Finite Group Databasebeta

← #30779211

Subgroups — #30779211

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863303C211yesmaximal, characteristic
2C2×#16863303C211yesmaximal, characteristic
3C2×#16863292C211yesmaximal, characteristic
4C2×C4×Dic67⋊C4C211yesmaximal, characteristic
5#22558472C212yesmaximal
6#22558468C212yesmaximal
7#22558442C212yesmaximal
8#22558442C212yesmaximal
9#22558439C211yesmaximal, characteristic
10#22558438C211yesmaximal, characteristic
11C22×C4×Q8×C67C211yesmaximal, characteristic
12C22×C4⋊Dic67C2211yescharacteristic
13C22×C4⋊Dic67C2211yescharacteristic
14C22×Dic67⋊C4C2211yescharacteristic
15C22×Dic67⋊C4C2212yes—
16C22×Dic67⋊C4C2211yescharacteristic
17C22×C4×Dic67C2211yescharacteristic
18C22×C4×Dic67C2211yescharacteristic
19#16863303—24no—
20#16863303C418yescomplemented
21#16863292—24no—
22C4×Dic67⋊C4—24no—
23C2×C67⋊#95C2211yescharacteristic
24C2×C67⋊#95C2212yes—
25C2×C67⋊#95C2212yes—
26C2×C67⋊#95C2212yes—
27C2×C67⋊#95C2212yes—
28C2×C67⋊#95C2212yes—
29C2×C67⋊#95C2211yescharacteristic
30C2×C67⋊#95C2212yes—
31C2×C67⋊#95C2212yes—
32C2×C67⋊#95C2212yes—
33C2×C67⋊#95C2212yes—
34C23×Q8×C67C2211yescharacteristic
35C2×C4×Q8×C67—24no—
36C2×C4×Q8×C67—24no—
37C2×C4×Q8×C67—24no—
38C22×C4⋊C4×C67C2212yes—
39C22×C4⋊C4×C67C2211yescharacteristic
40C22×C42×C67C2212yes—
41C22×C42×C67C2211yescharacteristic
42C23×Dic67C2312yes—
43C23×Dic67C2311yescharacteristic
44C23×Dic67C2312yes—
45C23×Dic67C2311yescharacteristic
46C23×Dic67C2311yescharacteristic
47C23×Dic67C2311yescharacteristic
48C2×C4⋊Dic67—22no—
49C2×C4⋊Dic67—22no—
50C2×C4⋊Dic67—22no—
51C2×C4⋊Dic67—22no—
52C2×C4⋊Dic67—22no—
53C2×C4⋊Dic67C2×C414yes—
54C2×Dic67⋊C4—22no—
55C2×Dic67⋊C4—22no—
56C2×Dic67⋊C4—24no—
57C2×Dic67⋊C4—22no—
58C2×Dic67⋊C4—22no—
59C2×Dic67⋊C4—24no—
60C2×Dic67⋊C4—22no—
61C2×Dic67⋊C4—42no—
62C2×Dic67⋊C4Q814yescomplemented
63C2×C4×Dic67—22no—
64C2×C4×Dic67—22no—
65C2×C4×Dic67—22no—
66C2×C4×Dic67—22no—
67C2×C4×Dic67—22no—
68C2×C4×Dic67C2×C414yes—
69C67⋊#95—24no—
70C67⋊#95—22no—
71C67⋊#95—22no—
72C67⋊#95—24no—
73C67⋊#95—24no—
74C67⋊#95—24no—
75C67⋊#95—24no—
76C67⋊#95—42no—
77C67⋊#95—42no—
78C67⋊#95C2×C418yes—
79C67⋊#95C2×C418yes—
80C22×Q8×C67—22no—
81C22×Q8×C67—22no—
82C22×Q8×C67—22no—
83C22×Q8×C67—22no—
84C22×Q8×C67C2×C414yes—
85C22×Q8×C67D414yes—
86C22×Q8×C67Q814yes—
87C23×C4×C67C2312yes—
88C23×C4×C67C2311yescharacteristic
89C23×C4×C67C2312yes—
90C23×C4×C67C2311yescharacteristic
91C23×C4×C67C2311yescharacteristic
92C4×Q8×C67—232no—
93C2×C4⋊C4×C67—24no—
94C2×C4⋊C4×C67—24no—
95C2×C4⋊C4×C67—24no—
96C2×C4⋊C4×C67—22no—
97C2×C4⋊C4×C67—22no—
98C2×C4⋊C4×C67D414yes—
99C2×C42×C67—24no—
100C2×C42×C67—24no—
101C2×C42×C67—24no—
102C2×C42×C67—22no—
103C2×C42×C67—22no—
104C2×C42×C67D414yes—
105C22×Dic67—21no—
106C22×Dic67—21no—
107C22×Dic67—21no—
108C22×Dic67—21no—
109C22×Dic67—21no—
110C22×Dic67—21no—
111C22×Dic67—21no—
112C22×Dic67—21no—
113C22×Dic67—21no—
114C22×Dic67—21no—
115C22×Dic67—22no—
116C22×Dic67—21no—
117C22×Dic67—22no—
118C22×Dic67—21no—
119C22×Dic67—22no—
120C22×Dic67—21no—
121C22×Dic67—21no—
122C22×Dic67—22no—
123C22×Dic67—21no—
124C22×Dic67—22no—
125C22×Dic67—21no—
126C22×Dic67—21no—
127C22×Dic67—21no—
128C22×Dic67—21no—
129C22×Dic67—21no—
130C22×Dic67—22no—
131C22×Dic67—21no—
132C22×Dic67—21no—
133C22×Dic67—22no—
134C22×Dic67—22no—
135C22×Dic67—22no—
136C22×Dic67—22no—
137C22×Dic67—22no—
138C22×Dic67—22no—
139C22×Dic67—22no—
140C22×Dic67C22×C412yes—
141C22×Dic67C22×C414yes—
142C22×Dic67C22×C412yes—
143C22×Dic67C2×Q812yes—
144C22×Dic67C2×Q812yes—
145C22×Dic67#4112yes—
146C22×Dic67#4112yes—
147C4⋊Dic67—28no—
148C4⋊Dic67—44no—
149Dic67⋊C4—28no—
150Dic67⋊C4—28no—
151Dic67⋊C4—48no—
152C4×Dic67—28no—
153C4×Dic67—44no—
154C24×C67C2411yescharacteristic
155C2×Q8×C67—28no—
156C2×Q8×C67—28no—
157C2×Q8×C67—28no—
158C2×Q8×C67—28no—
159C2×Q8×C67—28no—
160C2×Q8×C67—28no—
161C2×Q8×C67C4⋊C4116yescomplemented
162C22×C4×C67—21no—
163C22×C4×C67—21no—
164C22×C4×C67—22no—
165C22×C4×C67—22no—
166C22×C4×C67—22no—
167C22×C4×C67—22no—
168C22×C4×C67—21no—
169C22×C4×C67—21no—
170C22×C4×C67—22no—
171C22×C4×C67—21no—
172C22×C4×C67—22no—
173C22×C4×C67—21no—
174C22×C4×C67—22no—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—22no—
178C22×C4×C67—21no—
179C22×C4×C67—22no—
180C22×C4×C67—21no—
181C22×C4×C67—22no—
182C22×C4×C67C22×C414yes—
183C22×C4×C67C22×C412yes—
184C22×C4×C67C2×D414yes—
185C22×C4×C67C2×D412yes—
186C22×C4×C67C2×D414yes—
187C22×C4×C67C2×D412yes—
188C22×C4×C67C2×D412yes—
189C22×C4×C67C2×D412yes—
190C22×C4×C67C2×D412yes—
191C22×C4×C67C2×Q812yes—
192C22×C4×C67C2×Q814yes—
193C22×C4×C67C2×Q812yes—
194C22×C4×C67#4112yes—
195C22×C4×C67#4112yes—
196C22×C4×C67#4112yes—
197C4⋊C4×C67—216no—
198C4⋊C4×C67—28no—
199C42×C67—216no—
200C42×C67—28no—
201C23×C67C23×C411yescharacteristic
202C23×C67C22×D411yescharacteristic
203C23×C67C22×D411yescharacteristic
204C23×C67C22×D411yescharacteristic
205C23×C67C22×Q811yescharacteristic
206C23×C67C22×Q811yescharacteristic
207C23×C67C2×#4111yescharacteristic
208C23×C67C2×#4111yescharacteristic
209C23×C67C2×#4111yescharacteristic
210C23×C67C2×#4111yescharacteristic
211C23×C67C2×#4111yescharacteristic
212C23×C67H(5,𝔽2)11yescharacteristic
213C23×C672−1+411yescharacteristic
214C23×C672−1+411yescharacteristic
215C23×C672−1+411yescharacteristic
216Q8×C67—232no—
217C2×C4×C67—24no—
218C2×C4×C67—24no—
219C2×C4×C67—22no—
220C2×C4×C67—24no—
221C2×C4×C67—24no—
222C2×C4×C67—24no—
223C2×C4×C67—24no—
224C2×C4×C67—22no—
225C2×C4×C67—22no—
226C2×C4×C67—22no—
227C2×C4×C67—22no—
228C2×C4×C67—22no—
229C2×C4×C67—24no—
230C2×C4×C67—22no—
231C2×C4×C67—22no—
232C2×C4×C67—22no—
233C2×C4×C67—24no—
234C2×C4×C67—24no—
235C2×C4×C67—42no—
236C2×C4×C67—42no—
237C2×C4×C67—41no—
238C2×C4×C67—41no—
239C2×C4×C67—41no—
240C2×C4×C67—42no—
241C2×C4×C67—42no—
242C2×C4×C67—41no—
243C2×C4×C67C2×C4⋊C418yes—
244C2×C4×C67C2×C4⋊C414yes—
245C2×C4×C67C4×D414yes—
246C2×C4×C67C4×D414yes—
247C2×C4×C67#12014yes—
248C2×C4×C67C22⋊Q814yes—
249C2×C4×C67C22⋊Q814yes—
250C2×C4×C67C22⋊Q814yes—
251C2×C4×C67#12314yes—
252C2×Dic67—22no—
253C2×Dic67—22no—
254C2×Dic67—22no—
255C2×Dic67—22no—
256C2×Dic67—22no—
257C2×Dic67—22no—
258C2×Dic67—22no—
259C2×Dic67—24no—
260C2×Dic67—24no—
261C2×Dic67—22no—
262C2×Dic67—22no—
263C2×Dic67—24no—
264C2×Dic67—22no—
265C2×Dic67—22no—
266C2×Dic67—22no—
267C2×Dic67—22no—
268C2×Dic67—22no—
269C2×Dic67—22no—
270C2×Dic67—41no—
271C2×Dic67—41no—
272C2×Dic67—41no—
273C2×Dic67—41no—
274C2×Dic67—41no—
275C2×Dic67—41no—
276C2×Dic67—41no—
277C2×Dic67—41no—
278C2×Dic67—42no—
279C2×Dic67—41no—
280C2×Dic67—42no—
281C2×Dic67—41no—
282C2×Dic67—41no—
283C2×Dic67—41no—
284C2×Dic67—42no—
285C2×Dic67—42no—
286C2×Dic67—42no—
287C2×Dic67—42no—
288C2×Dic67—42no—
289C2×Dic67—42no—
290C2×Dic67—42no—
291C2×Dic67—42no—
292C2×Dic67—42no—
293C2×Dic67C4×Q814yescomplemented
294C22×C67C22×C4⋊C411yescharacteristic
295C22×C67C2×C4×D411yescharacteristic
296C22×C67C2×C4×D411yescharacteristic
297C22×C67C2×C4×Q811yescharacteristic
298C22×C67C4×#4111yescharacteristic
299C22×C67#51911yescharacteristic
300C22×C67#52011yescharacteristic
301C22×C67C2×#12011yescharacteristic
302C22×C67C2×C22⋊Q811yescharacteristic
303C22×C67C2×C22⋊Q811yescharacteristic
304C22×C67C2×C22⋊Q811yescharacteristic
305C22×C67C2×#12311yescharacteristic
306C22×C67#52511yescharacteristic
307C22×C67#52911yescharacteristic
308C22×C67#53311yescharacteristic
309C22×C67#53611yescharacteristic
310C22×C67#53711yescharacteristic
311C22×C67#54111yescharacteristic
312C22×C67#54211yescharacteristic
313C22×C67#54611yescharacteristic
314C22×C67#54711yescharacteristic
315C22×C67#54811yescharacteristic
316C22×C67#54811yescharacteristic
317C22×C67#54811yescharacteristic
318C22×C67D4×Q811yescharacteristic
319C22×C67D4×Q811yescharacteristic
320C22×C67#55011yescharacteristic
321C22×C67#55611yescharacteristic
322C22×C67#55611yescharacteristic
323C22×C67#55711yescharacteristic
324C22×C67#55711yescharacteristic
325C22×C67#55711yescharacteristic
326C22×C67#55711yescharacteristic
327C22×C67Q8211yescharacteristic
328C22×C67#55911yescharacteristic
329C4×C67—24no—
330C4×C67—28no—
331C4×C67—42no—
332C4×C67—44no—
333C4×C67#38518yes—
334Dic67—24no—
335Dic67—42no—
336Dic67—44no—
337Dic67—42no—
338Dic67—42no—
339Dic67—82no—
340#14017—671nomaximal, Sylow
341C2×C67C2×#38511yescharacteristic
342C2×C67C4×C22⋊Q811yescharacteristic
343C2×C67#232311yescharacteristic
344C2×C67Q8×C4⋊C411yescharacteristic
345C2×C67#235111yescharacteristic
346C2×C67#236511yescharacteristic
347C2×C67#236711yescharacteristic
348C2×C67#240711yescharacteristic
349C2×C67#240911yescharacteristic
350C2×C67#244611yescharacteristic
351C2×C67#244811yescharacteristic
352C2×C67#245111yescharacteristic
353C2×C67#245311yescharacteristic
354C2×C67#258111yescharacteristic
355C2×C67#258211yescharacteristic
356C22×C4×Q8D6711yescharacteristic
357C2×#391—671no—
358C2×#391—671no—
359C2×#389—671no—
360C2×C4×C4⋊C4—671no—
361#1444—672no—
362#1442—672no—
363#1436—672no—
364#1436—672no—
365C4⋊#95—671no—
366C4⋊#95—671no—
367C67#1401711yescharacteristic, complemented, Sylow
368C23×Q8C2×D6711yescharacteristic
369C2×C4×Q8—24no—
370C2×C4×Q8—24no—
371C2×C4×Q8—24no—
372C22×C4⋊C4—672no—
373C22×C4⋊C4—671no—
374C22×C4⋊C4—671no—
375C22×C4⋊C4—671no—
376C22×C4⋊C4—671no—
377C22×C4⋊C4C2×D6712yes—
378C22×C4⋊C4C2×D6711yescharacteristic
379C22×C42—671no—
380C22×C42—671no—
381C22×C42C2×D6712yes—
382C22×C42C2×D6711yescharacteristic
383#391—678no—
384#391—1344no—
385#389—1344no—
386C4×C4⋊C4—1344no—
387C2×#95—672no—
388C2×#95—672no—
389C2×#95—672no—
390C2×#95—672no—
391C2×#95—672no—
392C2×#95—672no—
393C2×#95—671no—
394C2×#95—672no—
395C2×#95—672no—
396C2×#95—672no—
397C2×#95—671no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8Dic13414yes—
403C22×Q8C4×D6714yes—
404C22×Q8C22⋊D6714yes—
405C23×C4—671no—
406C23×C4—671no—
407C23×C4—672no—
408C23×C4—671no—
409C23×C4—671no—
410C23×C4—672no—
411C23×C4C22×D6712yes—
412C23×C4C22×D6711yescharacteristic
413C23×C4C22×D6712yes—
414C23×C4C22×D6711yescharacteristic
415C23×C4C22×D6711yescharacteristic
416C4×Q8—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—2682no—
423C2×C4⋊C4—674no—
424C2×C4⋊C4—674no—
425C2×C4⋊C4—1344no—
426C2×C4⋊C4—1344no—
427C2×C4⋊C4—1342no—
428C2×C4⋊C4—1342no—
429C2×C4⋊C4—1342no—
430C2×C4⋊C4—1342no—
431C2×C4⋊C4—1342no—
432C2×C4⋊C4—1342no—
433C2×C4⋊C4—1342no—
434C2×C4⋊C4—1342no—
435C2×C4⋊C4—1342no—
436C2×C4⋊C4—1342no—
437C2×C4⋊C4C22⋊D6714yes—
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—674no—
444C2×C42—1342no—
445C2×C42—1342no—
446C2×C42—1342no—
447C2×C42—1342no—
448C2×C42—1342no—
449C2×C42C22⋊D6714yes—
450#95—2682no—
451#95—2682no—
452#95—678no—
453#95—678no—
454#95—1344no—
455#95—1342no—
456#95—1342no—
457#95—1344no—
458#95—1344no—
459#95—1344no—
460#95—1344no—
461C24C23×D6711yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8Dic67⋊C4116yescomplemented
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—672no—
490C22×C4—672no—
491C22×C4—672no—
492C22×C4—672no—
493C22×C4—674no—
494C22×C4—672no—
495C22×C4—672no—
496C22×C4—1342no—
497C22×C4—1342no—
498C22×C4—1342no—
499C22×C4—1342no—
500C22×C4—1342no—
501C22×C4—1342no—
502C22×C4—1342no—
503C22×C4—1341no—
504C22×C4—1341no—
505C22×C4—1341no—
506C22×C4—1341no—
507C22×C4—1341no—
508C22×C4—1341no—
509C22×C4—1342no—
510C22×C4—1341no—
511C22×C4—1342no—
512C22×C4—1341no—
513C22×C4—1341no—
514C22×C4—1342no—
515C22×C4—1342no—
516C22×C4—1341no—
517C22×C4—1341no—
518C22×C4—1342no—
519C22×C4—1341no—
520C22×C4—1341no—
521C22×C4—1341no—
522C22×C4—1341no—
523C22×C4—1341no—
524C22×C4—1342no—
525C22×C4—1341no—
526C22×C4—1341no—
527C22×C4—1341no—
528C22×C4—1341no—
529C22×C4—1341no—
530C22×C4—1341no—
531C22×C4C2×C4×D6714yes—
532C22×C4C2×C4×D6712yes—
533C22×C4C2×C22⋊D6714yes—
534C22×C4C2×C22⋊D6712yes—
535C22×C4C2×C22⋊D6714yes—
536C22×C4C2×C22⋊D6712yes—
537C22×C4C2×C22⋊D6712yes—
538C22×C4C2×C22⋊D6712yes—
539C22×C4C2×C22⋊D6712yes—
540C22×C4Q8×D6712yes—
541C22×C4C2×Dic13414yes—
542C22×C4C2×Dic13412yes—
543C22×C4#1176162812yes—
544C22×C4#1176162812yes—
545C22×C4#1176162912yes—
546C4⋊C4—216no—
547C4⋊C4—28no—
548C4⋊C4—2688no—
549C4⋊C4—2684no—
550C4⋊C4—1348no—
551C4⋊C4—1348no—
552C4⋊C4—1348no—
553C42—216no—
554C42—28no—
555C42—2684no—
556C42—1348no—
557C23C22×C4×D6711yescharacteristic
558C23C22×C22⋊D6711yescharacteristic
559C23C22×C22⋊D6711yescharacteristic
560C23C22×C22⋊D6711yescharacteristic
561C23C2×Q8×D6711yescharacteristic
562C23C22×Dic13411yescharacteristic
563C23#41×D6711yescharacteristic
564C23#41×D6711yescharacteristic
565C23C2×#1176162811yescharacteristic
566C23C2×#1176162811yescharacteristic
567C23C2×#1176162911yescharacteristic
568C23#1452408911yescharacteristic
569C23#1452409011yescharacteristic
570C23#1452409111yescharacteristic
571C23#1452409111yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—2681no—
600C2×C4—2681no—
601C2×C4—2682no—
602C2×C4—2681no—
603C2×C4—2682no—
604C2×C4—2681no—
605C2×C4—2681no—
606C2×C4—2681no—
607C2×C4—2682no—
608C2×C4—2682no—
609C2×C4—2681no—
610C2×C4—2681no—
611C2×C4—2681no—
612C2×C4—2681no—
613C2×C4—2681no—
614C2×C4—2681no—
615C2×C4—2682no—
616C2×C4—2682no—
617C2×C4—2682no—
618C2×C4—2682no—
619C2×C4—2682no—
620C2×C4—2682no—
621C2×C4—2682no—
622C2×C4—674no—
623C2×C4—1342no—
624C2×C4—1342no—
625C2×C4—1342no—
626C2×C4—1342no—
627C2×C4—1342no—
628C2×C4—1344no—
629C2×C4—1344no—
630C2×C4—1342no—
631C2×C4—1342no—
632C2×C4—1344no—
633C2×C4—1342no—
634C2×C4—1342no—
635C2×C4—1342no—
636C2×C4—1342no—
637C2×C4—1342no—
638C2×C4—1342no—
639C2×C4—1342no—
640C2×C4—1342no—
641C2×C4C2×Dic67⋊C418yes—
642C2×C4C2×Dic67⋊C414yes—
643C2×C4C4×C22⋊D6714yes—
644C2×C4C4×C22⋊D6714yes—
645C2×C4#1452401214yes—
646C2×C4#1452401914yes—
647C2×C4#1452402214yes—
648C2×C4#1452402214yes—
649C2×C4#1452402614yes—
650C22C22×Dic67⋊C411yescharacteristic
651C22C2×C4×C22⋊D6711yescharacteristic
652C22C2×C4×C22⋊D6711yescharacteristic
653C22C4×Q8×D6711yescharacteristic
654C22C4×#1176162911yescharacteristic
655C22#1686387211yescharacteristic
656C22#1686387811yescharacteristic
657C22C2×#1452401211yescharacteristic
658C22C2×#1452401911yescharacteristic
659C22C2×#1452402211yescharacteristic
660C22C2×#1452402211yescharacteristic
661C22C2×#1452402611yescharacteristic
662C22#1686390311yescharacteristic
663C22#1686393311yescharacteristic
664C22#1686395011yescharacteristic
665C22#1686397011yescharacteristic
666C22#1686397411yescharacteristic
667C22#1686400411yescharacteristic
668C22#1686401811yescharacteristic
669C22#1686403411yescharacteristic
670C22#1686404511yescharacteristic
671C22#1686405311yescharacteristic
672C22#1686405711yescharacteristic
673C22#1686405711yescharacteristic
674C22Q8×C22⋊D6711yescharacteristic
675C22Q8×C22⋊D6711yescharacteristic
676C22#1686406511yescharacteristic
677C22#1686411811yescharacteristic
678C22#1686411811yescharacteristic
679C22#1686412211yescharacteristic
680C22#1686412211yescharacteristic
681C22#1686412411yescharacteristic
682C22#1686412511yescharacteristic
683C22Q8×Dic13411yescharacteristic
684C22#1686413111yescharacteristic
685C4—28no—
686C4—24no—
687C4—44no—
688C4—42no—
689C4—2682no—
690C4—2684no—
691C4—2682no—
692C4—2682no—
693C4—5362no—
694C4—1344no—
695C4#1686326918yes—
696C2C2×#1686326911yescharacteristic
697C2C4×#1452401911yescharacteristic
698C2#2256288511yescharacteristic
699C2Q8×Dic67⋊C411yescharacteristic
700C2#2256312711yescharacteristic
701C2#2256326311yescharacteristic
702C2#2256327611yescharacteristic
703C2#2256354811yescharacteristic
704C2#2256356811yescharacteristic
705C2#2256397911yescharacteristic
706C2#2256400111yescharacteristic
707C2#2256404211yescharacteristic
708C2#2256406411yescharacteristic
709C2#2256557111yescharacteristic
710C2#2256557911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D67
commutatorC23×C67C23×C4
FittingC22×C4×Q8×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC22×C4×Q8D67
hypocenterC67#14017
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
20. #16863303C4semidirect
62. C2×Dic67⋊C4Q8semidirect
161. C2×Q8×C67C4⋊C4semidirect
293. C2×Dic67C4×Q8semidirect
367. C67#14017semidirect
468. C2×Q8Dic67⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168633032
C2×#168632922
C2×C4×Dic67⋊C42
#225584722
#225584682
#225584422
#225584392
#225584382
C22×C4×Q8×C672
#1401767