Finite Group Databasebeta

← C67×#21874 #30701125

Subgroups — C67×#21874 #30701125

Order 17152.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C67C211yesmaximal, characteristic
2C67×#2280C211yesmaximal, characteristic, complemented
3C2×#380×C67C211yesmaximal, characteristic, complemented
4C67×#1996C212yesmaximal, complemented
5C67×#1964C212yesmaximal, complemented
6C67×#1898C214yesmaximal, complemented
7C67×#1799C214yesmaximal, complemented
8C22×#41×C67C411yescharacteristic, complemented
9C24×C4×C67C2211yescharacteristic
10#525×C67—21no—
11#525×C67—21no—
12#525×C67—21no—
13#525×C67—21no—
14#525×C67—21no—
15#525×C67—21no—
16#525×C67—21no—
17#525×C67—21no—
18C2×#123×C67C412yescomplemented
19C2×C22⋊Q8×C67C411yescharacteristic, complemented
20C2×C22⋊Q8×C67C2211yescharacteristic
21C2×#121×C67C411yescharacteristic, complemented
22C2×#121×C67C2211yescharacteristic
23C2×#120×C67C2212yes—
24C2×C4×D4×C67C412yescomplemented
25C2×C4×D4×C67C2212yes—
26C2×#117×C67—21no—
27C2×#117×C67C411yescharacteristic, complemented
28C22×C4⋊C4×C67—21no—
29C22×C22⋊C4×C67C2212yes—
30C2×#99×C67C2218yes—
31#381×C67—21no—
32#380×C67—21no—
33#380×C67—21no—
34#380×C67—21no—
35#380×C67C2212yes—
36#380×C67C2212yes—
37#380×C67C2212yes—
38#379×C67C2212yes—
39C4×C22⋊C4×C67—21no—
40C4×C22⋊C4×C67C2212yes—
41C2×#95×C67—21no—
42#342×C67C2218yes—
43C25×C67C2311yescharacteristic
44C2×#41×C67—21no—
45C2×#41×C67—21no—
46C2×#41×C67—21no—
47C2×#41×C67—21no—
48C2×#41×C67—44no—
49C22×Q8×C67C2×C411yescharacteristic, complemented
50C22×D4×C67C2×C412yes—
51C22×D4×C67C2×C412yes—
52C22×D4×C67C2×C411yescharacteristic, complemented
53C22×D4×C67C2312yes—
54C23×C4×C67—22no—
55C23×C4×C67—44no—
56C23×C4×C67C2×C411yescharacteristic
57C23×C4×C67C2×C411yescharacteristic
58C23×C4×C67C2×C411yescharacteristic
59C23×C4×C67C2×C411yescharacteristic
60C23×C4×C67C2×C412yescomplemented
61C23×C4×C67D411yescharacteristic
62C23×C4×C67D411yescharacteristic
63C23×C4×C67D411yescharacteristic
64C23×C4×C67D411yescharacteristic
65C23×C4×C67D411yescharacteristic
66C23×C4×C67D411yescharacteristic
67C23×C4×C67D411yescharacteristic
68C23×C4×C67D411yescharacteristic
69C23×C4×C67C2311yescharacteristic
70C23×C4×C67C2311yescharacteristic
71#123×C67—22no—
72#123×C67—22no—
73#123×C67—22no—
74#123×C67—22no—
75C22⋊Q8×C67—21no—
76C22⋊Q8×C67—21no—
77C22⋊Q8×C67—21no—
78C22⋊Q8×C67—21no—
79C22⋊Q8×C67—21no—
80C22⋊Q8×C67—21no—
81C22⋊Q8×C67—21no—
82C22⋊Q8×C67—21no—
83#121×C67—21no—
84#121×C67—21no—
85#121×C67—21no—
86#121×C67—21no—
87#121×C67—21no—
88#121×C67—21no—
89#121×C67—21no—
90#121×C67—21no—
91#120×C67—22no—
92#120×C67—22no—
93#120×C67—22no—
94#120×C67—22no—
95C4×D4×C67—22no—
96C4×D4×C67—22no—
97C4×D4×C67—22no—
98C4×D4×C67—22no—
99C4×D4×C67—22no—
100C4×D4×C67—22no—
101C4×D4×C67—22no—
102C4×D4×C67—22no—
103#117×C67—21no—
104#117×C67—21no—
105#117×C67—21no—
106#117×C67—21no—
107#117×C67—44no—
108C2×C4⋊C4×C67—22no—
109C2×C4⋊C4×C67—22no—
110C2×C4⋊C4×C67—22no—
111C2×C4⋊C4×C67—44no—
112C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C67C2×C412yescomplemented
115C2×C4⋊C4×C67C2×C412yescomplemented
116C2×C22⋊C4×C67—22no—
117C2×C22⋊C4×C67—22no—
118C2×C22⋊C4×C67—22no—
119C2×C22⋊C4×C67—44no—
120C2×C22⋊C4×C67C2×C412yes—
121C2×C22⋊C4×C67C2×C412yes—
122C2×C22⋊C4×C67C2×C412yescomplemented
123C2×C22⋊C4×C67C2×C412yescomplemented
124C2×C22⋊C4×C67C2314yes—
125C2×C22⋊C4×C67C2314yes—
126C2×C22⋊C4×C67C2312yes—
127C2×C42×C67—22no—
128C2×C42×C67C2×C412yescomplemented
129#99×C67—48no—
130#95×C67—22no—
131#95×C67—22no—
132#95×C67—22no—
133#95×C67—22no—
134C24×C67—22no—
135C24×C67—22no—
136C24×C67—42no—
137C24×C67—42no—
138C24×C67C22×C411yescharacteristic
139C24×C67C22×C411yescharacteristic
140C24×C67C22×C412yes—
141C24×C67C2×D411yescharacteristic
142C24×C67C2×D411yescharacteristic
143C24×C67C2×D411yescharacteristic
144C24×C67C2×D411yescharacteristic
145C24×C67C2411yescharacteristic
146#41×C67—44no—
147#41×C67—44no—
148#41×C67—44no—
149#41×C67—44no—
150C2×Q8×C67—21no—
151C2×Q8×C67—21no—
152C2×Q8×C67—42no—
153C2×D4×C67—22no—
154C2×D4×C67—22no—
155C2×D4×C67—22no—
156C2×D4×C67—22no—
157C2×D4×C67—22no—
158C2×D4×C67—22no—
159C2×D4×C67—24no—
160C2×D4×C67—24no—
161C2×D4×C67—21no—
162C2×D4×C67—21no—
163C2×D4×C67—42no—
164C2×D4×C67—44no—
165C2×D4×C67—44no—
166C22×C4×C67—24no—
167C22×C4×C67—24no—
168C22×C4×C67—24no—
169C22×C4×C67—22no—
170C22×C4×C67—22no—
171C22×C4×C67—24no—
172C22×C4×C67—24no—
173C22×C4×C67—42no—
174C22×C4×C67—42no—
175C22×C4×C67—42no—
176C22×C4×C67—42no—
177C22×C4×C67—42no—
178C22×C4×C67—42no—
179C22×C4×C67—42no—
180C22×C4×C67—42no—
181C22×C4×C67—42no—
182C22×C4×C67—42no—
183C22×C4×C67—42no—
184C22×C4×C67—44no—
185C22×C4×C67—44no—
186C22×C4×C67—44no—
187C22×C4×C67—44no—
188C22×C4×C67C22⋊C411yescharacteristic
189C22×C4×C67C22⋊C411yescharacteristic
190C22×C4×C67C22⋊C411yescharacteristic
191C22×C4×C67C22⋊C411yescharacteristic
192C22×C4×C67C22⋊C411yescharacteristic
193C22×C4×C67C22⋊C411yescharacteristic
194C22×C4×C67C22⋊C411yescharacteristic
195C22×C4×C67C22⋊C411yescharacteristic
196C22×C4×C67C22⋊C411yescharacteristic
197C22×C4×C67C22⋊C411yescharacteristic
198C22×C4×C67C22⋊C411yescharacteristic
199C22×C4×C67C22⋊C411yescharacteristic
200C22×C4×C67C22⋊C411yescharacteristic
201C22×C4×C67C22⋊C411yescharacteristic
202C22×C4×C67C22⋊C411yescharacteristic
203C22×C4×C67C22⋊C411yescharacteristic
204C22×C4×C67C22×C412yes—
205C22×C4×C67C22×C411yescharacteristic
206C22×C4×C67C22×C411yescharacteristic
207C22×C4×C67C22×C412yes—
208C22×C4×C67C22×C412yes—
209C22×C4×C67C22×C411yescharacteristic
210C22×C4×C67C22×C411yescharacteristic
211C22×C4×C67C2×D411yescharacteristic
212C22×C4×C67C2×D411yescharacteristic
213C22×C4×C67C2×D411yescharacteristic
214C22×C4×C67C2×D411yescharacteristic
215C22×C4×C67C2×D411yescharacteristic
216C22×C4×C67C2×D411yescharacteristic
217C22×C4×C67C2×D411yescharacteristic
218C22×C4×C67C2×D411yescharacteristic
219C4⋊C4×C67—21no—
220C4⋊C4×C67—21no—
221C4⋊C4×C67—21no—
222C4⋊C4×C67—21no—
223C4⋊C4×C67—22no—
224C4⋊C4×C67—22no—
225C4⋊C4×C67—22no—
226C4⋊C4×C67—22no—
227C4⋊C4×C67—44no—
228C4⋊C4×C67—44no—
229C4⋊C4×C67—44no—
230C22⋊C4×C67—22no—
231C22⋊C4×C67—22no—
232C22⋊C4×C67—22no—
233C22⋊C4×C67—22no—
234C22⋊C4×C67—22no—
235C22⋊C4×C67—22no—
236C22⋊C4×C67—22no—
237C22⋊C4×C67—22no—
238C22⋊C4×C67—22no—
239C22⋊C4×C67—22no—
240C22⋊C4×C67—28no—
241C22⋊C4×C67—24no—
242C22⋊C4×C67—24no—
243C22⋊C4×C67—44no—
244C22⋊C4×C67—44no—
245C22⋊C4×C67—44no—
246C42×C67—22no—
247C42×C67—22no—
248C42×C67—44no—
249C23×C67—21no—
250C23×C67—21no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—22no—
255C23×C67—21no—
256C23×C67—21no—
257C23×C67—22no—
258C23×C67—22no—
259C23×C67—22no—
260C23×C67—22no—
261C23×C67—22no—
262C23×C67—22no—
263C23×C67—22no—
264C23×C67—24no—
265C23×C67—41no—
266C23×C67—41no—
267C23×C67—41no—
268C23×C67—41no—
269C23×C67—41no—
270C23×C67—41no—
271C23×C67—41no—
272C23×C67—41no—
273C23×C67—48no—
274C23×C67—48no—
275C23×C67—42no—
276C23×C67—42no—
277C23×C67C2×C22⋊C411yescharacteristic
278C23×C67C2×C22⋊C411yescharacteristic
279C23×C67C2×C22⋊C411yescharacteristic
280C23×C67C2×C22⋊C411yescharacteristic
281C23×C67C23×C411yescharacteristic
282C23×C67C22×D411yescharacteristic
283C23×C67C22×D411yescharacteristic
284C23×C67H(5,𝔽2)12yes—
285C23×C672−1+412yes—
286Q8×C67—42no—
287Q8×C67—42no—
288D4×C67—42no—
289D4×C67—44no—
290D4×C67—44no—
291D4×C67—42no—
292D4×C67—42no—
293D4×C67—44no—
294D4×C67—44no—
295D4×C67—44no—
296D4×C67—42no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—24no—
316C2×C4×C67—41no—
317C2×C4×C67—41no—
318C2×C4×C67—41no—
319C2×C4×C67—41no—
320C2×C4×C67—41no—
321C2×C4×C67—41no—
322C2×C4×C67—41no—
323C2×C4×C67—41no—
324C2×C4×C67—41no—
325C2×C4×C67—41no—
326C2×C4×C67—41no—
327C2×C4×C67—41no—
328C2×C4×C67—44no—
329C2×C4×C67—44no—
330C2×C4×C67—42no—
331C2×C4×C67—42no—
332C2×C4×C67—44no—
333C2×C4×C67—44no—
334C2×C4×C67—44no—
335C2×C4×C67—44no—
336C2×C4×C67—44no—
337C2×C4×C67—44no—
338C2×C4×C67—88no—
339C2×C4×C67#9914yescomplemented
340C2×C4×C67C2×C22⋊C411yescharacteristic
341C2×C4×C67C2×C22⋊C411yescharacteristic
342C2×C4×C67C2×C22⋊C411yescharacteristic
343C2×C4×C67C2×C22⋊C411yescharacteristic
344C2×C4×C67C2×C22⋊C411yescharacteristic
345C2×C4×C67C2×C22⋊C411yescharacteristic
346C2×C4×C67C2×C22⋊C411yescharacteristic
347C2×C4×C67C2×C22⋊C411yescharacteristic
348C22×C67—24no—
349C22×C67—24no—
350C22×C67—21no—
351C22×C67—21no—
352C22×C67—21no—
353C22×C67—21no—
354C22×C67—21no—
355C22×C67—21no—
356C22×C67—21no—
357C22×C67—21no—
358C22×C67—21no—
359C22×C67—21no—
360C22×C67—21no—
361C22×C67—21no—
362C22×C67—21no—
363C22×C67—21no—
364C22×C67—21no—
365C22×C67—21no—
366C22×C67—42no—
367C22×C67—42no—
368C22×C67—44no—
369C22×C67—44no—
370C22×C67—44no—
371C22×C67—44no—
372C22×C67—42no—
373C22×C67—42no—
374C22×C67—42no—
375C22×C67—42no—
376C22×C67—42no—
377C22×C67—84no—
378C22×C67C2×#9912yes—
379C22×C67#41012yes—
380C22×C67C22×C22⋊C411yescharacteristic
381C22×C67#52012yes—
382C22×C67#53511yescharacteristic
383C22×C67#53611yescharacteristic
384C22×C67#53712yes—
385C4×C67—21no—
386C4×C67—21no—
387C4×C67—21no—
388C4×C67—21no—
389C4×C67—21no—
390C4×C67—21no—
391C4×C67—42no—
392C4×C67—42no—
393C4×C67—42no—
394C4×C67—84no—
395C4×C67—84no—
396C4×C67C2×#9912yes—
397C4×C67C2×#9912yes—
398#21874C6711yesmaximal, characteristic, direct product factor, Sylow
399C2×C67—21no—
400C2×C67—22no—
401C2×C67—21no—
402C2×C67—22no—
403C2×C67—22no—
404C2×C67—22no—
405C2×C67—41no—
406C2×C67—41no—
407C2×C67—82no—
408C2×C67#231111yescharacteristic
409C2×C67C22×#9911yescharacteristic
410C2×C67C2×#41011yescharacteristic
411C2×#525C2×C6711yescharacteristic
412#2280C2×C6711yescharacteristic, complemented
413C2×#380C2×C6711yescharacteristic, complemented
414#1996C2×C6712yescomplemented
415#1964C2×C6712yescomplemented
416#1898C2×C6714yescomplemented
417#1799C2×C6714yescomplemented
418C67#2187411yescharacteristic, direct product factor, Sylow
419C22×#41C4×C6711yescharacteristic, complemented
420C24×C4C22×C6711yescharacteristic
421#525—21no—
422#525—21no—
423#525—21no—
424#525—21no—
425#525—21no—
426#525—21no—
427#525—21no—
428#525—21no—
429C2×#123C4×C6712yescomplemented
430C2×C22⋊Q8C4×C6711yescharacteristic, complemented
431C2×C22⋊Q8C22×C6711yescharacteristic
432C2×#121C4×C6711yescharacteristic, complemented
433C2×#121C22×C6711yescharacteristic
434C2×#120C22×C6712yes—
435C2×C4×D4C4×C6712yescomplemented
436C2×C4×D4C22×C6712yes—
437C2×#117—21no—
438C2×#117C4×C6711yescharacteristic, complemented
439C22×C4⋊C4—21no—
440C22×C22⋊C4C22×C6712yes—
441C2×#99C22×C6718yes—
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380C22×C6712yes—
447#380C22×C6712yes—
448#380C22×C6712yes—
449#379C22×C6712yes—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C22×C6712yes—
452C2×#95—21no—
453#342C22×C6718yes—
454C25C23×C6711yescharacteristic
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—44no—
460C22×Q8C2×C4×C6711yescharacteristic, complemented
461C22×D4C2×C4×C6712yes—
462C22×D4C2×C4×C6712yes—
463C22×D4C2×C4×C6711yescharacteristic, complemented
464C22×D4C23×C6712yes—
465C23×C4—22no—
466C23×C4—44no—
467C23×C4C2×C4×C6711yescharacteristic
468C23×C4C2×C4×C6711yescharacteristic
469C23×C4C2×C4×C6711yescharacteristic
470C23×C4C2×C4×C6711yescharacteristic
471C23×C4C2×C4×C6712yescomplemented
472C23×C4D4×C6711yescharacteristic
473C23×C4D4×C6711yescharacteristic
474C23×C4D4×C6711yescharacteristic
475C23×C4D4×C6711yescharacteristic
476C23×C4D4×C6711yescharacteristic
477C23×C4D4×C6711yescharacteristic
478C23×C4D4×C6711yescharacteristic
479C23×C4D4×C6711yescharacteristic
480C23×C4C23×C6711yescharacteristic
481C23×C4C23×C6711yescharacteristic
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
524C2×C4⋊C4C2×C4×C6711yescharacteristic, complemented
525C2×C4⋊C4C2×C4×C6712yescomplemented
526C2×C4⋊C4C2×C4×C6712yescomplemented
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—44no—
531C2×C22⋊C4C2×C4×C6712yes—
532C2×C22⋊C4C2×C4×C6712yes—
533C2×C22⋊C4C2×C4×C6712yescomplemented
534C2×C22⋊C4C2×C4×C6712yescomplemented
535C2×C22⋊C4C23×C6714yes—
536C2×C22⋊C4C23×C6714yes—
537C2×C22⋊C4C23×C6712yes—
538C2×C42—22no—
539C2×C42C2×C4×C6712yescomplemented
540#99—48no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×C4×C6711yescharacteristic
550C24C22×C4×C6711yescharacteristic
551C24C22×C4×C6712yes—
552C24C2×D4×C6711yescharacteristic
553C24C2×D4×C6711yescharacteristic
554C24C2×D4×C6711yescharacteristic
555C24C2×D4×C6711yescharacteristic
556C24C24×C6711yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C22⋊C4×C6711yescharacteristic
600C22×C4C22⋊C4×C6711yescharacteristic
601C22×C4C22⋊C4×C6711yescharacteristic
602C22×C4C22⋊C4×C6711yescharacteristic
603C22×C4C22⋊C4×C6711yescharacteristic
604C22×C4C22⋊C4×C6711yescharacteristic
605C22×C4C22⋊C4×C6711yescharacteristic
606C22×C4C22⋊C4×C6711yescharacteristic
607C22×C4C22⋊C4×C6711yescharacteristic
608C22×C4C22⋊C4×C6711yescharacteristic
609C22×C4C22⋊C4×C6711yescharacteristic
610C22×C4C22⋊C4×C6711yescharacteristic
611C22×C4C22⋊C4×C6711yescharacteristic
612C22×C4C22⋊C4×C6711yescharacteristic
613C22×C4C22⋊C4×C6711yescharacteristic
614C22×C4C22⋊C4×C6711yescharacteristic
615C22×C4C22×C4×C6712yes—
616C22×C4C22×C4×C6711yescharacteristic
617C22×C4C22×C4×C6711yescharacteristic
618C22×C4C22×C4×C6712yes—
619C22×C4C22×C4×C6712yes—
620C22×C4C22×C4×C6711yescharacteristic
621C22×C4C22×C4×C6711yescharacteristic
622C22×C4C2×D4×C6711yescharacteristic
623C22×C4C2×D4×C6711yescharacteristic
624C22×C4C2×D4×C6711yescharacteristic
625C22×C4C2×D4×C6711yescharacteristic
626C22×C4C2×D4×C6711yescharacteristic
627C22×C4C2×D4×C6711yescharacteristic
628C22×C4C2×D4×C6711yescharacteristic
629C22×C4C2×D4×C6711yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C42—22no—
658C42—22no—
659C42—44no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊C4×C6711yescharacteristic
689C23C2×C22⋊C4×C6711yescharacteristic
690C23C2×C22⋊C4×C6711yescharacteristic
691C23C2×C22⋊C4×C6711yescharacteristic
692C23C23×C4×C6711yescharacteristic
693C23C22×D4×C6711yescharacteristic
694C23C22×D4×C6711yescharacteristic
695C23H(5,𝔽2)×C6712yes—
696C232−1+4×C6712yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—88no—
750C2×C4#99×C6714yescomplemented
751C2×C4C2×C22⋊C4×C6711yescharacteristic
752C2×C4C2×C22⋊C4×C6711yescharacteristic
753C2×C4C2×C22⋊C4×C6711yescharacteristic
754C2×C4C2×C22⋊C4×C6711yescharacteristic
755C2×C4C2×C22⋊C4×C6711yescharacteristic
756C2×C4C2×C22⋊C4×C6711yescharacteristic
757C2×C4C2×C22⋊C4×C6711yescharacteristic
758C2×C4C2×C22⋊C4×C6711yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#99×C6712yes—
790C22#410×C6712yes—
791C22C22×C22⋊C4×C6711yescharacteristic
792C22#520×C6712yes—
793C22#535×C6711yescharacteristic
794C22#536×C6711yescharacteristic
795C22#537×C6712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×#99×C6712yes—
808C4C2×#99×C6712yes—
809C2—21no—
810C2—22no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C67×#231111yescharacteristic
819C2C22×#99×C6711yescharacteristic
820C2C2×#410×C6711yescharacteristic
subgroupG/H
center, socleC22×C67C22×C22⋊C4
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC2×#525×C67C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ C24×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C67×#2280C2semidirect
3. C2×#380×C67C2semidirect
4. C67×#1996C2semidirect
5. C67×#1964C2semidirect
6. C67×#1898C2semidirect
7. C67×#1799C2semidirect
8. C22×#41×C67C4semidirect
18. C2×#123×C67C4semidirect
19. C2×C22⋊Q8×C67C4semidirect
21. C2×#121×C67C4semidirect
24. C2×C4×D4×C67C4semidirect
27. C2×#117×C67C4semidirect
49. C22×Q8×C67C2×C4semidirect
52. C22×D4×C67C2×C4semidirect
60. C23×C4×C67C2×C4semidirect
112. C2×C4⋊C4×C67C2×C4semidirect
113. C2×C4⋊C4×C67C2×C4semidirect
114. C2×C4⋊C4×C67C2×C4semidirect
115. C2×C4⋊C4×C67C2×C4semidirect
122. C2×C22⋊C4×C67C2×C4semidirect
123. C2×C22⋊C4×C67C2×C4semidirect
128. C2×C42×C67C2×C4semidirect
339. C2×C4×C67#99semidirect
398. #21874C67direct (N × H)
412. #2280C2×C67semidirect
413. C2×#380C2×C67semidirect
414. #1996C2×C67semidirect
415. #1964C2×C67semidirect
416. #1898C2×C67semidirect
417. #1799C2×C67semidirect
418. C67#21874direct (N × H)
419. C22×#41C4×C67semidirect
429. C2×#123C4×C67semidirect
430. C2×C22⋊Q8C4×C67semidirect
432. C2×#121C4×C67semidirect
435. C2×C4×D4C4×C67semidirect
438. C2×#117C4×C67semidirect
460. C22×Q8C2×C4×C67semidirect
463. C22×D4C2×C4×C67semidirect
471. C23×C4C2×C4×C67semidirect
523. C2×C4⋊C4C2×C4×C67semidirect
524. C2×C4⋊C4C2×C4×C67semidirect
525. C2×C4⋊C4C2×C4×C67semidirect
526. C2×C4⋊C4C2×C4×C67semidirect
533. C2×C22⋊C4C2×C4×C67semidirect
534. C2×C22⋊C4C2×C4×C67semidirect
539. C2×C42C2×C4×C67semidirect
750. C2×C4#99×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C672
C67×#22802
C2×#380×C672
C67×#19962
C67×#19642
C67×#18982
C67×#17992
#2187467