Finite Group Databasebeta

← C67×#22405 #30701656

Subgroups — C67×#22405 #30701656

Order 17152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C67C211yesmaximal, characteristic
2C2×#410×C67C211yesmaximal, characteristic, complemented
3C22×#99×C67C211yesmaximal, characteristic, complemented
4C67×#2342C212yesmaximal, complemented
5C67×#1964C212yesmaximal, complemented
6C67×#1899C212yesmaximal, complemented
7C67×#1898C212yesmaximal, complemented
8C67×#1799C211yesmaximal, characteristic, complemented
9C67×#1782C211yesmaximal, characteristic, complemented
10C67×#1781C211yesmaximal, characteristic, complemented
11C4×#99×C67C211yesmaximal, characteristic, complemented
12C22×#41×C67C2211yescharacteristic
13C23×D4×C67C2211yescharacteristic
14#546×C67—22no—
15#546×C67—22no—
16#546×C67—22no—
17#546×C67—22no—
18C2×#124×C67C411yescharacteristic, complemented
19C2×#123×C67C411yescharacteristic, complemented
20C2×#123×C67C2211yescharacteristic
21C2×C22⋊Q8×C67C411yescharacteristic, complemented
22C2×#121×C67C411yescharacteristic, complemented
23C2×#121×C67C411yescharacteristic, complemented
24C2×#121×C67C2211yescharacteristic
25C2×#120×C67C411yescharacteristic, complemented
26C2×#120×C67C2211yescharacteristic
27C2×C4×D4×C67C411yescharacteristic, complemented
28C2×C4×D4×C67C2211yescharacteristic
29C2×#117×C67C2212yescomplemented
30C22×C22⋊C4×C67C411yescharacteristic, complemented
31C22×C22⋊C4×C67C2212yes—
32C22×C22⋊C4×C67C2211yescharacteristic
33#410×C67—24no—
34C2×#99×C67—24no—
35C2×#99×C67C2211yescharacteristic
36C2×#99×C67C2211yescharacteristic
37C2×#99×C67C2211yescharacteristic
38C2×#99×C67C2212yes—
39C2×#99×C67C2212yes—
40C2×#99×C67C2211yescharacteristic
41C2×#99×C67C2212yescomplemented
42C2×#99×C67C2212yescomplemented
43#388×C67—22no—
44#388×C67—22no—
45#385×C67—22no—
46#381×C67C2212yescomplemented
47#380×C67C2212yescomplemented
48#379×C67C2212yes—
49C4×C22⋊C4×C67—22no—
50C4×C22⋊C4×C67C2212yescomplemented
51#342×C67C2212yescomplemented
52#342×C67C2212yescomplemented
53C25×C67C2×C411yescharacteristic
54C25×C67C2311yescharacteristic
55C2×#41×C67—22no—
56C2×#41×C67—22no—
57C2×#41×C67—22no—
58C2×#41×C67—22no—
59C2×#41×C67—42no—
60C22×Q8×C67C2×C411yescharacteristic, complemented
61C22×D4×C67—22no—
62C22×D4×C67—22no—
63C22×D4×C67—22no—
64C22×D4×C67—22no—
65C22×D4×C67—42no—
66C22×D4×C67C2×C411yescharacteristic
67C22×D4×C67C2×C411yescharacteristic
68C22×D4×C67C2×C411yescharacteristic
69C22×D4×C67C2×C411yescharacteristic
70C22×D4×C67C2×C411yescharacteristic, complemented
71C22×D4×C67C2×C411yescharacteristic, complemented
72C22×D4×C67C2311yescharacteristic
73C22×D4×C67C2311yescharacteristic
74C22×D4×C67C2311yescharacteristic
75C23×C4×C67—22no—
76C23×C4×C67C2×C411yescharacteristic
77C23×C4×C67C2×C411yescharacteristic, complemented
78C23×C4×C67C2×C411yescharacteristic, complemented
79C23×C4×C67C2×C411yescharacteristic, complemented
80C23×C4×C67C2311yescharacteristic
81C23×C4×C67C2311yescharacteristic
82#124×C67—22no—
83#124×C67—22no—
84#123×C67—22no—
85#123×C67—22no—
86#123×C67—22no—
87#123×C67—22no—
88C22⋊Q8×C67—22no—
89C22⋊Q8×C67—22no—
90#121×C67—22no—
91#121×C67—22no—
92#121×C67—22no—
93#121×C67—22no—
94#121×C67—22no—
95#121×C67—22no—
96#120×C67—22no—
97#120×C67—22no—
98#120×C67—22no—
99#120×C67—22no—
100C4×D4×C67—22no—
101C4×D4×C67—22no—
102C4×D4×C67—21no—
103C4×D4×C67—21no—
104C4×D4×C67—21no—
105C4×D4×C67—21no—
106#117×C67—24no—
107#117×C67—42no—
108C2×C4⋊C4×C67—22no—
109C2×C4⋊C4×C67—22no—
110C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
111C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
112C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
114C2×C22⋊C4×C67—21no—
115C2×C22⋊C4×C67—21no—
116C2×C22⋊C4×C67—21no—
117C2×C22⋊C4×C67—21no—
118C2×C22⋊C4×C67—24no—
119C2×C22⋊C4×C67—22no—
120C2×C22⋊C4×C67—22no—
121C2×C22⋊C4×C67—22no—
122C2×C22⋊C4×C67—42no—
123C2×C22⋊C4×C67C2×C411yescharacteristic
124C2×C22⋊C4×C67C2×C411yescharacteristic
125C2×C22⋊C4×C67C2×C411yescharacteristic
126C2×C22⋊C4×C67C2×C411yescharacteristic
127C2×C22⋊C4×C67C2×C411yescharacteristic
128C2×C22⋊C4×C67C2×C411yescharacteristic
129C2×C22⋊C4×C67C2×C411yescharacteristic, complemented
130C2×C22⋊C4×C67C2×C411yescharacteristic, complemented
131C2×C22⋊C4×C67C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C67C2×C411yescharacteristic, complemented
133C2×C22⋊C4×C67C2×C411yescharacteristic, complemented
134C2×C22⋊C4×C67D412yes—
135C2×C22⋊C4×C67D412yes—
136C2×C22⋊C4×C67D412yes—
137C2×C22⋊C4×C67D412yes—
138C2×C22⋊C4×C67C2312yes—
139C2×C22⋊C4×C67C2312yes—
140C2×C22⋊C4×C67C2312yes—
141C2×C22⋊C4×C67C2311yescharacteristic
142C2×C22⋊C4×C67C2312yes—
143C2×C42×C67—22no—
144C2×C42×C67—22no—
145C2×C42×C67C2×C411yescharacteristic, complemented
146#99×C67—22no—
147#99×C67—22no—
148#99×C67—22no—
149#99×C67—24no—
150#99×C67—24no—
151#99×C67—42no—
152#99×C67—42no—
153#99×C67D414yescomplemented
154#95×C67—22no—
155#95×C67—22no—
156#95×C67—22no—
157#95×C67—22no—
158C24×C67—21no—
159C24×C67—21no—
160C24×C67—22no—
161C24×C67—21no—
162C24×C67—21no—
163C24×C67—22no—
164C24×C67—41no—
165C24×C67—42no—
166C24×C67—42no—
167C24×C67—81no—
168C24×C67—81no—
169C24×C67C22×C411yescharacteristic
170C24×C67C22×C411yescharacteristic
171C24×C67C22×C411yescharacteristic
172C24×C67C22×C411yescharacteristic
173C24×C67C22×C411yescharacteristic
174C24×C67C2×D412yes—
175C24×C67C2×D412yes—
176C24×C67C2411yescharacteristic
177#41×C67—44no—
178#41×C67—44no—
179#41×C67—44no—
180#41×C67—44no—
181C2×Q8×C67—22no—
182C2×Q8×C67—22no—
183C2×Q8×C67—41no—
184C2×D4×C67—22no—
185C2×D4×C67—22no—
186C2×D4×C67—21no—
187C2×D4×C67—21no—
188C2×D4×C67—22no—
189C2×D4×C67—22no—
190C2×D4×C67—22no—
191C2×D4×C67—22no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—21no—
195C2×D4×C67—21no—
196C2×D4×C67—21no—
197C2×D4×C67—21no—
198C2×D4×C67—22no—
199C2×D4×C67—22no—
200C2×D4×C67—22no—
201C2×D4×C67—22no—
202C2×D4×C67—22no—
203C2×D4×C67—22no—
204C2×D4×C67—41no—
205C2×D4×C67—41no—
206C2×D4×C67—41no—
207C2×D4×C67—44no—
208C2×D4×C67—44no—
209C2×D4×C67—44no—
210C2×D4×C67—44no—
211C2×D4×C67—42no—
212C2×D4×C67—81no—
213C2×D4×C67—81no—
214C2×D4×C67C2×D412yes—
215C2×D4×C67#4112yes—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—22no—
219C22×C4×C67—21no—
220C22×C4×C67—21no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—41no—
235C22×C4×C67—41no—
236C22×C4×C67—41no—
237C22×C4×C67—44no—
238C22×C4×C67—44no—
239C22×C4×C67—81no—
240C22×C4×C67—82no—
241C22×C4×C67—81no—
242C22×C4×C67C22×C411yescharacteristic
243C22×C4×C67C22×C411yescharacteristic
244C22×C4×C67C22×C411yescharacteristic
245C22×C4×C67C22×C411yescharacteristic
246C22×C4×C67C22×C411yescharacteristic
247C22×C4×C67C22×C411yescharacteristic
248C22×C4×C67C22×C411yescharacteristic
249C22×C4×C67C22×C411yescharacteristic
250C22×C4×C67C22×C411yescharacteristic
251C22×C4×C67C2×D412yes—
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2×D412yes—
254C22×C4×C67C2×D412yes—
255C4⋊C4×C67—22no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—22no—
259C4⋊C4×C67—22no—
260C4⋊C4×C67—44no—
261C4⋊C4×C67—82no—
262C22⋊C4×C67—21no—
263C22⋊C4×C67—21no—
264C22⋊C4×C67—22no—
265C22⋊C4×C67—22no—
266C22⋊C4×C67—22no—
267C22⋊C4×C67—21no—
268C22⋊C4×C67—21no—
269C22⋊C4×C67—21no—
270C22⋊C4×C67—21no—
271C22⋊C4×C67—22no—
272C22⋊C4×C67—21no—
273C22⋊C4×C67—21no—
274C22⋊C4×C67—22no—
275C22⋊C4×C67—22no—
276C22⋊C4×C67—22no—
277C22⋊C4×C67—22no—
278C22⋊C4×C67—22no—
279C22⋊C4×C67—22no—
280C22⋊C4×C67—22no—
281C22⋊C4×C67—44no—
282C22⋊C4×C67—44no—
283C22⋊C4×C67—82no—
284C22⋊C4×C67C22⋊C411yescharacteristic
285C22⋊C4×C67C22⋊C411yescharacteristic
286C22⋊C4×C67C22⋊C411yescharacteristic
287C22⋊C4×C67C22⋊C411yescharacteristic
288C22⋊C4×C67C22⋊C412yes—
289C22⋊C4×C67C22⋊C412yes—
290C22⋊C4×C67C22⋊C412yes—
291C22⋊C4×C67C22⋊C412yes—
292C22⋊C4×C67C22⋊C412yes—
293C22⋊C4×C67C22⋊C412yes—
294C22⋊C4×C67C2×D414yes—
295C42×C67—21no—
296C42×C67—21no—
297C42×C67—44no—
298C42×C67—82no—
299C23×C67—21no—
300C23×C67—21no—
301C23×C67—21no—
302C23×C67—21no—
303C23×C67—22no—
304C23×C67—22no—
305C23×C67—24no—
306C23×C67—22no—
307C23×C67—21no—
308C23×C67—21no—
309C23×C67—22no—
310C23×C67—22no—
311C23×C67—21no—
312C23×C67—21no—
313C23×C67—21no—
314C23×C67—21no—
315C23×C67—21no—
316C23×C67—21no—
317C23×C67—42no—
318C23×C67—41no—
319C23×C67—41no—
320C23×C67—41no—
321C23×C67—42no—
322C23×C67—41no—
323C23×C67—41no—
324C23×C67—42no—
325C23×C67—42no—
326C23×C67—42no—
327C23×C67—41no—
328C23×C67—41no—
329C23×C67—42no—
330C23×C67—41no—
331C23×C67—41no—
332C23×C67—41no—
333C23×C67—41no—
334C23×C67—42no—
335C23×C67—81no—
336C23×C67—81no—
337C23×C67—82no—
338C23×C67—82no—
339C23×C67—84no—
340C23×C67—84no—
341C23×C67—84no—
342C23×C67C2×C22⋊C411yescharacteristic
343C23×C67C2×C22⋊C412yes—
344C23×C67C2×C22⋊C411yescharacteristic
345C23×C67C4×D412yes—
346C23×C67C23×C411yescharacteristic
347C23×C67C22×D412yes—
348C23×C67C22×D411yescharacteristic
349C23×C67C2×#4111yescharacteristic
350C23×C67H(5,𝔽2)12yes—
351Q8×C67—44no—
352D4×C67—24no—
353D4×C67—24no—
354D4×C67—44no—
355D4×C67—44no—
356D4×C67—44no—
357D4×C67—42no—
358D4×C67—42no—
359D4×C67—42no—
360D4×C67—42no—
361D4×C67—42no—
362D4×C67—42no—
363D4×C67—82no—
364D4×C67—82no—
365C2×C4×C67—21no—
366C2×C4×C67—21no—
367C2×C4×C67—21no—
368C2×C4×C67—21no—
369C2×C4×C67—21no—
370C2×C4×C67—21no—
371C2×C4×C67—22no—
372C2×C4×C67—22no—
373C2×C4×C67—22no—
374C2×C4×C67—22no—
375C2×C4×C67—21no—
376C2×C4×C67—21no—
377C2×C4×C67—21no—
378C2×C4×C67—21no—
379C2×C4×C67—21no—
380C2×C4×C67—21no—
381C2×C4×C67—21no—
382C2×C4×C67—21no—
383C2×C4×C67—24no—
384C2×C4×C67—42no—
385C2×C4×C67—42no—
386C2×C4×C67—41no—
387C2×C4×C67—41no—
388C2×C4×C67—42no—
389C2×C4×C67—42no—
390C2×C4×C67—42no—
391C2×C4×C67—42no—
392C2×C4×C67—42no—
393C2×C4×C67—42no—
394C2×C4×C67—42no—
395C2×C4×C67—42no—
396C2×C4×C67—41no—
397C2×C4×C67—41no—
398C2×C4×C67—42no—
399C2×C4×C67—42no—
400C2×C4×C67—42no—
401C2×C4×C67—42no—
402C2×C4×C67—42no—
403C2×C4×C67—42no—
404C2×C4×C67—42no—
405C2×C4×C67—42no—
406C2×C4×C67—42no—
407C2×C4×C67—81no—
408C2×C4×C67—81no—
409C2×C4×C67—88no—
410C2×C4×C67C2×C22⋊C411yescharacteristic
411C2×C4×C67C2×C22⋊C411yescharacteristic
412C2×C4×C67C2×C22⋊C412yes—
413C2×C4×C67C2×C22⋊C411yescharacteristic
414C2×C4×C67C2×C22⋊C411yescharacteristic
415C2×C4×C67C2×C22⋊C412yes—
416C2×C4×C67C4×D412yes—
417C22×C67—21no—
418C22×C67—22no—
419C22×C67—21no—
420C22×C67—22no—
421C22×C67—21no—
422C22×C67—21no—
423C22×C67—22no—
424C22×C67—21no—
425C22×C67—22no—
426C22×C67—21no—
427C22×C67—22no—
428C22×C67—22no—
429C22×C67—21no—
430C22×C67—41no—
431C22×C67—41no—
432C22×C67—42no—
433C22×C67—44no—
434C22×C67—44no—
435C22×C67—42no—
436C22×C67—42no—
437C22×C67—42no—
438C22×C67—42no—
439C22×C67—41no—
440C22×C67—41no—
441C22×C67—41no—
442C22×C67—41no—
443C22×C67—41no—
444C22×C67—41no—
445C22×C67—41no—
446C22×C67—41no—
447C22×C67—82no—
448C22×C67—82no—
449C22×C67—81no—
450C22×C67—81no—
451C22×C67—84no—
452C22×C67—81no—
453C22×C67—81no—
454C22×C67—81no—
455C22×C67—81no—
456C22×C67—84no—
457C22×C67#41012yescomplemented
458C22×C67C22×C22⋊C411yescharacteristic
459C22×C67C2×C4×D411yescharacteristic
460C22×C67#51811yescharacteristic
461C22×C67D4212yes—
462C22×C67#54612yes—
463C4×C67—21no—
464C4×C67—21no—
465C4×C67—22no—
466C4×C67—22no—
467C4×C67—21no—
468C4×C67—21no—
469C4×C67—22no—
470C4×C67—44no—
471C4×C67—41no—
472C4×C67—41no—
473C4×C67—41no—
474C4×C67—41no—
475C4×C67—82no—
476C4×C67—82no—
477C4×C67—82no—
478#22405C6711yesmaximal, characteristic, direct product factor, Sylow
479C2×C67—22no—
480C2×C67—22no—
481C2×C67—21no—
482C2×C67—21no—
483C2×C67—22no—
484C2×C67—42no—
485C2×C67—41no—
486C2×C67—42no—
487C2×C67—81no—
488C2×C67—81no—
489C2×C67D4×C22⋊C411yescharacteristic
490C2×C67C2×#41011yescharacteristic
491C2×C67#288311yescharacteristic
492C2×#546C2×C6711yescharacteristic
493C2×#410C2×C6711yescharacteristic, complemented
494C22×#99C2×C6711yescharacteristic, complemented
495#2342C2×C6712yescomplemented
496#1964C2×C6712yescomplemented
497#1899C2×C6712yescomplemented
498#1898C2×C6712yescomplemented
499#1799C2×C6711yescharacteristic, complemented
500#1782C2×C6711yescharacteristic, complemented
501#1781C2×C6711yescharacteristic, complemented
502C4×#99C2×C6711yescharacteristic, complemented
503C67#2240511yescharacteristic, direct product factor, Sylow
504C22×#41C22×C6711yescharacteristic
505C23×D4C22×C6711yescharacteristic
506#546—22no—
507#546—22no—
508#546—22no—
509#546—22no—
510C2×#124C4×C6711yescharacteristic, complemented
511C2×#123C4×C6711yescharacteristic, complemented
512C2×#123C22×C6711yescharacteristic
513C2×C22⋊Q8C4×C6711yescharacteristic, complemented
514C2×#121C4×C6711yescharacteristic, complemented
515C2×#121C4×C6711yescharacteristic, complemented
516C2×#121C22×C6711yescharacteristic
517C2×#120C4×C6711yescharacteristic, complemented
518C2×#120C22×C6711yescharacteristic
519C2×C4×D4C4×C6711yescharacteristic, complemented
520C2×C4×D4C22×C6711yescharacteristic
521C2×#117C22×C6712yescomplemented
522C22×C22⋊C4C4×C6711yescharacteristic, complemented
523C22×C22⋊C4C22×C6712yes—
524C22×C22⋊C4C22×C6711yescharacteristic
525#410—24no—
526C2×#99—24no—
527C2×#99C22×C6711yescharacteristic
528C2×#99C22×C6711yescharacteristic
529C2×#99C22×C6712yes—
530C2×#99C22×C6711yescharacteristic
531C2×#99C22×C6712yes—
532C2×#99C22×C6711yescharacteristic
533C2×#99C22×C6712yescomplemented
534C2×#99C22×C6712yescomplemented
535#388—22no—
536#388—22no—
537#385—22no—
538#381C22×C6712yescomplemented
539#380C22×C6712yescomplemented
540#379C22×C6712yes—
541C4×C22⋊C4—22no—
542C4×C22⋊C4C22×C6712yescomplemented
543#342C22×C6712yescomplemented
544#342C22×C6712yescomplemented
545C25C2×C4×C6711yescharacteristic
546C25C23×C6711yescharacteristic
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—42no—
552C22×Q8C2×C4×C6711yescharacteristic, complemented
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4C2×C4×C6711yescharacteristic
559C22×D4C2×C4×C6711yescharacteristic
560C22×D4C2×C4×C6711yescharacteristic
561C22×D4C2×C4×C6711yescharacteristic
562C22×D4C2×C4×C6711yescharacteristic, complemented
563C22×D4C2×C4×C6711yescharacteristic, complemented
564C22×D4C23×C6711yescharacteristic
565C22×D4C23×C6711yescharacteristic
566C22×D4C23×C6711yescharacteristic
567C23×C4—22no—
568C23×C4C2×C4×C6711yescharacteristic
569C23×C4C2×C4×C6711yescharacteristic, complemented
570C23×C4C2×C4×C6711yescharacteristic, complemented
571C23×C4C2×C4×C6711yescharacteristic, complemented
572C23×C4C23×C6711yescharacteristic
573C23×C4C23×C6711yescharacteristic
574#124—22no—
575#124—22no—
576#123—22no—
577#123—22no—
578#123—22no—
579#123—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#120—22no—
589#120—22no—
590#120—22no—
591#120—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598#117—24no—
599#117—42no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
603C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
604C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
605C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—24no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—42no—
615C2×C22⋊C4C2×C4×C6711yescharacteristic
616C2×C22⋊C4C2×C4×C6711yescharacteristic
617C2×C22⋊C4C2×C4×C6711yescharacteristic
618C2×C22⋊C4C2×C4×C6711yescharacteristic
619C2×C22⋊C4C2×C4×C6711yescharacteristic
620C2×C22⋊C4C2×C4×C6711yescharacteristic
621C2×C22⋊C4C2×C4×C6711yescharacteristic, complemented
622C2×C22⋊C4C2×C4×C6711yescharacteristic, complemented
623C2×C22⋊C4C2×C4×C6711yescharacteristic, complemented
624C2×C22⋊C4C2×C4×C6711yescharacteristic, complemented
625C2×C22⋊C4C2×C4×C6711yescharacteristic, complemented
626C2×C22⋊C4D4×C6712yes—
627C2×C22⋊C4D4×C6712yes—
628C2×C22⋊C4D4×C6712yes—
629C2×C22⋊C4D4×C6712yes—
630C2×C22⋊C4C23×C6712yes—
631C2×C22⋊C4C23×C6712yes—
632C2×C22⋊C4C23×C6712yes—
633C2×C22⋊C4C23×C6711yescharacteristic
634C2×C22⋊C4C23×C6712yes—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42C2×C4×C6711yescharacteristic, complemented
638#99—22no—
639#99—22no—
640#99—22no—
641#99—24no—
642#99—24no—
643#99—42no—
644#99—42no—
645#99D4×C6714yescomplemented
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C22×C4×C6711yescharacteristic
662C24C22×C4×C6711yescharacteristic
663C24C22×C4×C6711yescharacteristic
664C24C22×C4×C6711yescharacteristic
665C24C22×C4×C6711yescharacteristic
666C24C2×D4×C6712yes—
667C24C2×D4×C6712yes—
668C24C24×C6711yescharacteristic
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C2×D4×C6712yes—
707C2×D4#41×C6712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—81no—
732C22×C4—82no—
733C22×C4—81no—
734C22×C4C22×C4×C6711yescharacteristic
735C22×C4C22×C4×C6711yescharacteristic
736C22×C4C22×C4×C6711yescharacteristic
737C22×C4C22×C4×C6711yescharacteristic
738C22×C4C22×C4×C6711yescharacteristic
739C22×C4C22×C4×C6711yescharacteristic
740C22×C4C22×C4×C6711yescharacteristic
741C22×C4C22×C4×C6711yescharacteristic
742C22×C4C22×C4×C6711yescharacteristic
743C22×C4C2×D4×C6712yes—
744C22×C4C2×D4×C6712yes—
745C22×C4C2×D4×C6712yes—
746C22×C4C2×D4×C6712yes—
747C4⋊C4—22no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—44no—
753C4⋊C4—82no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—22no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C22⋊C4C22⋊C4×C6711yescharacteristic
777C22⋊C4C22⋊C4×C6711yescharacteristic
778C22⋊C4C22⋊C4×C6711yescharacteristic
779C22⋊C4C22⋊C4×C6711yescharacteristic
780C22⋊C4C22⋊C4×C6712yes—
781C22⋊C4C22⋊C4×C6712yes—
782C22⋊C4C22⋊C4×C6712yes—
783C22⋊C4C22⋊C4×C6712yes—
784C22⋊C4C22⋊C4×C6712yes—
785C22⋊C4C22⋊C4×C6712yes—
786C22⋊C4C2×D4×C6714yes—
787C42—21no—
788C42—21no—
789C42—44no—
790C42—82no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—22no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—42no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—81no—
828C23—81no—
829C23—82no—
830C23—82no—
831C23—84no—
832C23—84no—
833C23—84no—
834C23C2×C22⋊C4×C6711yescharacteristic
835C23C2×C22⋊C4×C6712yes—
836C23C2×C22⋊C4×C6711yescharacteristic
837C23C4×D4×C6712yes—
838C23C23×C4×C6711yescharacteristic
839C23C22×D4×C6712yes—
840C23C22×D4×C6711yescharacteristic
841C23C2×#41×C6711yescharacteristic
842C23H(5,𝔽2)×C6712yes—
843Q8—44no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—44no—
849D4—42no—
850D4—42no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—82no—
856D4—82no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—24no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—88no—
902C2×C4C2×C22⋊C4×C6711yescharacteristic
903C2×C4C2×C22⋊C4×C6711yescharacteristic
904C2×C4C2×C22⋊C4×C6712yes—
905C2×C4C2×C22⋊C4×C6711yescharacteristic
906C2×C4C2×C22⋊C4×C6711yescharacteristic
907C2×C4C2×C22⋊C4×C6712yes—
908C2×C4C4×D4×C6712yes—
909C22—21no—
910C22—22no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—21no—
915C22—22no—
916C22—21no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—82no—
940C22—82no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—84no—
949C22#410×C6712yescomplemented
950C22C22×C22⋊C4×C6711yescharacteristic
951C22C2×C4×D4×C6711yescharacteristic
952C22#518×C6711yescharacteristic
953C22D42×C6712yes—
954C22#546×C6712yes—
955C4—21no—
956C4—21no—
957C4—22no—
958C4—22no—
959C4—21no—
960C4—21no—
961C4—22no—
962C4—44no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—41no—
967C4—82no—
968C4—82no—
969C4—82no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—81no—
980C2D4×C22⋊C4×C6711yescharacteristic
981C2C2×#410×C6711yescharacteristic
982C2C67×#288311yescharacteristic
subgroupG/H
center, socleC22×C67C22×C22⋊C4
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC2×#546×C67C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ C22×C22⋊C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#410×C67C2semidirect
3. C22×#99×C67C2semidirect
4. C67×#2342C2semidirect
5. C67×#1964C2semidirect
6. C67×#1899C2semidirect
7. C67×#1898C2semidirect
8. C67×#1799C2semidirect
9. C67×#1782C2semidirect
10. C67×#1781C2semidirect
11. C4×#99×C67C2semidirect
18. C2×#124×C67C4semidirect
19. C2×#123×C67C4semidirect
21. C2×C22⋊Q8×C67C4semidirect
22. C2×#121×C67C4semidirect
23. C2×#121×C67C4semidirect
25. C2×#120×C67C4semidirect
27. C2×C4×D4×C67C4semidirect
29. C2×#117×C67C22semidirect
30. C22×C22⋊C4×C67C4semidirect
41. C2×#99×C67C22semidirect
42. C2×#99×C67C22semidirect
46. #381×C67C22semidirect
47. #380×C67C22semidirect
50. C4×C22⋊C4×C67C22semidirect
51. #342×C67C22semidirect
52. #342×C67C22semidirect
60. C22×Q8×C67C2×C4semidirect
70. C22×D4×C67C2×C4semidirect
71. C22×D4×C67C2×C4semidirect
77. C23×C4×C67C2×C4semidirect
78. C23×C4×C67C2×C4semidirect
79. C23×C4×C67C2×C4semidirect
110. C2×C4⋊C4×C67C2×C4semidirect
111. C2×C4⋊C4×C67C2×C4semidirect
112. C2×C4⋊C4×C67C2×C4semidirect
113. C2×C4⋊C4×C67C2×C4semidirect
129. C2×C22⋊C4×C67C2×C4semidirect
130. C2×C22⋊C4×C67C2×C4semidirect
131. C2×C22⋊C4×C67C2×C4semidirect
132. C2×C22⋊C4×C67C2×C4semidirect
133. C2×C22⋊C4×C67C2×C4semidirect
145. C2×C42×C67C2×C4semidirect
153. #99×C67D4semidirect
457. C22×C67#410semidirect
478. #22405C67direct (N × H)
493. C2×#410C2×C67semidirect
494. C22×#99C2×C67semidirect
495. #2342C2×C67semidirect
496. #1964C2×C67semidirect
497. #1899C2×C67semidirect
498. #1898C2×C67semidirect
499. #1799C2×C67semidirect
500. #1782C2×C67semidirect
501. #1781C2×C67semidirect
502. C4×#99C2×C67semidirect
503. C67#22405direct (N × H)
510. C2×#124C4×C67semidirect
511. C2×#123C4×C67semidirect
513. C2×C22⋊Q8C4×C67semidirect
514. C2×#121C4×C67semidirect
515. C2×#121C4×C67semidirect
517. C2×#120C4×C67semidirect
519. C2×C4×D4C4×C67semidirect
521. C2×#117C22×C67semidirect
522. C22×C22⋊C4C4×C67semidirect
533. C2×#99C22×C67semidirect
534. C2×#99C22×C67semidirect
538. #381C22×C67semidirect
539. #380C22×C67semidirect
542. C4×C22⋊C4C22×C67semidirect
543. #342C22×C67semidirect
544. #342C22×C67semidirect
552. C22×Q8C2×C4×C67semidirect
562. C22×D4C2×C4×C67semidirect
563. C22×D4C2×C4×C67semidirect
569. C23×C4C2×C4×C67semidirect
570. C23×C4C2×C4×C67semidirect
571. C23×C4C2×C4×C67semidirect
602. C2×C4⋊C4C2×C4×C67semidirect
603. C2×C4⋊C4C2×C4×C67semidirect
604. C2×C4⋊C4C2×C4×C67semidirect
605. C2×C4⋊C4C2×C4×C67semidirect
621. C2×C22⋊C4C2×C4×C67semidirect
622. C2×C22⋊C4C2×C4×C67semidirect
623. C2×C22⋊C4C2×C4×C67semidirect
624. C2×C22⋊C4C2×C4×C67semidirect
625. C2×C22⋊C4C2×C4×C67semidirect
637. C2×C42C2×C4×C67semidirect
645. #99D4×C67semidirect
949. C22#410×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C672
C2×#410×C672
C22×#99×C672
C67×#23422
C67×#19642
C67×#18992
C67×#18982
C67×#17992
C67×#17822
C67×#17812
C4×#99×C672
#2240567