Finite Group Databasebeta

← C67×#22426 #30701677

Subgroups — C67×#22426 #30701677

Order 17152.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C67C211yesmaximal, characteristic
2C2×#435×C67C211yesmaximal, characteristic, complemented
3C2×#419×C67C211yesmaximal, characteristic, complemented
4C2×#416×C67C211yesmaximal, characteristic, complemented
5C67×#2354C211yesmaximal, characteristic, complemented
6C67×#1983C211yesmaximal, characteristic, complemented
7C67×#1959C211yesmaximal, characteristic, complemented
8C67×#1895C211yesmaximal, characteristic, complemented
9C67×#1892C211yesmaximal, characteristic, complemented
10C67×#1875C211yesmaximal, characteristic, complemented
11C67×#1873C211yesmaximal, characteristic, complemented
12C67×#1803C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1787C211yesmaximal, characteristic, complemented
15C67×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C23×Q8×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic
20#548×C67—24no—
21#548×C67C418yescomplemented
22C2×#124×C67—21no—
23C2×#124×C67C2211yescharacteristic
24C2×C22⋊Q8×C67—21no—
25C2×C22⋊Q8×C67C2211yescharacteristic
26C2×#121×C67—21no—
27C2×#121×C67C2211yescharacteristic
28C2×C4×Q8×C67C2211yescharacteristic
29C2×C4×D4×C67—21no—
30C2×C4×D4×C67C2211yescharacteristic
31C2×#117×C67C2211yescharacteristic
32C2×#117×C67C2211yescharacteristic
33#435×C67—24no—
34C2×C4⋊C8×C67C2211yescharacteristic
35#419×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#390×C67—21no—
53#388×C67—21no—
54#388×C67—21no—
55#384×C67C2211yescharacteristic
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic
58C4×C4⋊C4×C67—21no—
59C4×C4⋊C4×C67C2211yescharacteristic
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—41no—
68C2×#41×C67—41no—
69C2×#41×C67C2×C414yes—
70C22×Q8×C67—21no—
71C22×Q8×C67—22no—
72C22×Q8×C67—22no—
73C22×Q8×C67—22no—
74C22×Q8×C67—41no—
75C22×Q8×C67—41no—
76C22×Q8×C67C2×C414yes—
77C22×Q8×C67C2311yescharacteristic
78C22×Q8×C67C2311yescharacteristic
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67D411yescharacteristic
82C22×D4×C67C2311yescharacteristic
83C23×C4×C67—21no—
84C23×C4×C67—21no—
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C2×M16×C67—22no—
88C2×M16×C67—22no—
89C2×M16×C67—41no—
90C22×C8×C67—22no—
91C22×C8×C67—22no—
92C22×C8×C67—41no—
93C22×C8×C67C2311yescharacteristic
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97#124×C67—28no—
98#124×C67—22no—
99#124×C67C2×C414yes—
100C22⋊Q8×C67—22no—
101C22⋊Q8×C67—28no—
102C22⋊Q8×C67C2×C414yes—
103#121×C67—28no—
104#121×C67—22no—
105#121×C67C2×C414yes—
106C4×Q8×C67—22no—
107C4×Q8×C67C2×C414yes—
108C4×D4×C67—28no—
109C4×D4×C67C2×C414yes—
110C4×D4×C67D414yes—
111#117×C67—22no—
112#117×C67—22no—
113#117×C67—41no—
114#117×C67—41no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67—21no—
118C2×C4⋊C4×C67—21no—
119C2×C4⋊C4×C67D411yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C4⋊C4×C67C2311yescharacteristic
124C2×C4⋊C4×C67C2311yescharacteristic
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
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×C67—21no—
138C2×C42×C67—21no—
139C2×C42×C67C2311yescharacteristic
140C4⋊C8×C67—22no—
141#103×C67—22no—
142#103×C67—22no—
143#103×C67—22no—
144#103×C67—22no—
145#103×C67—22no—
146#103×C67—41no—
147#103×C67—41no—
148#103×C67D414yescomplemented
149#102×C67—22no—
150#102×C67—22no—
151#102×C67—41no—
152#102×C67—41no—
153C22⋊C8×C67—22no—
154C22⋊C8×C67—22no—
155#97×C67—22no—
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—44no—
164#41×C67—44no—
165#41×C67—44no—
166C2×Q8×C67—24no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67—21no—
170C2×Q8×C67—21no—
171C2×Q8×C67—28no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67—21no—
175C2×Q8×C67—21no—
176C2×Q8×C67—42no—
177C2×Q8×C67—42no—
178C2×Q8×C67—44no—
179C2×Q8×C67—44no—
180C2×Q8×C67—44no—
181C2×Q8×C67C22×C412yes—
182C2×Q8×C67C22×C412yes—
183C2×Q8×C67C2×D412yes—
184C2×Q8×C67#4112yes—
185C2×D4×C67—24no—
186C2×D4×C67—24no—
187C2×D4×C67—21no—
188C2×D4×C67—21no—
189C2×D4×C67—21no—
190C2×D4×C67—21no—
191C2×D4×C67—21no—
192C2×D4×C67—41no—
193C2×D4×C67—41no—
194C2×D4×C67—42no—
195C2×D4×C67—42no—
196C2×D4×C67—42no—
197C2×D4×C67—42no—
198C2×D4×C67C22⋊C414yes—
199C2×D4×C67C22×C412yes—
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—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—24no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—42no—
218C22×C4×C67—42no—
219C22×C4×C67—42no—
220C22×C4×C67—42no—
221C22×C4×C67C22×C412yes—
222C22×C4×C67C22×C412yes—
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67C2×D411yescharacteristic
226C22×C4×C67C2×D411yescharacteristic
227C22×C4×C67C2×D412yes—
228C22×C4×C67C2×D412yes—
229C22×C4×C67C2411yescharacteristic
230M16×C67—44no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
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—44no—
243C2×C8×C67C2×D412yes—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67—21no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—42no—
255C4⋊C4×C67—81no—
256C4⋊C4×C67C22⋊C414yes—
257C4⋊C4×C67C22×C412yes—
258C4⋊C4×C67C2×D412yes—
259C22⋊C4×C67—24no—
260C22⋊C4×C67—24no—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—42no—
264C22⋊C4×C67—42no—
265C22⋊C4×C67—81no—
266C22⋊C4×C67—81no—
267C22⋊C4×C67C22⋊C414yes—
268C22⋊C4×C67C22⋊C414yes—
269C42×C67—24no—
270C42×C67—42no—
271C42×C67—42no—
272C42×C67—42no—
273C42×C67C22×C412yes—
274C42×C67C2×D412yes—
275C23×C67—21no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—21no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—22no—
288C23×C67—41no—
289C23×C67—41no—
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—22no—
302Q8×C67—48no—
303Q8×C67—41no—
304Q8×C67—41no—
305Q8×C67C4×D414yes—
306D4×C67—22no—
307D4×C67—22no—
308D4×C67—44no—
309D4×C67—48no—
310D4×C67—48no—
311D4×C67—41no—
312D4×C67—41no—
313C2×C4×C67—22no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—22no—
317C2×C4×C67—21no—
318C2×C4×C67—21no—
319C2×C4×C67—22no—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
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—22no—
333C2×C4×C67—22no—
334C2×C4×C67—22no—
335C2×C4×C67—48no—
336C2×C4×C67—48no—
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×C67C2×C22⋊C412yes—
353C2×C4×C67C2×C22⋊C412yes—
354C2×C4×C67C2×C22⋊C412yes—
355C2×C4×C67C2×C22⋊C412yes—
356C2×C4×C67C23×C411yescharacteristic
357C2×C4×C67C22×D411yescharacteristic
358C2×C4×C67C22×D411yescharacteristic
359C2×C4×C67C2×#4111yescharacteristic
360C2×C4×C67H(5,𝔽2)11yescharacteristic
361C2×C4×C67H(5,𝔽2)11yescharacteristic
362C8×C67—22no—
363C8×C67—41no—
364C8×C67—41no—
365C8×C67—41no—
366C22×C67—22no—
367C22×C67—22no—
368C22×C67—22no—
369C22×C67—22no—
370C22×C67—22no—
371C22×C67—22no—
372C22×C67—41no—
373C22×C67—41no—
374C22×C67—41no—
375C22×C67—41no—
376C22×C67—41no—
377C22×C67—41no—
378C22×C67—41no—
379C22×C67—41no—
380C22×C67—42no—
381C22×C67—42no—
382C22×C67—42no—
383C22×C67—81no—
384C22×C67—81no—
385C22×C67—81no—
386C22×C67—81no—
387C22×C67C22×C22⋊C411yescharacteristic
388C22×C67D4211yescharacteristic
389C22×C67#54611yescharacteristic
390C22×C67#57511yescharacteristic
391C22×C67#57511yescharacteristic
392C22×C67#57711yescharacteristic
393C22×C67#57811yescharacteristic
394C4×C67—22no—
395C4×C67—22no—
396C4×C67—24no—
397C4×C67—22no—
398C4×C67—22no—
399C4×C67—42no—
400C4×C67—42no—
401C4×C67—42no—
402C4×C67—81no—
403C4×C67—81no—
404C4×C67—81no—
405C4×C67C2×C4×D411yescharacteristic
406C4×C67#51811yescharacteristic
407C4×C67D4211yescharacteristic
408C4×C67#54611yescharacteristic
409#22426C6711yesmaximal, characteristic, direct product factor, Sylow
410C2×C67—42no—
411C2×C67—42no—
412C2×C67—82no—
413C2×C67D4×C22⋊C411yescharacteristic
414C2×C67#289611yescharacteristic
415C2×C67#289811yescharacteristic
416C2×C67#326911yescharacteristic
417C2×C67#327111yescharacteristic
418C2×C67#331311yescharacteristic
419C2×C67#332111yescharacteristic
420C2×#548C2×C6711yescharacteristic
421C2×#435C2×C6711yescharacteristic, complemented
422C2×#419C2×C6711yescharacteristic, complemented
423C2×#416C2×C6711yescharacteristic, complemented
424#2354C2×C6711yescharacteristic, complemented
425#1983C2×C6711yescharacteristic, complemented
426#1959C2×C6711yescharacteristic, complemented
427#1895C2×C6711yescharacteristic, complemented
428#1892C2×C6711yescharacteristic, complemented
429#1875C2×C6711yescharacteristic, complemented
430#1873C2×C6711yescharacteristic, complemented
431#1803C2×C6711yescharacteristic, complemented
432#1788C2×C6711yescharacteristic, complemented
433#1787C2×C6711yescharacteristic, complemented
434#1763C2×C6711yescharacteristic, complemented
435C67#2242611yescharacteristic, direct product factor, Sylow
436C22×#41C22×C6711yescharacteristic
437C23×Q8C22×C6711yescharacteristic
438C22×M16C22×C6711yescharacteristic
439C23×C8C22×C6711yescharacteristic
440#548—24no—
441#548C4×C6718yescomplemented
442C2×#124—21no—
443C2×#124C22×C6711yescharacteristic
444C2×C22⋊Q8—21no—
445C2×C22⋊Q8C22×C6711yescharacteristic
446C2×#121—21no—
447C2×#121C22×C6711yescharacteristic
448C2×C4×Q8C22×C6711yescharacteristic
449C2×C4×D4—21no—
450C2×C4×D4C22×C6711yescharacteristic
451C2×#117C22×C6711yescharacteristic
452C2×#117C22×C6711yescharacteristic
453#435—24no—
454C2×C4⋊C8C22×C6711yescharacteristic
455#419—24no—
456#416—24no—
457C2×#103C22×C6711yescharacteristic
458C2×#103C22×C6711yescharacteristic
459C2×#103C22×C6711yescharacteristic
460C2×#103C22×C6711yescharacteristic
461C2×#103C22×C6711yescharacteristic
462C2×#103C22×C6711yescharacteristic
463C2×#103C22×C6711yescharacteristic
464C2×#103C22×C6711yescharacteristic
465C2×#102C22×C6711yescharacteristic
466C2×#102C22×C6711yescharacteristic
467C2×#102C22×C6711yescharacteristic
468C2×#102C22×C6711yescharacteristic
469C2×C22⋊C8C22×C6711yescharacteristic
470C2×C22⋊C8C22×C6711yescharacteristic
471C2×#97C22×C6711yescharacteristic
472#390—21no—
473#388—21no—
474#388—21no—
475#384C22×C6711yescharacteristic
476#380C22×C6711yescharacteristic
477#380C22×C6711yescharacteristic
478C4×C4⋊C4—21no—
479C4×C4⋊C4C22×C6711yescharacteristic
480#340C22×C6711yescharacteristic
481#340C22×C6711yescharacteristic
482#340C22×C6711yescharacteristic
483#340C22×C6711yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41C2×C4×C6714yes—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8C2×C4×C6714yes—
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×C4C23×C6711yescharacteristic
506C23×C4C23×C6711yescharacteristic
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C6711yescharacteristic
514C22×C8C23×C6711yescharacteristic
515C22×C8C23×C6711yescharacteristic
516C22×C8C23×C6711yescharacteristic
517#124—28no—
518#124—22no—
519#124C2×C4×C6714yes—
520C22⋊Q8—22no—
521C22⋊Q8—28no—
522C22⋊Q8C2×C4×C6714yes—
523#121—28no—
524#121—22no—
525#121C2×C4×C6714yes—
526C4×Q8—22no—
527C4×Q8C2×C4×C6714yes—
528C4×D4—28no—
529C4×D4C2×C4×C6714yes—
530C4×D4D4×C6714yes—
531#117—22no—
532#117—22no—
533#117—41no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4D4×C6711yescharacteristic
540C2×C4⋊C4C23×C6711yescharacteristic
541C2×C4⋊C4C23×C6711yescharacteristic
542C2×C4⋊C4C23×C6711yescharacteristic
543C2×C4⋊C4C23×C6711yescharacteristic
544C2×C4⋊C4C23×C6711yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4D4×C6711yescharacteristic
554C2×C22⋊C4D4×C6711yescharacteristic
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42C23×C6711yescharacteristic
560C4⋊C8—22no—
561#103—22no—
562#103—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#103—41no—
567#103—41no—
568#103D4×C6714yescomplemented
569#102—22no—
570#102—22no—
571#102—41no—
572#102—41no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579C24—21no—
580C24C2×D4×C6711yescharacteristic
581C24C2×D4×C6711yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—28no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8C22×C4×C6712yes—
602C2×Q8C22×C4×C6712yes—
603C2×Q8C2×D4×C6712yes—
604C2×Q8#41×C6712yes—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4C22⋊C4×C6714yes—
619C2×D4C22×C4×C6712yes—
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—24no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4C22×C4×C6712yes—
642C22×C4C22×C4×C6712yes—
643C22×C4C2×D4×C6711yescharacteristic
644C22×C4C2×D4×C6711yescharacteristic
645C22×C4C2×D4×C6711yescharacteristic
646C22×C4C2×D4×C6711yescharacteristic
647C22×C4C2×D4×C6712yes—
648C22×C4C2×D4×C6712yes—
649C22×C4C24×C6711yescharacteristic
650M16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8C2×D4×C6712yes—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C22⋊C4×C6714yes—
677C4⋊C4C22×C4×C6712yes—
678C4⋊C4C2×D4×C6712yes—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4C22⋊C4×C6714yes—
688C22⋊C4C22⋊C4×C6714yes—
689C42—24no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42C22×C4×C6712yes—
694C42C2×D4×C6712yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23C2×C22⋊C4×C6712yes—
715C23C2×C22⋊C4×C6712yes—
716C23C22×D4×C6711yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—41no—
724Q8—41no—
725Q8C4×D4×C6714yes—
726D4—22no—
727D4—22no—
728D4—44no—
729D4—48no—
730D4—48no—
731D4—41no—
732D4—41no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
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—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
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×C4C2×C22⋊C4×C6712yes—
773C2×C4C2×C22⋊C4×C6712yes—
774C2×C4C2×C22⋊C4×C6712yes—
775C2×C4C2×C22⋊C4×C6712yes—
776C2×C4C23×C4×C6711yescharacteristic
777C2×C4C22×D4×C6711yescharacteristic
778C2×C4C22×D4×C6711yescharacteristic
779C2×C4C2×#41×C6711yescharacteristic
780C2×C4H(5,𝔽2)×C6711yescharacteristic
781C2×C4H(5,𝔽2)×C6711yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C22×C22⋊C4×C6711yescharacteristic
808C22D42×C6711yescharacteristic
809C22#546×C6711yescharacteristic
810C22#575×C6711yescharacteristic
811C22#575×C6711yescharacteristic
812C22#577×C6711yescharacteristic
813C22#578×C6711yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—81no—
823C4—81no—
824C4—81no—
825C4C2×C4×D4×C6711yescharacteristic
826C4#518×C6711yescharacteristic
827C4D42×C6711yescharacteristic
828C4#546×C6711yescharacteristic
829C2—42no—
830C2—42no—
831C2—82no—
832C2D4×C22⋊C4×C6711yescharacteristic
833C2C67×#289611yescharacteristic
834C2C67×#289811yescharacteristic
835C2C67×#326911yescharacteristic
836C2C67×#327111yescharacteristic
837C2C67×#331311yescharacteristic
838C2C67×#332111yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC2×#548×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×#419×C67C2semidirect
4. C2×#416×C67C2semidirect
5. C67×#2354C2semidirect
6. C67×#1983C2semidirect
7. C67×#1959C2semidirect
8. C67×#1895C2semidirect
9. C67×#1892C2semidirect
10. C67×#1875C2semidirect
11. C67×#1873C2semidirect
12. C67×#1803C2semidirect
13. C67×#1788C2semidirect
14. C67×#1787C2semidirect
15. C67×#1763C2semidirect
21. #548×C67C4semidirect
148. #103×C67D4semidirect
409. #22426C67direct (N × H)
421. C2×#435C2×C67semidirect
422. C2×#419C2×C67semidirect
423. C2×#416C2×C67semidirect
424. #2354C2×C67semidirect
425. #1983C2×C67semidirect
426. #1959C2×C67semidirect
427. #1895C2×C67semidirect
428. #1892C2×C67semidirect
429. #1875C2×C67semidirect
430. #1873C2×C67semidirect
431. #1803C2×C67semidirect
432. #1788C2×C67semidirect
433. #1787C2×C67semidirect
434. #1763C2×C67semidirect
435. C67#22426direct (N × H)
441. #548C4×C67semidirect
568. #103D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C672
C2×#435×C672
C2×#419×C672
C2×#416×C672
C67×#23542
C67×#19832
C67×#19592
C67×#18952
C67×#18922
C67×#18752
C67×#18732
C67×#18032
C67×#17882
C67×#17872
C67×#17632
#2242667