Finite Group Databasebeta

← C2×C67×#3516 #30742036

Subgroups — C2×C67×#3516 #30742036

Order 17152.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3516C2132yesmaximal, direct product factor
2C2×#557×C67C211yesmaximal, characteristic, complemented
3C2×#556×C67C213yesmaximal, complemented
4C2×#554×C67C213yesmaximal, complemented
5C2×#553×C67C213yesmaximal, complemented
6C2×#552×C67C213yesmaximal, complemented
7C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
8C2×#548×C67C211yesmaximal, characteristic, complemented
9C2×#548×C67C211yesmaximal, characteristic, complemented
10C2×#542×C67C213yesmaximal, complemented
11C2×#541×C67C213yesmaximal, complemented
12C2×#529×C67C213yesmaximal, complemented
13C2×#529×C67C213yesmaximal, complemented
14C2×#520×C67C211yesmaximal, characteristic, complemented
15C2×#519×C67C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
17C22×#41×C67C2211yescharacteristic
18C23×Q8×C67C2211yescharacteristic
19C23×Q8×C67C2211yescharacteristic
20#557×C67C22116yescomplemented
21#556×C67C22148yescomplemented
22#554×C67C22148yescomplemented
23#553×C67C22148yescomplemented
24#552×C67C22148yescomplemented
25D4×Q8×C67C22116yescomplemented
26#548×C67C22116yescomplemented
27#548×C67C22116yescomplemented
28#542×C67C22148yescomplemented
29#541×C67C22148yescomplemented
30C2×C4⋊Q8×C67C2213yes—
31C2×C4⋊Q8×C67C2213yes—
32#529×C67C22148yescomplemented
33#529×C67C22148yescomplemented
34C2×#126×C67C2216yes—
35C2×#126×C67C2213yes—
36C2×#126×C67C2213yes—
37C2×#126×C67C2216yes—
38C2×#125×C67C2213yes—
39C2×#125×C67C2213yes—
40C2×#125×C67C2216yes—
41C2×#125×C67C2213yes—
42C2×#124×C67C2213yes—
43C2×#124×C67C2213yes—
44C2×#124×C67C2213yes—
45C2×#123×C67C2211yescharacteristic
46C2×#123×C67C2213yes—
47C2×#123×C67C2216yes—
48C2×C22⋊Q8×C67C2213yes—
49C2×C22⋊Q8×C67C2213yes—
50C2×C22⋊Q8×C67C2213yes—
51C2×C22⋊Q8×C67C2213yes—
52C2×C22⋊Q8×C67C2213yes—
53C2×C22⋊Q8×C67C2216yes—
54C2×#121×C67C2213yes—
55C2×#121×C67C2213yes—
56C2×#121×C67C2213yes—
57#520×C67C22116yescomplemented
58#519×C67C22116yescomplemented
59C2×C4×Q8×C67C2211yescharacteristic
60C2×C4×Q8×C67C2213yes—
61C2×C4×Q8×C67C2211yescharacteristic
62C2×C4×Q8×C67C2213yes—
63C2×C4×Q8×C67C2213yes—
64C2×C4×Q8×C67C2211yescharacteristic
65C2×C4×Q8×C67C2213yes—
66C2×C4×Q8×C67C2211yescharacteristic
67C2×C4×Q8×C67C2213yes—
68C2×C4×Q8×C67C22116yescomplemented
69C2×C4×D4×C67C2213yes—
70C2×C4×D4×C67C2213yes—
71C2×C4×D4×C67C2213yes—
72C2×C4×D4×C67C2213yes—
73C2×C4×D4×C67C2213yes—
74C2×C4×D4×C67C2216yes—
75C2×#117×C67C2213yes—
76C2×#117×C67C2213yes—
77C2×#117×C67C2213yes—
78C2×#117×C67C2216yes—
79C22×C4⋊C4×C67C2213yes—
80C22×C4⋊C4×C67C2213yes—
81C22×C42×C67C2213yes—
82C2×#41×C67—28no—
83C2×#41×C67C2318yes—
84C22×Q8×C67—28no—
85C22×Q8×C67—28no—
86C22×Q8×C67C2313yes—
87C22×Q8×C67C2313yes—
88C22×Q8×C67C2318yes—
89C22×Q8×C67C2318yes—
90C22×Q8×C67C2313yes—
91C22×Q8×C67C2311yescharacteristic
92C22×D4×C67C2313yes—
93C22×D4×C67C2311yescharacteristic
94C22×D4×C67C2313yes—
95C22×D4×C67C2313yes—
96C23×C4×C67C2311yescharacteristic
97C23×C4×C67C2313yes—
98C23×C4×C67C2313yes—
99C23×C4×C67C2313yes—
100C23×C4×C67C2313yes—
101C23×C4×C67C2316yes—
102C4⋊Q8×C67C23124yes—
103C4⋊Q8×C67C23124yes—
104#126×C67C23148yes—
105#126×C67C23124yes—
106#126×C67C23124yes—
107#126×C67C23148yes—
108#125×C67C23124yes—
109#125×C67C23124yes—
110#125×C67C23148yes—
111#125×C67C23124yes—
112#124×C67C23124yes—
113#124×C67C23124yes—
114#124×C67C23124yes—
115#123×C67C2318yes—
116#123×C67C23124yes—
117#123×C67C23148yes—
118C22⋊Q8×C67C23124yes—
119C22⋊Q8×C67C23124yes—
120C22⋊Q8×C67C23124yes—
121C22⋊Q8×C67C23124yes—
122C22⋊Q8×C67C23124yes—
123C22⋊Q8×C67C23148yes—
124#121×C67C23124yes—
125#121×C67C23124yes—
126#121×C67C23124yes—
127C4×Q8×C67C2318yes—
128C4×Q8×C67C23124yes—
129C4×Q8×C67C2318yes—
130C4×Q8×C67C23124yes—
131C4×Q8×C67C23124yes—
132C4×Q8×C67C2318yes—
133C4×Q8×C67C23124yes—
134C4×Q8×C67C2318yes—
135C4×Q8×C67C23124yes—
136C4×D4×C67C23124yes—
137C4×D4×C67C23124yes—
138C4×D4×C67C23124yes—
139C4×D4×C67C23124yes—
140C4×D4×C67C23124yes—
141C4×D4×C67C23148yes—
142#117×C67C23124yes—
143#117×C67C23124yes—
144#117×C67C23124yes—
145#117×C67C23148yes—
146C2×C4⋊C4×C67C2313yes—
147C2×C4⋊C4×C67C2313yes—
148C2×C4⋊C4×C67C2313yes—
149C2×C4⋊C4×C67C2313yes—
150C2×C4⋊C4×C67C2316yes—
151C2×C4⋊C4×C67C23124yes—
152C2×C4⋊C4×C67C23124yes—
153C2×C4⋊C4×C67C2311yescharacteristic
154C2×C4⋊C4×C67C2313yes—
155C2×C4⋊C4×C67C2313yes—
156C2×C4⋊C4×C67C2313yes—
157C2×C4⋊C4×C67C2313yes—
158C2×C4⋊C4×C67C2316yes—
159C2×C4⋊C4×C67C2313yes—
160C2×C4⋊C4×C67C2313yes—
161C2×C4⋊C4×C67C2316yes—
162C2×C4⋊C4×C67C2313yes—
163C2×C4⋊C4×C67C2311yescharacteristic
164C2×C4⋊C4×C67C2313yes—
165C2×C22⋊C4×C67C2313yes—
166C2×C22⋊C4×C67C2311yescharacteristic
167C2×C22⋊C4×C67C2313yes—
168C2×C22⋊C4×C67C2313yes—
169C2×C22⋊C4×C67C2313yes—
170C2×C22⋊C4×C67C2316yes—
171C2×C22⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67C2313yes—
173C2×C22⋊C4×C67C2311yescharacteristic
174C2×C22⋊C4×C67C2316yes—
175C2×C22⋊C4×C67C2313yes—
176C2×C22⋊C4×C67C2313yes—
177C2×C42×C67C2313yes—
178C2×C42×C67C2313yes—
179C2×C42×C67C2313yes—
180C2×C42×C67C2313yes—
181C2×C42×C67C23124yes—
182C2×C42×C67C2316yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C2313yes—
185C24×C67C2411yescharacteristic
186C24×C67C2413yes—
187C24×C67C2411yescharacteristic
188#41×C67—232no—
189C2×Q8×C67—232no—
190C2×Q8×C67—232no—
191C2×Q8×C67—212no—
192C2×Q8×C67—212no—
193C2×Q8×C67—46no—
194C2×Q8×C67#4118yes—
195C2×Q8×C67C24112yes—
196C2×Q8×C67C24112yes—
197C2×Q8×C67C24112yes—
198C2×Q8×C67C2414yes—
199C2×D4×C67—212no—
200C2×D4×C67—24no—
201C2×D4×C67—212no—
202C2×D4×C67—46no—
203C2×D4×C67C24112yes—
204C2×D4×C67C2414yes—
205C2×D4×C67C24112yes—
206C2×D4×C67C24112yes—
207C22×C4×C67—24no—
208C22×C4×C67—212no—
209C22×C4×C67—212no—
210C22×C4×C67—212no—
211C22×C4×C67—412no—
212C22×C4×C67—46no—
213C22×C4×C67C2414yes—
214C22×C4×C67C24112yes—
215C22×C4×C67C24112yes—
216C22×C4×C67C24112yes—
217C22×C4×C67C2411yescharacteristic
218C22×C4×C67C2411yescharacteristic
219C22×C4×C67C2413yes—
220C22×C4×C67C2411yescharacteristic
221C22×C4×C67C2413yes—
222C22×C4×C67C2411yescharacteristic
223C22×C4×C67C2413yes—
224C22×C4×C67C2413yes—
225C22×C4×C67C2413yes—
226C22×C4×C67C2413yes—
227C22×C4×C67C2411yescharacteristic
228C22×C4×C67C24112yes—
229C22×C4×C67C24124yes—
230C22×C4×C67C2413yes—
231C4⋊C4×C67C24112yes—
232C4⋊C4×C67C24112yes—
233C4⋊C4×C67C24112yes—
234C4⋊C4×C67C24112yes—
235C4⋊C4×C67C24124yes—
236C4⋊C4×C67C2414yes—
237C4⋊C4×C67C24112yes—
238C4⋊C4×C67C24112yes—
239C4⋊C4×C67C24112yes—
240C4⋊C4×C67C24112yes—
241C4⋊C4×C67C24124yes—
242C4⋊C4×C67C24112yes—
243C4⋊C4×C67C24112yes—
244C4⋊C4×C67C24124yes—
245C4⋊C4×C67C24112yes—
246C4⋊C4×C67C2414yes—
247C4⋊C4×C67C24112yes—
248C22⋊C4×C67C24112yes—
249C22⋊C4×C67C2414yes—
250C22⋊C4×C67C24112yes—
251C22⋊C4×C67C24112yes—
252C22⋊C4×C67C24112yes—
253C22⋊C4×C67C24124yes—
254C22⋊C4×C67C2414yes—
255C22⋊C4×C67C24112yes—
256C22⋊C4×C67C2414yes—
257C22⋊C4×C67C24124yes—
258C22⋊C4×C67C24112yes—
259C22⋊C4×C67C24112yes—
260C42×C67C24112yes—
261C42×C67C24112yes—
262C42×C67C24112yes—
263C42×C67C24112yes—
264C42×C67C24124yes—
265C42×C67C24112yes—
266C42×C67C24112yes—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—26no—
271C23×C67—22no—
272C23×C67—26no—
273C23×C67—26no—
274C23×C67—22no—
275C23×C672−1+414yes—
276C23×C67C2512yes—
277C23×C67C2516yes—
278C23×C67C2512yes—
279C23×C67C2511yescharacteristic
280Q8×C67—224no—
281Q8×C67—224no—
282Q8×C67—412no—
283Q8×C67C2×#41116yes—
284D4×C67—224no—
285D4×C67—28no—
286D4×C67—224no—
287D4×C67—412no—
288C2×C4×C67—22no—
289C2×C4×C67—26no—
290C2×C4×C67—26no—
291C2×C4×C67—28no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—26no—
295C2×C4×C67—22no—
296C2×C4×C67—26no—
297C2×C4×C67—26no—
298C2×C4×C67—26no—
299C2×C4×C67—22no—
300C2×C4×C67—224no—
301C2×C4×C67—224no—
302C2×C4×C67—224no—
303C2×C4×C67—424no—
304C2×C4×C67—412no—
305C2×C4×C67C2×#41112yes—
306C2×C4×C67C2512yes—
307C2×C4×C67C2512yes—
308C2×C4×C67C2516yes—
309C2×C4×C67C2512yes—
310C2×C4×C67C2516yes—
311C2×C4×C67C2512yes—
312C2×C4×C67C2516yes—
313C2×C4×C67C2516yes—
314C2×C4×C67C2516yes—
315C2×C4×C67C2516yes—
316C2×C4×C67C2512yes—
317C2×C4×C67C2516yes—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—28no—
321C22×C67—22no—
322C22×C67—26no—
323C22×C67—22no—
324C22×C67—26no—
325C22×C67—26no—
326C22×C67—22no—
327C22×C67—44no—
328C22×C67—412no—
329C22×C67C22×#4112yes—
330C22×C67C2×2−1+414yes—
331C22×C67C2×2−1+412yes—
332C22×C67#58512yes—
333C22×C67C2611yescharacteristic
334C4×C67—22no—
335C4×C67—26no—
336C4×C67—26no—
337C4×C67—22no—
338C4×C67—22no—
339C4×C67—26no—
340C4×C67—22no—
341C4×C67—26no—
342C4×C67—26no—
343C4×C67—26no—
344C4×C67—22no—
345C4×C67C22×#41112yes—
346C2×#3516C6711yesmaximal, characteristic, direct product factor, Sylow
347C2×C67—24no—
348C2×C67—42no—
349C2×C67—46no—
350C2×C67#351614yesdirect product factor
351C2×C67C23×#4111yescharacteristic
352C2×C67C22×2−1+411yescharacteristic
353C2×C67C2×#58511yescharacteristic
354#3516C2×C67132yesdirect product factor
355C2×#557C2×C6711yescharacteristic, complemented
356C2×#556C2×C6713yescomplemented
357C2×#554C2×C6713yescomplemented
358C2×#553C2×C6713yescomplemented
359C2×#552C2×C6713yescomplemented
360C2×D4×Q8C2×C6711yescharacteristic, complemented
361C2×#548C2×C6711yescharacteristic, complemented
362C2×#548C2×C6711yescharacteristic, complemented
363C2×#542C2×C6713yescomplemented
364C2×#541C2×C6713yescomplemented
365C2×#529C2×C6713yescomplemented
366C2×#529C2×C6713yescomplemented
367C2×#520C2×C6711yescharacteristic, complemented
368C2×#519C2×C6711yescharacteristic, complemented
369C22×C4×Q8C2×C6711yescharacteristic, complemented
370C67C2×#351611yescharacteristic, direct product factor, Sylow
371C22×#41C22×C6711yescharacteristic
372C23×Q8C22×C6711yescharacteristic
373C23×Q8C22×C6711yescharacteristic
374#557C22×C67116yescomplemented
375#556C22×C67148yescomplemented
376#554C22×C67148yescomplemented
377#553C22×C67148yescomplemented
378#552C22×C67148yescomplemented
379D4×Q8C22×C67116yescomplemented
380#548C22×C67116yescomplemented
381#548C22×C67116yescomplemented
382#542C22×C67148yescomplemented
383#541C22×C67148yescomplemented
384C2×C4⋊Q8C22×C6713yes—
385C2×C4⋊Q8C22×C6713yes—
386#529C22×C67148yescomplemented
387#529C22×C67148yescomplemented
388C2×#126C22×C6716yes—
389C2×#126C22×C6713yes—
390C2×#126C22×C6713yes—
391C2×#126C22×C6716yes—
392C2×#125C22×C6713yes—
393C2×#125C22×C6713yes—
394C2×#125C22×C6716yes—
395C2×#125C22×C6713yes—
396C2×#124C22×C6713yes—
397C2×#124C22×C6713yes—
398C2×#124C22×C6713yes—
399C2×#123C22×C6711yescharacteristic
400C2×#123C22×C6713yes—
401C2×#123C22×C6716yes—
402C2×C22⋊Q8C22×C6713yes—
403C2×C22⋊Q8C22×C6713yes—
404C2×C22⋊Q8C22×C6713yes—
405C2×C22⋊Q8C22×C6713yes—
406C2×C22⋊Q8C22×C6713yes—
407C2×C22⋊Q8C22×C6716yes—
408C2×#121C22×C6713yes—
409C2×#121C22×C6713yes—
410C2×#121C22×C6713yes—
411#520C22×C67116yescomplemented
412#519C22×C67116yescomplemented
413C2×C4×Q8C22×C6711yescharacteristic
414C2×C4×Q8C22×C6713yes—
415C2×C4×Q8C22×C6711yescharacteristic
416C2×C4×Q8C22×C6713yes—
417C2×C4×Q8C22×C6713yes—
418C2×C4×Q8C22×C6711yescharacteristic
419C2×C4×Q8C22×C6713yes—
420C2×C4×Q8C22×C6711yescharacteristic
421C2×C4×Q8C22×C6713yes—
422C2×C4×Q8C22×C67116yescomplemented
423C2×C4×D4C22×C6713yes—
424C2×C4×D4C22×C6713yes—
425C2×C4×D4C22×C6713yes—
426C2×C4×D4C22×C6713yes—
427C2×C4×D4C22×C6713yes—
428C2×C4×D4C22×C6716yes—
429C2×#117C22×C6713yes—
430C2×#117C22×C6713yes—
431C2×#117C22×C6713yes—
432C2×#117C22×C6716yes—
433C22×C4⋊C4C22×C6713yes—
434C22×C4⋊C4C22×C6713yes—
435C22×C42C22×C6713yes—
436C2×#41—28no—
437C2×#41C23×C6718yes—
438C22×Q8—28no—
439C22×Q8—28no—
440C22×Q8C23×C6713yes—
441C22×Q8C23×C6713yes—
442C22×Q8C23×C6718yes—
443C22×Q8C23×C6718yes—
444C22×Q8C23×C6713yes—
445C22×Q8C23×C6711yescharacteristic
446C22×D4C23×C6713yes—
447C22×D4C23×C6711yescharacteristic
448C22×D4C23×C6713yes—
449C22×D4C23×C6713yes—
450C23×C4C23×C6713yes—
451C23×C4C23×C6713yes—
452C23×C4C23×C6713yes—
453C23×C4C23×C6711yescharacteristic
454C23×C4C23×C6713yes—
455C23×C4C23×C6716yes—
456C4⋊Q8C23×C67124yes—
457C4⋊Q8C23×C67124yes—
458#126C23×C67148yes—
459#126C23×C67124yes—
460#126C23×C67124yes—
461#126C23×C67148yes—
462#125C23×C67124yes—
463#125C23×C67124yes—
464#125C23×C67148yes—
465#125C23×C67124yes—
466#124C23×C67124yes—
467#124C23×C67124yes—
468#124C23×C67124yes—
469#123C23×C6718yes—
470#123C23×C67124yes—
471#123C23×C67148yes—
472C22⋊Q8C23×C67124yes—
473C22⋊Q8C23×C67124yes—
474C22⋊Q8C23×C67124yes—
475C22⋊Q8C23×C67124yes—
476C22⋊Q8C23×C67124yes—
477C22⋊Q8C23×C67148yes—
478#121C23×C67124yes—
479#121C23×C67124yes—
480#121C23×C67124yes—
481C4×Q8C23×C6718yes—
482C4×Q8C23×C67124yes—
483C4×Q8C23×C6718yes—
484C4×Q8C23×C67124yes—
485C4×Q8C23×C67124yes—
486C4×Q8C23×C6718yes—
487C4×Q8C23×C67124yes—
488C4×Q8C23×C6718yes—
489C4×Q8C23×C67124yes—
490C4×D4C23×C67124yes—
491C4×D4C23×C67124yes—
492C4×D4C23×C67124yes—
493C4×D4C23×C67124yes—
494C4×D4C23×C67124yes—
495C4×D4C23×C67148yes—
496#117C23×C67124yes—
497#117C23×C67124yes—
498#117C23×C67124yes—
499#117C23×C67148yes—
500C2×C4⋊C4C23×C6713yes—
501C2×C4⋊C4C23×C6713yes—
502C2×C4⋊C4C23×C6713yes—
503C2×C4⋊C4C23×C6713yes—
504C2×C4⋊C4C23×C6716yes—
505C2×C4⋊C4C23×C67124yes—
506C2×C4⋊C4C23×C67124yes—
507C2×C4⋊C4C23×C6711yescharacteristic
508C2×C4⋊C4C23×C6713yes—
509C2×C4⋊C4C23×C6713yes—
510C2×C4⋊C4C23×C6713yes—
511C2×C4⋊C4C23×C6713yes—
512C2×C4⋊C4C23×C6716yes—
513C2×C4⋊C4C23×C6713yes—
514C2×C4⋊C4C23×C6713yes—
515C2×C4⋊C4C23×C6716yes—
516C2×C4⋊C4C23×C6713yes—
517C2×C4⋊C4C23×C6711yescharacteristic
518C2×C4⋊C4C23×C6713yes—
519C2×C22⋊C4C23×C6713yes—
520C2×C22⋊C4C23×C6711yescharacteristic
521C2×C22⋊C4C23×C6713yes—
522C2×C22⋊C4C23×C6713yes—
523C2×C22⋊C4C23×C6713yes—
524C2×C22⋊C4C23×C6716yes—
525C2×C22⋊C4C23×C6711yescharacteristic
526C2×C22⋊C4C23×C6713yes—
527C2×C22⋊C4C23×C6711yescharacteristic
528C2×C22⋊C4C23×C6716yes—
529C2×C22⋊C4C23×C6713yes—
530C2×C22⋊C4C23×C6713yes—
531C2×C42C23×C6713yes—
532C2×C42C23×C6716yes—
533C2×C42C23×C6713yes—
534C2×C42C23×C6713yes—
535C2×C42C23×C6713yes—
536C2×C42C23×C6713yes—
537C2×C42C23×C6713yes—
538C2×C42C23×C67124yes—
539C24C24×C6711yescharacteristic
540C24C24×C6713yes—
541C24C24×C6711yescharacteristic
542#41—232no—
543C2×Q8—232no—
544C2×Q8—232no—
545C2×Q8—212no—
546C2×Q8—212no—
547C2×Q8—46no—
548C2×Q8#41×C6718yes—
549C2×Q8C24×C67112yes—
550C2×Q8C24×C67112yes—
551C2×Q8C24×C67112yes—
552C2×Q8C24×C6714yes—
553C2×D4—212no—
554C2×D4—24no—
555C2×D4—212no—
556C2×D4—46no—
557C2×D4C24×C67112yes—
558C2×D4C24×C6714yes—
559C2×D4C24×C67112yes—
560C2×D4C24×C67112yes—
561C22×C4—24no—
562C22×C4—212no—
563C22×C4—212no—
564C22×C4—212no—
565C22×C4—412no—
566C22×C4—46no—
567C22×C4C24×C6711yescharacteristic
568C22×C4C24×C6711yescharacteristic
569C22×C4C24×C6714yes—
570C22×C4C24×C6713yes—
571C22×C4C24×C6711yescharacteristic
572C22×C4C24×C6713yes—
573C22×C4C24×C6711yescharacteristic
574C22×C4C24×C6713yes—
575C22×C4C24×C6713yes—
576C22×C4C24×C6713yes—
577C22×C4C24×C67112yes—
578C22×C4C24×C6713yes—
579C22×C4C24×C6711yescharacteristic
580C22×C4C24×C67112yes—
581C22×C4C24×C67112yes—
582C22×C4C24×C67112yes—
583C22×C4C24×C67124yes—
584C22×C4C24×C6713yes—
585C4⋊C4C24×C67112yes—
586C4⋊C4C24×C67112yes—
587C4⋊C4C24×C67112yes—
588C4⋊C4C24×C67112yes—
589C4⋊C4C24×C67124yes—
590C4⋊C4C24×C6714yes—
591C4⋊C4C24×C67112yes—
592C4⋊C4C24×C67112yes—
593C4⋊C4C24×C67112yes—
594C4⋊C4C24×C67112yes—
595C4⋊C4C24×C67124yes—
596C4⋊C4C24×C67112yes—
597C4⋊C4C24×C67112yes—
598C4⋊C4C24×C67124yes—
599C4⋊C4C24×C67112yes—
600C4⋊C4C24×C6714yes—
601C4⋊C4C24×C67112yes—
602C22⋊C4C24×C67112yes—
603C22⋊C4C24×C6714yes—
604C22⋊C4C24×C67112yes—
605C22⋊C4C24×C67112yes—
606C22⋊C4C24×C67112yes—
607C22⋊C4C24×C67124yes—
608C22⋊C4C24×C6714yes—
609C22⋊C4C24×C67112yes—
610C22⋊C4C24×C6714yes—
611C22⋊C4C24×C67124yes—
612C22⋊C4C24×C67112yes—
613C22⋊C4C24×C67112yes—
614C42C24×C67112yes—
615C42C24×C67112yes—
616C42C24×C67112yes—
617C42C24×C67112yes—
618C42C24×C67124yes—
619C42C24×C67112yes—
620C42C24×C67112yes—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—26no—
625C23—22no—
626C23—26no—
627C23—26no—
628C23—22no—
629C232−1+4×C6714yes—
630C23C25×C6712yes—
631C23C25×C6716yes—
632C23C25×C6712yes—
633C23C25×C6711yescharacteristic
634Q8—224no—
635Q8—224no—
636Q8—412no—
637Q8C2×#41×C67116yes—
638D4—224no—
639D4—28no—
640D4—224no—
641D4—412no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—26no—
652C2×C4—26no—
653C2×C4—22no—
654C2×C4—224no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—424no—
658C2×C4—412no—
659C2×C4C2×#41×C67112yes—
660C2×C4C25×C6712yes—
661C2×C4C25×C6712yes—
662C2×C4C25×C6716yes—
663C2×C4C25×C6712yes—
664C2×C4C25×C6716yes—
665C2×C4C25×C6712yes—
666C2×C4C25×C6716yes—
667C2×C4C25×C6716yes—
668C2×C4C25×C6716yes—
669C2×C4C25×C6716yes—
670C2×C4C25×C6712yes—
671C2×C4C25×C6716yes—
672C22—22no—
673C22—22no—
674C22—28no—
675C22—22no—
676C22—26no—
677C22—22no—
678C22—26no—
679C22—26no—
680C22—22no—
681C22—44no—
682C22—412no—
683C22C22×#41×C6712yes—
684C22C2×2−1+4×C6714yes—
685C22C2×2−1+4×C6712yes—
686C22#585×C6712yes—
687C22C26×C6711yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—22no—
693C4—26no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—26no—
698C4—22no—
699C4C22×#41×C67112yes—
700C2—24no—
701C2—42no—
702C2—46no—
703C2C67×#351614yesdirect product factor
704C2C23×#41×C6711yescharacteristic
705C2C22×2−1+4×C6711yescharacteristic
706C2C2×#585×C6711yescharacteristic
subgroupG/H
center, socleC23×C67C25
commutator, Frattini, cosocleC22C26×C67
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#3516C2direct (N × H)
2. C2×#557×C67C2semidirect
3. C2×#556×C67C2semidirect
4. C2×#554×C67C2semidirect
5. C2×#553×C67C2semidirect
6. C2×#552×C67C2semidirect
7. C2×D4×Q8×C67C2semidirect
8. C2×#548×C67C2semidirect
9. C2×#548×C67C2semidirect
10. C2×#542×C67C2semidirect
11. C2×#541×C67C2semidirect
12. C2×#529×C67C2semidirect
13. C2×#529×C67C2semidirect
14. C2×#520×C67C2semidirect
15. C2×#519×C67C2semidirect
16. C22×C4×Q8×C67C2semidirect
20. #557×C67C22semidirect
21. #556×C67C22semidirect
22. #554×C67C22semidirect
23. #553×C67C22semidirect
24. #552×C67C22semidirect
25. D4×Q8×C67C22semidirect
26. #548×C67C22semidirect
27. #548×C67C22semidirect
28. #542×C67C22semidirect
29. #541×C67C22semidirect
32. #529×C67C22semidirect
33. #529×C67C22semidirect
57. #520×C67C22semidirect
58. #519×C67C22semidirect
68. C2×C4×Q8×C67C22semidirect
346. C2×#3516C67direct (N × H)
350. C2×C67#3516direct (N × H)
354. #3516C2×C67direct (N × H)
355. C2×#557C2×C67semidirect
356. C2×#556C2×C67semidirect
357. C2×#554C2×C67semidirect
358. C2×#553C2×C67semidirect
359. C2×#552C2×C67semidirect
360. C2×D4×Q8C2×C67semidirect
361. C2×#548C2×C67semidirect
362. C2×#548C2×C67semidirect
363. C2×#542C2×C67semidirect
364. C2×#541C2×C67semidirect
365. C2×#529C2×C67semidirect
366. C2×#529C2×C67semidirect
367. C2×#520C2×C67semidirect
368. C2×#519C2×C67semidirect
369. C22×C4×Q8C2×C67semidirect
370. C67C2×#3516direct (N × H)
374. #557C22×C67semidirect
375. #556C22×C67semidirect
376. #554C22×C67semidirect
377. #553C22×C67semidirect
378. #552C22×C67semidirect
379. D4×Q8C22×C67semidirect
380. #548C22×C67semidirect
381. #548C22×C67semidirect
382. #542C22×C67semidirect
383. #541C22×C67semidirect
386. #529C22×C67semidirect
387. #529C22×C67semidirect
411. #520C22×C67semidirect
412. #519C22×C67semidirect
422. C2×C4×Q8C22×C67semidirect
703. C2C67×#3516direct (N × H)

Maximal subgroups

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

subgroupindex
C67×#35162
C2×#557×C672
C2×#556×C672
C2×#554×C672
C2×#553×C672
C2×#552×C672
C2×D4×Q8×C672
C2×#548×C672
C2×#542×C672
C2×#541×C672
C2×#529×C672
C2×#520×C672
C2×#519×C672
C22×C4×Q8×C672
C2×#351667