊C8×C67C2211yescharacteristic
44C2×#97×C67C2211yescharacteristic
45C2×C4×C8×C67C2211yescharacteristic
46#396×C67—21no—
47#396×C67—21no—
48#394×C67—21no—
49#394×C67—21no—
50#391×C67C2211yescharacteristic
51#390×C67C2211yescharacteristic
52#384×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C22×Q8×C67—21no—
64C22×Q8×C67—21no—
65C22×Q8×C67C2311yescharacteristic
66C22×D4×C67—21no—
67C22×D4×C67C2311yescharacteristic
68C23×C4×C67—21no—
69C23×C4×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22×C8×C67C2311yescharacteristic
73C22×C8×C67C2311yescharacteristic
74C4⋊Q8×C67—28no—
75C4⋊Q8×C67—22no—
76C4⋊Q8×C67—22no—
77C4⋊Q8×C67—22no—
78C4⋊Q8×C67D414yescomplemented
79#125×C67—28no—
80#125×C67—22no—
81#125×C67—22no—
82#125×C67—22no—
83#125×C67D414yescomplemented
84#124×C67—22no—
85#124×C67—22no—
86C22⋊Q8×C67—28no—
87C22⋊Q8×C67—28no—
88C22⋊Q8×C67—22no—
89C22⋊Q8×C67—22no—
90#121×C67—22no—
91#121×C67—22no—
92#117×C67—22no—
93#117×C67—22no—
94#117×C67—22no—
95#117×C67—22no—
96C2×C4⋊C4×C67—21no—
97C2×C4⋊C4×C67—21no—
98C2×C4⋊C4×C67—21no—
99C2×C4⋊C4×C67—21no—
100C2×C4⋊C4×C67—21no—
101C2×C4⋊C4×C67—21no—
102C2×C4⋊C4×C67—21no—
103C2×C4⋊C4×C67—22no—
104C2×C4⋊C4×C67—22no—
105C2×C4⋊C4×C67—21no—
106C2×C4⋊C4×C67—21no—
107C2×C4⋊C4×C67—21no—
108C2×C4⋊C4×C67D411yescharacteristic
109C2×C4⋊C4×C67D411yescharacteristic
110C2×C4⋊C4×C67C2311yescharacteristic
111C2×C4⋊C4×C67C2311yescharacteristic
112C2×C4⋊C4×C67C2311yescharacteristic
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C4⋊C4×C67C2311yescharacteristic
115C2×C4⋊C4×C67C2311yescharacteristic
116C2×C22⋊C4×C67—21no—
117C2×C22⋊C4×C67—21no—
118C2×C22⋊C4×C67—21no—
119C2×C22⋊C4×C67—21no—
120C2×C22⋊C4×C67—21no—
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67D411yescharacteristic
124C2×C22⋊C4×C67D411yescharacteristic
125C2×C42×C67—21no—
126C2×C42×C67C2311yescharacteristic
127C2×C42×C67C2311yescharacteristic
128#103×C67—22no—
129#103×C67—22no—
130#103×C67—22no—
131#103×C67—22no—
132#102×C67—22no—
133#102×C67—22no—
134#102×C67—22no—
135#102×C67—22no—
136C22⋊C8×C67—22no—
137C22⋊C8×C67—22no—
138#97×C67—22no—
139C4×C8×C67—22no—
140#95×C67—21no—
141#95×C67—21no—
142C24×C67—21no—
143C24×C67C2×D411yescharacteristic
144C2×Q8×C67—24no—
145C2×Q8×C67—24no—
146C2×Q8×C67—21no—
147C2×Q8×C67—21no—
148C2×Q8×C67—21no—
149C2×Q8×C67—21no—
150C2×Q8×C67—21no—
151C2×Q8×C67—21no—
152C2×Q8×C67—81no—
153C2×Q8×C67—81no—
154C2×Q8×C67—81no—
155C2×Q8×C67—81no—
156C2×D4×C67—21no—
157C2×D4×C67—21no—
158C2×D4×C67—21no—
159C2×D4×C67—21no—
160C2×D4×C67—21no—
161C2×D4×C67—21no—
162C2×D4×C67—42no—
163C2×D4×C67—81no—
164C2×D4×C67—81no—
165C22×C4×C67—21no—
166C22×C4×C67—21no—
167C22×C4×C67—21no—
168C22×C4×C67—21no—
169C22×C4×C67—21no—
170C22×C4×C67—21no—
171C22×C4×C67—21no—
172C22×C4×C67—21no—
173C22×C4×C67—24no—
174C22×C4×C67—21no—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—81no—
178C22×C4×C67—81no—
179C22×C4×C67C2×D411yescharacteristic
180C22×C4×C67C2×D411yescharacteristic
181C22×C4×C67C2×D411yescharacteristic
182C22×C4×C67C2×D411yescharacteristic
183C22×C4×C67C2×D411yescharacteristic
184C22×C4×C67#4112yes—
185C22×C4×C67#4112yes—
186C22×C4×C67C2411yescharacteristic
187C2×C8×C67—21no—
188C2×C8×C67—21no—
189C2×C8×C67—21no—
190C2×C8×C67—21no—
191C2×C8×C67—21no—
192C2×C8×C67—21no—
193C2×C8×C67—21no—
194C2×C8×C67—21no—
195C2×C8×C67—21no—
196C2×C8×C67—21no—
197C2×C8×C67—21no—
198C2×C8×C67—21no—
199C4⋊C4×C67—24no—
200C4⋊C4×C67—24no—
201C4⋊C4×C67—24no—
202C4⋊C4×C67—24no—
203C4⋊C4×C67—24no—
204C4⋊C4×C67—24no—
205C4⋊C4×C67—24no—
206C4⋊C4×C67—22no—
207C4⋊C4×C67—22no—
208C4⋊C4×C67—21no—
209C4⋊C4×C67—21no—
210C4⋊C4×C67—21no—
211C4⋊C4×C67—21no—
212C4⋊C4×C67—21no—
213C4⋊C4×C67—21no—
214C4⋊C4×C67—21no—
215C4⋊C4×C67—21no—
216C4⋊C4×C67—42no—
217C4⋊C4×C67—81no—
218C4⋊C4×C67—81no—
219C4⋊C4×C67C2×D412yes—
220C4⋊C4×C67C2×D412yes—
221C4⋊C4×C67C2×D412yes—
222C4⋊C4×C67C2×D412yes—
223C22⋊C4×C67—24no—
224C22⋊C4×C67—22no—
225C22⋊C4×C67—22no—
226C22⋊C4×C67—42no—
227C22⋊C4×C67—42no—
228C22⋊C4×C67—42no—
229C22⋊C4×C67—42no—
230C22⋊C4×C67—81no—
231C22⋊C4×C67—81no—
232C42×C67—24no—
233C42×C67—21no—
234C42×C67—21no—
235C42×C67C2×D412yes—
236C42×C67C2×D412yes—
237C23×C67—21no—
238C23×C67—21no—
239C23×C67—21no—
240C23×C67—21no—
241C23×C67—21no—
242C23×C67—21no—
243C23×C67—41no—
244C23×C67—41no—
245C23×C67—41no—
246C23×C67—41no—
247C23×C67—41no—
248C23×C67—41no—
249C23×C67—41no—
250C23×C67#12412yes—
251C23×C67C22×D411yescharacteristic
252Q8×C67—41no—
253Q8×C67—41no—
254Q8×C67—41no—
255Q8×C67—41no—
256Q8×C67—84no—
257Q8×C67—84no—
258D4×C67—41no—
259D4×C67—41no—
260D4×C67—41no—
261D4×C67—41no—
262D4×C67—84no—
263C2×C4×C67—21no—
264C2×C4×C67—21no—
265C2×C4×C67—21no—
266C2×C4×C67—21no—
267C2×C4×C67—21no—
268C2×C4×C67—21no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—21no—
274C2×C4×C67—22no—
275C2×C4×C67—21no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—21no—
280C2×C4×C67—21no—
281C2×C4×C67—21no—
282C2×C4×C67—21no—
283C2×C4×C67—41no—
284C2×C4×C67—41no—
285C2×C4×C67—41no—
286C2×C4×C67—41no—
287C2×C4×C67—41no—
288C2×C4×C67—41no—
289C2×C4×C67—41no—
290C2×C4×C67—41no—
291C2×C4×C67—41no—
292C2×C4×C67—41no—
293C2×C4×C67—41no—
294C2×C4×C67—41no—
295C2×C4×C67—41no—
296C2×C4×C67—41no—
297C2×C4×C67—41no—
298C2×C4×C67—41no—
299C2×C4×C67—41no—
300C2×C4×C67—84no—
301C2×C4×C67#12012yes—
302C2×C4×C67#12012yes—
303C2×C4×C67#12412yes—
304C2×C4×C67C22×D411yescharacteristic
305C2×C4×C67C22×D411yescharacteristic
306C2×C4×C67C2×#4111yescharacteristic
307C2×C4×C67C2×#4111yescharacteristic
308C2×C4×C672−1+411yescharacteristic
309C2×C4×C672−1+411yescharacteristic
310C8×C67—41no—
311C8×C67—41no—
312C8×C67—41no—
313C8×C67—41no—
314C22×C67—22no—
315C22×C67—22no—
316C22×C67—22no—
317C22×C67—41no—
318C22×C67—41no—
319C22×C67—41no—
320C22×C67—41no—
321C22×C67—81no—
322C22×C67—81no—
323C22×C67—81no—
324C22×C67—81no—
325C22×C67—81no—
326C22×C67—81no—
327C22×C67—81no—
328C22×C67C2×#12011yescharacteristic
329C22×C67C2×#12411yescharacteristic
330C22×C67#53611yescharacteristic
331C22×C67#57611yescharacteristic
332C22×C67#57711yescharacteristic
333C22×C67#57711yescharacteristic
334C22×C67#57811yescharacteristic
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—22no—
338C4×C67—41no—
339C4×C67—42no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67—41no—
343C4×C67—42no—
344C4×C67—81no—
345C4×C67—81no—
346C4×C67—81no—
347C4×C67#54811yescharacteristic
348C4×C67#54811yescharacteristic
349C4×C67#54811yescharacteristic
350C4×C67#54811yescharacteristic
351#25916C6711yesmaximal, characteristic, direct product factor, Sylow
352C2×C67—42no—
353C2×C67—161no—
354C2×C67#243611yescharacteristic
355C2×C67#301211yescharacteristic
356C2×C67#301311yescharacteristic
357C2×C67#313611yescharacteristic
358C2×C67#313711yescharacteristic
359C2×C67#324311yescharacteristic
360C2×C67#324411yescharacteristic
361C2×#544C2×C6711yescharacteristic, complemented
362C2×#489C2×C6711yescharacteristic, complemented
363C2×#488C2×C6711yescharacteristic, complemented
364#2620C2×C6711yescharacteristic
365#2026C2×C6711yescharacteristic, complemented
366#2025C2×C6711yescharacteristic, complemented
367#2024C2×C6711yescharacteristic, complemented
368#2023C2×C6711yescharacteristic, complemented
369#1992C2×C6711yescharacteristic, complemented
370#1990C2×C6711yescharacteristic, complemented
371#1875C2×C6711yescharacteristic
372#1874C2×C6711yescharacteristic
373#1873C2×C6711yescharacteristic, complemented
374#1872C2×C6711yescharacteristic, complemented
375#1750C2×C6711yescharacteristic, complemented
376C67#2591611yescharacteristic, direct product factor, Sylow
377#544—24no—
378#544—24no—
379C2×C4⋊Q8—21no—
380C2×C4⋊Q8C22×C6711yescharacteristic
381C2×C4⋊Q8C22×C6711yescharacteristic
382C2×#125—21no—
383C2×#125C22×C6711yescharacteristic
384C2×#125C22×C6711yescharacteristic
385C2×#124C22×C6711yescharacteristic
386C2×C22⋊Q8—21no—
387C2×C22⋊Q8—21no—
388C2×C22⋊Q8C22×C6711yescharacteristic
389C2×#121C22×C6711yescharacteristic
390C2×#117C22×C6711yescharacteristic
391C2×#117C22×C6711yescharacteristic
392C22×C4⋊C4C22×C6711yescharacteristic
393#489—24no—
394#488—24no—
395C2×#103C22×C6711yescharacteristic
396C2×#103C22×C6711yescharacteristic
397C2×#103C22×C6711yescharacteristic
398C2×#103C22×C6711yescharacteristic
399C2×#102C22×C6711yescharacteristic
400C2×#102C22×C6711yescharacteristic
401C2×#102C22×C6711yescharacteristic
402C2×#102C22×C6711yescharacteristic
403C2×C22⋊C8C22×C6711yescharacteristic
404C2×C22⋊C8C22×C6711yescharacteristic
405C2×#97C22×C6711yescharacteristic
406C2×C4×C8C22×C6711yescharacteristic
407#396—21no—
408#396—21no—
409#394—21no—
410#394—21no—
411#391C22×C6711yescharacteristic
412#390C22×C6711yescharacteristic
413#384C22×C6711yescharacteristic
414#340C22×C6711yescharacteristic
415#340C22×C6711yescharacteristic
416#340C22×C6711yescharacteristic
417#340C22×C6711yescharacteristic
418#340C22×C6711yescharacteristic
419#340C22×C6711yescharacteristic
420#340C22×C6711yescharacteristic
421#340C22×C6711yescharacteristic
422#336C22×C6711yescharacteristic
423#336C22×C6711yescharacteristic
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8C23×C6711yescharacteristic
427C22×D4—21no—
428C22×D4C23×C6711yescharacteristic
429C23×C4—21no—
430C23×C4C23×C6711yescharacteristic
431C22×C8C23×C6711yescharacteristic
432C22×C8C23×C6711yescharacteristic
433C22×C8C23×C6711yescharacteristic
434C22×C8C23×C6711yescharacteristic
435C4⋊Q8—28no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8D4×C6714yescomplemented
440#125—28no—
441#125—22no—
442#125—22no—
443#125—22no—
444#125D4×C6714yescomplemented
445#124—22no—
446#124—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451#121—22no—
452#121—22no—
453#117—22no—
454#117—22no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4D4×C6711yescharacteristic
470C2×C4⋊C4D4×C6711yescharacteristic
471C2×C4⋊C4C23×C6711yescharacteristic
472C2×C4⋊C4C23×C6711yescharacteristic
473C2×C4⋊C4C23×C6711yescharacteristic
474C2×C4⋊C4C23×C6711yescharacteristic
475C2×C4⋊C4C23×C6711yescharacteristic
476C2×C4⋊C4C23×C6711yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4D4×C6711yescharacteristic
485C2×C22⋊C4D4×C6711yescharacteristic
486C2×C42—21no—
487C2×C42C23×C6711yescharacteristic
488C2×C42C23×C6711yescharacteristic
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499#97—22no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503C24—21no—
504C24C2×D4×C6711yescharacteristic
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—81no—
514C2×Q8—81no—
515C2×Q8—81no—
516C2×Q8—81no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C6711yescharacteristic
541C22×C4C2×D4×C6711yescharacteristic
542C22×C4C2×D4×C6711yescharacteristic
543C22×C4C2×D4×C6711yescharacteristic
544C22×C4C2×D4×C6711yescharacteristic
545C22×C4#41×C6712yes—
546C22×C4#41×C6712yes—
547C22×C4C24×C6711yescharacteristic
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C6712yes—
581C4⋊C4C2×D4×C6712yes—
582C4⋊C4C2×D4×C6712yes—
583C4⋊C4C2×D4×C6712yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—24no—
594C42—21no—
595C42—21no—
596C42C2×D4×C6712yes—
597C42C2×D4×C6712yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23#124×C6712yes—
612C23C22×D4×C6711yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—84no—
618Q8—84no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4#120×C6712yes—
663C2×C4#120×C6712yes—
664C2×C4#124×C6712yes—
665C2×C4C22×D4×C6711yescharacteristic
666C2×C4C22×D4×C6711yescharacteristic
667C2×C4C2×#41×C6711yescharacteristic
668C2×C4C2×#41×C6711yescharacteristic
669C2×C42−1+4×C6711yescharacteristic
670C2×C42−1+4×C6711yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#120×C6711yescharacteristic
690C22C2×#124×C6711yescharacteristic
691C22#536×C6711yescharacteristic
692C22#576×C6711yescharacteristic
693C22#577×C6711yescharacteristic
694C22#577×C6711yescharacteristic
695C22#578×C6711yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4#548×C6711yescharacteristic
709C4#548×C6711yescharacteristic
710C4#548×C6711yescharacteristic
711C4#548×C6711yescharacteristic
712C2—42no—
713C2—161no—
714C2C67×#243611yescharacteristic
715C2C67×#301211yescharacteristic
716C2C67×#301311yescharacteristic
717C2C67×#313611yescharacteristic
718C2C67×#313711yescharacteristic
719C2C67×#324311yescharacteristic
720C2C67×#324411yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#121×C67C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#544×C67C2semidirect
2. C2×#489×C67C2semidirect
3. C2×#488×C67C2semidirect
5. C67×#2026C2semidirect
6. C67×#2025C2semidirect
7. C67×#2024C2semidirect
8. C67×#2023C2semidirect
9. C67×#1992C2semidirect
10. C67×#1990C2semidirect
13. C67×#1873C2semidirect
14. C67×#1872C2semidirect
15. C67×#1750C2semidirect
78. C4⋊Q8×C67D4semidirect
83. #125×C67D4semidirect
351. #25916C67direct (N × H)
361. C2×#544C2×C67semidirect
362. C2×#489C2×C67semidirect
363. C2×#488C2×C67semidirect
365. #2026C2×C67semidirect
366. #2025C2×C67semidirect
367. #2024C2×C67semidirect
368. #2023C2×C67semidirect
369. #1992C2×C67semidirect
370. #1990C2×C67semidirect
373. #1873C2×C67semidirect
374. #1872C2×C67semidirect
375. #1750C2×C67semidirect
376. C67#25916direct (N × H)
439. C4⋊Q8D4×C67semidirect
444. #125D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C672
C2×#489×C672
C2×#488×C672
C67×#26202
C67×#20262
C67×#20252
C67×#20242
C67×#20232
C67×#19922
C67×#19902
C67×#18752
C67×#18742
C67×#18732
C67×#18722
C67×#17502
#2591667