Finite Group Databasebeta

← #30874603

Subgroups — #30874603

Order 17152.

796 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11761612C211yesmaximal, characteristic
2C2×#16863468C211yesmaximal, characteristic
3#22560984C211yesmaximal, characteristic, complemented
4#22560982C211yesmaximal, characteristic, complemented
5#22560414C211yesmaximal, characteristic, complemented
6#22560414C211yesmaximal, characteristic, complemented
7#22560413C211yesmaximal, characteristic, complemented
8#22560413C211yesmaximal, characteristic, complemented
9#22560349C211yesmaximal, characteristic, complemented
10#22560249C211yesmaximal, characteristic, complemented
11#22560245C211yesmaximal, characteristic, complemented
12#22560116C211yesmaximal, characteristic, complemented
13#22559935C211yesmaximal, characteristic, complemented
14C2×#16863160C211yesmaximal, characteristic, complemented
15D4×M16×C67C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C22×#11761612C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20#16863474—21no—
21#16863468—21no—
22#16863468—21no—
23#16863468C412yes—
24#16863468C412yes—
25#16863468C412yes—
26#16863468C412yes—
27D4×C67⋊C8—21no—
28C2×#14523978C2211yescharacteristic
29C2×#14523978C2211yescharacteristic
30C2×#14523978C2211yescharacteristic
31C2×#14523978C2211yescharacteristic
32C2×#14523978C2211yescharacteristic
33C2×#14523978C2211yescharacteristic
34#16863420C2211yescharacteristic
35C2×C4⋊(C67⋊C8)C2211yescharacteristic
36#16863360C2211yescharacteristic
37#16863360C2211yescharacteristic
38C2×C22⋊(C67⋊C8)C2211yescharacteristic
39C2×C22⋊(C67⋊C8)C2211yescharacteristic
40C4×#11761612C2211yescharacteristic
41C2×#14523954C2211yescharacteristic
42#16863160C2211yescharacteristic
43#16863160C2211yescharacteristic
44#16863160C2211yescharacteristic
45#16863160C2211yescharacteristic
46#16863160C2211yescharacteristic
47#16863160C2211yescharacteristic
48#16863160C2211yescharacteristic
49#16863160C2211yescharacteristic
50#16863160C2211yescharacteristic
51#16863160C2211yescharacteristic
52C22×M16×C67C2211yescharacteristic
53C22×M16×C67C2211yescharacteristic
54C2×C4×D4×C67C2211yescharacteristic
55#436×C67—21no—
56#435×C67—21no—
57#435×C67—21no—
58C8×D4×C67—21no—
59#423×C67C2211yescharacteristic
60#407×C67C2211yescharacteristic
61#407×C67C2211yescharacteristic
62C4×M16×C67C2211yescharacteristic
63C2×#11761612—22no—
64C2×#11761612—22no—
65C2×#11761612—21no—
66C2×#11761612—21no—
67C2×#11761612—41no—
68C2×#11761612—41no—
69C2×#11761612—41no—
70C2×#11761612—41no—
71C2×#11761612C2×C412yes—
72C2×#11761612C2×C412yes—
73C2×#11761612C2311yescharacteristic
74C2×#11761612C2311yescharacteristic
75C2×#11761612C2311yescharacteristic
76C2×#11761612C2311yescharacteristic
77C22×C67⋊C8—21no—
78C22×C67⋊C8—21no—
79C22×C67⋊C8—41no—
80C22×C67⋊C8—41no—
81C22×C67⋊C8C2×C412yes—
82C22×C67⋊C8C2×C412yes—
83C22×C67⋊C8C2311yescharacteristic
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87#14523978—22no—
88#14523978—22no—
89#14523978—41no—
90#14523978—41no—
91#14523978—41no—
92#14523978—41no—
93C4⋊(C67⋊C8)—21no—
94C4⋊(C67⋊C8)—21no—
95C4⋊(C67⋊C8)C2×C412yes—
96C4⋊(C67⋊C8)C2×C412yes—
97C22⋊(C67⋊C8)—21no—
98C22⋊(C67⋊C8)—21no—
99C22⋊(C67⋊C8)—21no—
100C22⋊(C67⋊C8)—21no—
101C22⋊(C67⋊C8)C2×C412yes—
102C22⋊(C67⋊C8)C2×C412yes—
103C22⋊(C67⋊C8)C2×C412yes—
104C22⋊(C67⋊C8)C2×C412yes—
105#14523954—21no—
106#14523954C2×C412yes—
107#14523954C2×C412yes—
108C4×C67⋊C8—21no—
109C22×D4×C67Q811yescharacteristic
110C23×C4×C67C2311yescharacteristic
111C23×C4×C67C2311yescharacteristic
112C2×M16×C67—21no—
113C2×M16×C67—21no—
114C2×M16×C67—22no—
115C2×M16×C67—22no—
116C2×M16×C67—41no—
117C2×M16×C67—41no—
118C2×M16×C67C2311yescharacteristic
119C2×M16×C67C2311yescharacteristic
120C2×M16×C67C2311yescharacteristic
121C2×M16×C67C2311yescharacteristic
122C22×C8×C67—21no—
123C22×C8×C67—21no—
124C4×D4×C67C2×C411yescharacteristic
125C4×D4×C67C2×C411yescharacteristic
126C4×D4×C67C2×C411yescharacteristic
127C4×D4×C67C2×C411yescharacteristic
128C4×D4×C67D411yescharacteristic
129C4×D4×C67D411yescharacteristic
130C4×D4×C67D411yescharacteristic
131C4×D4×C67D411yescharacteristic
132C2×C4⋊C4×C67Q811yescharacteristic
133C2×C22⋊C4×C67Q811yescharacteristic
134C2×C22⋊C4×C67Q811yescharacteristic
135C2×C42×C67C2311yescharacteristic
136C4⋊C8×C67—21no—
137C4⋊C8×C67—21no—
138C22⋊C8×C67—21no—
139C22⋊C8×C67—21no—
140C22⋊C8×C67—21no—
141C22⋊C8×C67—21no—
142#97×C67—21no—
143C4×C8×C67—21no—
144#11761612—21no—
145#11761612—21no—
146#11761612—21no—
147#11761612—21no—
148#11761612—21no—
149#11761612—21no—
150#11761612—21no—
151#11761612—42no—
152#11761612—42no—
153#11761612—42no—
154#11761612—42no—
155#11761612#4112yes—
156C2×C67⋊C8—21no—
157C2×C67⋊C8—21no—
158C2×C67⋊C8—21no—
159C2×C67⋊C8—21no—
160C2×C67⋊C8—21no—
161C2×C67⋊C8—21no—
162C2×C67⋊C8—21no—
163C2×C67⋊C8—21no—
164C2×C67⋊C8—21no—
165C2×C67⋊C8—21no—
166C2×C67⋊C8—21no—
167C2×C67⋊C8—21no—
168C2×C67⋊C8—42no—
169C2×C67⋊C8—42no—
170C2×C67⋊C8—42no—
171C2×C67⋊C8—42no—
172C2×C67⋊C8C22×C412yes—
173C2×C67⋊C8C22×C412yes—
174C2×C67⋊C8C22×C412yes—
175C2×C67⋊C8C22×C412yes—
176C24×C67C2×Q811yescharacteristic
177C24×C67C2×Q811yescharacteristic
178C2×D4×C67—42no—
179C2×D4×C67C4⋊C411yescharacteristic
180C2×D4×C67C4⋊C411yescharacteristic
181C2×D4×C67C4⋊C411yescharacteristic
182C2×D4×C67C4⋊C411yescharacteristic
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67C22×C411yescharacteristic
192C22×C4×C67C22×C411yescharacteristic
193C22×C4×C67C22×C411yescharacteristic
194C22×C4×C67C22×C411yescharacteristic
195C22×C4×C67C2×D411yescharacteristic
196C22×C4×C67C2×D411yescharacteristic
197C22×C4×C67C2×D411yescharacteristic
198C22×C4×C67C2×D411yescharacteristic
199C22×C4×C67C2×Q811yescharacteristic
200C22×C4×C67C2×Q811yescharacteristic
201C22×C4×C67C2×Q811yescharacteristic
202C22×C4×C67C2×Q811yescharacteristic
203C22×C4×C67C2411yescharacteristic
204M16×C67—21no—
205M16×C67—21no—
206M16×C67—21no—
207M16×C67—21no—
208M16×C67—21no—
209M16×C67—21no—
210M16×C67—21no—
211M16×C67—42no—
212M16×C67—42no—
213M16×C67#4112yes—
214C2×C8×C67—21no—
215C2×C8×C67—21no—
216C2×C8×C67—21no—
217C2×C8×C67—21no—
218C2×C8×C67—42no—
219C2×C8×C67—42no—
220C4⋊C4×C67C4⋊C411yescharacteristic
221C4⋊C4×C67C4⋊C411yescharacteristic
222C4⋊C4×C67C4⋊C411yescharacteristic
223C4⋊C4×C67C4⋊C411yescharacteristic
224C22⋊C4×C67C4⋊C411yescharacteristic
225C22⋊C4×C67C4⋊C411yescharacteristic
226C22⋊C4×C67C4⋊C411yescharacteristic
227C22⋊C4×C67C4⋊C411yescharacteristic
228C22⋊C4×C67C4⋊C411yescharacteristic
229C22⋊C4×C67C4⋊C411yescharacteristic
230C22⋊C4×C67C4⋊C411yescharacteristic
231C22⋊C4×C67C4⋊C411yescharacteristic
232C42×C67C22×C411yescharacteristic
233C42×C67C22×C411yescharacteristic
234C42×C67C2×D411yescharacteristic
235C42×C67C2×D411yescharacteristic
236C23×C67—21no—
237C23×C67—21no—
238C23×C67—22no—
239C23×C67—21no—
240C23×C67—21no—
241C23×C67—41no—
242C23×C67—41no—
243C23×C67—41no—
244C23×C67C2×C4⋊C411yescharacteristic
245C23×C67C2×C4⋊C411yescharacteristic
246C23×C67C2×C4⋊C411yescharacteristic
247C23×C67C2×C4⋊C411yescharacteristic
248C23×C67C22×Q811yescharacteristic
249D4×C67—22no—
250D4×C67—22no—
251D4×C67—41no—
252D4×C67—41no—
253C2×C4×C67—21no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—21no—
259C2×C4×C67—21no—
260C2×C4×C67—21no—
261C2×C4×C67—21no—
262C2×C4×C67—21no—
263C2×C4×C67—21no—
264C2×C4×C67—21no—
265C2×C4×C67—21no—
266C2×C4×C67—21no—
267C2×C4×C67—21no—
268C2×C4×C67—21no—
269C2×C4×C67—21no—
270C2×C4×C67—21no—
271C2×C4×C67—21no—
272C2×C4×C67—21no—
273C2×C4×C67—41no—
274C2×C4×C67—41no—
275C2×C4×C67C2×C4⋊C411yescharacteristic
276C2×C4×C67C2×C4⋊C411yescharacteristic
277C2×C4×C67C2×C4⋊C411yescharacteristic
278C2×C4×C67C2×C4⋊C411yescharacteristic
279C2×C4×C67C2×C4⋊C411yescharacteristic
280C2×C4×C67C2×C4⋊C411yescharacteristic
281C2×C4×C67C2×C4⋊C411yescharacteristic
282C2×C4×C67C2×C4⋊C411yescharacteristic
283C2×C4×C67C23×C411yescharacteristic
284C2×C4×C67C22×D411yescharacteristic
285C2×C4×C67C2×#4111yescharacteristic
286C2×C4×C67C2×#4111yescharacteristic
287C2×C4×C67H(5,𝔽2)11yescharacteristic
288C2×C4×C67H(5,𝔽2)11yescharacteristic
289C8×C67—22no—
290C8×C67—41no—
291C8×C67—41no—
292C8×C67—41no—
293C67⋊C8—22no—
294C67⋊C8—22no—
295C67⋊C8—22no—
296C67⋊C8—22no—
297C67⋊C8—22no—
298C67⋊C8—41no—
299C67⋊C8—41no—
300C67⋊C8—41no—
301C22×C67—21no—
302C22×C67—21no—
303C22×C67—21no—
304C22×C67—21no—
305C22×C67—21no—
306C22×C67—21no—
307C22×C67—21no—
308C22×C67—21no—
309C22×C67—21no—
310C22×C67—21no—
311C22×C67—21no—
312C22×C67—21no—
313C22×C67—21no—
314C22×C67—42no—
315C22×C67—42no—
316C22×C67—81no—
317C22×C67—81no—
318C22×C67#43012yes—
319C22×C67C22×C4⋊C411yescharacteristic
320C22×C67#55411yescharacteristic
321C22×C67#55411yescharacteristic
322C4×C67—21no—
323C4×C67—21no—
324C4×C67—21no—
325C4×C67—21no—
326C4×C67—21no—
327C4×C67—21no—
328C4×C67—21no—
329C4×C67—21no—
330C4×C67C4×#4111yescharacteristic
331C4×C67#51811yescharacteristic
332C4×C67#54611yescharacteristic
333C4×C67#54611yescharacteristic
334#22718—671nomaximal, Sylow
335C2×C67—21no—
336C2×C67—21no—
337C2×C67—22no—
338C2×C67—41no—
339C2×C67—41no—
340C2×C67—41no—
341C2×C67#234911yescharacteristic
342C2×C67C2×#43011yescharacteristic
343C2×C67#291611yescharacteristic
344D4×M16—671no—
345D4×M16D6711yescharacteristic
346C2×#435—671no—
347#1950—671no—
348#1950—671no—
349#1855—671no—
350#1855—671no—
351#1855—671no—
352#1855—671no—
353#1838—671no—
354#1811—671no—
355#1810—671no—
356#1778—671no—
357#1738—671no—
358C2×#341—671no—
359C67#2271811yescharacteristic, complemented, Sylow
360C22×M16—671no—
361C22×M16—671no—
362C22×M16—671no—
363C22×M16C2×D6711yescharacteristic
364C22×M16C2×D6711yescharacteristic
365C23×C8—671no—
366C2×C4×D4C2×D6711yescharacteristic
367#436—21no—
368#436—1341no—
369#435—21no—
370#435—21no—
371#435—672no—
372#435—672no—
373#435—672no—
374#435—672no—
375#435—1341no—
376#435—1341no—
377C8×D4—21no—
378C8×D4—1341no—
379C2×#108—671no—
380C2×#108—671no—
381C2×#108—671no—
382C2×#108—671no—
383C2×#108—671no—
384C2×#108—671no—
385#423—671no—
386#423C2×D6711yescharacteristic
387C2×C4⋊C8—671no—
388#407—671no—
389#407—671no—
390#407C2×D6711yescharacteristic
391#407C2×D6711yescharacteristic
392C2×C22⋊C8—671no—
393C2×C22⋊C8—671no—
394C4×M16—671no—
395C4×M16C2×D6711yescharacteristic
396C2×#97—671no—
397#341—671no—
398#341—671no—
399#341—671no—
400#341—671no—
401#341—671no—
402#341—671no—
403#341—671no—
404#341—671no—
405#341—671no—
406#341—671no—
407C22×D4Dic13411yescharacteristic
408C23×C4C22×D6711yescharacteristic
409C23×C4C22×D6711yescharacteristic
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—41no—
415C2×M16—41no—
416C2×M16—2681no—
417C2×M16—2681no—
418C2×M16—2681no—
419C2×M16—2681no—
420C2×M16—672no—
421C2×M16—672no—
422C2×M16—671no—
423C2×M16—671no—
424C2×M16—671no—
425C2×M16—671no—
426C2×M16—1342no—
427C2×M16—1342no—
428C2×M16—1341no—
429C2×M16—1341no—
430C2×M16C22×D6711yescharacteristic
431C2×M16C22×D6711yescharacteristic
432C2×M16C22×D6711yescharacteristic
433C2×M16C22×D6711yescharacteristic
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—2681no—
437C22×C8—2681no—
438C22×C8—672no—
439C22×C8—672no—
440C22×C8—671no—
441C22×C8—671no—
442C22×C8—671no—
443C22×C8—671no—
444C22×C8—1341no—
445C22×C8—1341no—
446C4×D4C4×D6711yescharacteristic
447C4×D4C4×D6711yescharacteristic
448C4×D4C4×D6711yescharacteristic
449C4×D4C4×D6711yescharacteristic
450C4×D4C22⋊D6711yescharacteristic
451C4×D4C22⋊D6711yescharacteristic
452C4×D4C22⋊D6711yescharacteristic
453C4×D4C22⋊D6711yescharacteristic
454C2×C4⋊C4Dic13411yescharacteristic
455C2×C22⋊C4Dic13411yescharacteristic
456C2×C22⋊C4Dic13411yescharacteristic
457C2×C42C22×D6711yescharacteristic
458#108—2681no—
459#108—2681no—
460#108—2681no—
461#108—2681no—
462#108—1342no—
463#108—1342no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—672no—
467C4⋊C8—672no—
468C4⋊C8—1341no—
469C4⋊C8—1341no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—672no—
475C22⋊C8—672no—
476C22⋊C8—672no—
477C22⋊C8—672no—
478C22⋊C8—1341no—
479C22⋊C8—1341no—
480C22⋊C8—1341no—
481C22⋊C8—1341no—
482#97—21no—
483#97—672no—
484#97—672no—
485#97—1341no—
486C4×C8—21no—
487C4×C8—1341no—
488C24C2×Dic13411yescharacteristic
489C24C2×Dic13411yescharacteristic
490C2×D4—42no—
491C2×D4Dic67⋊C411yescharacteristic
492C2×D4Dic67⋊C411yescharacteristic
493C2×D4Dic67⋊C411yescharacteristic
494C2×D4Dic67⋊C411yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4C2×C4×D6711yescharacteristic
504C22×C4C2×C4×D6711yescharacteristic
505C22×C4C2×C4×D6711yescharacteristic
506C22×C4C2×C4×D6711yescharacteristic
507C22×C4C2×C22⋊D6711yescharacteristic
508C22×C4C2×C22⋊D6711yescharacteristic
509C22×C4C2×C22⋊D6711yescharacteristic
510C22×C4C2×C22⋊D6711yescharacteristic
511C22×C4C2×Dic13411yescharacteristic
512C22×C4C2×Dic13411yescharacteristic
513C22×C4C2×Dic13411yescharacteristic
514C22×C4C2×Dic13411yescharacteristic
515C22×C4C23×D6711yescharacteristic
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—42no—
524M16—42no—
525M16—2682no—
526M16—2682no—
527M16—2682no—
528M16—2682no—
529M16—672no—
530M16—1341no—
531M16—1341no—
532M16—1341no—
533M16—1341no—
534M16—1341no—
535M16—1341no—
536M16—1341no—
537M16#1176162712yes—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—2682no—
545C2×C8—2682no—
546C2×C8—2682no—
547C2×C8—2682no—
548C2×C8—672no—
549C2×C8—672no—
550C2×C8—672no—
551C2×C8—672no—
552C2×C8—1341no—
553C2×C8—1341no—
554C2×C8—1341no—
555C2×C8—1341no—
556C2×C8—1341no—
557C2×C8—1341no—
558C2×C8—1341no—
559C2×C8—1341no—
560C2×C8—1341no—
561C2×C8—1341no—
562C2×C8—1341no—
563C2×C8—1341no—
564C4⋊C4Dic67⋊C411yescharacteristic
565C4⋊C4Dic67⋊C411yescharacteristic
566C4⋊C4Dic67⋊C411yescharacteristic
567C4⋊C4Dic67⋊C411yescharacteristic
568C22⋊C4Dic67⋊C411yescharacteristic
569C22⋊C4Dic67⋊C411yescharacteristic
570C22⋊C4Dic67⋊C411yescharacteristic
571C22⋊C4Dic67⋊C411yescharacteristic
572C22⋊C4Dic67⋊C411yescharacteristic
573C22⋊C4Dic67⋊C411yescharacteristic
574C22⋊C4Dic67⋊C411yescharacteristic
575C22⋊C4Dic67⋊C411yescharacteristic
576C42C2×C4×D6711yescharacteristic
577C42C2×C4×D6711yescharacteristic
578C42C2×C22⋊D6711yescharacteristic
579C42C2×C22⋊D6711yescharacteristic
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C2×Dic67⋊C411yescharacteristic
589C23C2×Dic67⋊C411yescharacteristic
590C23C2×Dic67⋊C411yescharacteristic
591C23C2×Dic67⋊C411yescharacteristic
592C23C22×Dic13411yescharacteristic
593D4—22no—
594D4—22no—
595D4—41no—
596D4—41no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4C2×Dic67⋊C411yescharacteristic
620C2×C4C2×Dic67⋊C411yescharacteristic
621C2×C4C2×Dic67⋊C411yescharacteristic
622C2×C4C2×Dic67⋊C411yescharacteristic
623C2×C4C2×Dic67⋊C411yescharacteristic
624C2×C4C2×Dic67⋊C411yescharacteristic
625C2×C4C2×Dic67⋊C411yescharacteristic
626C2×C4C2×Dic67⋊C411yescharacteristic
627C2×C4C22×C4×D6711yescharacteristic
628C2×C4C22×C22⋊D6711yescharacteristic
629C2×C4#41×D6711yescharacteristic
630C2×C4C2×#1176162711yescharacteristic
631C2×C4#1452408811yescharacteristic
632C2×C4#1452408911yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C8—2681no—
638C8—2681no—
639C8—2681no—
640C8—1342no—
641C8—1342no—
642C8—1342no—
643C8—1342no—
644C8—1342no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22#1686344412yes—
663C22C22×Dic67⋊C411yescharacteristic
664C22#1686410311yescharacteristic
665C22#1686410511yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4C4×#1176162711yescharacteristic
675C4#1686386811yescharacteristic
676C4#1686403411yescharacteristic
677C4#1686404011yescharacteristic
678C2—21no—
679C2—21no—
680C2—22no—
681C2—41no—
682C2—41no—
683C2—41no—
684C2#2256311411yescharacteristic
685C2C2×#1686344411yescharacteristic
686C2#2256881811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingD4×M16×C67C2
socleC22×C67C22×C4⋊C4
prime radicalC22×D4×C67Q8
cosocleC22×C4×C67C24
hypercenterD4×M16D67
hypocenterC67#22718
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #22560984C2semidirect
4. #22560982C2semidirect
5. #22560414C2semidirect
6. #22560414C2semidirect
7. #22560413C2semidirect
8. #22560413C2semidirect
9. #22560349C2semidirect
10. #22560249C2semidirect
11. #22560245C2semidirect
12. #22560116C2semidirect
13. #22559935C2semidirect
14. C2×#16863160C2semidirect
359. C67#22718semidirect

Maximal subgroups

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

subgroupindex
D4×#117616122
C2×#168634682
#225609842
#225609822
#225604142
#225604132
#225603492
#225602492
#225602452
#225601162
#225599352
C2×#168631602
D4×M16×C672
#2271867