Finite Group Databasebeta

← C67×#14043 #30693294

Subgroups — C67×#14043 #30693294

Order 17152.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C67C211yesmaximal, characteristic
2C2×#389×C67C212yesmaximal, complemented
3C2×#385×C67C211yesmaximal, characteristic
4C2×#385×C67C211yesmaximal, characteristic
5C2×#385×C67C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
7C67×#1444C212yesmaximal, complemented
8C67×#1441C212yesmaximal, complemented
9C67×#1436C212yesmaximal, complemented
10C67×C22⋊#95C211yesmaximal, characteristic
11C67×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C67C2211yescharacteristic
13C24×C4×C67C2211yescharacteristic
14C24×C4×C67C2211yescharacteristic
15C22×C4⋊C4×C67—24no—
16C22×C4⋊C4×C67—28no—
17C22×C4⋊C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2212yes—
19C22×C4⋊C4×C67C2212yes—
20C22×C4⋊C4×C67C2212yes—
21C22×C4⋊C4×C67C2212yes—
22C22×C4⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C22⋊C4×C67C2211yescharacteristic
26C22×C22⋊C4×C67C2211yescharacteristic
27C22×C42×C67C2212yes—
28#389×C67—28no—
29#385×C67—24no—
30#385×C67—24no—
31#385×C67C418yescomplemented
32C4×C22⋊C4×C67—24no—
33C2×#95×C67C2212yes—
34C2×#95×C67C2211yescharacteristic
35C2×#95×C67C2212yes—
36C2×#95×C67C2211yescharacteristic
37C2×#95×C67C2212yes—
38C2×#95×C67C2212yes—
39C2×#95×C67C2212yes—
40C2×#95×C67C2212yes—
41C2×#95×C67C2212yes—
42C25×C67C2311yescharacteristic
43C23×C4×C67—22no—
44C23×C4×C67—22no—
45C23×C4×C67—24no—
46C23×C4×C67—24no—
47C23×C4×C67—22no—
48C23×C4×C67—22no—
49C23×C4×C67—22no—
50C23×C4×C67—24no—
51C23×C4×C67—24no—
52C23×C4×C67—22no—
53C23×C4×C67—22no—
54C23×C4×C67—42no—
55C23×C4×C67—42no—
56C23×C4×C67C2×C414yes—
57C23×C4×C67D414yes—
58C23×C4×C67C2311yescharacteristic
59C23×C4×C67C2311yescharacteristic
60C23×C4×C67C2311yescharacteristic
61C23×C4×C67C2311yescharacteristic
62C23×C4×C67C2312yes—
63C23×C4×C67C2311yescharacteristic
64C23×C4×C67C2312yes—
65C23×C4×C67C2312yes—
66C23×C4×C67C2312yes—
67C23×C4×C67C2311yescharacteristic
68C2×C4⋊C4×C67—232no—
69C2×C4⋊C4×C67—24no—
70C2×C4⋊C4×C67—24no—
71C2×C4⋊C4×C67—24no—
72C2×C4⋊C4×C67—24no—
73C2×C4⋊C4×C67—24no—
74C2×C4⋊C4×C67—24no—
75C2×C4⋊C4×C67—24no—
76C2×C4⋊C4×C67—24no—
77C2×C4⋊C4×C67—22no—
78C2×C4⋊C4×C67—22no—
79C2×C4⋊C4×C67—24no—
80C2×C4⋊C4×C67—24no—
81C2×C4⋊C4×C67—42no—
82C2×C4⋊C4×C67—42no—
83C2×C4⋊C4×C67C2×C418yescomplemented
84C2×C4⋊C4×C67D418yes—
85C2×C22⋊C4×C67—22no—
86C2×C22⋊C4×C67—22no—
87C2×C22⋊C4×C67—22no—
88C2×C22⋊C4×C67—22no—
89C2×C22⋊C4×C67—22no—
90C2×C22⋊C4×C67—22no—
91C2×C22⋊C4×C67—22no—
92C2×C22⋊C4×C67C2×C414yes—
93C2×C22⋊C4×C67C2×C414yes—
94C2×C22⋊C4×C67D414yes—
95C2×C22⋊C4×C67Q814yes—
96C2×C22⋊C4×C67Q814yes—
97C2×C42×C67—24no—
98C2×C42×C67—24no—
99C2×C42×C67—42no—
100#95×C67—24no—
101#95×C67—22no—
102#95×C67—22no—
103#95×C67—24no—
104#95×C67—24no—
105#95×C67—24no—
106#95×C67—24no—
107#95×C67—42no—
108#95×C67C2×C418yescomplemented
109C24×C67—22no—
110C24×C67—22no—
111C24×C67—22no—
112C24×C67—22no—
113C24×C67C22×C412yes—
114C24×C67C2×D412yes—
115C24×C67C2×D412yes—
116C24×C67C2×Q812yes—
117C24×C67C2×Q812yes—
118C24×C67#4112yes—
119C24×C67#4112yes—
120C24×C67C2411yescharacteristic
121C22×C4×C67—28no—
122C22×C4×C67—216no—
123C22×C4×C67—28no—
124C22×C4×C67—28no—
125C22×C4×C67—21no—
126C22×C4×C67—22no—
127C22×C4×C67—22no—
128C22×C4×C67—22no—
129C22×C4×C67—22no—
130C22×C4×C67—22no—
131C22×C4×C67—22no—
132C22×C4×C67—21no—
133C22×C4×C67—22no—
134C22×C4×C67—22no—
135C22×C4×C67—22no—
136C22×C4×C67—216no—
137C22×C4×C67—28no—
138C22×C4×C67—28no—
139C22×C4×C67—22no—
140C22×C4×C67—22no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—22no—
144C22×C4×C67—22no—
145C22×C4×C67—22no—
146C22×C4×C67—22no—
147C22×C4×C67—22no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—21no—
151C22×C4×C67—22no—
152C22×C4×C67—22no—
153C22×C4×C67—21no—
154C22×C4×C67—22no—
155C22×C4×C67—22no—
156C22×C4×C67—22no—
157C22×C4×C67—22no—
158C22×C4×C67—22no—
159C22×C4×C67—22no—
160C22×C4×C67—22no—
161C22×C4×C67—22no—
162C22×C4×C67—22no—
163C22×C4×C67—28no—
164C22×C4×C67—21no—
165C22×C4×C67—21no—
166C22×C4×C67—21no—
167C22×C4×C67—21no—
168C22×C4×C67—22no—
169C22×C4×C67—21no—
170C22×C4×C67—21no—
171C22×C4×C67—22no—
172C22×C4×C67—22no—
173C22×C4×C67—22no—
174C22×C4×C67—44no—
175C22×C4×C67—48no—
176C22×C4×C67—48no—
177C22×C4×C67—48no—
178C22×C4×C67—48no—
179C22×C4×C67—44no—
180C22×C4×C67—44no—
181C22×C4×C67C22×C412yes—
182C22×C4×C67C22×C412yes—
183C22×C4×C67C22×C414yes—
184C22×C4×C67C22×C414yes—
185C22×C4×C67C2×D412yes—
186C22×C4×C67C2×D414yes—
187C22×C4×C67C2×D414yes—
188C22×C4×C67C2×D414yes—
189C22×C4×C67C2×D414yes—
190C22×C4×C67C2×D412yes—
191C22×C4×C67C2×Q814yes—
192C22×C4×C67C2×Q814yes—
193C22×C4×C67#4114yes—
194C4⋊C4×C67—216no—
195C4⋊C4×C67—216no—
196C4⋊C4×C67—216no—
197C4⋊C4×C67—48no—
198C4⋊C4×C67—44no—
199C4⋊C4×C67—44no—
200C22⋊C4×C67—28no—
201C22⋊C4×C67—28no—
202C22⋊C4×C67—44no—
203C22⋊C4×C67C4⋊C4116yescomplemented
204C42×C67—48no—
205C23×C67—24no—
206C23×C67—24no—
207C23×C67—22no—
208C23×C67—22no—
209C23×C67—24no—
210C23×C67—22no—
211C23×C67—22no—
212C23×C67—24no—
213C23×C67—24no—
214C23×C67—24no—
215C23×C67—24no—
216C23×C67—24no—
217C23×C67—24no—
218C23×C67—24no—
219C23×C67—24no—
220C23×C67—24no—
221C23×C67C2×C4⋊C414yes—
222C23×C67C4×D414yes—
223C23×C67C4×Q814yes—
224C23×C67#12114yes—
225C23×C67C22⋊Q814yes—
226C23×C67#12514yes—
227C23×C67C4⋊Q814yes—
228C23×C67C23×C411yescharacteristic
229C23×C67C22×D411yescharacteristic
230C23×C67C22×D411yescharacteristic
231C23×C67C22×D412yes—
232C23×C67C22×Q811yescharacteristic
233C23×C67C22×Q811yescharacteristic
234C23×C67C2×#4111yescharacteristic
235C23×C67C2×#4112yes—
236C23×C67C2×#4111yescharacteristic
237C23×C67H(5,𝔽2)12yes—
238C23×C672−1+412yes—
239C2×C4×C67—232no—
240C2×C4×C67—24no—
241C2×C4×C67—24no—
242C2×C4×C67—24no—
243C2×C4×C67—24no—
244C2×C4×C67—24no—
245C2×C4×C67—22no—
246C2×C4×C67—24no—
247C2×C4×C67—24no—
248C2×C4×C67—24no—
249C2×C4×C67—22no—
250C2×C4×C67—24no—
251C2×C4×C67—24no—
252C2×C4×C67—24no—
253C2×C4×C67—24no—
254C2×C4×C67—24no—
255C2×C4×C67—24no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—24no—
259C2×C4×C67—24no—
260C2×C4×C67—22no—
261C2×C4×C67—24no—
262C2×C4×C67—22no—
263C2×C4×C67—24no—
264C2×C4×C67—22no—
265C2×C4×C67—24no—
266C2×C4×C67—24no—
267C2×C4×C67—24no—
268C2×C4×C67—24no—
269C2×C4×C67—416no—
270C2×C4×C67—416no—
271C2×C4×C67—41no—
272C2×C4×C67—42no—
273C2×C4×C67—42no—
274C2×C4×C67—41no—
275C2×C4×C67—42no—
276C2×C4×C67—41no—
277C2×C4×C67—42no—
278C2×C4×C67—41no—
279C2×C4×C67—42no—
280C2×C4×C67—42no—
281C2×C4×C67—42no—
282C2×C4×C67—42no—
283C2×C4×C67—42no—
284C2×C4×C67—42no—
285C2×C4×C67—42no—
286C2×C4×C67—42no—
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—42no—
294C2×C4×C67—42no—
295C2×C4×C67—42no—
296C2×C4×C67—42no—
297C2×C4×C67C2×C4⋊C418yescomplemented
298C2×C4×C67C4×D418yes—
299C2×C4×C67#12014yes—
300C22×C67—24no—
301C22×C67—24no—
302C22×C67—28no—
303C22×C67—28no—
304C22×C67—24no—
305C22×C67—24no—
306C22×C67—24no—
307C22×C67—28no—
308C22×C67—28no—
309C22×C67—24no—
310C22×C67#38918yescomplemented
311C22×C67C22×C4⋊C411yescharacteristic
312C22×C67C2×C4×D411yescharacteristic
313C22×C67C2×C4×D412yes—
314C22×C67C2×C4×Q811yescharacteristic
315C22×C67#52012yes—
316C22×C67C2×#12011yescharacteristic
317C22×C67C2×#12111yescharacteristic
318C22×C67C2×C22⋊Q811yescharacteristic
319C22×C67#52511yescharacteristic
320C22×C67#52512yes—
321C22×C67C2×#12511yescharacteristic
322C22×C67C2×C4⋊Q811yescharacteristic
323C22×C67#53411yescharacteristic
324C22×C67#53611yescharacteristic
325C22×C67#53912yes—
326C22×C67D4212yes—
327C22×C67#54612yes—
328C22×C67#54712yes—
329C22×C67D4×Q812yes—
330C22×C67D4×Q812yes—
331C22×C67#55212yes—
332C22×C67#55412yes—
333C22×C67#55412yes—
334C4×C67—28no—
335C4×C67—24no—
336C4×C67—28no—
337C4×C67—42no—
338C4×C67—42no—
339C4×C67—44no—
340C4×C67—44no—
341C4×C67—42no—
342C4×C67—81no—
343C4×C67—81no—
344#14043C6711yesmaximal, characteristic, direct product factor, Sylow
345C2×C67—28no—
346C2×C67C2×#38911yescharacteristic
347C2×C67C4×#12011yescharacteristic
348C2×C67#232211yescharacteristic
349C2×C67D4×C4⋊C412yes—
350C2×C67#236012yes—
351C2×C67#241011yescharacteristic
352C2×C67#241311yescharacteristic
353C2×C67#243411yescharacteristic
354C2×C67#244912yes—
355C2×C67#247312yes—
356C2×C67#258311yescharacteristic
357C23×C4⋊C4C2×C6711yescharacteristic
358C2×#389C2×C6712yescomplemented
359C2×#385C2×C6711yescharacteristic
360C2×#385C2×C6711yescharacteristic
361C2×#385C2×C6711yescharacteristic
362C2×C4×C22⋊C4C2×C6711yescharacteristic
363#1444C2×C6712yescomplemented
364#1441C2×C6712yescomplemented
365#1436C2×C6712yescomplemented
366C22⋊#95C2×C6711yescharacteristic
367C22⋊#95C2×C6711yescharacteristic
368C67#1404311yescharacteristic, direct product factor, Sylow
369C24×C4C22×C6711yescharacteristic
370C24×C4C22×C6711yescharacteristic
371C24×C4C22×C6711yescharacteristic
372C22×C4⋊C4—24no—
373C22×C4⋊C4—28no—
374C22×C4⋊C4C22×C6712yes—
375C22×C4⋊C4C22×C6711yescharacteristic
376C22×C4⋊C4C22×C6712yes—
377C22×C4⋊C4C22×C6712yes—
378C22×C4⋊C4C22×C6712yes—
379C22×C4⋊C4C22×C6711yescharacteristic
380C22×C22⋊C4C22×C6711yescharacteristic
381C22×C22⋊C4C22×C6711yescharacteristic
382C22×C22⋊C4C22×C6711yescharacteristic
383C22×C22⋊C4C22×C6711yescharacteristic
384C22×C42C22×C6712yes—
385#389—28no—
386#385—24no—
387#385—24no—
388#385C4×C6718yescomplemented
389C4×C22⋊C4—24no—
390C2×#95C22×C6712yes—
391C2×#95C22×C6712yes—
392C2×#95C22×C6712yes—
393C2×#95C22×C6711yescharacteristic
394C2×#95C22×C6712yes—
395C2×#95C22×C6711yescharacteristic
396C2×#95C22×C6712yes—
397C2×#95C22×C6712yes—
398C2×#95C22×C6712yes—
399C25C23×C6711yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×C4×C6714yes—
414C23×C4D4×C6714yes—
415C23×C4C23×C6711yescharacteristic
416C23×C4C23×C6711yescharacteristic
417C23×C4C23×C6711yescharacteristic
418C23×C4C23×C6711yescharacteristic
419C23×C4C23×C6711yescharacteristic
420C23×C4C23×C6712yes—
421C23×C4C23×C6712yes—
422C23×C4C23×C6712yes—
423C23×C4C23×C6712yes—
424C23×C4C23×C6711yescharacteristic
425C2×C4⋊C4—232no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4C2×C4×C6718yescomplemented
441C2×C4⋊C4D4×C6718yes—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4C2×C4×C6714yes—
450C2×C22⋊C4C2×C4×C6714yes—
451C2×C22⋊C4D4×C6714yes—
452C2×C22⋊C4Q8×C6714yes—
453C2×C22⋊C4Q8×C6714yes—
454C2×C42—24no—
455C2×C42—24no—
456C2×C42—42no—
457#95—24no—
458#95—22no—
459#95—22no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—42no—
465#95C2×C4×C6718yescomplemented
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C22×C4×C6712yes—
471C24C2×D4×C6712yes—
472C24C2×D4×C6712yes—
473C24C2×Q8×C6712yes—
474C24C2×Q8×C6712yes—
475C24#41×C6712yes—
476C24#41×C6712yes—
477C24C24×C6711yescharacteristic
478C22×C4—28no—
479C22×C4—216no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4C22×C4×C6712yes—
539C22×C4C22×C4×C6712yes—
540C22×C4C22×C4×C6714yes—
541C22×C4C22×C4×C6714yes—
542C22×C4C2×D4×C6712yes—
543C22×C4C2×D4×C6714yes—
544C22×C4C2×D4×C6714yes—
545C22×C4C2×D4×C6714yes—
546C22×C4C2×D4×C6712yes—
547C22×C4C2×D4×C6714yes—
548C22×C4C2×Q8×C6714yes—
549C22×C4C2×Q8×C6714yes—
550C22×C4#41×C6714yes—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—216no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4—44no—
560C22⋊C4C4⋊C4×C67116yescomplemented
561C42—48no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—24no—
567C23—22no—
568C23—22no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23C2×C4⋊C4×C6714yes—
579C23C4×D4×C6714yes—
580C23C4×Q8×C6714yes—
581C23#121×C6714yes—
582C23C22⋊Q8×C6714yes—
583C23#125×C6714yes—
584C23C4⋊Q8×C6714yes—
585C23C23×C4×C6711yescharacteristic
586C23C22×D4×C6711yescharacteristic
587C23C22×D4×C6711yescharacteristic
588C23C22×D4×C6712yes—
589C23C22×Q8×C6711yescharacteristic
590C23C22×Q8×C6711yescharacteristic
591C23C2×#41×C6711yescharacteristic
592C23C2×#41×C6712yes—
593C23C2×#41×C6711yescharacteristic
594C23H(5,𝔽2)×C6712yes—
595C232−1+4×C6712yes—
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—416no—
627C2×C4—416no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4C2×C4⋊C4×C6718yescomplemented
655C2×C4C4×D4×C6718yes—
656C2×C4#120×C6714yes—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—28no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22#389×C6718yescomplemented
668C22C22×C4⋊C4×C6711yescharacteristic
669C22C2×C4×D4×C6711yescharacteristic
670C22C2×C4×D4×C6712yes—
671C22C2×C4×Q8×C6711yescharacteristic
672C22#520×C6712yes—
673C22C2×#120×C6711yescharacteristic
674C22C2×#121×C6711yescharacteristic
675C22C2×C22⋊Q8×C6711yescharacteristic
676C22#525×C6711yescharacteristic
677C22#525×C6712yes—
678C22C2×#125×C6711yescharacteristic
679C22C2×C4⋊Q8×C6711yescharacteristic
680C22#534×C6711yescharacteristic
681C22#536×C6711yescharacteristic
682C22#539×C6712yes—
683C22D42×C6712yes—
684C22#546×C6712yes—
685C22#547×C6712yes—
686C22D4×Q8×C6712yes—
687C22D4×Q8×C6712yes—
688C22#552×C6712yes—
689C22#554×C6712yes—
690C22#554×C6712yes—
691C4—28no—
692C4—28no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—44no—
698C4—44no—
699C4—81no—
700C4—81no—
701C2—28no—
702C2C2×#389×C6711yescharacteristic
703C2C4×#120×C6711yescharacteristic
704C2C67×#232211yescharacteristic
705C2D4×C4⋊C4×C6712yes—
706C2C67×#236012yes—
707C2C67×#241011yescharacteristic
708C2C67×#241311yescharacteristic
709C2C67×#243411yescharacteristic
710C2C67×#244912yes—
711C2C67×#247312yes—
712C2C67×#258311yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
prime radicalC25×C67C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#389×C67C2semidirect
7. C67×#1444C2semidirect
8. C67×#1441C2semidirect
9. C67×#1436C2semidirect
31. #385×C67C4semidirect
83. C2×C4⋊C4×C67C2×C4semidirect
108. #95×C67C2×C4semidirect
203. C22⋊C4×C67C4⋊C4semidirect
297. C2×C4×C67C2×C4⋊C4semidirect
310. C22×C67#389semidirect
344. #14043C67direct (N × H)
358. C2×#389C2×C67semidirect
363. #1444C2×C67semidirect
364. #1441C2×C67semidirect
365. #1436C2×C67semidirect
368. C67#14043direct (N × H)
388. #385C4×C67semidirect
440. C2×C4⋊C4C2×C4×C67semidirect
465. #95C2×C4×C67semidirect
560. C22⋊C4C4⋊C4×C67semidirect
654. C2×C4C2×C4⋊C4×C67semidirect
667. C22#389×C67semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C672
C2×#389×C672
C2×#385×C672
C2×C4×C22⋊C4×C672
C67×#14442
C67×#14412
C67×#14362
C67×C22⋊#952
#1404367