Finite Group Databasebeta

← #31723468

Subgroups — #31723468

Order 17152.

2030 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573410C211yesmaximal, characteristic
2#22570067C214yesmaximal, complemented
3#22570056C214yesmaximal, complemented
4#22570045C214yesmaximal, complemented
5#22570034C214yesmaximal, complemented
6#22570027C214yesmaximal, complemented
7#22570018C214yesmaximal, complemented
8#22568798C211yesmaximal, characteristic, complemented
9C2×#16863436C211yesmaximal, characteristic, complemented
10#22568773C211yesmaximal, characteristic, complemented
11#22568726C211yesmaximal, characteristic
12C2×#16863395C211yesmaximal, characteristic
13C2×#544×C67C211yesmaximal, characteristic, complemented
14C22×#11761628C2211yescharacteristic
15C22×#11761612C2211yescharacteristic
16C22×#11761612C2211yescharacteristic
17#16863877—21no—
18#16863877—21no—
19#16863876C2212yes—
20#16863876C2212yes—
21#16863873C2212yes—
22#16863870C2212yes—
23#16863869—22no—
24C4×#11761628C2214yes—
25#16863864—22no—
26C2×#14524002C2211yescharacteristic
27#117×D67—22no—
28#16863700C2218yescomplemented
29#16863700C2218yescomplemented
30#16863693C2218yescomplemented
31#16863693C2218yescomplemented
32#16863688C2218yescomplemented
33#16863683C2218yescomplemented
34#16863678C2218yescomplemented
35#16863673C2218yescomplemented
36#16863439C2212yescomplemented
37#16863439C2212yescomplemented
38#16863436C2214yes—
39#16863436C2212yescomplemented
40#16863436C2214yescomplemented
41#16863436C2212yescomplemented
42#16863432C2214yes—
43C2×#14523976C2212yescomplemented
44C2×#14523974C2212yescomplemented
45#16863423C2214yes—
46#16863423C2214yescomplemented
47#16863420C2214yescomplemented
48#16863404C2212yes—
49#16863400C2212yes—
50#16863395C2214yes—
51#16863395C2214yes—
52#16863395C2212yes—
53#16863395C2212yes—
54#16863390C2214yes—
55C2×#14523966C2212yes—
56C2×#14523963C2212yes—
57#544×C67—22no—
58#544×C67—22no—
59#544×C67C2214yes—
60#544×C67C2214yescomplemented
61C2×C4⋊Q8×C67—21no—
62C2×C4⋊Q8×C67C2212yescomplemented
63C2×#125×C67—21no—
64C2×#125×C67C2212yescomplemented
65C2×C22⋊Q8×C67—22no—
66C2×#117×C67C2211yescharacteristic
67C2×#117×C67C2211yescharacteristic
68C22×C4⋊C4×C67C2211yescharacteristic
69C2×#11761628—21no—
70C2×#11761628—21no—
71C2×#11761628—24no—
72C2×#11761628Q818yescomplemented
73C2×#11761628C2312yes—
74C2×#11761628C2312yes—
75C22×Dic134C2311yescharacteristic
76C22×D268C2311yescharacteristic
77C22×C22⋊D67—21no—
78C22×C4×D67—21no—
79C2×#11761612—24no—
80C2×#11761612—24no—
81C2×#11761612C2312yes—
82C2×#11761612C2312yes—
83C2×#11761612C2312yes—
84C2×#11761612C2312yes—
85C22×C67⋊C8C2312yes—
86C22×C67⋊C8C2312yes—
87C4×Dic134C2314yes—
88C4×Dic134C2314yes—
89#14524008—22no—
90#14524008—22no—
91C4×D268C2314yes—
92C4×D268C2314yes—
93#14524005—22no—
94#14524005—22no—
95C4×C22⋊D67—24no—
96C4×C22⋊D67—24no—
97(C22⋊D67)⋊C4—24no—
98(C22⋊D67)⋊C4—24no—
99#14524002—21no—
100#14524002—21no—
101#14524002C2312yes—
102#14524002C2312yes—
103#14524001—22no—
104#14524001—22no—
105#14524000—24no—
106#14523999—24no—
107C2×C4⋊Dic67C2311yescharacteristic
108C2×C4⋊Dic67C2311yescharacteristic
109C4⋊C4×D67—22no—
110C4⋊C4×D67—22no—
111C2×C22⋊Dic67—21no—
112C22⋊C4×D67—24no—
113C2×C4×Dic67—21no—
114C42×D67—24no—
115#14523976C2314yes—
116#14523976C2318yes—
117#14523976C2314yes—
118#14523974C2314yes—
119#14523974C2318yes—
120#14523974C2314yes—
121C4⋊(C67⋊C8)C2318yes—
122C4⋊(C67⋊C8)C2318yes—
123#14523966C2318yes—
124#14523966C2314yes—
125#14523966C2314yes—
126#14523963C2318yes—
127#14523963C2314yes—
128#14523963C2314yes—
129C22×Q8×C67—22no—
130C23×C4×C67—21no—
131C23×C4×C67C2311yescharacteristic
132C4⋊Q8×C67—24no—
133C4⋊Q8×C67—24no—
134C4⋊Q8×C67—24no—
135C4⋊Q8×C67C2318yes—
136#125×C67—24no—
137#125×C67—24no—
138#125×C67—24no—
139#125×C67C2318yes—
140C22⋊Q8×C67—28no—
141C22⋊Q8×C67—28no—
142#117×C67—21no—
143#117×C67—21no—
144#117×C67D412yes—
145#117×C67D412yes—
146#117×C67C2312yes—
147#117×C67C2312yes—
148#117×C67C2312yes—
149#117×C67C2312yes—
150C2×C4⋊C4×C67—21no—
151C2×C4⋊C4×C67—21no—
152C2×C4⋊C4×C67—21no—
153C2×C4⋊C4×C67—22no—
154C2×C4⋊C4×C67—22no—
155C2×C4⋊C4×C67—22no—
156C2×C4⋊C4×C67D411yescharacteristic
157C2×C4⋊C4×C67D411yescharacteristic
158C2×C4⋊C4×C67C2312yes—
159C2×C4⋊C4×C67C2312yes—
160C2×C4⋊C4×C67C2312yes—
161C2×C4⋊C4×C67C2311yescharacteristic
162C2×C4⋊C4×C67C2311yescharacteristic
163C2×C22⋊C4×C67—21no—
164C2×C22⋊C4×C67D412yes—
165C2×C42×C67—21no—
166C2×C42×C67C2312yes—
167C23×D67—21no—
168#11761628—28no—
169#11761628—28no—
170#11761628—24no—
171#11761628—24no—
172#11761628C2×Q818yes—
173#11761628C2×Q818yescomplemented
174C2×Dic134—21no—
175C2×Dic134—22no—
176C2×Dic134C2×Q814yescomplemented
177C2×Dic134C2412yes—
178C2×D268—21no—
179C2×D268—22no—
180C2×D268C2×Q814yescomplemented
181C2×D268C2412yes—
182C2×C22⋊D67—28no—
183C2×C22⋊D67—22no—
184C2×C22⋊D67—22no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C2×C4×D67—28no—
189C2×C4×D67—22no—
190C2×C4×D67—22no—
191C2×C4×D67—24no—
192C2×C4×D67—24no—
193#11761612—24no—
194#11761612—24no—
195#11761612—24no—
196#11761612—24no—
197C2×C67⋊C8—24no—
198C2×C67⋊C8—24no—
199C2×C67⋊C8C2414yes—
200C2×C67⋊C8C2414yes—
201C4⋊Dic67—21no—
202C4⋊Dic67—21no—
203C4⋊Dic67C2412yes—
204C4⋊Dic67C2412yes—
205Dic67⋊C4—24no—
206Dic67⋊C4—24no—
207C22⋊Dic67—22no—
208C22⋊Dic67—22no—
209(C2×D67)⋊C4—24no—
210(C2×D67)⋊C4—24no—
211C4×Dic67—22no—
212C4×Dic67—24no—
213C4×Dic67—24no—
214C4×Dic67—22no—
215C24×C67C2×D411yescharacteristic
216C2×Q8×C67—28no—
217C2×Q8×C67—84no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67—22no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67—82no—
224C22×C4×C67C2×D412yes—
225C22×C4×C67C2×D412yes—
226C22×C4×C67C2×D411yescharacteristic
227C22×C4×C67C2×D411yescharacteristic
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×Q814yes—
230C22×C4×C67#4114yes—
231C22×C4×C67C2411yescharacteristic
232C22×C4×C67C2411yescharacteristic
233C22×C4×C67C2411yescharacteristic
234C4⋊C4×C67—22no—
235C4⋊C4×C67—22no—
236C4⋊C4×C67—22no—
237C4⋊C4×C67—28no—
238C4⋊C4×C67—28no—
239C4⋊C4×C67—28no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67C2×D412yes—
243C4⋊C4×C67C2×D412yes—
244C4⋊C4×C67C2×D412yes—
245C4⋊C4×C67C2×D412yes—
246C4⋊C4×C67C2414yes—
247C4⋊C4×C67C2412yes—
248C4⋊C4×C67C2412yes—
249C22⋊C4×C67—22no—
250C22⋊C4×C67—22no—
251C22⋊C4×C67C2×D414yes—
252C22⋊C4×C67C2×D414yes—
253C42×C67—22no—
254C42×C67—22no—
255C42×C67C2×D414yes—
256C42×C67C2414yes—
257C23×C67—41no—
258C23×C67—41no—
259C23×C67C22⋊Q814yes—
260C23×C67C22×D411yescharacteristic
261C23×C67C22×D411yescharacteristic
262C23×C67C22×D411yescharacteristic
263C22×D67—22no—
264C22×D67—24no—
265C22×D67—81no—
266C22×D67—81no—
267Q8×C67—88no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—24no—
271C2×C4×C67—42no—
272C2×C4×C67—42no—
273C2×C4×C67—42no—
274C2×C4×C67—44no—
275C2×C4×C67—42no—
276C2×C4×C67—82no—
277C2×C4×C67—82no—
278C2×C4×C67C22⋊Q814yes—
279C2×C4×C67C22⋊Q814yes—
280C2×C4×C67C22⋊Q814yes—
281C2×C4×C67C22×D414yes—
282C2×C4×C67C22×D414yes—
283C2×C4×C67C22×D411yescharacteristic
284C2×C4×C67C22×D411yescharacteristic
285C2×C4×C67C22×D411yescharacteristic
286C2×C4×C67C22×Q812yes—
287C2×C4×C67C22×Q812yes—
288C2×C4×C67C22×Q812yes—
289C2×C4×C67C2×#4112yes—
290C2×C4×C67C2×#4112yes—
291C2×C4×C67C2×#4112yes—
292C2×C4×C67C2511yescharacteristic
293C22⋊D67—28no—
294C22⋊D67—28no—
295C2×Dic67—24no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—81no—
300C2×Dic67—81no—
301D268—24no—
302D268—22no—
303D268C22×Q814yes—
304C4×D67—28no—
305C4×D67—28no—
306C4×D67—84no—
307C4×D67—84no—
308Dic134—24no—
309Dic134—22no—
310Dic134C22×Q814yes—
311C67⋊C8—24no—
312C67⋊C8—24no—
313C22×C67—21no—
314C22×C67—21no—
315C22×C67—21no—
316C22×C67—21no—
317C22×C67—21no—
318C22×C67—21no—
319C22×C67—44no—
320C22×C67C2×C22⋊Q812yes—
321C22×C67C2×C22⋊Q812yes—
322C22×C67C2×C22⋊Q812yes—
323C22×C67C23×D411yescharacteristic
324C2×D67—24no—
325C2×D67—42no—
326C2×D67—42no—
327C2×D67—84no—
328C4×C67—24no—
329C4×C67—24no—
330C4×C67—44no—
331C4×C67—42no—
332C4×C67—42no—
333C4×C67C2×C22⋊Q812yes—
334C4×C67C2×C22⋊Q812yes—
335C4×C67C2×C22⋊Q812yes—
336C4×C67C23×Q811yescharacteristic
337C4×C67C22×#4111yescharacteristic
338Dic67—24no—
339Dic67—42no—
340Dic67—42no—
341#60493—671nomaximal, Sylow
342C2×C67—22no—
343C2×C67—22no—
344C2×C67—22no—
345C2×C67C22×C22⋊Q811yescharacteristic
346C2×C67#358511yescharacteristic
347C2×C67#358611yescharacteristic
348D67—44no—
349C2×#544D6711yescharacteristic, complemented
350#3428—671no—
351#3084—674no—
352#3083—674no—
353#3082—674no—
354#3081—674no—
355#3080—674no—
356#3079—674no—
357#2911—671no—
358C2×#428—671no—
359#2905—671no—
360#2896—671no—
361C2×#417—671no—
362C67#6049311yescharacteristic, complemented, Sylow
363C22×#41—671no—
364C22×M16—671no—
365C22×M16—671no—
366#544—22no—
367#544—22no—
368#544C2×D6714yes—
369#544C2×D6714yescomplemented
370C2×C4⋊Q8—21no—
371C2×C4⋊Q8C2×D6712yescomplemented
372C2×#125—21no—
373C2×#125C2×D6712yescomplemented
374C2×C22⋊Q8—22no—
375#520—672no—
376#520—672no—
377#520—1341no—
378#520—1341no—
379#519—672no—
380#518—672no—
381#518—1342no—
382C4×#41—674no—
383C4×#41—1342no—
384C2×#117—671no—
385C2×#117—1342no—
386C2×#117C2×D6711yescharacteristic
387C2×#117C2×D6711yescharacteristic
388C22×C4⋊C4C2×D6711yescharacteristic
389#479—678no—
390#479—678no—
391#478—678no—
392#478—678no—
393#477—678no—
394#476—678no—
395#475—678no—
396#474—678no—
397#428—672no—
398#428—672no—
399#428—672no—
400#428—674no—
401#428—672no—
402#428—674no—
403#427—674no—
404C2×#107—672no—
405C2×#106—672no—
406#424—674no—
407#424—674no—
408#423—674no—
409#419—672no—
410#418—672no—
411#417—672no—
412#417—674no—
413#417—672no—
414#417—674no—
415#416—674no—
416C2×#103—672no—
417C2×#102—672no—
418C2×#41—678no—
419C2×#41—672no—
420C2×#41—672no—
421C2×#41—1341no—
422C2×#41—1341no—
423C2×#41—1344no—
424C22×Q8—22no—
425C22×Q8—671no—
426C22×D4—671no—
427C22×D4—1341no—
428C23×C4—21no—
429C23×C4—1341no—
430C23×C4C22×D6711yescharacteristic
431C2×M16—672no—
432C2×M16—672no—
433C2×M16—672no—
434C2×M16—672no—
435C2×M16—1344no—
436C2×M16—1344no—
437C22×C8—672no—
438C22×C8—672no—
439C4⋊Q8—24no—
440C4⋊Q8—24no—
441C4⋊Q8—24no—
442C4⋊Q8C22×D6718yes—
443#125—24no—
444#125—24no—
445#125—24no—
446#125C22×D6718yes—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C4×Q8—674no—
450C4×Q8—674no—
451C4×Q8—1342no—
452C4×Q8—1342no—
453C4×D4—674no—
454C4×D4—674no—
455C4×D4—1344no—
456C4×D4—1344no—
457C4×D4—1342no—
458C4×D4—1342no—
459C4×D4—1344no—
460C4×D4—1344no—
461#117—21no—
462#117—21no—
463#117—672no—
464#117—672no—
465#117—1341no—
466#117—1341no—
467#117—1342no—
468#117—1342no—
469#117—1344no—
470#117—1344no—
471#117C22⋊D6712yes—
472#117C22⋊D6712yes—
473#117C22×D6712yes—
474#117C22×D6712yes—
475#117C22×D6712yes—
476#117C22×D6712yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—671no—
484C2×C4⋊C4—671no—
485C2×C4⋊C4—1342no—
486C2×C4⋊C4—1342no—
487C2×C4⋊C4C22⋊D6711yescharacteristic
488C2×C4⋊C4C22⋊D6711yescharacteristic
489C2×C4⋊C4C22×D6712yes—
490C2×C4⋊C4C22×D6712yes—
491C2×C4⋊C4C22×D6712yes—
492C2×C4⋊C4C22×D6711yescharacteristic
493C2×C4⋊C4C22×D6711yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—1341no—
496C2×C22⋊C4—1344no—
497C2×C22⋊C4C22⋊D6712yes—
498C2×C42—21no—
499C2×C42—1341no—
500C2×C42—1344no—
501C2×C42C22×D6712yes—
502#107—678no—
503#107—674no—
504#107—674no—
505#106—678no—
506#106—674no—
507#106—674no—
508C4⋊C8—678no—
509C4⋊C8—678no—
510#103—678no—
511#103—674no—
512#103—674no—
513#102—678no—
514#102—674no—
515#102—674no—
516C24—1341no—
517C24C2×C22⋊D6711yescharacteristic
518#41—678no—
519#41—678no—
520#41—1348no—
521#41—1348no—
522#41—1344no—
523#41—1344no—
524C2×Q8—28no—
525C2×Q8—84no—
526C2×Q8—674no—
527C2×Q8—672no—
528C2×Q8—1341no—
529C2×Q8—1342no—
530C2×D4—674no—
531C2×D4—672no—
532C2×D4—1348no—
533C2×D4—1342no—
534C2×D4—1342no—
535C2×D4—1341no—
536C2×D4—1342no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—82no—
543C22×C4—1341no—
544C22×C4—1341no—
545C22×C4—1344no—
546C22×C4—1344no—
547C22×C4—1341no—
548C22×C4—1348no—
549C22×C4—1342no—
550C22×C4—1342no—
551C22×C4C2×C22⋊D6712yes—
552C22×C4C2×C22⋊D6712yes—
553C22×C4C2×C22⋊D6711yescharacteristic
554C22×C4C2×C22⋊D6711yescharacteristic
555C22×C4C2×C22⋊D6711yescharacteristic
556C22×C4Q8×D6714yes—
557C22×C4#1176162914yes—
558C22×C4C23×D6711yescharacteristic
559C22×C4C23×D6711yescharacteristic
560C22×C4C23×D6711yescharacteristic
561M16—1344no—
562M16—1344no—
563M16—1344no—
564M16—1344no—
565C2×C8—674no—
566C2×C8—674no—
567C2×C8—1344no—
568C2×C8—1344no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—672no—
578C4⋊C4—672no—
579C4⋊C4—1341no—
580C4⋊C4—1341no—
581C4⋊C4—1344no—
582C4⋊C4—1344no—
583C4⋊C4C2×C22⋊D6712yes—
584C4⋊C4C2×C22⋊D6712yes—
585C4⋊C4C2×C22⋊D6712yes—
586C4⋊C4C2×C22⋊D6712yes—
587C4⋊C4C23×D6714yes—
588C4⋊C4C23×D6712yes—
589C4⋊C4C23×D6712yes—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—1342no—
593C22⋊C4—1342no—
594C22⋊C4—1344no—
595C22⋊C4—1344no—
596C22⋊C4C2×C22⋊D6714yes—
597C22⋊C4C2×C22⋊D6714yes—
598C42—22no—
599C42—22no—
600C42—1342no—
601C42—1342no—
602C42—1344no—
603C42—1344no—
604C42C2×C22⋊D6714yes—
605C42C23×D6714yes—
606C23—41no—
607C23—41no—
608C23—5361no—
609C23—5361no—
610C23—1342no—
611C23—1344no—
612C23#1452401914yes—
613C23C22×C22⋊D6711yescharacteristic
614C23C22×C22⋊D6711yescharacteristic
615C23C22×C22⋊D6711yescharacteristic
616Q8—88no—
617Q8—674no—
618Q8—1344no—
619Q8—1342no—
620D4—674no—
621D4—1348no—
622D4—1348no—
623D4—1344no—
624D4—1342no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—5364no—
636C2×C4—5364no—
637C2×C4—5361no—
638C2×C4—5361no—
639C2×C4—1342no—
640C2×C4—1342no—
641C2×C4—1344no—
642C2×C4—1342no—
643C2×C4—1348no—
644C2×C4—1348no—
645C2×C4#1452401914yes—
646C2×C4#1452401914yes—
647C2×C4#1452401914yes—
648C2×C4C22×C22⋊D6714yes—
649C2×C4C22×C22⋊D6714yes—
650C2×C4C22×C22⋊D6711yescharacteristic
651C2×C4C22×C22⋊D6711yescharacteristic
652C2×C4C22×C22⋊D6711yescharacteristic
653C2×C4C2×Q8×D6712yes—
654C2×C4C2×Q8×D6712yes—
655C2×C4C2×Q8×D6712yes—
656C2×C4C2×#1176162912yes—
657C2×C4C2×#1176162912yes—
658C2×C4C2×#1176162912yes—
659C2×C4C24×D6711yescharacteristic
660C8—1344no—
661C8—1344no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—44no—
669C22—2682no—
670C22—2682no—
671C22—5364no—
672C22—1344no—
673C22C2×#1452401912yes—
674C22C2×#1452401912yes—
675C22C2×#1452401912yes—
676C22C23×C22⋊D6711yescharacteristic
677C4—24no—
678C4—24no—
679C4—44no—
680C4—42no—
681C4—42no—
682C4—2682no—
683C4—2682no—
684C4—1344no—
685C4C2×#1452401912yes—
686C4C2×#1452401912yes—
687C4C2×#1452401912yes—
688C4C22×Q8×D6711yescharacteristic
689C4C22×#1176162911yescharacteristic
690C2—22no—
691C2—22no—
692C2—22no—
693C2—2684no—
694C2C22×#1452401911yescharacteristic
695C2#2257498911yescharacteristic
696C2#2257499611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#544×C67C2
socleC22×C67C23×D4
prime radicalC22×#11761628C22
hypercenterC2×#544D67
hypocenterC67#60493
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22570067C2semidirect
3. #22570056C2semidirect
4. #22570045C2semidirect
5. #22570034C2semidirect
6. #22570027C2semidirect
7. #22570018C2semidirect
8. #22568798C2semidirect
9. C2×#16863436C2semidirect
10. #22568773C2semidirect
13. C2×#544×C67C2semidirect
28. #16863700C22semidirect
29. #16863700C22semidirect
30. #16863693C22semidirect
31. #16863693C22semidirect
32. #16863688C22semidirect
33. #16863683C22semidirect
34. #16863678C22semidirect
35. #16863673C22semidirect
36. #16863439C22semidirect
37. #16863439C22semidirect
39. #16863436C22semidirect
40. #16863436C22semidirect
41. #16863436C22semidirect
43. C2×#14523976C22semidirect
44. C2×#14523974C22semidirect
46. #16863423C22semidirect
47. #16863420C22semidirect
60. #544×C67C22semidirect
62. C2×C4⋊Q8×C67C22semidirect
64. C2×#125×C67C22semidirect
72. C2×#11761628Q8semidirect
173. #11761628C2×Q8semidirect
176. C2×Dic134C2×Q8semidirect
180. C2×D268C2×Q8semidirect
349. C2×#544D67semidirect
362. C67#60493semidirect
369. #544C2×D67semidirect
371. C2×C4⋊Q8C2×D67semidirect
373. C2×#125C2×D67semidirect

Maximal subgroups

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

subgroupindex
#225734102
#225700672
#225700562
#225700452
#225700342
#225700272
#225700182
#225687982
C2×#168634362
#225687732
#225687262
C2×#168633952
C2×#544×C672
#6049367