Finite Group Databasebeta

← C67×#22420 #30701671

Subgroups — C67×#22420 #30701671

Order 17152.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C67C211yesmaximal, characteristic
2C2×#435×C67C211yesmaximal, characteristic, complemented
3C2×#417×C67C211yesmaximal, characteristic, complemented
4C2×#416×C67C211yesmaximal, characteristic, complemented
5C67×#2352C211yesmaximal, characteristic, complemented
6C67×#1981C211yesmaximal, characteristic, complemented
7C67×#1960C211yesmaximal, characteristic, complemented
8C67×#1894C211yesmaximal, characteristic, complemented
9C67×#1892C211yesmaximal, characteristic, complemented
10C67×#1873C211yesmaximal, characteristic, complemented
11C67×#1872C211yesmaximal, characteristic, complemented
12C67×#1804C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic, complemented
15C67×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic
20#547×C67—24no—
21#547×C67C418yescomplemented
22C2×C4⋊Q8×C67C2211yescharacteristic
23C2×#123×C67—21no—
24C2×#123×C67—21no—
25C2×C22⋊Q8×C67C2211yescharacteristic
26C2×C22⋊Q8×C67C2211yescharacteristic
27C2×#121×C67—21no—
28C2×C4×D4×C67C2211yescharacteristic
29C2×C4×D4×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31C22×C4⋊C4×C67—21no—
32C22×C4⋊C4×C67C2211yescharacteristic
33#435×C67—24no—
34C2×C4⋊C8×C67C2211yescharacteristic
35#417×C67—24no—
36#416×C67—24no—
37C2×#103×C67C2211yescharacteristic
38C2×#103×C67C2211yescharacteristic
39C2×#103×C67C2211yescharacteristic
40C2×#103×C67C2211yescharacteristic
41C2×#103×C67C2211yescharacteristic
42C2×#103×C67C2211yescharacteristic
43C2×#103×C67C2211yescharacteristic
44C2×#103×C67C2211yescharacteristic
45C2×#102×C67C2211yescharacteristic
46C2×#102×C67C2211yescharacteristic
47C2×#102×C67C2211yescharacteristic
48C2×#102×C67C2211yescharacteristic
49C2×C22⋊C8×C67C2211yescharacteristic
50C2×C22⋊C8×C67C2211yescharacteristic
51C2×#97×C67C2211yescharacteristic
52#388×C67—21no—
53#387×C67—21no—
54#386×C67—21no—
55#382×C67C2211yescharacteristic
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic
58C4×C4⋊C4×C67C2211yescharacteristic
59C4×C22⋊C4×C67—21no—
60#340×C67C2211yescharacteristic
61#340×C67C2211yescharacteristic
62#340×C67C2211yescharacteristic
63#340×C67C2211yescharacteristic
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67—22no—
69C2×#41×C67—22no—
70C2×#41×C67—41no—
71C2×#41×C67—41no—
72C2×#41×C67—41no—
73C2×#41×C67—41no—
74C2×#41×C67C2×C414yes—
75C2×#41×C67C2×C414yescomplemented
76C22×Q8×C67C2311yescharacteristic
77C22×Q8×C67C2311yescharacteristic
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67D411yescharacteristic
81C22×D4×C67C2311yescharacteristic
82C23×C4×C67—21no—
83C23×C4×C67—21no—
84C23×C4×C67—21no—
85C23×C4×C67—21no—
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2311yescharacteristic
88C2×M16×C67—22no—
89C2×M16×C67—22no—
90C2×M16×C67—41no—
91C22×C8×C67—22no—
92C22×C8×C67—22no—
93C22×C8×C67—41no—
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C4⋊Q8×C67—22no—
99C4⋊Q8×C67C2×C414yescomplemented
100#123×C67—28no—
101#123×C67—28no—
102C22⋊Q8×C67—22no—
103C22⋊Q8×C67—22no—
104C22⋊Q8×C67C2×C414yes—
105C22⋊Q8×C67C2×C414yescomplemented
106#121×C67—28no—
107C4×D4×C67—22no—
108C4×D4×C67C2×C414yes—
109C4×D4×C67C2×C414yescomplemented
110C4×D4×C67D414yes—
111#117×C67—22no—
112#117×C67—41no—
113C2×C4⋊C4×C67—21no—
114C2×C4⋊C4×C67—21no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67—28no—
118C2×C4⋊C4×C67—22no—
119C2×C4⋊C4×C67—21no—
120C2×C4⋊C4×C67—41no—
121C2×C4⋊C4×C67D411yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C4⋊C4×C67C2311yescharacteristic
124C2×C4⋊C4×C67C2311yescharacteristic
125C2×C4⋊C4×C67C2311yescharacteristic
126C2×C4⋊C4×C67C2311yescharacteristic
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—21no—
130C2×C22⋊C4×C67—21no—
131C2×C22⋊C4×C67—21no—
132C2×C22⋊C4×C67—21no—
133C2×C22⋊C4×C67D411yescharacteristic
134C2×C22⋊C4×C67D411yescharacteristic
135C2×C42×C67—21no—
136C2×C42×C67—21no—
137C2×C42×C67C2311yescharacteristic
138C4⋊C8×C67—22no—
139#103×C67—22no—
140#103×C67—22no—
141#103×C67—22no—
142#103×C67—22no—
143#103×C67—41no—
144#103×C67—41no—
145#103×C67—41no—
146#103×C67—41no—
147#102×C67—22no—
148#102×C67—22no—
149#102×C67—22no—
150#102×C67D414yescomplemented
151C22⋊C8×C67—22no—
152C22⋊C8×C67—22no—
153#97×C67—22no—
154#95×C67—21no—
155#95×C67—21no—
156#95×C67—21no—
157#95×C67—21no—
158#95×C67—21no—
159C24×C67—21no—
160C24×C67C2×D411yescharacteristic
161C24×C67C2×D411yescharacteristic
162#41×C67—28no—
163#41×C67—28no—
164#41×C67—44no—
165#41×C67—44no—
166#41×C67—44no—
167#41×C67—44no—
168#41×C67—44no—
169#41×C67—44no—
170C2×Q8×C67—21no—
171C2×Q8×C67—21no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67—21no—
175C2×Q8×C67—21no—
176C2×Q8×C67—21no—
177C2×Q8×C67—21no—
178C2×Q8×C67—21no—
179C2×Q8×C67—21no—
180C2×Q8×C67C22×C412yes—
181C2×Q8×C67C22×C412yes—
182C2×D4×C67—24no—
183C2×D4×C67—24no—
184C2×D4×C67—21no—
185C2×D4×C67—21no—
186C2×D4×C67—21no—
187C2×D4×C67—41no—
188C2×D4×C67—41no—
189C2×D4×C67—42no—
190C2×D4×C67—42no—
191C2×D4×C67—42no—
192C2×D4×C67—42no—
193C2×D4×C67C22⋊C414yes—
194C2×D4×C67C22×C412yes—
195C2×D4×C67C2×D412yes—
196C2×D4×C67#4112yes—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—24no—
210C22×C4×C67—24no—
211C22×C4×C67—24no—
212C22×C4×C67—21no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—42no—
216C22×C4×C67—42no—
217C22×C4×C67—42no—
218C22×C4×C67—42no—
219C22×C4×C67—42no—
220C22×C4×C67—42no—
221C22×C4×C67—42no—
222C22×C4×C67—42no—
223C22×C4×C67—81no—
224C22×C4×C67C22×C412yes—
225C22×C4×C67C22×C412yes—
226C22×C4×C67C2×D411yescharacteristic
227C22×C4×C67C2×D411yescharacteristic
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×D411yescharacteristic
230C22×C4×C67C2×D412yes—
231C22×C4×C67C2×D412yes—
232C22×C4×C67C2411yescharacteristic
233M16×C67—44no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67—21no—
242C2×C8×C67—21no—
243C2×C8×C67—21no—
244C2×C8×C67—21no—
245C2×C8×C67—44no—
246C2×C8×C67C2×D412yes—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—42no—
260C4⋊C4×C67C22⋊C414yes—
261C4⋊C4×C67C22×C412yes—
262C4⋊C4×C67C2×D412yes—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—24no—
265C22⋊C4×C67—24no—
266C22⋊C4×C67—42no—
267C22⋊C4×C67—42no—
268C22⋊C4×C67—81no—
269C22⋊C4×C67C22⋊C414yes—
270C22⋊C4×C67C22⋊C414yes—
271C42×C67—42no—
272C42×C67—81no—
273C42×C67C22×C412yes—
274C42×C67C2×D412yes—
275C23×C67—22no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—22no—
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—22no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—21no—
289C23×C67—21no—
290C23×C67—41no—
291C23×C67—41no—
292C23×C67—41no—
293C23×C67—41no—
294C23×C67C2×C22⋊C412yes—
295C23×C67C2×C22⋊C412yes—
296C23×C67C22×D411yescharacteristic
297Q8×C67—22no—
298Q8×C67—22no—
299Q8×C67—22no—
300Q8×C67—22no—
301Q8×C67—41no—
302Q8×C67—41no—
303Q8×C67—41no—
304Q8×C67—41no—
305D4×C67—22no—
306D4×C67—22no—
307D4×C67—22no—
308D4×C67—44no—
309D4×C67—48no—
310D4×C67—48no—
311D4×C67C4×D414yes—
312C2×C4×C67—21no—
313C2×C4×C67—21no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—21no—
317C2×C4×C67—21no—
318C2×C4×C67—21no—
319C2×C4×C67—21no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—48no—
333C2×C4×C67—48no—
334C2×C4×C67—48no—
335C2×C4×C67—41no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67—41no—
340C2×C4×C67—41no—
341C2×C4×C67—41no—
342C2×C4×C67—41no—
343C2×C4×C67—41no—
344C2×C4×C67—41no—
345C2×C4×C67—41no—
346C2×C4×C67—41no—
347C2×C4×C67—41no—
348C2×C4×C67—41no—
349C2×C4×C67—41no—
350C2×C4×C67—41no—
351C2×C4×C67—41no—
352C2×C4×C67—84no—
353C2×C4×C67C2×C22⋊C412yes—
354C2×C4×C67C2×C22⋊C412yes—
355C2×C4×C67C2×C22⋊C412yes—
356C2×C4×C67C2×C22⋊C412yes—
357C2×C4×C67C23×C411yescharacteristic
358C2×C4×C67C22×D411yescharacteristic
359C2×C4×C67C22×D411yescharacteristic
360C2×C4×C67C2×#4111yescharacteristic
361C2×C4×C67H(5,𝔽2)11yescharacteristic
362C2×C4×C67H(5,𝔽2)11yescharacteristic
363C8×C67—22no—
364C8×C67—41no—
365C8×C67—41no—
366C8×C67—41no—
367C22×C67—22no—
368C22×C67—22no—
369C22×C67—24no—
370C22×C67—22no—
371C22×C67—22no—
372C22×C67—22no—
373C22×C67—22no—
374C22×C67—42no—
375C22×C67—42no—
376C22×C67—41no—
377C22×C67—41no—
378C22×C67—42no—
379C22×C67—41no—
380C22×C67—41no—
381C22×C67—42no—
382C22×C67—41no—
383C22×C67—41no—
384C22×C67—42no—
385C22×C67—41no—
386C22×C67—41no—
387C22×C67—42no—
388C22×C67C22×C22⋊C411yescharacteristic
389C22×C67D4211yescharacteristic
390C22×C67#54611yescharacteristic
391C22×C67#57511yescharacteristic
392C22×C67#57511yescharacteristic
393C22×C67#57711yescharacteristic
394C22×C67#57811yescharacteristic
395C4×C67—22no—
396C4×C67—22no—
397C4×C67—22no—
398C4×C67—22no—
399C4×C67—42no—
400C4×C67—42no—
401C4×C67—42no—
402C4×C67—42no—
403C4×C67—81no—
404C4×C67—81no—
405C4×C67—81no—
406C4×C67C2×C4×D411yescharacteristic
407C4×C67#51811yescharacteristic
408C4×C67D4211yescharacteristic
409C4×C67#54611yescharacteristic
410#22420C6711yesmaximal, characteristic, direct product factor, Sylow
411C2×C67—42no—
412C2×C67—42no—
413C2×C67—44no—
414C2×C67D4×C22⋊C411yescharacteristic
415C2×C67#289611yescharacteristic
416C2×C67#289811yescharacteristic
417C2×C67#326711yescharacteristic
418C2×C67#326911yescharacteristic
419C2×C67#330711yescharacteristic
420C2×C67#331511yescharacteristic
421C2×#547C2×C6711yescharacteristic
422C2×#435C2×C6711yescharacteristic, complemented
423C2×#417C2×C6711yescharacteristic, complemented
424C2×#416C2×C6711yescharacteristic, complemented
425#2352C2×C6711yescharacteristic, complemented
426#1981C2×C6711yescharacteristic, complemented
427#1960C2×C6711yescharacteristic, complemented
428#1894C2×C6711yescharacteristic, complemented
429#1892C2×C6711yescharacteristic, complemented
430#1873C2×C6711yescharacteristic, complemented
431#1872C2×C6711yescharacteristic, complemented
432#1804C2×C6711yescharacteristic, complemented
433#1788C2×C6711yescharacteristic, complemented
434#1788C2×C6711yescharacteristic, complemented
435#1762C2×C6711yescharacteristic, complemented
436C67#2242011yescharacteristic, direct product factor, Sylow
437C22×#41C22×C6711yescharacteristic
438C22×#41C22×C6711yescharacteristic
439C22×M16C22×C6711yescharacteristic
440C23×C8C22×C6711yescharacteristic
441#547—24no—
442#547C4×C6718yescomplemented
443C2×C4⋊Q8C22×C6711yescharacteristic
444C2×#123—21no—
445C2×#123—21no—
446C2×C22⋊Q8C22×C6711yescharacteristic
447C2×C22⋊Q8C22×C6711yescharacteristic
448C2×#121—21no—
449C2×C4×D4C22×C6711yescharacteristic
450C2×C4×D4C22×C6711yescharacteristic
451C2×#117C22×C6711yescharacteristic
452C22×C4⋊C4—21no—
453C22×C4⋊C4C22×C6711yescharacteristic
454#435—24no—
455C2×C4⋊C8C22×C6711yescharacteristic
456#417—24no—
457#416—24no—
458C2×#103C22×C6711yescharacteristic
459C2×#103C22×C6711yescharacteristic
460C2×#103C22×C6711yescharacteristic
461C2×#103C22×C6711yescharacteristic
462C2×#103C22×C6711yescharacteristic
463C2×#103C22×C6711yescharacteristic
464C2×#103C22×C6711yescharacteristic
465C2×#103C22×C6711yescharacteristic
466C2×#102C22×C6711yescharacteristic
467C2×#102C22×C6711yescharacteristic
468C2×#102C22×C6711yescharacteristic
469C2×#102C22×C6711yescharacteristic
470C2×C22⋊C8C22×C6711yescharacteristic
471C2×C22⋊C8C22×C6711yescharacteristic
472C2×#97C22×C6711yescharacteristic
473#388—21no—
474#387—21no—
475#386—21no—
476#382C22×C6711yescharacteristic
477#380C22×C6711yescharacteristic
478#380C22×C6711yescharacteristic
479C4×C4⋊C4C22×C6711yescharacteristic
480C4×C22⋊C4—21no—
481#340C22×C6711yescharacteristic
482#340C22×C6711yescharacteristic
483#340C22×C6711yescharacteristic
484#340C22×C6711yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41C2×C4×C6714yes—
496C2×#41C2×C4×C6714yescomplemented
497C22×Q8C23×C6711yescharacteristic
498C22×Q8C23×C6711yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4D4×C6711yescharacteristic
502C22×D4C23×C6711yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C6711yescharacteristic
508C23×C4C23×C6711yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8C23×C6711yescharacteristic
516C22×C8C23×C6711yescharacteristic
517C22×C8C23×C6711yescharacteristic
518C22×C8C23×C6711yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8C2×C4×C6714yescomplemented
521#123—28no—
522#123—28no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8C2×C4×C6714yes—
526C22⋊Q8C2×C4×C6714yescomplemented
527#121—28no—
528C4×D4—22no—
529C4×D4C2×C4×C6714yes—
530C4×D4C2×C4×C6714yescomplemented
531C4×D4D4×C6714yes—
532#117—22no—
533#117—41no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4D4×C6711yescharacteristic
543C2×C4⋊C4C23×C6711yescharacteristic
544C2×C4⋊C4C23×C6711yescharacteristic
545C2×C4⋊C4C23×C6711yescharacteristic
546C2×C4⋊C4C23×C6711yescharacteristic
547C2×C4⋊C4C23×C6711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4D4×C6711yescharacteristic
555C2×C22⋊C4D4×C6711yescharacteristic
556C2×C42—21no—
557C2×C42—21no—
558C2×C42C23×C6711yescharacteristic
559C4⋊C8—22no—
560#103—22no—
561#103—22no—
562#103—22no—
563#103—22no—
564#103—41no—
565#103—41no—
566#103—41no—
567#103—41no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102D4×C6714yescomplemented
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580C24—21no—
581C24C2×D4×C6711yescharacteristic
582C24C2×D4×C6711yescharacteristic
583#41—28no—
584#41—28no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C22×C4×C6712yes—
602C2×Q8C22×C4×C6712yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4C22⋊C4×C6714yes—
615C2×D4C22×C4×C6712yes—
616C2×D4C2×D4×C6712yes—
617C2×D4#41×C6712yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C22×C4×C6712yes—
646C22×C4C22×C4×C6712yes—
647C22×C4C2×D4×C6711yescharacteristic
648C22×C4C2×D4×C6711yescharacteristic
649C22×C4C2×D4×C6711yescharacteristic
650C22×C4C2×D4×C6711yescharacteristic
651C22×C4C2×D4×C6712yes—
652C22×C4C2×D4×C6712yes—
653C22×C4C24×C6711yescharacteristic
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—44no—
667C2×C8C2×D4×C6712yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—42no—
681C4⋊C4C22⋊C4×C6714yes—
682C4⋊C4C22×C4×C6712yes—
683C4⋊C4C2×D4×C6712yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4C22⋊C4×C6714yes—
691C22⋊C4C22⋊C4×C6714yes—
692C42—42no—
693C42—81no—
694C42C22×C4×C6712yes—
695C42C2×D4×C6712yes—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊C4×C6712yes—
716C23C2×C22⋊C4×C6712yes—
717C23C22×D4×C6711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4C4×D4×C6714yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4C2×C22⋊C4×C6712yes—
775C2×C4C2×C22⋊C4×C6712yes—
776C2×C4C2×C22⋊C4×C6712yes—
777C2×C4C2×C22⋊C4×C6712yes—
778C2×C4C23×C4×C6711yescharacteristic
779C2×C4C22×D4×C6711yescharacteristic
780C2×C4C22×D4×C6711yescharacteristic
781C2×C4C2×#41×C6711yescharacteristic
782C2×C4H(5,𝔽2)×C6711yescharacteristic
783C2×C4H(5,𝔽2)×C6711yescharacteristic
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22C22×C22⋊C4×C6711yescharacteristic
810C22D42×C6711yescharacteristic
811C22#546×C6711yescharacteristic
812C22#575×C6711yescharacteristic
813C22#575×C6711yescharacteristic
814C22#577×C6711yescharacteristic
815C22#578×C6711yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4C2×C4×D4×C6711yescharacteristic
828C4#518×C6711yescharacteristic
829C4D42×C6711yescharacteristic
830C4#546×C6711yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C22⋊C4×C6711yescharacteristic
835C2C67×#289611yescharacteristic
836C2C67×#289811yescharacteristic
837C2C67×#326711yescharacteristic
838C2C67×#326911yescharacteristic
839C2C67×#330711yescharacteristic
840C2C67×#331511yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC2×#547×C67C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C67C2semidirect
3. C2×#417×C67C2semidirect
4. C2×#416×C67C2semidirect
5. C67×#2352C2semidirect
6. C67×#1981C2semidirect
7. C67×#1960C2semidirect
8. C67×#1894C2semidirect
9. C67×#1892C2semidirect
10. C67×#1873C2semidirect
11. C67×#1872C2semidirect
12. C67×#1804C2semidirect
13. C67×#1788C2semidirect
14. C67×#1788C2semidirect
15. C67×#1762C2semidirect
21. #547×C67C4semidirect
75. C2×#41×C67C2×C4semidirect
99. C4⋊Q8×C67C2×C4semidirect
105. C22⋊Q8×C67C2×C4semidirect
109. C4×D4×C67C2×C4semidirect
150. #102×C67D4semidirect
410. #22420C67direct (N × H)
422. C2×#435C2×C67semidirect
423. C2×#417C2×C67semidirect
424. C2×#416C2×C67semidirect
425. #2352C2×C67semidirect
426. #1981C2×C67semidirect
427. #1960C2×C67semidirect
428. #1894C2×C67semidirect
429. #1892C2×C67semidirect
430. #1873C2×C67semidirect
431. #1872C2×C67semidirect
432. #1804C2×C67semidirect
433. #1788C2×C67semidirect
434. #1788C2×C67semidirect
435. #1762C2×C67semidirect
436. C67#22420direct (N × H)
442. #547C4×C67semidirect
496. C2×#41C2×C4×C67semidirect
520. C4⋊Q8C2×C4×C67semidirect
526. C22⋊Q8C2×C4×C67semidirect
530. C4×D4C2×C4×C67semidirect
571. #102D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C672
C2×#435×C672
C2×#417×C672
C2×#416×C672
C67×#23522
C67×#19812
C67×#19602
C67×#18942
C67×#18922
C67×#18732
C67×#18722
C67×#18042
C67×#17882
C67×#17622
#2242067