Finite Group Databasebeta

← #30823609

Subgroups — #30823609

Order 17152.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22569238C211yesmaximal, characteristic, complemented
2#22563119C211yesmaximal, characteristic, complemented
3#22558781C211yesmaximal, characteristic, complemented
4#22558777C211yesmaximal, characteristic, complemented
5#22558752C212yesmaximal, complemented
6#22558747C212yesmaximal, complemented
7#22558734C212yesmaximal, complemented
8#22558713C212yesmaximal, complemented
9C2×#16863133C211yesmaximal, characteristic, complemented
10C2×#16863130C211yesmaximal, characteristic, complemented
11C67×#3505C211yesmaximal, characteristic
12C2×D4×Dic67—21no—
13#16863468—22no—
14#16863468—22no—
15#16863453C2212yescomplemented
16#16863360C2212yescomplemented
17C2×C22⋊(C67⋊C8)C2211yescharacteristic
18C2×C22⋊(C67⋊C8)C2211yescharacteristic
19#16863295—21no—
20#16863271—21no—
21#16863271—21no—
22#16863262C2211yescharacteristic, complemented
23#16863256C2211yescharacteristic
24#16863256C2211yescharacteristic, complemented
25C4×C4⋊Dic67C2211yescharacteristic, complemented
26C2×C67⋊#95C2211yescharacteristic
27C2×C67⋊#95C2211yescharacteristic, complemented
28#16863133C2212yescomplemented
29#16863133C2212yescomplemented
30#16863133C2212yescomplemented
31#16863133C2212yescomplemented
32#16863130C2212yes—
33#16863130C2212yes—
34#16863130C2212yes—
35#16863130C2212yes—
36#553×C67—22no—
37#553×C67C412yescomplemented
38#552×C67C412yescomplemented
39#551×C67—22no—
40#548×C67C412yescomplemented
41#546×C67C412yescomplemented
42#539×C67—21no—
43#538×C67—21no—
44#534×C67—21no—
45#529×C67C2212yes—
46#525×C67C2212yes—
47C2×C22⋊Q8×C67C2211yescharacteristic
48C2×#121×C67C2211yescharacteristic
49#518×C67—21no—
50C2×C4×D4×C67C2211yescharacteristic
51C23×Dic67—21no—
52C23×Dic67—21no—
53C2×#11761612—22no—
54C22×C67⋊C8—21no—
55C22×C67⋊C8—21no—
56D4×Dic67—44no—
57C2×C4⋊Dic67—21no—
58C2×C4⋊Dic67—21no—
59C2×C4⋊Dic67—21no—
60C2×C4⋊Dic67—21no—
61C2×C22⋊Dic67—21no—
62C2×C22⋊Dic67—21no—
63C2×C4×Dic67—21no—
64C4⋊(C67⋊C8)—22no—
65C22⋊(C67⋊C8)—21no—
66C22⋊(C67⋊C8)—21no—
67C22⋊(C67⋊C8)—22no—
68C22⋊(C67⋊C8)C2312yes—
69C22⋊(C67⋊C8)C2312yes—
70#14523954—22no—
71C67⋊#95—21no—
72C67⋊#95—21no—
73C67⋊#95—21no—
74C67⋊#95C2311yescharacteristic
75C67⋊#95C2311yescharacteristic
76C67⋊#95C2311yescharacteristic
77C67⋊#95C2311yescharacteristic
78C2×#41×C67C2×C412yescomplemented
79C22×Q8×C67C2×C411yescharacteristic, complemented
80C22×D4×C67—21no—
81C22×D4×C67C2×C411yescharacteristic, complemented
82C22×D4×C67D411yescharacteristic
83C23×C4×C67C2311yescharacteristic
84C23×C4×C67C2311yescharacteristic
85#126×C67—22no—
86#126×C67—22no—
87#126×C67—22no—
88#125×C67—22no—
89#125×C67C2×C412yescomplemented
90#124×C67—22no—
91#124×C67C2×C412yescomplemented
92#123×C67—22no—
93#123×C67—22no—
94#123×C67—22no—
95#123×C67—22no—
96#123×C67—22no—
97C22⋊Q8×C67—21no—
98C22⋊Q8×C67—21no—
99C22⋊Q8×C67—22no—
100C22⋊Q8×C67C2×C412yescomplemented
101C22⋊Q8×C67C2×C412yescomplemented
102C22⋊Q8×C67C2312yes—
103#121×C67—22no—
104#121×C67—22no—
105#121×C67—21no—
106#121×C67—21no—
107#121×C67—22no—
108#121×C67C2×C412yescomplemented
109#121×C67C2×C412yescomplemented
110#121×C67C2312yes—
111#120×C67—22no—
112#120×C67—22no—
113C4×Q8×C67C2×C412yescomplemented
114C4×D4×C67—22no—
115C4×D4×C67—22no—
116C4×D4×C67—22no—
117C4×D4×C67—22no—
118C4×D4×C67—22no—
119C4×D4×C67C2×C412yes—
120C4×D4×C67C2×C412yes—
121C4×D4×C67C2×C412yescomplemented
122C4×D4×C67D412yes—
123C4×D4×C67D412yes—
124#117×C67—22no—
125#117×C67—22no—
126#117×C67C2×C412yescomplemented
127C2×C4⋊C4×C67—21no—
128C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C67D411yescharacteristic
131C2×C22⋊C4×C67—21no—
132C2×C22⋊C4×C67—21no—
133C2×C22⋊C4×C67—22no—
134C2×C22⋊C4×C67D411yescharacteristic
135C2×C22⋊C4×C67D411yescharacteristic
136C2×C42×C67C2311yescharacteristic
137C22×Dic67—21no—
138C22×Dic67—21no—
139C22×Dic67—21no—
140C22×Dic67—21no—
141C22×Dic67—42no—
142C22×Dic67—42no—
143C22×Dic67—42no—
144C22×Dic67—42no—
145C22×Dic67—81no—
146C22×Dic67—81no—
147#11761612—82no—
148C2×C67⋊C8—22no—
149C2×C67⋊C8—22no—
150C2×C67⋊C8—81no—
151C2×C67⋊C8—81no—
152C4⋊Dic67—42no—
153C4⋊Dic67—42no—
154C4⋊Dic67—81no—
155C4⋊Dic67—81no—
156C22⋊Dic67—42no—
157C22⋊Dic67—42no—
158C4×Dic67—42no—
159C24×C67—21no—
160C24×C67C2×D411yescharacteristic
161C24×C67C2×D411yescharacteristic
162#41×C67—82no—
163C2×Q8×C67—21no—
164C2×Q8×C67—81no—
165C2×Q8×C67C22×C412yes—
166C2×D4×C67—22no—
167C2×D4×C67—22no—
168C2×D4×C67—22no—
169C2×D4×C67—22no—
170C2×D4×C67—22no—
171C2×D4×C67—22no—
172C2×D4×C67—21no—
173C2×D4×C67—42no—
174C2×D4×C67—42no—
175C2×D4×C67—81no—
176C2×D4×C67C22⋊C412yes—
177C2×D4×C67C22⋊C412yes—
178C2×D4×C67C22×C412yes—
179C22×C4×C67—21no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—22no—
183C22×C4×C67—22no—
184C22×C4×C67—81no—
185C22×C4×C67—81no—
186C22×C4×C67C22×C411yescharacteristic
187C22×C4×C67C22×C411yescharacteristic
188C22×C4×C67C22×C412yes—
189C22×C4×C67C2×D411yescharacteristic
190C22×C4×C67C2×D411yescharacteristic
191C22×C4×C67C2×D411yescharacteristic
192C22×C4×C67C2×D411yescharacteristic
193C22×C4×C67C2×D411yescharacteristic
194C22×C4×C67C2×D411yescharacteristic
195C22×C4×C67C2×D412yes—
196C22×C4×C67C2411yescharacteristic
197C4⋊C4×C67—22no—
198C4⋊C4×C67—21no—
199C4⋊C4×C67—21no—
200C4⋊C4×C67—22no—
201C4⋊C4×C67—22no—
202C4⋊C4×C67—22no—
203C4⋊C4×C67—22no—
204C4⋊C4×C67—22no—
205C4⋊C4×C67C22⋊C412yes—
206C4⋊C4×C67C22⋊C412yes—
207C4⋊C4×C67C22×C412yes—
208C4⋊C4×C67C22×C412yes—
209C22⋊C4×C67—22no—
210C22⋊C4×C67—22no—
211C22⋊C4×C67—22no—
212C22⋊C4×C67—22no—
213C22⋊C4×C67—22no—
214C22⋊C4×C67—22no—
215C22⋊C4×C67—22no—
216C22⋊C4×C67—22no—
217C22⋊C4×C67—22no—
218C22⋊C4×C67—22no—
219C22⋊C4×C67C22⋊C412yes—
220C22⋊C4×C67C22⋊C412yes—
221C22⋊C4×C67C22⋊C412yes—
222C22⋊C4×C67C22⋊C412yes—
223C42×C67—22no—
224C42×C67—22no—
225C42×C67C22×C412yes—
226C42×C67C2×D412yes—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—22no—
230C23×C67—41no—
231C23×C67—41no—
232C23×C67—41no—
233C23×C67—41no—
234C23×C67—42no—
235C23×C67—81no—
236C23×C67—81no—
237C23×C67C2×C22⋊C412yes—
238C23×C67C2×C22⋊C411yescharacteristic
239C23×C67C2×C22⋊C411yescharacteristic
240C23×C67AGL(1,ℤ/8)12yes—
241C23×C67#13712yes—
242C23×C67C22×D411yescharacteristic
243Q8×C67—42no—
244Q8×C67—81no—
245D4×C67—24no—
246D4×C67—24no—
247D4×C67—42no—
248D4×C67—42no—
249D4×C67—42no—
250D4×C67—44no—
251D4×C67—81no—
252D4×C67—82no—
253D4×C67—82no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—42no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—42no—
268C2×C4×C67—41no—
269C2×C4×C67—42no—
270C2×C4×C67—82no—
271C2×C4×C67—82no—
272C2×C4×C67—81no—
273C2×C4×C67—81no—
274C2×C4×C67C2×C22⋊C412yes—
275C2×C4×C67C2×C22⋊C412yes—
276C2×C4×C67C2×C22⋊C412yes—
277C2×C4×C67C2×C22⋊C411yescharacteristic
278C2×C4×C67C2×C22⋊C411yescharacteristic
279C2×C4×C67C23×C411yescharacteristic
280C2×C4×C67C22×D411yescharacteristic
281C2×Dic67—22no—
282C2×Dic67—41no—
283C2×Dic67—41no—
284C2×Dic67—41no—
285C2×Dic67—41no—
286C2×Dic67—41no—
287C2×Dic67—41no—
288C2×Dic67—41no—
289C2×Dic67—41no—
290C2×Dic67—41no—
291C2×Dic67—41no—
292C2×Dic67—41no—
293C2×Dic67—84no—
294C2×Dic67—84no—
295C67⋊C8—42no—
296C67⋊C8—42no—
297C22×C67—21no—
298C22×C67—21no—
299C22×C67—21no—
300C22×C67—21no—
301C22×C67—21no—
302C22×C67—21no—
303C22×C67—22no—
304C22×C67—22no—
305C22×C67—22no—
306C22×C67—42no—
307C22×C67—42no—
308C22×C67—42no—
309C22×C67—42no—
310C22×C67—42no—
311C22×C67—42no—
312C22×C67—42no—
313C22×C67—162no—
314C22×C67#41712yes—
315C22×C67#41712yes—
316C22×C67C22×C22⋊C411yescharacteristic
317C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C67C2×#13711yescharacteristic
319C4×C67—21no—
320C4×C67—21no—
321C4×C67—22no—
322C4×C67—21no—
323C4×C67—21no—
324C4×C67—22no—
325C4×C67—22no—
326C4×C67—42no—
327C4×C67—42no—
328C4×C67—42no—
329Dic67—42no—
330Dic67—81no—
331Dic67—81no—
332Dic67—81no—
333#17622—671nomaximal, Sylow
334C2×C67—21no—
335C2×C67—21no—
336C2×C67—22no—
337C2×C67—22no—
338C2×C67—42no—
339C2×C67—82no—
340C2×C67#288311yescharacteristic
341C2×C67C2×#41711yescharacteristic
342C2×C67#290111yescharacteristic
343#3505D6711yescharacteristic
344#2973—671no—
345#2349—671no—
346#1520—671no—
347#1519—671no—
348#1513—672no—
349#1512—672no—
350#1509—672no—
351#1504—672no—
352C2×#328—671no—
353C2×#327—671no—
354C67#1762211yescharacteristic, complemented, Sylow
355#553—22no—
356#553Dic6712yescomplemented
357#552Dic6712yescomplemented
358#551—22no—
359#548Dic6712yescomplemented
360#546Dic6712yescomplemented
361#539—21no—
362#538—21no—
363#534—21no—
364#529C2×D6712yes—
365#525C2×D6712yes—
366C2×C22⋊Q8C2×D6711yescharacteristic
367C2×#121C2×D6711yescharacteristic
368#518—21no—
369C2×C4×D4—1341no—
370C2×C4×D4C2×D6711yescharacteristic
371#435—1342no—
372#435—1342no—
373#432—672no—
374#407—672no—
375C2×C22⋊C8—671no—
376C2×C22⋊C8—671no—
377#389—1341no—
378#385—1341no—
379#385—1341no—
380#382—671no—
381#380—671no—
382#380—671no—
383C4×C4⋊C4—671no—
384C2×#95—671no—
385C2×#95—671no—
386#328—672no—
387#328—672no—
388#328—672no—
389#328—672no—
390#327—672no—
391#327—672no—
392#327—672no—
393#327—672no—
394C2×#41C2×Dic6712yescomplemented
395C22×Q8C2×Dic6711yescharacteristic, complemented
396C22×D4—21no—
397C22×D4C2×Dic6711yescharacteristic, complemented
398C22×D4C22⋊D6711yescharacteristic
399C23×C4—1341no—
400C23×C4—1341no—
401C23×C4C22×D6711yescharacteristic
402C23×C4C22×D6711yescharacteristic
403C2×M16—1342no—
404C22×C8—1341no—
405C22×C8—1341no—
406#126—22no—
407#126—22no—
408#126—22no—
409#125—22no—
410#125C2×Dic6712yescomplemented
411#124—22no—
412#124C2×Dic6712yescomplemented
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8C2×Dic6712yescomplemented
422C22⋊Q8C2×Dic6712yescomplemented
423C22⋊Q8C22×D6712yes—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121—22no—
429#121C2×Dic6712yescomplemented
430#121C2×Dic6712yescomplemented
431#121C22×D6712yes—
432#120—22no—
433#120—22no—
434C4×Q8C2×Dic6712yescomplemented
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—2684no—
441C4×D4C2×Dic6712yes—
442C4×D4C2×Dic6712yes—
443C4×D4C2×Dic6712yescomplemented
444C4×D4C22⋊D6712yes—
445C4×D4C22⋊D6712yes—
446#117—22no—
447#117—22no—
448#117C2×Dic6712yescomplemented
449C2×C4⋊C4—21no—
450C2×C4⋊C4—1341no—
451C2×C4⋊C4—1341no—
452C2×C4⋊C4—1341no—
453C2×C4⋊C4—1341no—
454C2×C4⋊C4C2×Dic6711yescharacteristic, complemented
455C2×C4⋊C4C2×Dic6711yescharacteristic, complemented
456C2×C4⋊C4C22⋊D6711yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—1341no—
461C2×C22⋊C4—1341no—
462C2×C22⋊C4C22⋊D6711yescharacteristic
463C2×C22⋊C4C22⋊D6711yescharacteristic
464C2×C42—1341no—
465C2×C42C22×D6711yescharacteristic
466C4⋊C8—1342no—
467C22⋊C8—672no—
468C22⋊C8—672no—
469C22⋊C8—1341no—
470C22⋊C8—1341no—
471C22⋊C8—1342no—
472#97—1342no—
473#95—671no—
474#95—671no—
475#95—671no—
476#95—671no—
477#95—1341no—
478#95—1341no—
479#95—1341no—
480C24—21no—
481C24C2×C22⋊D6711yescharacteristic
482C24C2×C22⋊D6711yescharacteristic
483#41—82no—
484C2×Q8—21no—
485C2×Q8—81no—
486C2×Q8C22×Dic6712yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4C22⋊Dic6712yes—
498C2×D4C22⋊Dic6712yes—
499C2×D4C22×Dic6712yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—2682no—
508C22×C4—2682no—
509C22×C4—2682no—
510C22×C4—2682no—
511C22×C4—5361no—
512C22×C4—5361no—
513C22×C4—1341no—
514C22×C4—1341no—
515C22×C4—1341no—
516C22×C4—1341no—
517C22×C4C22×Dic6711yescharacteristic
518C22×C4C22×Dic6711yescharacteristic
519C22×C4C22×Dic6712yes—
520C22×C4C2×C22⋊D6711yescharacteristic
521C22×C4C2×C22⋊D6711yescharacteristic
522C22×C4C2×C22⋊D6711yescharacteristic
523C22×C4C2×C22⋊D6711yescharacteristic
524C22×C4C2×C22⋊D6711yescharacteristic
525C22×C4C2×C22⋊D6711yescharacteristic
526C22×C4C2×C22⋊D6712yes—
527C22×C4C23×D6711yescharacteristic
528M16—5362no—
529C2×C8—5361no—
530C2×C8—5361no—
531C2×C8—1342no—
532C2×C8—1342no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—2682no—
542C4⋊C4—2682no—
543C4⋊C4—5361no—
544C4⋊C4—5361no—
545C4⋊C4C22⋊Dic6712yes—
546C4⋊C4C22⋊Dic6712yes—
547C4⋊C4C22×Dic6712yes—
548C4⋊C4C22×Dic6712yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—2682no—
560C22⋊C4—2682no—
561C22⋊C4C22⋊Dic6712yes—
562C22⋊C4C22⋊Dic6712yes—
563C22⋊C4C22⋊Dic6712yes—
564C22⋊C4C22⋊Dic6712yes—
565C42—22no—
566C42—22no—
567C42—2682no—
568C42C22×Dic6712yes—
569C42C2×C22⋊D6712yes—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—81no—
579C23—81no—
580C23C2×C22⋊Dic6712yes—
581C23C2×C22⋊Dic6711yescharacteristic
582C23C2×C22⋊Dic6711yescharacteristic
583C23#1452406812yes—
584C23#1452407312yes—
585C23C22×C22⋊D6711yescharacteristic
586Q8—42no—
587Q8—81no—
588D4—24no—
589D4—24no—
590D4—42no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—82no—
596D4—82no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—2681no—
618C2×C4—2681no—
619C2×C4—2681no—
620C2×C4—2681no—
621C2×C4—2681no—
622C2×C4—2681no—
623C2×C4—2681no—
624C2×C4—2681no—
625C2×C4—2681no—
626C2×C4—2681no—
627C2×C4—2681no—
628C2×C4—5364no—
629C2×C4—5364no—
630C2×C4—1342no—
631C2×C4C2×C22⋊Dic6712yes—
632C2×C4C2×C22⋊Dic6712yes—
633C2×C4C2×C22⋊Dic6712yes—
634C2×C4C2×C22⋊Dic6711yescharacteristic
635C2×C4C2×C22⋊Dic6711yescharacteristic
636C2×C4C23×Dic6711yescharacteristic
637C2×C4C22×C22⋊D6711yescharacteristic
638C8—2682no—
639C8—2682no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—162no—
657C22#1686339712yes—
658C22#1686339712yes—
659C22C22×C22⋊Dic6711yescharacteristic
660C22C2×#1452406811yescharacteristic
661C22C2×#1452407311yescharacteristic
662C4—22no—
663C4—22no—
664C4—21no—
665C4—21no—
666C4—22no—
667C4—21no—
668C4—21no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—2682no—
673C4—5361no—
674C4—5361no—
675C4—5361no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—42no—
681C2—82no—
682C2#2256867011yescharacteristic
683C2C2×#1686339711yescharacteristic
684C2#2256875611yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC67×#3505C2
socleC22×C67C22×C22⋊C4
cosocleC22×C4×C67C24
hypercenter#3505D67
hypocenterC67#17622
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #22569238C2semidirect
2. #22563119C2semidirect
3. #22558781C2semidirect
4. #22558777C2semidirect
5. #22558752C2semidirect
6. #22558747C2semidirect
7. #22558734C2semidirect
8. #22558713C2semidirect
9. C2×#16863133C2semidirect
10. C2×#16863130C2semidirect
15. #16863453C22semidirect
16. #16863360C22semidirect
22. #16863262C22semidirect
24. #16863256C22semidirect
25. C4×C4⋊Dic67C22semidirect
27. C2×C67⋊#95C22semidirect
28. #16863133C22semidirect
29. #16863133C22semidirect
30. #16863133C22semidirect
31. #16863133C22semidirect
37. #553×C67C4semidirect
38. #552×C67C4semidirect
40. #548×C67C4semidirect
41. #546×C67C4semidirect
78. C2×#41×C67C2×C4semidirect
79. C22×Q8×C67C2×C4semidirect
81. C22×D4×C67C2×C4semidirect
89. #125×C67C2×C4semidirect
91. #124×C67C2×C4semidirect
100. C22⋊Q8×C67C2×C4semidirect
101. C22⋊Q8×C67C2×C4semidirect
108. #121×C67C2×C4semidirect
109. #121×C67C2×C4semidirect
113. C4×Q8×C67C2×C4semidirect
121. C4×D4×C67C2×C4semidirect
126. #117×C67C2×C4semidirect
128. C2×C4⋊C4×C67C2×C4semidirect
129. C2×C4⋊C4×C67C2×C4semidirect
354. C67#17622semidirect
356. #553Dic67semidirect
357. #552Dic67semidirect
359. #548Dic67semidirect
360. #546Dic67semidirect
394. C2×#41C2×Dic67semidirect
395. C22×Q8C2×Dic67semidirect
397. C22×D4C2×Dic67semidirect
410. #125C2×Dic67semidirect
412. #124C2×Dic67semidirect
421. C22⋊Q8C2×Dic67semidirect
422. C22⋊Q8C2×Dic67semidirect
429. #121C2×Dic67semidirect
430. #121C2×Dic67semidirect
434. C4×Q8C2×Dic67semidirect
443. C4×D4C2×Dic67semidirect
448. #117C2×Dic67semidirect
454. C2×C4⋊C4C2×Dic67semidirect
455. C2×C4⋊C4C2×Dic67semidirect

Maximal subgroups

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

subgroupindex
#225692382
#225631192
#225587812
#225587772
#225587522
#225587472
#225587342
#225587132
C2×#168631332
C2×#168631302
C67×#35052
#1762267