Finite Group Databasebeta

← #29727821

Subgroups — #29727821

Order 15616.

1094 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839984C211yesmaximal, characteristic, complemented
2C2×#16839918C211yesmaximal, characteristic, complemented
3C2×#16839901C211yesmaximal, characteristic
4C2×#16839860C211yesmaximal, characteristic, complemented
5#21449396C211yesmaximal, characteristic
6#21447214C211yesmaximal, characteristic, complemented
7#21447022C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic
9#21446912C211yesmaximal, characteristic, complemented
10#21446689C211yesmaximal, characteristic, complemented
11#21446434C211yesmaximal, characteristic, complemented
12#21446160C211yesmaximal, characteristic, complemented
13#21446156C211yesmaximal, characteristic, complemented
14#21446087C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24#16839984—24no—
25#16839918—24no—
26#16839901—24no—
27#16839860—24no—
28C2×#14519710C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42#16839691—21no—
43#16839677—21no—
44#16839668C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839638—21no—
47#16839621—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C23×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C61×#391—21no—
56C61×#391—21no—
57C61×#391C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#380—21no—
60C61×#380C2211yescharacteristic
61C4×C22⋊C4×C61—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—41no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—41no—
78C2×#11758201D414yes—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519765—22no—
84#14519765—41no—
85#14519756—22no—
86#14519756—41no—
87#14519751—22no—
88#14519751—41no—
89C4×D244—22no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519710—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701D414yescomplemented
107#14519700—22no—
108#14519700—41no—
109#14519697—22no—
110#14519697—22no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113#14519688—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×Q8×C61—22no—
118C22×Q8×C61—22no—
119C22×Q8×C61—21no—
120C22×Q8×C61—22no—
121C22×Q8×C61—22no—
122C22×Q8×C61—41no—
123C22×Q8×C61—41no—
124C22×Q8×C61C2311yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C4×Q8×C61—22no—
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C4×Q8×C61—41no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61—21no—
140C2×C42×C61—21no—
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C23×D61—21no—
152C2×Q8×C61—24no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—42no—
162C2×Q8×C61—42no—
163C2×Q8×C61—44no—
164C2×Q8×C61—44no—
165C2×Q8×C61—44no—
166C2×Q8×C61—44no—
167C2×Q8×C61C2×D412yes—
168C2×Q8×C61C2×D412yes—
169C2×Q8×C61#4112yes—
170C2×Q8×C61#4112yes—
171C22×C4×C61—21no—
172C22×C4×C61—24no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—81no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244C2×D412yes—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—81no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—42no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—42no—
225C42×C61—42no—
226C22⋊Dic61—42no—
227#11758202—44no—
228#11758202—44no—
229#11758201—28no—
230#11758201—44no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C2×D412yes—
239#11758196—42no—
240#11758196—81no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61#13712yes—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—48no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61#12114yes—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—48no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C22⋊D61—84no—
316C2×Dic61—22no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325D244—22no—
326D244—22no—
327D244—41no—
328D244—41no—
329C4×D61—84no—
330Dic122—41no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334#92418—22no—
335#92418—22no—
336#92418—41no—
337#92418—41no—
338#25177—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61#52511yescharacteristic
347C22×C61D4211yescharacteristic
348C22×C61D4211yescharacteristic
349C22×C61C2×#13711yescharacteristic
350C22×C61#57511yescharacteristic
351C22×C61#57711yescharacteristic
352C22×C61#57811yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C4×C61—24no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61C2×#12111yescharacteristic
370C4×C61#53811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#54611yescharacteristic
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376C2×#464—611no—
377C2×#451—611no—
378C2×#448—611no—
379C2×#440—611no—
380#2427—611no—
381Q8×C22⋊C4D6111yescharacteristic, complemented
382#2068—611no—
383#2036—611no—
384#2034—611no—
385#2015—611no—
386#1971—611no—
387#1924—611no—
388#1878—611no—
389#1877—611no—
390#1865—611no—
391C2×C61—42no—
392C2×C61#242411yescharacteristic
393C2×C61#311711yescharacteristic
394C2×C61#312111yescharacteristic
395C2×C61#326611yescharacteristic
396C2×C61#326911yescharacteristic
397C2×C61#327011yescharacteristic
398C2×C61#327511yescharacteristic
399D61—82no—
400C23×Q8C2×D6111yescharacteristic
401C22×Q16—611no—
402C22×Q16—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C2×#124—611no—
406C2×C22⋊Q8—611no—
407C2×#121—611no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×Q8C2×D6111yescharacteristic
410C2×C4×D4—611no—
411#464—1224no—
412#451—1224no—
413#448—1224no—
414#440—1224no—
415C2×#107—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428C2×#97—611no—
429#397—1221no—
430#394—1221no—
431#391—21no—
432#391—21no—
433#391—611no—
434#391C2×D6111yescharacteristic
435#391C2×D6111yescharacteristic
436#389—611no—
437#386—1221no—
438#380—21no—
439#380—1221no—
440#380C2×D6111yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2517711yescharacteristic, complemented, Sylow
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—41no—
454C22×Q8—41no—
455C22×Q8—611no—
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—1222no—
464C2×Q16—1222no—
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—1222no—
468C2×Q16—2441no—
469C2×SD16—614no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—1222no—
474C2×SD16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479#124—1222no—
480#124—2441no—
481C22⋊Q8—1222no—
482C22⋊Q8—2441no—
483#121—1222no—
484#121—2441no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—41no—
488C4×Q8—41no—
489C4×D4—1222no—
490C4×D4—2441no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4C22⋊D6111yescharacteristic
506C2×C22⋊C4C22⋊D6111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C22×D6111yescharacteristic
510C2×C42C22×D6111yescharacteristic
511#107—1222no—
512#106—2441no—
513C4⋊C8—1222no—
514#103—614no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—2441no—
520#102—1222no—
521#102—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524#97—1222no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95C22⋊D6111yescharacteristic
534#95C22⋊D6111yescharacteristic
535C24—1221no—
536C24C2×C22⋊D6111yescharacteristic
537C2×Q8—24no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—44no—
549C2×Q8—44no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8#1175822212yes—
559C2×Q8#1175822212yes—
560C2×Q8D4×D6112yes—
561C2×Q8D4×D6112yes—
562C2×D4—612no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—4881no—
569C2×D4—2442no—
570C2×D4—2442no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C23×D6111yescharacteristic
596Q16—2444no—
597Q16—2444no—
598SD16—1228no—
599SD16—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—612no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—4881no—
623C4⋊C4—2442no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—42no—
627C22⋊C4—2442no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—42no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—1222no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23#1451980812yes—
652C23C22×C22⋊D6111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—48no—
659Q8—41no—
660Q8—41no—
661Q8—2441no—
662Q8—2441no—
663Q8—2441no—
664Q8—2441no—
665Q8#1451975014yes—
666D4—1222no—
667D4—1222no—
668D4—4884no—
669D4—2441no—
670D4—2441no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—1222no—
704C2×C4—4884no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822211yescharacteristic
716C2×C4C2×#1175822211yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C8—1222no—
720C8—1222no—
721C8—2441no—
722C8—2441no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—4881no—
731C22—4881no—
732C22—4881no—
733C22—4881no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22#1684027311yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22D4×C22⋊D6111yescharacteristic
740C22C2×#1451980811yescharacteristic
741C22#1684056011yescharacteristic
742C22#1684057011yescharacteristic
743C22#1684057711yescharacteristic
744C4—24no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—4881no—
754C4—4881no—
755C4—2442no—
756C4C2×#1451975011yescharacteristic
757C4#1684035011yescharacteristic
758C4#1684040211yescharacteristic
759C4#1684040211yescharacteristic
760C2—42no—
761C2—4882no—
762C2#2144935511yescharacteristic
763C2#2145599011yescharacteristic
764C2#2145604811yescharacteristic
765C2#2145733011yescharacteristic
766C2#2145737511yescharacteristic
767C2#2145739011yescharacteristic
768C2#2145745111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingQ8×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterQ8×C22⋊C4D61
hypocenterC61#25177
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839984C2semidirect
2. C2×#16839918C2semidirect
4. C2×#16839860C2semidirect
6. #21447214C2semidirect
7. #21447022C2semidirect
9. #21446912C2semidirect
10. #21446689C2semidirect
11. #21446434C2semidirect
12. #21446160C2semidirect
13. #21446156C2semidirect
14. #21446087C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
106. #14519701D4semidirect
381. Q8×C22⋊C4D61semidirect
447. C61#25177semidirect

Maximal subgroups

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

subgroupindex
C2×#168399842
C2×#168399182
C2×#168399012
C2×#168398602
#214493962
#214472142
#214470222
#214470082
#214469122
#214466892
#214464342
#214461602
#214461562
#214460872
Q8×C22⋊C4×C612
#2517761