Finite Group Databasebeta

← #30873985

Subgroups — #30873985

Order 17152.

1042 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
1C2×#16863438C211yesmaximal, characteristic, complemented
2C22×#14523975C211yesmaximal, characteristic, complemented
3#22563138C211yesmaximal, characteristic
4D4×C4⋊Dic67C211yesmaximal, characteristic
5#22560979C211yesmaximal, characteristic, complemented
6#22560973C211yesmaximal, characteristic, complemented
7#22560410C211yesmaximal, characteristic, complemented
8#22560404C211yesmaximal, characteristic, complemented
9#22560404C211yesmaximal, characteristic, complemented
10#22560399C211yesmaximal, characteristic, complemented
11#22560377C211yesmaximal, characteristic, complemented
12#22560242C211yesmaximal, characteristic, complemented
13#22560238C211yesmaximal, characteristic, complemented
14#22560106C211yesmaximal, characteristic, complemented
15C2×#435×C67C211yesmaximal, characteristic
16C2×D4×Dic67—21no—
17C2×#14524002C2211yescharacteristic
18C22×C4⋊Dic67C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21#16863438—24no—
22C2×#14523977C2211yescharacteristic
23C2×#14523977C2211yescharacteristic
24C2×#14523977C2211yescharacteristic
25C2×#14523977C2211yescharacteristic
26C2×#14523975—24no—
27C2×#14523975C2211yescharacteristic
28C2×#14523975C2211yescharacteristic
29C2×#14523975C2211yescharacteristic
30C2×#14523975C2211yescharacteristic
31C2×#14523975C2211yescharacteristic
32C2×#14523975C2211yescharacteristic
33#16863295—21no—
34#16863289—21no—
35#16863282—21no—
36#16863276—21no—
37#16863271—21no—
38#16863271—21no—
39#16863266C2211yescharacteristic
40#16863262C2211yescharacteristic
41#16863256C2211yescharacteristic
42#16863256C2211yescharacteristic
43#16863256C2211yescharacteristic
44#16863256C2211yescharacteristic
45C4×C4⋊Dic67C2211yescharacteristic
46C4×C4⋊Dic67C2211yescharacteristic
47C22⋊C4×Dic67—21no—
48#16863159C2211yescharacteristic
49#16863159C2211yescharacteristic
50#16863159C2211yescharacteristic
51#16863159C2211yescharacteristic
52#16863159C2211yescharacteristic
53#16863159C2211yescharacteristic
54C22×M16×C67C2211yescharacteristic
55C23×C8×C67C2211yescharacteristic
56C2×C4×D4×C67C2211yescharacteristic
57#435×C67C418yescomplemented
58C2×C4⋊C8×C67C2211yescharacteristic
59C2×C22⋊C8×C67C2211yescharacteristic
60C2×C22⋊C8×C67C2211yescharacteristic
61C2×#97×C67C2211yescharacteristic
62C23×Dic67—21no—
63C23×Dic67—21no—
64C23×Dic67—21no—
65D4×Dic67—44no—
66#14524002—22no—
67#14524002—41no—
68C2×C4⋊Dic67—22no—
69C2×C4⋊Dic67—22no—
70C2×C4⋊Dic67—22no—
71C2×C4⋊Dic67—21no—
72C2×C4⋊Dic67—21no—
73C2×C4⋊Dic67—21no—
74C2×C4⋊Dic67—21no—
75C2×C4⋊Dic67—21no—
76C2×C4⋊Dic67—41no—
77C2×C4⋊Dic67—41no—
78C2×C4⋊Dic67—41no—
79C2×C4⋊Dic67C2311yescharacteristic
80C2×C4⋊Dic67C2311yescharacteristic
81C2×C4⋊Dic67C2311yescharacteristic
82C2×C4⋊Dic67C2311yescharacteristic
83C2×C4⋊Dic67C2311yescharacteristic
84C2×C4⋊Dic67C2311yescharacteristic
85C2×C4⋊Dic67C2311yescharacteristic
86C2×C4⋊Dic67C2311yescharacteristic
87C2×C22⋊Dic67—21no—
88C2×C22⋊Dic67—21no—
89C2×C22⋊Dic67—21no—
90C2×C22⋊Dic67—21no—
91C2×C22⋊Dic67—21no—
92C2×C4×Dic67—21no—
93C2×C4×Dic67—21no—
94C2×C4×Dic67—21no—
95#14523977—22no—
96#14523977—22no—
97#14523977—22no—
98#14523977—41no—
99#14523975—22no—
100#14523975—22no—
101#14523975—22no—
102#14523975—22no—
103#14523975—41no—
104#14523975D414yescomplemented
105C67⋊#95—21no—
106C67⋊#95—21no—
107C67⋊#95—21no—
108C67⋊#95—21no—
109C67⋊#95—21no—
110C67⋊#95—21no—
111C67⋊#95—21no—
112C67⋊#95—21no—
113C22×D4×C67D411yescharacteristic
114C23×C4×C67C2311yescharacteristic
115C23×C4×C67C2311yescharacteristic
116C2×M16×C67—22no—
117C2×M16×C67—22no—
118C2×M16×C67C2×C414yescomplemented
119C22×C8×C67—22no—
120C22×C8×C67—22no—
121C22×C8×C67C2×C414yescomplemented
122C22×C8×C67C2311yescharacteristic
123C22×C8×C67C2311yescharacteristic
124C22×C8×C67C2311yescharacteristic
125C22×C8×C67C2311yescharacteristic
126C4×D4×C67C2×C414yes—
127C4×D4×C67Q814yes—
128C2×C4⋊C4×C67D411yescharacteristic
129C2×C22⋊C4×C67D411yescharacteristic
130C2×C22⋊C4×C67D411yescharacteristic
131C2×C42×C67C2311yescharacteristic
132C4⋊C8×C67C2×C414yescomplemented
133C22⋊C8×C67C2×C414yescomplemented
134C22⋊C8×C67C2×C414yescomplemented
135#97×C67C2×C414yescomplemented
136C22×Dic67—21no—
137C22×Dic67—21no—
138C22×Dic67—21no—
139C22×Dic67—21no—
140C22×Dic67—21no—
141C22×Dic67—21no—
142C22×Dic67—21no—
143C22×Dic67—21no—
144C22×Dic67—42no—
145C22×Dic67—42no—
146C22×Dic67—42no—
147C22×Dic67—42no—
148C22×Dic67—42no—
149C22×Dic67—42no—
150C22×Dic67—81no—
151C22×Dic67—81no—
152C22×Dic67—81no—
153C4⋊Dic67—21no—
154C4⋊Dic67—21no—
155C4⋊Dic67—21no—
156C4⋊Dic67—21no—
157C4⋊Dic67—21no—
158C4⋊Dic67—21no—
159C4⋊Dic67—21no—
160C4⋊Dic67—21no—
161C4⋊Dic67—21no—
162C4⋊Dic67—21no—
163C4⋊Dic67—21no—
164C4⋊Dic67—21no—
165C4⋊Dic67—21no—
166C4⋊Dic67—21no—
167C4⋊Dic67—42no—
168C4⋊Dic67—42no—
169C4⋊Dic67—42no—
170C4⋊Dic67—42no—
171C4⋊Dic67—81no—
172C4⋊Dic67C2×D412yes—
173C4⋊Dic67C2×D412yes—
174C22⋊Dic67—42no—
175C22⋊Dic67—42no—
176C22⋊Dic67—42no—
177C22⋊Dic67—42no—
178C22⋊Dic67—81no—
179C4×Dic67—42no—
180C4×Dic67—42no—
181C4×Dic67—81no—
182C24×C67C2×D411yescharacteristic
183C24×C67C2×D411yescharacteristic
184C2×D4×C67—22no—
185C2×D4×C67—22no—
186C2×D4×C67C4⋊C414yes—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67C22×C412yes—
196C22×C4×C67C22×C412yes—
197C22×C4×C67C2×D411yescharacteristic
198C22×C4×C67C2×D411yescharacteristic
199C22×C4×C67C2×D411yescharacteristic
200C22×C4×C67C2×D411yescharacteristic
201C22×C4×C67C2×Q812yes—
202C22×C4×C67C2×Q812yes—
203C22×C4×C67C2411yescharacteristic
204M16×C67—28no—
205C2×C8×C67—21no—
206C2×C8×C67—21no—
207C2×C8×C67—21no—
208C2×C8×C67—21no—
209C2×C8×C67—21no—
210C2×C8×C67—21no—
211C2×C8×C67—28no—
212C2×C8×C67C22×C412yes—
213C2×C8×C67C22×C412yes—
214C2×C8×C67C22×C412yes—
215C2×C8×C67C22×C412yes—
216C2×C8×C67C2×D412yes—
217C2×C8×C67#4112yes—
218C4⋊C4×C67C4⋊C414yes—
219C22⋊C4×C67C4⋊C414yes—
220C22⋊C4×C67C4⋊C414yes—
221C42×C67C22×C412yes—
222C42×C67C2×Q812yes—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—21no—
230C23×C67—21no—
231C23×C67—21no—
232C23×C67—21no—
233C23×C67C2×C4⋊C412yes—
234C23×C67C2×C4⋊C412yes—
235C23×C67AGL(1,ℤ/8)12yes—
236C23×C67#13712yes—
237C23×C67C22×D411yescharacteristic
238D4×C67—28no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—21no—
242C2×C4×C67—21no—
243C2×C4×C67—21no—
244C2×C4×C67—21no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—22no—
248C2×C4×C67—22no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67C2×C4⋊C412yes—
256C2×C4×C67C2×C4⋊C412yes—
257C2×C4×C67C2×C4⋊C412yes—
258C2×C4×C67C2×C4⋊C412yes—
259C2×C4×C67C23×C411yescharacteristic
260C2×C4×C67C22×D411yescharacteristic
261C2×C4×C67C22×Q811yescharacteristic
262C2×C4×C67C2×#4111yescharacteristic
263C2×C4×C67H(5,𝔽2)11yescharacteristic
264C2×C4×C672−1+411yescharacteristic
265C2×Dic67—22no—
266C2×Dic67—22no—
267C2×Dic67—41no—
268C2×Dic67—41no—
269C2×Dic67—41no—
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—41no—
279C2×Dic67—41no—
280C2×Dic67—41no—
281C2×Dic67—41no—
282C2×Dic67—41no—
283C2×Dic67—41no—
284C2×Dic67—41no—
285C2×Dic67—41no—
286C2×Dic67—41no—
287C2×Dic67—41no—
288C2×Dic67—41no—
289C2×Dic67—84no—
290C2×Dic67—84no—
291C2×Dic67—84no—
292C8×C67—22no—
293C8×C67—22no—
294C8×C67—22no—
295C8×C67C4×D414yescomplemented
296C22×C67—22no—
297C22×C67—22no—
298C22×C67—22no—
299C22×C67—22no—
300C22×C67—22no—
301C22×C67—22no—
302C22×C67—22no—
303C22×C67—22no—
304C22×C67—22no—
305C22×C67—41no—
306C22×C67—41no—
307C22×C67—41no—
308C22×C67—41no—
309C22×C67#42814yescomplemented
310C22×C67C22×C4⋊C411yescharacteristic
311C22×C67D4211yescharacteristic
312C22×C67#54711yescharacteristic
313C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C67C2×#13711yescharacteristic
315C22×C67#57711yescharacteristic
316C22×C67#57711yescharacteristic
317C4×C67—22no—
318C4×C67—22no—
319C4×C67—22no—
320C4×C67—22no—
321C4×C67C2×C4×D411yescharacteristic
322C4×C67#52011yescharacteristic
323C4×C67D4×Q811yescharacteristic
324C4×C67#55411yescharacteristic
325Dic67—42no—
326Dic67—42no—
327Dic67—81no—
328Dic67—81no—
329Dic67—81no—
330Dic67—81no—
331Dic67—81no—
332Dic67—81no—
333#22659—671nomaximal, Sylow
334C2×C67—24no—
335C2×C67—42no—
336C2×C67D4×C4⋊C411yescharacteristic
337C2×C67C2×#42811yescharacteristic
338C2×C67#291211yescharacteristic
339C2×C67#326511yescharacteristic
340C2×C67#326611yescharacteristic
341C2×C67#334411yescharacteristic
342C2×C67#334511yescharacteristic
343C2×#435D6711yescharacteristic
344C2×#428—671no—
345C22×#106—671no—
346#2352—671no—
347D4×C4⋊C4—671no—
348#1949—671no—
349#1948—671no—
350#1854—671no—
351#1853—671no—
352#1853—671no—
353#1852—671no—
354#1847—671no—
355#1809—671no—
356#1808—671no—
357#1776—671no—
358C67#2265911yescharacteristic, complemented, Sylow
359C22×M16C2×D6711yescharacteristic
360C23×C8C2×D6711yescharacteristic
361C2×C4×D4—1341no—
362C2×C4×D4C2×D6711yescharacteristic
363C2×#117—671no—
364C22×C4⋊C4—671no—
365C22×C4⋊C4—671no—
366C22×C4⋊C4—671no—
367#435Dic6718yescomplemented
368#428—1344no—
369C2×#107—671no—
370C2×#107—671no—
371C2×#107—671no—
372C2×#107—671no—
373C2×#106—671no—
374C2×#106—671no—
375C2×#106—671no—
376C2×#106—671no—
377C2×#106—671no—
378C2×#106—671no—
379C2×#106—1344no—
380C2×C4⋊C8C2×D6711yescharacteristic
381C2×C22⋊C8C2×D6711yescharacteristic
382C2×C22⋊C8C2×D6711yescharacteristic
383C2×#97C2×D6711yescharacteristic
384#389—1341no—
385#388—1341no—
386#387—1341no—
387#386—1341no—
388#385—1341no—
389#385—1341no—
390#384—671no—
391#382—671no—
392#380—671no—
393#380—671no—
394#380—671no—
395#380—671no—
396C4×C4⋊C4—671no—
397C4×C4⋊C4—671no—
398C4×C22⋊C4—1341no—
399#340—671no—
400#340—671no—
401#340—671no—
402#340—671no—
403#340—671no—
404#340—671no—
405C22×D4D26811yescharacteristic
406C23×C4—1341no—
407C23×C4—1341no—
408C23×C4—1341no—
409C23×C4C22×D6711yescharacteristic
410C23×C4C22×D6711yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×Dic6714yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×Dic6714yescomplemented
417C22×C8C22×D6711yescharacteristic
418C22×C8C22×D6711yescharacteristic
419C22×C8C22×D6711yescharacteristic
420C22×C8C22×D6711yescharacteristic
421C4×D4—2684no—
422C4×D4Dic13414yes—
423C4×D4C2×Dic6714yes—
424#117—2681no—
425#117—1342no—
426C2×C4⋊C4—2681no—
427C2×C4⋊C4—2681no—
428C2×C4⋊C4—2681no—
429C2×C4⋊C4—671no—
430C2×C4⋊C4—671no—
431C2×C4⋊C4—671no—
432C2×C4⋊C4—671no—
433C2×C4⋊C4—671no—
434C2×C4⋊C4—671no—
435C2×C4⋊C4—671no—
436C2×C4⋊C4—671no—
437C2×C4⋊C4—1341no—
438C2×C4⋊C4—1341no—
439C2×C4⋊C4—1341no—
440C2×C4⋊C4—1341no—
441C2×C4⋊C4—1342no—
442C2×C4⋊C4—1342no—
443C2×C4⋊C4—1342no—
444C2×C4⋊C4—1341no—
445C2×C4⋊C4D26811yescharacteristic
446C2×C22⋊C4—1341no—
447C2×C22⋊C4—1341no—
448C2×C22⋊C4—1341no—
449C2×C22⋊C4—1341no—
450C2×C22⋊C4—1341no—
451C2×C22⋊C4D26811yescharacteristic
452C2×C22⋊C4D26811yescharacteristic
453C2×C42—1341no—
454C2×C42—1341no—
455C2×C42—1341no—
456C2×C42C22×D6711yescharacteristic
457#107—2681no—
458#107—1342no—
459#107—1342no—
460#107—1342no—
461#106—2681no—
462#106—674no—
463#106—1342no—
464#106—1342no—
465#106—1342no—
466#106—1342no—
467C4⋊C8C2×Dic6714yescomplemented
468C22⋊C8C2×Dic6714yescomplemented
469C22⋊C8C2×Dic6714yescomplemented
470#97C2×Dic6714yescomplemented
471#95—1341no—
472#95—1341no—
473#95—1341no—
474#95—1341no—
475#95—1341no—
476#95—1341no—
477#95—1341no—
478#95—1341no—
479C24C2×D26811yescharacteristic
480C24C2×D26811yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊Dic6714yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—2682no—
493C22×C4—2682no—
494C22×C4—2682no—
495C22×C4—2682no—
496C22×C4—2682no—
497C22×C4—2682no—
498C22×C4—5361no—
499C22×C4—5361no—
500C22×C4—5361no—
501C22×C4—1341no—
502C22×C4—1341no—
503C22×C4—1341no—
504C22×C4—1341no—
505C22×C4—1341no—
506C22×C4—1341no—
507C22×C4—1341no—
508C22×C4—1341no—
509C22×C4C22×Dic6712yes—
510C22×C4C22×Dic6712yes—
511C22×C4C2×D26811yescharacteristic
512C22×C4C2×D26811yescharacteristic
513C22×C4C2×D26811yescharacteristic
514C22×C4C2×D26811yescharacteristic
515C22×C4C2×Dic13412yes—
516C22×C4C2×Dic13412yes—
517C22×C4C23×D6711yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8C22×Dic6712yes—
527C2×C8C22×Dic6712yes—
528C2×C8C22×Dic6712yes—
529C2×C8C22×Dic6712yes—
530C2×C8D4×D6712yes—
531C2×C8#1176162712yes—
532C4⋊C4—2682no—
533C4⋊C4—2682no—
534C4⋊C4—2682no—
535C4⋊C4—2682no—
536C4⋊C4—5361no—
537C4⋊C4—672no—
538C4⋊C4—672no—
539C4⋊C4—1341no—
540C4⋊C4—1341no—
541C4⋊C4—1341no—
542C4⋊C4—1341no—
543C4⋊C4—1341no—
544C4⋊C4—1341no—
545C4⋊C4—1341no—
546C4⋊C4—1341no—
547C4⋊C4—1341no—
548C4⋊C4—1341no—
549C4⋊C4—1341no—
550C4⋊C4—1341no—
551C4⋊C4—1341no—
552C4⋊C4—1341no—
553C4⋊C4C4⋊Dic6714yes—
554C22⋊C4—2682no—
555C22⋊C4—2682no—
556C22⋊C4—2682no—
557C22⋊C4—2682no—
558C22⋊C4—5361no—
559C22⋊C4C4⋊Dic6714yes—
560C22⋊C4C4⋊Dic6714yes—
561C42—2682no—
562C42—2682no—
563C42—5361no—
564C42C22×Dic6712yes—
565C42C2×Dic13412yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊Dic6712yes—
577C23C2×C4⋊Dic6712yes—
578C23#1452407112yes—
579C23#1452407612yes—
580C23C22×D26811yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—2681no—
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—2681no—
611C2×C4—2681no—
612C2×C4—2681no—
613C2×C4—2681no—
614C2×C4—2681no—
615C2×C4—2681no—
616C2×C4—2681no—
617C2×C4—2681no—
618C2×C4—2681no—
619C2×C4—2681no—
620C2×C4—5364no—
621C2×C4—5364no—
622C2×C4—5364no—
623C2×C4—1342no—
624C2×C4—1342no—
625C2×C4C2×C4⋊Dic6712yes—
626C2×C4C2×C4⋊Dic6712yes—
627C2×C4C2×C4⋊Dic6712yes—
628C2×C4C2×C4⋊Dic6712yes—
629C2×C4C23×Dic6711yescharacteristic
630C2×C4C2×D4×D6711yescharacteristic
631C2×C4C22×Dic13411yescharacteristic
632C2×C4C2×#1176162711yescharacteristic
633C2×C4#1452408911yescharacteristic
634C2×C4#1452409011yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8D4×Dic6714yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1686343814yescomplemented
653C22C22×C4⋊Dic6711yescharacteristic
654C22D4×D26811yescharacteristic
655C22#1686405011yescharacteristic
656C22C2×#1452407111yescharacteristic
657C22C2×#1452407611yescharacteristic
658C22#1686420811yescharacteristic
659C22#1686420811yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—2682no—
665C4—2682no—
666C4—5361no—
667C4—5361no—
668C4—5361no—
669C4—5361no—
670C4—5361no—
671C4—5361no—
672C4C2×D4×Dic6711yescharacteristic
673C4#1686387911yescharacteristic
674C4D4×Dic13411yescharacteristic
675C4#1686410311yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊Dic6711yescharacteristic
679C2C2×#1686343811yescharacteristic
680C2#2256880411yescharacteristic
681C2#2257170911yescharacteristic
682C2#2257172411yescharacteristic
683C2#2257266611yescharacteristic
684C2#2257268111yescharacteristic
subgroupG/H
centerC23C22×D268
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
cosocleC22×C4×C67C24
hypercenterC2×#435D67
hypocenterC67#22659
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16863438C2semidirect
2. C22×#14523975C2semidirect
5. #22560979C2semidirect
6. #22560973C2semidirect
7. #22560410C2semidirect
8. #22560404C2semidirect
9. #22560404C2semidirect
10. #22560399C2semidirect
11. #22560377C2semidirect
12. #22560242C2semidirect
13. #22560238C2semidirect
14. #22560106C2semidirect
57. #435×C67C4semidirect
104. #14523975D4semidirect
118. C2×M16×C67C2×C4semidirect
121. C22×C8×C67C2×C4semidirect
132. C4⋊C8×C67C2×C4semidirect
133. C22⋊C8×C67C2×C4semidirect
134. C22⋊C8×C67C2×C4semidirect
135. #97×C67C2×C4semidirect
295. C8×C67C4×D4semidirect
309. C22×C67#428semidirect
358. C67#22659semidirect
367. #435Dic67semidirect
413. C2×M16C2×Dic67semidirect
416. C22×C8C2×Dic67semidirect
467. C4⋊C8C2×Dic67semidirect
468. C22⋊C8C2×Dic67semidirect
469. C22⋊C8C2×Dic67semidirect
470. #97C2×Dic67semidirect
638. C8D4×Dic67semidirect
652. C22#16863438semidirect

Maximal subgroups

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

subgroupindex
C2×#168634382
C22×#145239752
#225631382
D4×C4⋊Dic672
#225609792
#225609732
#225604102
#225604042
#225603992
#225603772
#225602422
#225602382
#225601062
C2×#435×C672
#2265967