Finite Group Databasebeta

← #30867711

Subgroups — #30867711

Order 17152.

712 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#22568913C211yesmaximal, characteristic
2#22568773C211yesmaximal, characteristic, complemented
3#22560963C211yesmaximal, characteristic, complemented
4#22560958C211yesmaximal, characteristic, complemented
5#22560922C211yesmaximal, characteristic, complemented
6#22560915C211yesmaximal, characteristic, complemented
7#22560810C211yesmaximal, characteristic, complemented
8#22560810C211yesmaximal, characteristic, complemented
9#22560512C211yesmaximal, characteristic
10#22560486C211yesmaximal, characteristic, complemented
11#22560486C211yesmaximal, characteristic, complemented
12#22560416C211yesmaximal, characteristic, complemented
13#22560308C211yesmaximal, characteristic, complemented
14#22559995C211yesmaximal, characteristic, complemented
15C67×#3091C211yesmaximal, characteristic
16C2×#14524050C2211yescharacteristic
17C22×#11761612C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19#16863474—21no—
20#16863474—21no—
21#16863468—21no—
22#16863468—21no—
23C2×#14523979C2211yescharacteristic
24C2×#14523979C2211yescharacteristic
25#16863423—21no—
26#16863423—21no—
27#16863423C2211yescharacteristic
28#16863423C2211yescharacteristic
29#16863423C2211yescharacteristic
30#16863423C2211yescharacteristic
31#16863423C2211yescharacteristic
32#16863420—21no—
33#16863420—21no—
34C2×#14523970C2211yescharacteristic
35C2×#14523970C2211yescharacteristic
36#16863363C2211yescharacteristic
37#16863360C2211yescharacteristic
38#16863352C2211yescharacteristic
39C2×#14523953C2211yescharacteristic
40C2×C8×Dic67C2211yescharacteristic
41C4×C22⋊Dic67C2211yescharacteristic
42#16863161C2211yescharacteristic
43#16863161C2211yescharacteristic
44#16863155C2211yescharacteristic
45#16863155C2211yescharacteristic
46#16863155C2211yescharacteristic
47#16863155C2211yescharacteristic
48#16863155C2211yescharacteristic
49#16863155C2211yescharacteristic
50#16863150C2211yescharacteristic
51#16863150C2211yescharacteristic
52#525×C67C2211yescharacteristic
53C2×#117×C67C2211yescharacteristic
54#485×C67C411yescharacteristic, complemented
55#485×C67C411yescharacteristic, complemented
56#484×C67C411yescharacteristic, complemented
57#483×C67C411yescharacteristic, complemented
58#482×C67C411yescharacteristic, complemented
59#482×C67C411yescharacteristic, complemented
60#481×C67C411yescharacteristic, complemented
61#480×C67C411yescharacteristic, complemented
62#427×C67C2211yescharacteristic
63#427×C67C2211yescharacteristic
64#416×C67C2211yescharacteristic
65#416×C67C2211yescharacteristic
66C2×C22⋊C8×C67C2211yescharacteristic
67#14524050—41no—
68#14524050—41no—
69C2×#11761612—21no—
70C2×#11761612—21no—
71C2×#11761612—41no—
72C2×#11761612—41no—
73C2×#11761612—41no—
74C2×#11761612—41no—
75C2×#11761612D411yescharacteristic
76C2×#11761612D411yescharacteristic
77C2×#11761612D411yescharacteristic
78C2×#11761612D411yescharacteristic
79C2×#11761612C2311yescharacteristic
80C2×#11761612C2311yescharacteristic
81C2×#11761612C2311yescharacteristic
82C2×#11761612C2311yescharacteristic
83C22×C67⋊C8—21no—
84C22×C67⋊C8—21no—
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C2×C22⋊Dic67—21no—
88C2×C4×Dic67C2311yescharacteristic
89C2×C4×Dic67C2311yescharacteristic
90#14523979—41no—
91#14523979—41no—
92C4⋊(C67⋊C8)—21no—
93C4⋊(C67⋊C8)—21no—
94C4⋊(C67⋊C8)—21no—
95C4⋊(C67⋊C8)—21no—
96C4⋊(C67⋊C8)—21no—
97C4⋊(C67⋊C8)—21no—
98C4⋊(C67⋊C8)—21no—
99C4⋊(C67⋊C8)—21no—
100C4⋊(C67⋊C8)—21no—
101C4⋊(C67⋊C8)—21no—
102#14523970—41no—
103#14523970—41no—
104C22⋊(C67⋊C8)—21no—
105C22⋊(C67⋊C8)—21no—
106C22⋊(C67⋊C8)—21no—
107C22⋊(C67⋊C8)—21no—
108#14523954—21no—
109#14523953—41no—
110C4×C67⋊C8—21no—
111C8×Dic67—41no—
112C67⋊#95—21no—
113C2×#41×C67C2311yescharacteristic
114C23×C4×C67C2311yescharacteristic
115C22×C8×C67C2311yescharacteristic
116C22×C8×C67C2311yescharacteristic
117#123×C67—21no—
118C22⋊Q8×C67C2×C411yescharacteristic
119C22⋊Q8×C67C2×C411yescharacteristic
120#121×C67C2×C411yescharacteristic
121#121×C67C2×C411yescharacteristic
122#120×C67—21no—
123C4×D4×C67—21no—
124C4×D4×C67—21no—
125#117×C67—21no—
126#117×C67—21no—
127#117×C67C2×C411yescharacteristic
128#117×C67C2×C411yescharacteristic
129#117×C67C2311yescharacteristic
130#117×C67C2311yescharacteristic
131#117×C67C2311yescharacteristic
132C2×C4⋊C4×C67C2×C411yescharacteristic
133C2×C4⋊C4×C67C2×C411yescharacteristic
134C2×C22⋊C4×C67—21no—
135C2×C42×C67—21no—
136#107×C67C2×C411yescharacteristic
137#107×C67C2×C411yescharacteristic
138#107×C67C2×C411yescharacteristic
139#107×C67C2×C411yescharacteristic
140#106×C67C2×C411yescharacteristic
141#106×C67C2×C411yescharacteristic
142#106×C67C2×C411yescharacteristic
143#106×C67C2×C411yescharacteristic
144#103×C67C2×C411yescharacteristic
145#103×C67C2×C411yescharacteristic
146#103×C67C2×C411yescharacteristic
147#103×C67C2×C411yescharacteristic
148#102×C67C2×C411yescharacteristic
149#102×C67C2×C411yescharacteristic
150#102×C67C2×C411yescharacteristic
151#102×C67C2×C411yescharacteristic
152C22⋊C8×C67C2×C411yescharacteristic
153C22⋊C8×C67C2×C411yescharacteristic
154C22⋊C8×C67C2×C411yescharacteristic
155C22⋊C8×C67C2×C411yescharacteristic
156C22×Dic67—21no—
157C22×Dic67—21no—
158#11761612—21no—
159#11761612—21no—
160#11761612—21no—
161#11761612—21no—
162#11761612—21no—
163#11761612—21no—
164#11761612—21no—
165#11761612—21no—
166#11761612—41no—
167#11761612—41no—
168#11761612—41no—
169#11761612—41no—
170#11761612—42no—
171#11761612—42no—
172C2×C67⋊C8—21no—
173C2×C67⋊C8—21no—
174C2×C67⋊C8—21no—
175C2×C67⋊C8—21no—
176C2×C67⋊C8—21no—
177C2×C67⋊C8—21no—
178C2×C67⋊C8—21no—
179C2×C67⋊C8—21no—
180C2×C67⋊C8—42no—
181C2×C67⋊C8—42no—
182C2×C67⋊C8C2×D411yescharacteristic
183C2×C67⋊C8C2×D411yescharacteristic
184C2×C67⋊C8C2×D411yescharacteristic
185C2×C67⋊C8C2×D411yescharacteristic
186C22⋊Dic67—42no—
187C4×Dic67—21no—
188C4×Dic67—21no—
189C4×Dic67—21no—
190C4×Dic67—21no—
191C24×C67#4111yescharacteristic
192#41×C67—21no—
193#41×C67—21no—
194#41×C67—21no—
195#41×C67—21no—
196C2×Q8×C67C22×C411yescharacteristic
197C2×D4×C67—21no—
198C2×D4×C67—21no—
199C2×D4×C67—21no—
200C2×D4×C67C22×C411yescharacteristic
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67C22×C411yescharacteristic
209C22×C4×C67C22×C411yescharacteristic
210C22×C4×C67C2×D411yescharacteristic
211C22×C4×C67C2×D411yescharacteristic
212C22×C4×C67#4111yescharacteristic
213C22×C4×C67C2411yescharacteristic
214C2×C8×C67—21no—
215C2×C8×C67—21no—
216C2×C8×C67—21no—
217C2×C8×C67—21no—
218C2×C8×C67C22×C411yescharacteristic
219C2×C8×C67C22×C411yescharacteristic
220C2×C8×C67C22×C411yescharacteristic
221C2×C8×C67C22×C411yescharacteristic
222C4⋊C4×C67—21no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—21no—
226C4⋊C4×C67C22×C411yescharacteristic
227C4⋊C4×C67C22×C411yescharacteristic
228C4⋊C4×C67C22×C411yescharacteristic
229C4⋊C4×C67C22×C411yescharacteristic
230C4⋊C4×C67C22×C411yescharacteristic
231C4⋊C4×C67C22×C411yescharacteristic
232C22⋊C4×C67—21no—
233C22⋊C4×C67—21no—
234C22⋊C4×C67—21no—
235C22⋊C4×C67—21no—
236C22⋊C4×C67—21no—
237C22⋊C4×C67—21no—
238C22⋊C4×C67—21no—
239C22⋊C4×C67—21no—
240C22⋊C4×C67—21no—
241C42×C67—21no—
242C42×C67—21no—
243C42×C67—21no—
244C42×C67—21no—
245C42×C67—21no—
246C23×C67—21no—
247C23×C67—21no—
248C23×C67—21no—
249C23×C67—41no—
250C23×C67—41no—
251C23×C67C4×D411yescharacteristic
252C23×C67C4×D411yescharacteristic
253C23×C67C2×#4111yescharacteristic
254Q8×C67—21no—
255Q8×C67—21no—
256D4×C67—21no—
257D4×C67—21no—
258D4×C67—41no—
259D4×C67—41no—
260D4×C67—81no—
261D4×C67—81no—
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—21no—
274C2×C4×C67—21no—
275C2×C4×C67—21no—
276C2×C4×C67—21no—
277C2×C4×C67—21no—
278C2×C4×C67—21no—
279C2×C4×C67—41no—
280C2×C4×C67—41no—
281C2×C4×C67—81no—
282C2×C4×C67—81no—
283C2×C4×C67C4×D411yescharacteristic
284C2×C4×C67C4×D411yescharacteristic
285C2×C4×C67C23×C411yescharacteristic
286C2×C4×C67C22×D411yescharacteristic
287C2×C4×C67H(5,𝔽2)11yescharacteristic
288C2×C4×C67H(5,𝔽2)11yescharacteristic
289C2×C4×C672−1+411yescharacteristic
290C2×C4×C672−1+411yescharacteristic
291C2×Dic67—22no—
292C2×Dic67—41no—
293C2×Dic67—41no—
294C2×Dic67—41no—
295C2×Dic67—41no—
296C2×Dic67—41no—
297C8×C67—21no—
298C8×C67—21no—
299C8×C67—21no—
300C8×C67—21no—
301C67⋊C8—21no—
302C67⋊C8—21no—
303C67⋊C8—21no—
304C67⋊C8—21no—
305C67⋊C8—41no—
306C67⋊C8—41no—
307C67⋊C8—41no—
308C67⋊C8—41no—
309C22×C67—21no—
310C22×C67—21no—
311C22×C67—21no—
312C22×C67—21no—
313C22×C67—21no—
314C22×C67—21no—
315C22×C67—21no—
316C22×C67—21no—
317C22×C67—41no—
318C22×C67—41no—
319C22×C67—41no—
320C22×C67—81no—
321C22×C67—81no—
322C22×C67C2×C4×D411yescharacteristic
323C22×C67#53911yescharacteristic
324C22×C67#53911yescharacteristic
325C4×C67—21no—
326C4×C67—21no—
327C4×C67—41no—
328C4×C67—41no—
329C4×C67—41no—
330C4×C67—41no—
331C4×C67—41no—
332C4×C67—41no—
333C4×C67—41no—
334C4×C67#52011yescharacteristic
335C4×C67#52011yescharacteristic
336C4×C67#53411yescharacteristic
337C4×C67#53611yescharacteristic
338Dic67—42no—
339Dic67—81no—
340#22097—671nomaximal, Sylow
341C2×C67—21no—
342C2×C67—21no—
343C2×C67—41no—
344C2×C67—41no—
345C2×C67—81no—
346C2×C67#232211yescharacteristic
347C2×C67#295611yescharacteristic
348C2×C67#295711yescharacteristic
349#3091D6711yescharacteristic
350#2930—671no—
351#2905—671no—
352#1946—671no—
353#1945—671no—
354#1938—671no—
355#1937—671no—
356#1922—671no—
357#1922—671no—
358#1871—671no—
359#1866—671no—
360#1866—671no—
361#1855—671no—
362#1826—671no—
363#1753—671no—
364C67#2209711yescharacteristic, complemented, Sylow
365C2×#131—671no—
366C22×M16—671no—
367C22×M16—671no—
368#525C2×D6711yescharacteristic
369C2×#117C2×D6711yescharacteristic
370#485Dic6711yescharacteristic, complemented
371#485Dic6711yescharacteristic, complemented
372#484Dic6711yescharacteristic, complemented
373#483Dic6711yescharacteristic, complemented
374#482Dic6711yescharacteristic, complemented
375#482Dic6711yescharacteristic, complemented
376#481Dic6711yescharacteristic, complemented
377#480Dic6711yescharacteristic, complemented
378#436—1341no—
379#436—1341no—
380#435—1341no—
381#435—1341no—
382C2×#108—671no—
383C2×#108—671no—
384#427C2×D6711yescharacteristic
385#427C2×D6711yescharacteristic
386#424—671no—
387#424—671no—
388#424—671no—
389#424—671no—
390#424—671no—
391#424—1341no—
392#424—1341no—
393#423—1341no—
394#423—1341no—
395C2×#104—671no—
396C2×#104—671no—
397#416C2×D6711yescharacteristic
398#416C2×D6711yescharacteristic
399#408—671no—
400#407—671no—
401C2×C22⋊C8C2×D6711yescharacteristic
402#405—671no—
403C2×#97—671no—
404C2×C4×C8—671no—
405C4×C22⋊C4—671no—
406#341—671no—
407#341—671no—
408#339—671no—
409#339—671no—
410#339—671no—
411#339—671no—
412#339—671no—
413#339—671no—
414#336—671no—
415#336—671no—
416C2×#41C22×D6711yescharacteristic
417C23×C4C22×D6711yescharacteristic
418#131—2681no—
419#131—2681no—
420C2×M16—2681no—
421C2×M16—2681no—
422C2×M16—2681no—
423C2×M16—2681no—
424C2×M16—671no—
425C2×M16—671no—
426C2×M16—671no—
427C2×M16—671no—
428C2×M16—671no—
429C2×M16—671no—
430C2×M16—671no—
431C2×M16—671no—
432C2×M16—1341no—
433C2×M16—1341no—
434C22×C8—671no—
435C22×C8—671no—
436C22×C8—1341no—
437C22×C8—1341no—
438C22×C8C22×D6711yescharacteristic
439C22×C8C22×D6711yescharacteristic
440#123—21no—
441C22⋊Q8C2×Dic6711yescharacteristic
442C22⋊Q8C2×Dic6711yescharacteristic
443#121C2×Dic6711yescharacteristic
444#121C2×Dic6711yescharacteristic
445#120—21no—
446C4×D4—21no—
447C4×D4—21no—
448#117—21no—
449#117—21no—
450#117C2×Dic6711yescharacteristic
451#117C2×Dic6711yescharacteristic
452#117C22×D6711yescharacteristic
453#117C22×D6711yescharacteristic
454#117C22×D6711yescharacteristic
455C2×C4⋊C4C2×Dic6711yescharacteristic
456C2×C4⋊C4C2×Dic6711yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—1341no—
459C2×C42—21no—
460C2×C42—671no—
461C2×C42—671no—
462#108—2681no—
463#108—2681no—
464#107C2×Dic6711yescharacteristic
465#107C2×Dic6711yescharacteristic
466#107C2×Dic6711yescharacteristic
467#107C2×Dic6711yescharacteristic
468#106C2×Dic6711yescharacteristic
469#106C2×Dic6711yescharacteristic
470#106C2×Dic6711yescharacteristic
471#106C2×Dic6711yescharacteristic
472C4⋊C8—1341no—
473C4⋊C8—1341no—
474C4⋊C8—1341no—
475C4⋊C8—1341no—
476C4⋊C8—1341no—
477C4⋊C8—1341no—
478C4⋊C8—1341no—
479C4⋊C8—1341no—
480C4⋊C8—1341no—
481C4⋊C8—1341no—
482#104—2681no—
483#104—2681no—
484#103C2×Dic6711yescharacteristic
485#103C2×Dic6711yescharacteristic
486#103C2×Dic6711yescharacteristic
487#103C2×Dic6711yescharacteristic
488#102C2×Dic6711yescharacteristic
489#102C2×Dic6711yescharacteristic
490#102C2×Dic6711yescharacteristic
491#102C2×Dic6711yescharacteristic
492C22⋊C8—1341no—
493C22⋊C8—1341no—
494C22⋊C8—1341no—
495C22⋊C8—1341no—
496C22⋊C8C2×Dic6711yescharacteristic
497C22⋊C8C2×Dic6711yescharacteristic
498C22⋊C8C2×Dic6711yescharacteristic
499C22⋊C8C2×Dic6711yescharacteristic
500#97—2681no—
501#97—1341no—
502C4×C8—2681no—
503C4×C8—1341no—
504#95—1341no—
505C24#1176162711yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×Dic6711yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×Dic6711yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—1341no—
523C22×C4—1341no—
524C22×C4C22×Dic6711yescharacteristic
525C22×C4C22×Dic6711yescharacteristic
526C22×C4D4×D6711yescharacteristic
527C22×C4D4×D6711yescharacteristic
528C22×C4#1176162711yescharacteristic
529C22×C4C23×D6711yescharacteristic
530M16—2682no—
531M16—2682no—
532M16—2681no—
533M16—2681no—
534M16—2681no—
535M16—2681no—
536M16—1341no—
537M16—1341no—
538M16—1341no—
539M16—1341no—
540M16—1341no—
541M16—1341no—
542M16—1341no—
543M16—1341no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—2682no—
549C2×C8—2682no—
550C2×C8—671no—
551C2×C8—671no—
552C2×C8—671no—
553C2×C8—671no—
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×C8C22×Dic6711yescharacteristic
563C2×C8C22×Dic6711yescharacteristic
564C2×C8C22×Dic6711yescharacteristic
565C2×C8C22×Dic6711yescharacteristic
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4C22×Dic6711yescharacteristic
571C4⋊C4C22×Dic6711yescharacteristic
572C4⋊C4C22×Dic6711yescharacteristic
573C4⋊C4C22×Dic6711yescharacteristic
574C4⋊C4C22×Dic6711yescharacteristic
575C4⋊C4C22×Dic6711yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—2682no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—1341no—
592C42—1341no—
593C42—1341no—
594C42—1341no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23D4×Dic6711yescharacteristic
601C23D4×Dic6711yescharacteristic
602C23C2×#1176162711yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—2681no—
633C2×C4—2681no—
634C2×C4—2681no—
635C2×C4—2681no—
636C2×C4—2681no—
637C2×C4—1342no—
638C2×C4D4×Dic6711yescharacteristic
639C2×C4D4×Dic6711yescharacteristic
640C2×C4C23×Dic6711yescharacteristic
641C2×C4C2×D4×D6711yescharacteristic
642C2×C4#1452408911yescharacteristic
643C2×C4#1452408911yescharacteristic
644C2×C4#1452409011yescharacteristic
645C2×C4#1452409011yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—2681no—
651C8—2681no—
652C8—2681no—
653C8—2681no—
654C8—1341no—
655C8—1341no—
656C8—1341no—
657C8—1341no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×D4×Dic6711yescharacteristic
672C22#1686399011yescharacteristic
673C22#1686399011yescharacteristic
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—2682no—
684C4—5361no—
685C4#1686387911yescharacteristic
686C4#1686387911yescharacteristic
687C4#1686395711yescharacteristic
688C4#1686396811yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2#2256288111yescharacteristic
695C2#2256911911yescharacteristic
696C2#2256912611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#3091C2
socleC22×C67C2×C4×D4
prime radical#525×C67C22
cosocleC22×C4×C67C24
hypercenter#3091D67
hypocenterC67#22097
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #22568773C2semidirect
3. #22560963C2semidirect
4. #22560958C2semidirect
5. #22560922C2semidirect
6. #22560915C2semidirect
7. #22560810C2semidirect
8. #22560810C2semidirect
10. #22560486C2semidirect
11. #22560486C2semidirect
12. #22560416C2semidirect
13. #22560308C2semidirect
14. #22559995C2semidirect
54. #485×C67C4semidirect
55. #485×C67C4semidirect
56. #484×C67C4semidirect
57. #483×C67C4semidirect
58. #482×C67C4semidirect
59. #482×C67C4semidirect
60. #481×C67C4semidirect
61. #480×C67C4semidirect
364. C67#22097semidirect
370. #485Dic67semidirect
371. #485Dic67semidirect
372. #484Dic67semidirect
373. #483Dic67semidirect
374. #482Dic67semidirect
375. #482Dic67semidirect
376. #481Dic67semidirect
377. #480Dic67semidirect

Maximal subgroups

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

subgroupindex
#225689132
#225687732
#225609632
#225609582
#225609222
#225609152
#225608102
#225605122
#225604862
#225604162
#225603082
#225599952
C67×#30912
#2209767