Finite Group Databasebeta

← #30873979

Subgroups — #30873979

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×#16863468C211yesmaximal, characteristic
2C2×#16863436C211yesmaximal, characteristic, complemented
3C22×#14523974C211yesmaximal, characteristic, complemented
4#22563138C211yesmaximal, characteristic
5#22560977C211yesmaximal, characteristic, complemented
6#22560970C211yesmaximal, characteristic, complemented
7#22560406C211yesmaximal, characteristic, complemented
8#22560402C211yesmaximal, characteristic, complemented
9#22560401C211yesmaximal, characteristic, complemented
10#22560397C211yesmaximal, characteristic, complemented
11#22560375C211yesmaximal, characteristic, complemented
12#22560240C211yesmaximal, characteristic, complemented
13#22560236C211yesmaximal, characteristic, complemented
14#22560107C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C67C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C23×C67⋊C8C2211yescharacteristic
18C2×#14524002C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20#16863468C418yescomplemented
21#16863436—24no—
22C2×#14523976C2211yescharacteristic
23C2×#14523976C2211yescharacteristic
24C2×#14523976C2211yescharacteristic
25C2×#14523976C2211yescharacteristic
26C2×#14523974—24no—
27C2×#14523974C2211yescharacteristic
28C2×#14523974C2211yescharacteristic
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#16863289—21no—
38#16863282—21no—
39#16863276—21no—
40#16863262C2211yescharacteristic
41#16863256C2211yescharacteristic
42#16863256C2211yescharacteristic
43C4×C4⋊Dic67C2211yescharacteristic
44C22⋊C4×Dic67—21no—
45#16863158C2211yescharacteristic
46#16863158C2211yescharacteristic
47#16863158C2211yescharacteristic
48#16863158C2211yescharacteristic
49#16863158C2211yescharacteristic
50#16863158C2211yescharacteristic
51C2×C4×D4×C67—21no—
52C2×C4×D4×C67C2211yescharacteristic
53C22×C4⋊C4×C67C2211yescharacteristic
54C22×C4⋊C4×C67C2211yescharacteristic
55#389×C67—21no—
56#385×C67—21no—
57#385×C67—21no—
58#384×C67C2211yescharacteristic
59#380×C67C2211yescharacteristic
60#380×C67C2211yescharacteristic
61C4×C4⋊C4×C67C2211yescharacteristic
62C23×Dic67—21no—
63C2×#11761612—22no—
64C2×#11761612—22no—
65C2×#11761612C2×C414yescomplemented
66C22×C67⋊C8—22no—
67C22×C67⋊C8—22no—
68C22×C67⋊C8C2×C414yescomplemented
69C22×C67⋊C8C2311yescharacteristic
70C22×C67⋊C8C2311yescharacteristic
71C22×C67⋊C8C2311yescharacteristic
72C22×C67⋊C8C2311yescharacteristic
73#14524002—22no—
74#14524002—41no—
75C2×C4⋊Dic67—22no—
76C2×C4⋊Dic67—21no—
77C2×C4⋊Dic67—41no—
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×C4×Dic67—21no—
86C2×C4×Dic67—21no—
87#14523976—22no—
88#14523976—22no—
89#14523976—22no—
90#14523976—41no—
91#14523974—22no—
92#14523974—22no—
93#14523974—22no—
94#14523974—22no—
95#14523974—41no—
96#14523974D414yescomplemented
97C4⋊(C67⋊C8)C2×C414yescomplemented
98C22⋊(C67⋊C8)C2×C414yescomplemented
99C22⋊(C67⋊C8)C2×C414yescomplemented
100#14523954C2×C414yescomplemented
101C67⋊#95—21no—
102C67⋊#95—21no—
103C67⋊#95—21no—
104C67⋊#95—21no—
105C67⋊#95—21no—
106C22×D4×C67D411yescharacteristic
107C23×C4×C67—21no—
108C23×C4×C67—21no—
109C23×C4×C67C2311yescharacteristic
110C23×C4×C67C2311yescharacteristic
111C4×D4×C67—44no—
112C4×D4×C67C2×C414yes—
113C4×D4×C67Q814yes—
114C2×C4⋊C4×C67—22no—
115C2×C4⋊C4×C67—22no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67—21no—
118C2×C4⋊C4×C67—21no—
119C2×C4⋊C4×C67—21no—
120C2×C4⋊C4×C67—41no—
121C2×C4⋊C4×C67—41no—
122C2×C4⋊C4×C67D411yescharacteristic
123C2×C4⋊C4×C67C2311yescharacteristic
124C2×C4⋊C4×C67C2311yescharacteristic
125C2×C4⋊C4×C67C2311yescharacteristic
126C2×C4⋊C4×C67C2311yescharacteristic
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67D411yescharacteristic
130C2×C22⋊C4×C67D411yescharacteristic
131C2×C42×C67—21no—
132C2×C42×C67C2311yescharacteristic
133#95×C67—21no—
134#95×C67—21no—
135#95×C67—21no—
136C22×Dic67—21no—
137C22×Dic67—21no—
138C22×Dic67—21no—
139C22×Dic67—21no—
140C22×Dic67—42no—
141C22×Dic67—42no—
142C22×Dic67—81no—
143#11761612—28no—
144C2×C67⋊C8—21no—
145C2×C67⋊C8—21no—
146C2×C67⋊C8—21no—
147C2×C67⋊C8—21no—
148C2×C67⋊C8—21no—
149C2×C67⋊C8—21no—
150C2×C67⋊C8—28no—
151C2×C67⋊C8C22×C412yes—
152C2×C67⋊C8C22×C412yes—
153C2×C67⋊C8C22×C412yes—
154C2×C67⋊C8C22×C412yes—
155C2×C67⋊C8C2×D412yes—
156C2×C67⋊C8#4112yes—
157C4⋊Dic67—21no—
158C4⋊Dic67—21no—
159C4⋊Dic67—21no—
160C4⋊Dic67—21no—
161C4⋊Dic67—21no—
162C4⋊Dic67—21no—
163C4⋊Dic67—21no—
164C4⋊Dic67—42no—
165C4⋊Dic67C2×D412yes—
166C22⋊Dic67—42no—
167C22⋊Dic67—42no—
168C22⋊Dic67—81no—
169C4×Dic67—42no—
170C4×Dic67—81no—
171C24×C67C2×D411yescharacteristic
172C24×C67C2×D411yescharacteristic
173C2×D4×C67—22no—
174C2×D4×C67—22no—
175C2×D4×C67C4⋊C414yes—
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—21no—
188C22×C4×C67—42no—
189C22×C4×C67—42no—
190C22×C4×C67—42no—
191C22×C4×C67—42no—
192C22×C4×C67—81no—
193C22×C4×C67—81no—
194C22×C4×C67C22×C412yes—
195C22×C4×C67C22×C412yes—
196C22×C4×C67C2×D411yescharacteristic
197C22×C4×C67C2×D411yescharacteristic
198C22×C4×C67C2×D411yescharacteristic
199C22×C4×C67C2×D411yescharacteristic
200C22×C4×C67C2×Q812yes—
201C22×C4×C67C2×Q812yes—
202C22×C4×C67C2411yescharacteristic
203C4⋊C4×C67—21no—
204C4⋊C4×C67—21no—
205C4⋊C4×C67—21no—
206C4⋊C4×C67—21no—
207C4⋊C4×C67—21no—
208C4⋊C4×C67—21no—
209C4⋊C4×C67—21no—
210C4⋊C4×C67—42no—
211C4⋊C4×C67—42no—
212C4⋊C4×C67—42no—
213C4⋊C4×C67—81no—
214C4⋊C4×C67C4⋊C414yes—
215C4⋊C4×C67C2×D412yes—
216C22⋊C4×C67—42no—
217C22⋊C4×C67—42no—
218C22⋊C4×C67C4⋊C414yes—
219C22⋊C4×C67C4⋊C414yes—
220C42×C67—42no—
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×C67—22no—
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—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—84no—
268C2×C4×C67—84no—
269C2×C4×C67C2×C4⋊C412yes—
270C2×C4×C67C2×C4⋊C412yes—
271C2×C4×C67C2×C4⋊C412yes—
272C2×C4×C67C2×C4⋊C412yes—
273C2×C4×C67C23×C411yescharacteristic
274C2×C4×C67C22×D411yescharacteristic
275C2×C4×C67C22×Q811yescharacteristic
276C2×C4×C67C2×#4111yescharacteristic
277C2×C4×C67H(5,𝔽2)11yescharacteristic
278C2×C4×C672−1+411yescharacteristic
279C2×Dic67—22no—
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—41no—
290C2×Dic67—41no—
291C2×Dic67—84no—
292C67⋊C8—22no—
293C67⋊C8—22no—
294C67⋊C8—22no—
295C67⋊C8C4×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×C67—42no—
322C4×C67—81no—
323C4×C67—81no—
324C4×C67—81no—
325C4×C67C2×C4×D411yescharacteristic
326C4×C67#52011yescharacteristic
327C4×C67D4×Q811yescharacteristic
328C4×C67#55411yescharacteristic
329Dic67—42no—
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×#435—671no—
344C2×#428—671no—
345C22×#106—671no—
346#2352—671no—
347D4×C4⋊C4D6711yescharacteristic
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×M16—671no—
360C23×C8—671no—
361C2×C4×D4—21no—
362C2×C4×D4C2×D6711yescharacteristic
363C2×#117—671no—
364C22×C4⋊C4—671no—
365C22×C4⋊C4C2×D6711yescharacteristic
366C22×C4⋊C4C2×D6711yescharacteristic
367#435—678no—
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⋊C8—671no—
381C2×C22⋊C8—671no—
382C2×C22⋊C8—671no—
383C2×#97—671no—
384#389—21no—
385#388—1341no—
386#387—1341no—
387#386—1341no—
388#385—21no—
389#385—21no—
390#384C2×D6711yescharacteristic
391#382—671no—
392#380—671no—
393#380—671no—
394#380C2×D6711yescharacteristic
395#380C2×D6711yescharacteristic
396C4×C4⋊C4—671no—
397C4×C4⋊C4C2×D6711yescharacteristic
398C4×C22⋊C4—1341no—
399#340—671no—
400#340—671no—
401#340—671no—
402#340—671no—
403#340—671no—
404#340—671no—
405C22×D4C22⋊D6711yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—1341no—
409C23×C4C22×D6711yescharacteristic
410C23×C4C22×D6711yescharacteristic
411C2×M16—674no—
412C2×M16—1342no—
413C2×M16—1342no—
414C22×C8—671no—
415C22×C8—674no—
416C22×C8—671no—
417C22×C8—671no—
418C22×C8—671no—
419C22×C8—1342no—
420C22×C8—1342no—
421C4×D4—44no—
422C4×D4Dic13414yes—
423C4×D4C4×D6714yes—
424#117—2681no—
425#117—1342no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—2681no—
435C2×C4⋊C4—671no—
436C2×C4⋊C4—671no—
437C2×C4⋊C4—671no—
438C2×C4⋊C4—671no—
439C2×C4⋊C4—1341no—
440C2×C4⋊C4—1342no—
441C2×C4⋊C4C22⋊D6711yescharacteristic
442C2×C4⋊C4C22×D6711yescharacteristic
443C2×C4⋊C4C22×D6711yescharacteristic
444C2×C4⋊C4C22×D6711yescharacteristic
445C2×C4⋊C4C22×D6711yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—1341no—
449C2×C22⋊C4—1341no—
450C2×C22⋊C4—1341no—
451C2×C22⋊C4C22⋊D6711yescharacteristic
452C2×C22⋊C4C22⋊D6711yescharacteristic
453C2×C42—21no—
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⋊C8—674no—
468C22⋊C8—674no—
469C22⋊C8—674no—
470#97—674no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—1341no—
475#95—1341no—
476#95—1341no—
477#95—1341no—
478#95—1341no—
479C24C2×C22⋊D6711yescharacteristic
480C24C2×C22⋊D6711yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic67⋊C414yes—
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—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—2682no—
503C22×C4—2682no—
504C22×C4—5361no—
505C22×C4—1341no—
506C22×C4—1341no—
507C22×C4—1341no—
508C22×C4—1341no—
509C22×C4C2×C4×D6712yes—
510C22×C4C2×C4×D6712yes—
511C22×C4C2×C22⋊D6711yescharacteristic
512C22×C4C2×C22⋊D6711yescharacteristic
513C22×C4C2×C22⋊D6711yescharacteristic
514C22×C4C2×C22⋊D6711yescharacteristic
515C22×C4C2×Dic13412yes—
516C22×C4C2×Dic13412yes—
517C22×C4C23×D6711yescharacteristic
518M16—1348no—
519C2×C8—672no—
520C2×C8—672no—
521C2×C8—672no—
522C2×C8—672no—
523C2×C8—672no—
524C2×C8—672no—
525C2×C8—1348no—
526C2×C8—1341no—
527C2×C8—1341no—
528C2×C8—1341no—
529C2×C8—1341no—
530C2×C8—1341no—
531C2×C8—1341no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—2682no—
544C4⋊C4—672no—
545C4⋊C4—1341no—
546C4⋊C4—1341no—
547C4⋊C4—1341no—
548C4⋊C4—1341no—
549C4⋊C4—1341no—
550C4⋊C4—1341no—
551C4⋊C4—1341no—
552C4⋊C4Dic67⋊C414yes—
553C4⋊C4D4×D6712yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—2682no—
557C22⋊C4—2682no—
558C22⋊C4—5361no—
559C22⋊C4Dic67⋊C414yes—
560C22⋊C4Dic67⋊C414yes—
561C42—42no—
562C42—2682no—
563C42—5361no—
564C42C2×C4×D6712yes—
565C42C2×Dic13412yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic67⋊C412yes—
577C23C2×Dic67⋊C412yes—
578C23#1452406912yes—
579C23#1452407412yes—
580C23C22×C22⋊D6711yescharacteristic
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—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—84no—
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—2681no—
621C2×C4—2681no—
622C2×C4—2681no—
623C2×C4—5364no—
624C2×C4—1342no—
625C2×C4C2×Dic67⋊C412yes—
626C2×C4C2×Dic67⋊C412yes—
627C2×C4C2×Dic67⋊C412yes—
628C2×C4C2×Dic67⋊C412yes—
629C2×C4C22×C4×D6711yescharacteristic
630C2×C4C2×D4×D6711yescharacteristic
631C2×C4C22×Dic13411yescharacteristic
632C2×C4#41×D6711yescharacteristic
633C2×C4#1452408811yescharacteristic
634C2×C4#1452409011yescharacteristic
635C8—674no—
636C8—1342no—
637C8—1342no—
638C8—1342no—
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#1686343614yescomplemented
653C22C22×Dic67⋊C411yescharacteristic
654C22D4×C22⋊D6711yescharacteristic
655C22#1686404511yescharacteristic
656C22C2×#1452406911yescharacteristic
657C22C2×#1452407411yescharacteristic
658C22#1686420411yescharacteristic
659C22#1686420711yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—2682no—
669C4—5361no—
670C4—5361no—
671C4—5361no—
672C4C4×D4×D6711yescharacteristic
673C4#1686387511yescharacteristic
674C4D4×Dic13411yescharacteristic
675C4#1686410511yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic67⋊C411yescharacteristic
679C2C2×#1686343611yescharacteristic
680C2#2256880211yescharacteristic
681C2#2257170011yescharacteristic
682C2#2257172011yescharacteristic
683C2#2257265811yescharacteristic
684C2#2257267911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingD4×C4⋊C4×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
cosocleC22×C4×C67C24
hypercenterD4×C4⋊C4D67
hypocenterC67#22659
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16863436C2semidirect
3. C22×#14523974C2semidirect
5. #22560977C2semidirect
6. #22560970C2semidirect
7. #22560406C2semidirect
8. #22560402C2semidirect
9. #22560401C2semidirect
10. #22560397C2semidirect
11. #22560375C2semidirect
12. #22560240C2semidirect
13. #22560236C2semidirect
14. #22560107C2semidirect
20. #16863468C4semidirect
65. C2×#11761612C2×C4semidirect
68. C22×C67⋊C8C2×C4semidirect
96. #14523974D4semidirect
97. C4⋊(C67⋊C8)C2×C4semidirect
98. C22⋊(C67⋊C8)C2×C4semidirect
99. C22⋊(C67⋊C8)C2×C4semidirect
100. #14523954C2×C4semidirect
295. C67⋊C8C4×D4semidirect
309. C22×C67#428semidirect
358. C67#22659semidirect
652. C22#16863436semidirect

Maximal subgroups

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

subgroupindex
C2×#168634682
C2×#168634362
C22×#145239742
#225631382
#225609772
#225609702
#225604062
#225604022
#225604012
#225603972
#225603752
#225602402
#225602362
#225601072
D4×C4⋊C4×C672
#2265967