Finite Group Databasebeta

← #30873994

Subgroups — #30873994

Order 17152.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863468C211yesmaximal, characteristic
2C2×#16863436C211yesmaximal, characteristic, complemented
3C2×#16863432C211yesmaximal, characteristic, complemented
4#22563158C211yesmaximal, characteristic
5#22560975C211yesmaximal, characteristic, complemented
6#22560967C211yesmaximal, characteristic, complemented
7#22560408C211yesmaximal, characteristic, complemented
8#22560406C211yesmaximal, characteristic, complemented
9#22560406C211yesmaximal, characteristic, complemented
10#22560397C211yesmaximal, characteristic, complemented
11#22560378C211yesmaximal, characteristic, complemented
12#22560240C211yesmaximal, characteristic, complemented
13#22560236C211yesmaximal, characteristic, complemented
14#22560107C211yesmaximal, characteristic, complemented
15C67×#2352C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C23×C67⋊C8C2211yescharacteristic
18C2×#14524002C2211yescharacteristic
19C2×#14524002C2211yescharacteristic
20#16863468C418yescomplemented
21#16863436—24no—
22#16863432—24no—
23C2×#14523976C2211yescharacteristic
24C2×#14523976C2211yescharacteristic
25C2×#14523976C2211yescharacteristic
26C2×#14523976C2211yescharacteristic
27C2×#14523976C2211yescharacteristic
28C2×#14523976C2211yescharacteristic
29C2×#14523974C2211yescharacteristic
30C2×#14523974C2211yescharacteristic
31C2×#14523974C2211yescharacteristic
32C2×#14523974C2211yescharacteristic
33C2×C4⋊(C67⋊C8)C2211yescharacteristic
34C2×C22⋊(C67⋊C8)C2211yescharacteristic
35C2×C22⋊(C67⋊C8)C2211yescharacteristic
36C2×#14523954C2211yescharacteristic
37#16863299—21no—
38#16863289—21no—
39#16863289—21no—
40#16863266C2211yescharacteristic
41#16863256C2211yescharacteristic
42#16863256C2211yescharacteristic
43C4⋊C4×Dic67—21no—
44C4×C4⋊Dic67C2211yescharacteristic
45#16863158C2211yescharacteristic
46#16863158C2211yescharacteristic
47#16863158C2211yescharacteristic
48#16863158C2211yescharacteristic
49#16863158C2211yescharacteristic
50#16863158C2211yescharacteristic
51C2×C4×D4×C67C2211yescharacteristic
52C2×#117×C67C2211yescharacteristic
53C22×C4⋊C4×C67C2211yescharacteristic
54#388×C67—21no—
55#387×C67—21no—
56#386×C67—21no—
57#382×C67C2211yescharacteristic
58#380×C67C2211yescharacteristic
59#380×C67C2211yescharacteristic
60C4×C4⋊C4×C67C2211yescharacteristic
61C4×C22⋊C4×C67—21no—
62C2×#11761612—22no—
63C2×#11761612—22no—
64C2×#11761612C2×C414yes—
65C22×C67⋊C8—22no—
66C22×C67⋊C8—22no—
67C22×C67⋊C8C2×C414yescomplemented
68C22×C67⋊C8C2311yescharacteristic
69C22×C67⋊C8C2311yescharacteristic
70C22×C67⋊C8C2311yescharacteristic
71C22×C67⋊C8C2311yescharacteristic
72#14524002—22no—
73#14524002—22no—
74#14524002—41no—
75#14524002—41no—
76C2×C4⋊Dic67—21no—
77C2×C4⋊Dic67—21no—
78C2×C4⋊Dic67C2311yescharacteristic
79C2×C4⋊Dic67C2311yescharacteristic
80C2×C4⋊Dic67C2311yescharacteristic
81C2×C4⋊Dic67C2311yescharacteristic
82C2×C22⋊Dic67—21no—
83C2×C22⋊Dic67—21no—
84C2×C22⋊Dic67—21no—
85C2×C22⋊Dic67—21no—
86C2×C4×Dic67—21no—
87C2×C4×Dic67—21no—
88C2×C4×Dic67—21no—
89#14523976—22no—
90#14523976—22no—
91#14523976—22no—
92#14523976—22no—
93#14523976—22no—
94#14523976—41no—
95#14523974—22no—
96#14523974—22no—
97#14523974—41no—
98#14523974D414yescomplemented
99C4⋊(C67⋊C8)C2×C414yescomplemented
100C22⋊(C67⋊C8)C2×C414yes—
101C22⋊(C67⋊C8)C2×C414yescomplemented
102#14523954C2×C414yescomplemented
103C67⋊#95—21no—
104C67⋊#95—21no—
105C67⋊#95—21no—
106C22×D4×C67D411yescharacteristic
107C23×C4×C67—21no—
108C23×C4×C67C2311yescharacteristic
109C23×C4×C67C2311yescharacteristic
110C4×D4×C67C2×C414yes—
111C4×D4×C67Q814yes—
112#117×C67—22no—
113#117×C67—41no—
114C2×C4⋊C4×C67—22no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—41no—
117C2×C4⋊C4×C67D411yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67D411yescharacteristic
126C2×C22⋊C4×C67D411yescharacteristic
127C2×C42×C67—21no—
128C2×C42×C67—21no—
129C2×C42×C67C2311yescharacteristic
130#95×C67—21no—
131#95×C67—21no—
132#95×C67—21no—
133#95×C67—21no—
134#95×C67—21no—
135C22×Dic67—21no—
136C22×Dic67—21no—
137C22×Dic67—21no—
138C22×Dic67—21no—
139#11761612—28no—
140C2×C67⋊C8—21no—
141C2×C67⋊C8—21no—
142C2×C67⋊C8—21no—
143C2×C67⋊C8—21no—
144C2×C67⋊C8—21no—
145C2×C67⋊C8—21no—
146C2×C67⋊C8—28no—
147C2×C67⋊C8C22×C412yes—
148C2×C67⋊C8C22×C412yes—
149C2×C67⋊C8C22×C412yes—
150C2×C67⋊C8C22×C412yes—
151C2×C67⋊C8C2×D412yes—
152C2×C67⋊C8#4112yes—
153C4⋊Dic67—21no—
154C4⋊Dic67—21no—
155C4⋊Dic67—21no—
156C4⋊Dic67—21no—
157C4⋊Dic67—21no—
158C4⋊Dic67—21no—
159C4⋊Dic67—21no—
160C4⋊Dic67—42no—
161C4⋊Dic67—81no—
162C4⋊Dic67C2×D412yes—
163C22⋊Dic67—42no—
164C22⋊Dic67—42no—
165C22⋊Dic67—81no—
166C22⋊Dic67—81no—
167C4×Dic67—42no—
168C4×Dic67—42no—
169C4×Dic67—42no—
170C24×C67C2×D411yescharacteristic
171C24×C67C2×D411yescharacteristic
172C2×D4×C67—41no—
173C2×D4×C67—41no—
174C2×D4×C67C4⋊C414yes—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—21no—
178C22×C4×C67—21no—
179C22×C4×C67—21no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—42no—
188C22×C4×C67—42no—
189C22×C4×C67—81no—
190C22×C4×C67C22×C412yes—
191C22×C4×C67C22×C412yes—
192C22×C4×C67C2×D411yescharacteristic
193C22×C4×C67C2×D411yescharacteristic
194C22×C4×C67C2×D411yescharacteristic
195C22×C4×C67C2×D411yescharacteristic
196C22×C4×C67C2×Q812yes—
197C22×C4×C67C2×Q812yes—
198C22×C4×C67C2411yescharacteristic
199C4⋊C4×C67—21no—
200C4⋊C4×C67—21no—
201C4⋊C4×C67—21no—
202C4⋊C4×C67—21no—
203C4⋊C4×C67—21no—
204C4⋊C4×C67—21no—
205C4⋊C4×C67—21no—
206C4⋊C4×C67—42no—
207C4⋊C4×C67C4⋊C414yes—
208C4⋊C4×C67C2×D412yes—
209C22⋊C4×C67—42no—
210C22⋊C4×C67—42no—
211C22⋊C4×C67—81no—
212C22⋊C4×C67C4⋊C414yes—
213C22⋊C4×C67C4⋊C414yes—
214C42×C67—42no—
215C42×C67—81no—
216C42×C67C22×C412yes—
217C42×C67C2×Q812yes—
218C23×C67—21no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—21no—
230C23×C67C2×C4⋊C412yes—
231C23×C67C2×C4⋊C412yes—
232C23×C67C22×D411yescharacteristic
233D4×C67—44no—
234C2×C4×C67—21no—
235C2×C4×C67—21no—
236C2×C4×C67—21no—
237C2×C4×C67—21no—
238C2×C4×C67—21no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—22no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—22no—
248C2×C4×C67—22no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—41no—
252C2×C4×C67—41no—
253C2×C4×C67—41no—
254C2×C4×C67—41no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—84no—
263C2×C4×C67C2×C4⋊C412yes—
264C2×C4×C67C2×C4⋊C412yes—
265C2×C4×C67C2×C4⋊C412yes—
266C2×C4×C67C2×C4⋊C412yes—
267C2×C4×C67C23×C411yescharacteristic
268C2×C4×C67C22×D411yescharacteristic
269C2×C4×C67C22×Q811yescharacteristic
270C2×C4×C67C2×#4111yescharacteristic
271C2×C4×C67H(5,𝔽2)11yescharacteristic
272C2×C4×C672−1+411yescharacteristic
273C2×Dic67—22no—
274C2×Dic67—41no—
275C2×Dic67—41no—
276C2×Dic67—41no—
277C2×Dic67—41no—
278C2×Dic67—41no—
279C2×Dic67—41no—
280C2×Dic67—41no—
281C2×Dic67—41no—
282C2×Dic67—41no—
283C2×Dic67—41no—
284C2×Dic67—41no—
285C67⋊C8—22no—
286C67⋊C8—22no—
287C67⋊C8—22no—
288C67⋊C8C4×D414yes—
289C22×C67—22no—
290C22×C67—22no—
291C22×C67—22no—
292C22×C67—22no—
293C22×C67—22no—
294C22×C67—22no—
295C22×C67—41no—
296C22×C67—41no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67—41no—
302C22×C67—41no—
303C22×C67C22×C4⋊C411yescharacteristic
304C22×C67D4211yescharacteristic
305C22×C67#54711yescharacteristic
306C22×C67#57511yescharacteristic
307C22×C67#57511yescharacteristic
308C22×C67#57611yescharacteristic
309C22×C67#57811yescharacteristic
310C4×C67—22no—
311C4×C67—22no—
312C4×C67—22no—
313C4×C67—22no—
314C4×C67—42no—
315C4×C67—81no—
316C4×C67—81no—
317C4×C67—81no—
318C4×C67C2×C4×D411yescharacteristic
319C4×C67#52011yescharacteristic
320C4×C67D4×Q811yescharacteristic
321C4×C67#55411yescharacteristic
322Dic67—42no—
323Dic67—81no—
324Dic67—81no—
325Dic67—81no—
326#22660—671nomaximal, Sylow
327C2×C67—42no—
328C2×C67—42no—
329C2×C67D4×C4⋊C411yescharacteristic
330C2×C67#291111yescharacteristic
331C2×C67#291311yescharacteristic
332C2×C67#326811yescharacteristic
333C2×C67#326911yescharacteristic
334C2×C67#334711yescharacteristic
335C2×C67#334911yescharacteristic
336C2×#435—671no—
337C2×#428—671no—
338C2×#427—671no—
339#2354—671no—
340#2352D6711yescharacteristic
341#1949—671no—
342#1947—671no—
343#1854—671no—
344#1854—671no—
345#1854—671no—
346#1852—671no—
347#1847—671no—
348#1809—671no—
349#1808—671no—
350#1776—671no—
351C67#2266011yescharacteristic, complemented, Sylow
352C22×M16—671no—
353C23×C8—671no—
354C2×C4×D4C2×D6711yescharacteristic
355C2×#117—671no—
356C2×#117—671no—
357C2×#117C2×D6711yescharacteristic
358C22×C4⋊C4C2×D6711yescharacteristic
359#435—678no—
360#428—1344no—
361#427—1344no—
362C2×#107—671no—
363C2×#107—671no—
364C2×#107—671no—
365C2×#107—671no—
366C2×#107—671no—
367C2×#107—671no—
368C2×#106—671no—
369C2×#106—671no—
370C2×#106—671no—
371C2×#106—671no—
372C2×C4⋊C8—671no—
373C2×C22⋊C8—671no—
374C2×C22⋊C8—671no—
375C2×#97—671no—
376#390—1341no—
377#388—21no—
378#388—1341no—
379#388—1341no—
380#387—21no—
381#386—21no—
382#384—671no—
383#382C2×D6711yescharacteristic
384#380—671no—
385#380—671no—
386#380C2×D6711yescharacteristic
387#380C2×D6711yescharacteristic
388C4×C4⋊C4—671no—
389C4×C4⋊C4—1341no—
390C4×C4⋊C4C2×D6711yescharacteristic
391C4×C22⋊C4—21no—
392#340—671no—
393#340—671no—
394#340—671no—
395#340—671no—
396#340—671no—
397#340—671no—
398C22×D4C22⋊D6711yescharacteristic
399C23×C4—21no—
400C23×C4C22×D6711yescharacteristic
401C23×C4C22×D6711yescharacteristic
402C2×M16—674no—
403C2×M16—1342no—
404C2×M16—1342no—
405C22×C8—671no—
406C22×C8—674no—
407C22×C8—671no—
408C22×C8—671no—
409C22×C8—671no—
410C22×C8—1342no—
411C22×C8—1342no—
412C4×D4Dic13414yes—
413C4×D4C4×D6714yes—
414#117—22no—
415#117—41no—
416#117—2681no—
417#117—2681no—
418#117—1342no—
419#117—1342no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—671no—
424C2×C4⋊C4—671no—
425C2×C4⋊C4—671no—
426C2×C4⋊C4—671no—
427C2×C4⋊C4—1341no—
428C2×C4⋊C4—1341no—
429C2×C4⋊C4C22⋊D6711yescharacteristic
430C2×C4⋊C4C22×D6711yescharacteristic
431C2×C4⋊C4C22×D6711yescharacteristic
432C2×C4⋊C4C22×D6711yescharacteristic
433C2×C4⋊C4C22×D6711yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1341no—
438C2×C22⋊C4—1341no—
439C2×C22⋊C4—1341no—
440C2×C22⋊C4—1341no—
441C2×C22⋊C4C22⋊D6711yescharacteristic
442C2×C22⋊C4C22⋊D6711yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—1341no—
446C2×C42—1341no—
447C2×C42—1341no—
448C2×C42C22×D6711yescharacteristic
449#107—2681no—
450#107—1342no—
451#107—1342no—
452#107—1342no—
453#107—1342no—
454#107—1342no—
455#106—2681no—
456#106—674no—
457#106—1342no—
458#106—1342no—
459C4⋊C8—674no—
460C22⋊C8—674no—
461C22⋊C8—674no—
462#97—674no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—1341no—
469#95—1341no—
470#95—1341no—
471C24C2×C22⋊D6711yescharacteristic
472C24C2×C22⋊D6711yescharacteristic
473C2×D4—41no—
474C2×D4—41no—
475C2×D4Dic67⋊C414yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—81no—
491C22×C4—1341no—
492C22×C4—1341no—
493C22×C4—1341no—
494C22×C4—1341no—
495C22×C4C2×C4×D6712yes—
496C22×C4C2×C4×D6712yes—
497C22×C4C2×C22⋊D6711yescharacteristic
498C22×C4C2×C22⋊D6711yescharacteristic
499C22×C4C2×C22⋊D6711yescharacteristic
500C22×C4C2×C22⋊D6711yescharacteristic
501C22×C4C2×Dic13412yes—
502C22×C4C2×Dic13412yes—
503C22×C4C23×D6711yescharacteristic
504M16—1348no—
505C2×C8—672no—
506C2×C8—672no—
507C2×C8—672no—
508C2×C8—672no—
509C2×C8—672no—
510C2×C8—672no—
511C2×C8—1348no—
512C2×C8—1341no—
513C2×C8—1341no—
514C2×C8—1341no—
515C2×C8—1341no—
516C2×C8—1341no—
517C2×C8—1341no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—2682no—
527C4⋊C4—5361no—
528C4⋊C4—672no—
529C4⋊C4—1341no—
530C4⋊C4—1341no—
531C4⋊C4—1341no—
532C4⋊C4—1341no—
533C4⋊C4—1341no—
534C4⋊C4—1341no—
535C4⋊C4—1341no—
536C4⋊C4Dic67⋊C414yes—
537C4⋊C4D4×D6712yes—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—2682no—
542C22⋊C4—2682no—
543C22⋊C4—5361no—
544C22⋊C4—5361no—
545C22⋊C4Dic67⋊C414yes—
546C22⋊C4Dic67⋊C414yes—
547C42—42no—
548C42—81no—
549C42—2682no—
550C42—2682no—
551C42—2682no—
552C42C2×C4×D6712yes—
553C42C2×Dic13412yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C2×Dic67⋊C412yes—
567C23C2×Dic67⋊C412yes—
568C23C22×C22⋊D6711yescharacteristic
569D4—44no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—2681no—
600C2×C4—2681no—
601C2×C4—2681no—
602C2×C4—2681no—
603C2×C4—2681no—
604C2×C4—2681no—
605C2×C4—2681no—
606C2×C4—2681no—
607C2×C4—2681no—
608C2×C4—2681no—
609C2×C4—2681no—
610C2×C4—1342no—
611C2×C4C2×Dic67⋊C412yes—
612C2×C4C2×Dic67⋊C412yes—
613C2×C4C2×Dic67⋊C412yes—
614C2×C4C2×Dic67⋊C412yes—
615C2×C4C22×C4×D6711yescharacteristic
616C2×C4C2×D4×D6711yescharacteristic
617C2×C4C22×Dic13411yescharacteristic
618C2×C4#41×D6711yescharacteristic
619C2×C4#1452408811yescharacteristic
620C2×C4#1452409011yescharacteristic
621C8—674no—
622C8—1342no—
623C8—1342no—
624C8—1342no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×Dic67⋊C411yescharacteristic
640C22D4×C22⋊D6711yescharacteristic
641C22#1686404511yescharacteristic
642C22#1686419411yescharacteristic
643C22#1686419411yescharacteristic
644C22#1686419911yescharacteristic
645C22#1686421111yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—2682no—
655C4—5361no—
656C4—5361no—
657C4—5361no—
658C4C4×D4×D6711yescharacteristic
659C4#1686387511yescharacteristic
660C4D4×Dic13411yescharacteristic
661C4#1686410511yescharacteristic
662C2—42no—
663C2—42no—
664C2D4×Dic67⋊C411yescharacteristic
665C2#2256879811yescharacteristic
666C2#2256880711yescharacteristic
667C2#2257174511yescharacteristic
668C2#2257176511yescharacteristic
669C2#2257270311yescharacteristic
670C2#2257273911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#2352C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
cosocleC22×C4×C67C24
hypercenter#2352D67
hypocenterC67#22660
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16863436C2semidirect
3. C2×#16863432C2semidirect
5. #22560975C2semidirect
6. #22560967C2semidirect
7. #22560408C2semidirect
8. #22560406C2semidirect
9. #22560406C2semidirect
10. #22560397C2semidirect
11. #22560378C2semidirect
12. #22560240C2semidirect
13. #22560236C2semidirect
14. #22560107C2semidirect
20. #16863468C4semidirect
67. C22×C67⋊C8C2×C4semidirect
98. #14523974D4semidirect
99. C4⋊(C67⋊C8)C2×C4semidirect
101. C22⋊(C67⋊C8)C2×C4semidirect
102. #14523954C2×C4semidirect
351. C67#22660semidirect

Maximal subgroups

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

subgroupindex
C2×#168634682
C2×#168634362
C2×#168634322
#225631582
#225609752
#225609672
#225604082
#225604062
#225603972
#225603782
#225602402
#225602362
#225601072
C67×#23522
#2266067