Finite Group Databasebeta

← C67×#32968 #30712219

Subgroups — C67×#32968 #30712219

Order 17152.

1274 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C67C211yesmaximal, characteristic
2C2×#479×C67C211yesmaximal, characteristic, complemented
3C2×#478×C67C211yesmaximal, characteristic, complemented
4C67×#2629C211yesmaximal, characteristic, complemented
5C67×#1865C211yesmaximal, characteristic, complemented
6C67×#1864C211yesmaximal, characteristic, complemented
7C67×#1863C211yesmaximal, characteristic, complemented
8C67×#1862C211yesmaximal, characteristic, complemented
9C67×#1853C211yesmaximal, characteristic, complemented
10C67×#1852C211yesmaximal, characteristic, complemented
11C67×#1803C211yesmaximal, characteristic, complemented
12C67×#1802C211yesmaximal, characteristic, complemented
13C67×#1798C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic
15C67×#1788C211yesmaximal, characteristic
16C22×#41×C67C2211yescharacteristic
17C2×#125×C67C2211yescharacteristic
18#520×C67—24no—
19#520×C67—24no—
20C2×C4×Q8×C67C2211yescharacteristic
21C2×C4×Q8×C67C2211yescharacteristic
22C2×C4×D4×C67—21no—
23C2×C4×D4×C67—21no—
24C2×C4×D4×C67C2211yescharacteristic
25C2×C4×D4×C67C2211yescharacteristic
26C2×#117×C67—21no—
27C2×#117×C67C2211yescharacteristic
28C22×C4⋊C4×C67—21no—
29C22×C4⋊C4×C67C2211yescharacteristic
30#479×C67—24no—
31#478×C67—24no—
32C2×#107×C67C2211yescharacteristic
33C2×#107×C67C2211yescharacteristic
34C2×#106×C67C2211yescharacteristic
35C2×#106×C67C2211yescharacteristic
36C2×C4⋊C8×C67C2211yescharacteristic
37C2×C4⋊C8×C67C2211yescharacteristic
38C2×#103×C67C2211yescharacteristic
39C2×#103×C67C2211yescharacteristic
40C2×#103×C67C2211yescharacteristic
41C2×#103×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×#102×C67C2211yescharacteristic
44C2×#102×C67C2211yescharacteristic
45C2×#102×C67C2211yescharacteristic
46C2×C22⋊C8×C67C2211yescharacteristic
47C2×C22⋊C8×C67C2211yescharacteristic
48#398×C67—21no—
49#398×C67—21no—
50#396×C67—21no—
51#396×C67—21no—
52#389×C67C2211yescharacteristic
53#389×C67C2211yescharacteristic
54#384×C67C2211yescharacteristic
55#380×C67C2211yescharacteristic
56#380×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C2×#41×C67—22no—
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67Q814yes—
69C22×Q8×C67C2311yescharacteristic
70C22×D4×C67—21no—
71C22×D4×C67C2311yescharacteristic
72C23×C4×C67—21no—
73C23×C4×C67—21no—
74C23×C4×C67—21no—
75C23×C4×C67—21no—
76C23×C4×C67C2311yescharacteristic
77C22×C8×C67C2311yescharacteristic
78C22×C8×C67C2311yescharacteristic
79C22×C8×C67C2311yescharacteristic
80C22×C8×C67C2311yescharacteristic
81#125×C67—22no—
82#125×C67—22no—
83C4×Q8×C67—22no—
84C4×Q8×C67—22no—
85C4×Q8×C67—22no—
86C4×Q8×C67D414yes—
87C4×D4×C67—28no—
88C4×D4×C67—28no—
89C4×D4×C67—22no—
90C4×D4×C67—22no—
91C4×D4×C67—22no—
92C4×D4×C67D414yes—
93#117×C67—28no—
94#117×C67—22no—
95#117×C67—22no—
96C2×C4⋊C4×C67—28no—
97C2×C4⋊C4×C67—21no—
98C2×C4⋊C4×C67—21no—
99C2×C4⋊C4×C67—21no—
100C2×C4⋊C4×C67—22no—
101C2×C4⋊C4×C67—22no—
102C2×C4⋊C4×C67—21no—
103C2×C4⋊C4×C67—21no—
104C2×C4⋊C4×C67—21no—
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×C67D411yescharacteristic
121C2×C22⋊C4×C67D411yescharacteristic
122C2×C42×C67—21no—
123C2×C42×C67—21no—
124C2×C42×C67C2311yescharacteristic
125C2×C42×C67C2311yescharacteristic
126#107×C67—22no—
127#107×C67—22no—
128#106×C67—22no—
129#106×C67—22no—
130C4⋊C8×C67—22no—
131C4⋊C8×C67—22no—
132#103×C67—22no—
133#103×C67—22no—
134#103×C67—22no—
135#103×C67—22no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140C22⋊C8×C67—22no—
141C22⋊C8×C67—22no—
142#95×C67—21no—
143#95×C67—21no—
144#95×C67—21no—
145#95×C67—21no—
146C24×C67—21no—
147C24×C67C2×D411yescharacteristic
148#41×C67—28no—
149#41×C67—28no—
150#41×C67—28no—
151#41×C67—28no—
152C2×Q8×C67—21no—
153C2×Q8×C67—21no—
154C2×Q8×C67—21no—
155C2×Q8×C67C2×D412yes—
156C2×Q8×C67C2×Q812yes—
157C2×Q8×C67#4112yes—
158C2×D4×C67—24no—
159C2×D4×C67—24no—
160C2×D4×C67—24no—
161C2×D4×C67—21no—
162C2×D4×C67—21no—
163C2×D4×C67—21no—
164C2×D4×C67C2×D412yes—
165C2×D4×C67C2×Q812yes—
166C2×D4×C67#4112yes—
167C22×C4×C67—24no—
168C22×C4×C67—24no—
169C22×C4×C67—21no—
170C22×C4×C67—24no—
171C22×C4×C67—21no—
172C22×C4×C67—21no—
173C22×C4×C67—21no—
174C22×C4×C67—21no—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—24no—
178C22×C4×C67—24no—
179C22×C4×C67—24no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—81no—
185C22×C4×C67—81no—
186C22×C4×C67—81no—
187C22×C4×C67—81no—
188C22×C4×C67—81no—
189C22×C4×C67—81no—
190C22×C4×C67C2×D411yescharacteristic
191C22×C4×C67C2×D411yescharacteristic
192C22×C4×C67C2×D411yescharacteristic
193C22×C4×C67C2×D411yescharacteristic
194C22×C4×C67C2×D411yescharacteristic
195C22×C4×C67C2×Q812yes—
196C22×C4×C67#4112yes—
197C22×C4×C67C2411yescharacteristic
198C2×C8×C67—21no—
199C2×C8×C67—21no—
200C2×C8×C67—21no—
201C2×C8×C67—21no—
202C2×C8×C67—21no—
203C2×C8×C67—21no—
204C2×C8×C67—21no—
205C2×C8×C67—21no—
206C2×C8×C67—21no—
207C2×C8×C67—21no—
208C2×C8×C67—21no—
209C2×C8×C67—21no—
210C4⋊C4×C67—24no—
211C4⋊C4×C67—24no—
212C4⋊C4×C67—22no—
213C4⋊C4×C67—24no—
214C4⋊C4×C67—22no—
215C4⋊C4×C67—21no—
216C4⋊C4×C67—21no—
217C4⋊C4×C67—21no—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67—21no—
221C4⋊C4×C67—21no—
222C4⋊C4×C67—21no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—42no—
226C4⋊C4×C67—42no—
227C4⋊C4×C67—81no—
228C4⋊C4×C67—81no—
229C4⋊C4×C67—81no—
230C4⋊C4×C67—81no—
231C4⋊C4×C67C2×D412yes—
232C4⋊C4×C67C2×D412yes—
233C22⋊C4×C67—24no—
234C22⋊C4×C67—24no—
235C22⋊C4×C67—22no—
236C22⋊C4×C67—22no—
237C22⋊C4×C67—81no—
238C22⋊C4×C67—81no—
239C42×C67—24no—
240C42×C67—24no—
241C42×C67—21no—
242C42×C67—21no—
243C42×C67C2×D412yes—
244C42×C67C2×D412yes—
245C23×C67—21no—
246C23×C67—22no—
247C23×C67—22no—
248C23×C67—21no—
249C23×C67—22no—
250C23×C67—21no—
251C23×C67—21no—
252C23×C67—21no—
253C23×C67—21no—
254C23×C67—41no—
255C23×C67—41no—
256C23×C67—41no—
257C23×C67—41no—
258C23×C67C22⋊Q812yes—
259C23×C67C22×D411yescharacteristic
260Q8×C67—22no—
261Q8×C67—22no—
262Q8×C67—22no—
263Q8×C67C22⋊Q814yes—
264D4×C67—216no—
265D4×C67—22no—
266D4×C67—22no—
267D4×C67—22no—
268D4×C67C22⋊Q814yes—
269C2×C4×C67—216no—
270C2×C4×C67—22no—
271C2×C4×C67—21no—
272C2×C4×C67—22no—
273C2×C4×C67—21no—
274C2×C4×C67—22no—
275C2×C4×C67—21no—
276C2×C4×C67—21no—
277C2×C4×C67—21no—
278C2×C4×C67—21no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—21no—
284C2×C4×C67—21no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—21no—
288C2×C4×C67—21no—
289C2×C4×C67—21no—
290C2×C4×C67—21no—
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—41no—
301C2×C4×C67—41no—
302C2×C4×C67—41no—
303C2×C4×C67—41no—
304C2×C4×C67—41no—
305C2×C4×C67—41no—
306C2×C4×C67—41no—
307C2×C4×C67—84no—
308C2×C4×C67—84no—
309C2×C4×C67—84no—
310C2×C4×C67#12012yes—
311C2×C4×C67#12012yes—
312C2×C4×C67C22⋊Q812yes—
313C2×C4×C67C22×D411yescharacteristic
314C2×C4×C67C22×D411yescharacteristic
315C2×C4×C67C22×Q811yescharacteristic
316C2×C4×C67C2×#4111yescharacteristic
317C2×C4×C67C2×#4111yescharacteristic
318C2×C4×C67C2×#4111yescharacteristic
319C8×C67—41no—
320C8×C67—41no—
321C8×C67—41no—
322C8×C67—41no—
323C22×C67—22no—
324C22×C67—22no—
325C22×C67—22no—
326C22×C67—24no—
327C22×C67—42no—
328C22×C67—42no—
329C22×C67—41no—
330C22×C67—42no—
331C22×C67—41no—
332C22×C67—42no—
333C22×C67—41no—
334C22×C67—42no—
335C22×C67—41no—
336C22×C67—42no—
337C22×C67C2×#12011yescharacteristic
338C22×C67C2×C22⋊Q811yescharacteristic
339C22×C67#52511yescharacteristic
340C22×C67#57611yescharacteristic
341C22×C67#57711yescharacteristic
342C22×C67#57711yescharacteristic
343C22×C67#57811yescharacteristic
344C4×C67—22no—
345C4×C67—24no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—41no—
349C4×C67—42no—
350C4×C67—42no—
351C4×C67—41no—
352C4×C67—81no—
353C4×C67—81no—
354C4×C67—81no—
355C4×C67—81no—
356C4×C67C2×C22⋊Q811yescharacteristic
357C4×C67C2×C22⋊Q811yescharacteristic
358C4×C67#52511yescharacteristic
359C4×C67#52511yescharacteristic
360#32968C6711yesmaximal, characteristic, direct product factor, Sylow
361C2×C67—42no—
362C2×C67—44no—
363C2×C67#284811yescharacteristic
364C2×C67#301211yescharacteristic
365C2×C67#301311yescharacteristic
366C2×C67#308311yescharacteristic
367C2×C67#308411yescharacteristic
368C2×C67#311911yescharacteristic
369C2×C67#312011yescharacteristic
370C2×#520C2×C6711yescharacteristic
371C2×#479C2×C6711yescharacteristic, complemented
372C2×#478C2×C6711yescharacteristic, complemented
373#2629C2×C6711yescharacteristic, complemented
374#1865C2×C6711yescharacteristic, complemented
375#1864C2×C6711yescharacteristic, complemented
376#1863C2×C6711yescharacteristic, complemented
377#1862C2×C6711yescharacteristic, complemented
378#1853C2×C6711yescharacteristic, complemented
379#1852C2×C6711yescharacteristic, complemented
380#1803C2×C6711yescharacteristic, complemented
381#1802C2×C6711yescharacteristic, complemented
382#1798C2×C6711yescharacteristic, complemented
383#1788C2×C6711yescharacteristic
384#1788C2×C6711yescharacteristic
385C67#3296811yescharacteristic, direct product factor, Sylow
386C22×#41C22×C6711yescharacteristic
387C2×#125C22×C6711yescharacteristic
388#520—24no—
389#520—24no—
390C2×C4×Q8C22×C6711yescharacteristic
391C2×C4×Q8C22×C6711yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4—21no—
394C2×C4×D4C22×C6711yescharacteristic
395C2×C4×D4C22×C6711yescharacteristic
396C2×#117—21no—
397C2×#117C22×C6711yescharacteristic
398C22×C4⋊C4—21no—
399C22×C4⋊C4C22×C6711yescharacteristic
400#479—24no—
401#478—24no—
402C2×#107C22×C6711yescharacteristic
403C2×#107C22×C6711yescharacteristic
404C2×#106C22×C6711yescharacteristic
405C2×#106C22×C6711yescharacteristic
406C2×C4⋊C8C22×C6711yescharacteristic
407C2×C4⋊C8C22×C6711yescharacteristic
408C2×#103C22×C6711yescharacteristic
409C2×#103C22×C6711yescharacteristic
410C2×#103C22×C6711yescharacteristic
411C2×#103C22×C6711yescharacteristic
412C2×#102C22×C6711yescharacteristic
413C2×#102C22×C6711yescharacteristic
414C2×#102C22×C6711yescharacteristic
415C2×#102C22×C6711yescharacteristic
416C2×C22⋊C8C22×C6711yescharacteristic
417C2×C22⋊C8C22×C6711yescharacteristic
418#398—21no—
419#398—21no—
420#396—21no—
421#396—21no—
422#389C22×C6711yescharacteristic
423#389C22×C6711yescharacteristic
424#384C22×C6711yescharacteristic
425#380C22×C6711yescharacteristic
426#380C22×C6711yescharacteristic
427#340C22×C6711yescharacteristic
428#340C22×C6711yescharacteristic
429#340C22×C6711yescharacteristic
430#340C22×C6711yescharacteristic
431#336C22×C6711yescharacteristic
432#336C22×C6711yescharacteristic
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41Q8×C6714yes—
439C22×Q8C23×C6711yescharacteristic
440C22×D4—21no—
441C22×D4C23×C6711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4C23×C6711yescharacteristic
447C22×C8C23×C6711yescharacteristic
448C22×C8C23×C6711yescharacteristic
449C22×C8C23×C6711yescharacteristic
450C22×C8C23×C6711yescharacteristic
451#125—22no—
452#125—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8D4×C6714yes—
457C4×D4—28no—
458C4×D4—28no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4D4×C6714yes—
463#117—28no—
464#117—22no—
465#117—22no—
466C2×C4⋊C4—28no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4D4×C6711yescharacteristic
479C2×C4⋊C4D4×C6711yescharacteristic
480C2×C4⋊C4C23×C6711yescharacteristic
481C2×C4⋊C4C23×C6711yescharacteristic
482C2×C4⋊C4C23×C6711yescharacteristic
483C2×C4⋊C4C23×C6711yescharacteristic
484C2×C4⋊C4C23×C6711yescharacteristic
485C2×C4⋊C4C23×C6711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C6711yescharacteristic
491C2×C22⋊C4D4×C6711yescharacteristic
492C2×C42—21no—
493C2×C42—21no—
494C2×C42C23×C6711yescharacteristic
495C2×C42C23×C6711yescharacteristic
496#107—22no—
497#107—22no—
498#106—22no—
499#106—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502#103—22no—
503#103—22no—
504#103—22no—
505#103—22no—
506#102—22no—
507#102—22no—
508#102—22no—
509#102—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24—21no—
517C24C2×D4×C6711yescharacteristic
518#41—28no—
519#41—28no—
520#41—28no—
521#41—28no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8C2×D4×C6712yes—
526C2×Q8C2×Q8×C6712yes—
527C2×Q8#41×C6712yes—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4C2×D4×C6712yes—
535C2×D4C2×Q8×C6712yes—
536C2×D4#41×C6712yes—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4C2×D4×C6711yescharacteristic
561C22×C4C2×D4×C6711yescharacteristic
562C22×C4C2×D4×C6711yescharacteristic
563C22×C4C2×D4×C6711yescharacteristic
564C22×C4C2×D4×C6711yescharacteristic
565C22×C4C2×Q8×C6712yes—
566C22×C4#41×C6712yes—
567C22×C4C24×C6711yescharacteristic
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—81no—
598C4⋊C4—81no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C4⋊C4C2×D4×C6712yes—
602C4⋊C4C2×D4×C6712yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C42—24no—
610C42—24no—
611C42—21no—
612C42—21no—
613C42C2×D4×C6712yes—
614C42C2×D4×C6712yes—
615C23—21no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22⋊Q8×C6712yes—
629C23C22×D4×C6711yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8C22⋊Q8×C6714yes—
634D4—216no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4C22⋊Q8×C6714yes—
639C2×C4—216no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4#120×C6712yes—
681C2×C4#120×C6712yes—
682C2×C4C22⋊Q8×C6712yes—
683C2×C4C22×D4×C6711yescharacteristic
684C2×C4C22×D4×C6711yescharacteristic
685C2×C4C22×Q8×C6711yescharacteristic
686C2×C4C2×#41×C6711yescharacteristic
687C2×C4C2×#41×C6711yescharacteristic
688C2×C4C2×#41×C6711yescharacteristic
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—24no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22C2×#120×C6711yescharacteristic
708C22C2×C22⋊Q8×C6711yescharacteristic
709C22#525×C6711yescharacteristic
710C22#576×C6711yescharacteristic
711C22#577×C6711yescharacteristic
712C22#577×C6711yescharacteristic
713C22#578×C6711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—24no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4C2×C22⋊Q8×C6711yescharacteristic
727C4C2×C22⋊Q8×C6711yescharacteristic
728C4#525×C6711yescharacteristic
729C4#525×C6711yescharacteristic
730C2—42no—
731C2—44no—
732C2C67×#284811yescharacteristic
733C2C67×#301211yescharacteristic
734C2C67×#301311yescharacteristic
735C2C67×#308311yescharacteristic
736C2C67×#308411yescharacteristic
737C2C67×#311911yescharacteristic
738C2C67×#312011yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC22×#41×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
2. C2×#479×C67C2semidirect
3. C2×#478×C67C2semidirect
4. C67×#2629C2semidirect
5. C67×#1865C2semidirect
6. C67×#1864C2semidirect
7. C67×#1863C2semidirect
8. C67×#1862C2semidirect
9. C67×#1853C2semidirect
10. C67×#1852C2semidirect
11. C67×#1803C2semidirect
12. C67×#1802C2semidirect
13. C67×#1798C2semidirect
360. #32968C67direct (N × H)
371. C2×#479C2×C67semidirect
372. C2×#478C2×C67semidirect
373. #2629C2×C67semidirect
374. #1865C2×C67semidirect
375. #1864C2×C67semidirect
376. #1863C2×C67semidirect
377. #1862C2×C67semidirect
378. #1853C2×C67semidirect
379. #1852C2×C67semidirect
380. #1803C2×C67semidirect
381. #1802C2×C67semidirect
382. #1798C2×C67semidirect
385. C67#32968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#520×C672
C2×#479×C672
C2×#478×C672
C67×#26292
C67×#18652
C67×#18642
C67×#18632
C67×#18622
C67×#18532
C67×#18522
C67×#18032
C67×#18022
C67×#17982
C67×#17882
#3296867