Finite Group Databasebeta

← #29714832

Subgroups — #29714832

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic, complemented
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21451177C211yesmaximal, characteristic, complemented
4#21447055C211yesmaximal, characteristic, complemented
5#21447050C211yesmaximal, characteristic, complemented
6#21446896C211yesmaximal, characteristic, complemented
7#21446890C211yesmaximal, characteristic
8#21446756C211yesmaximal, characteristic, complemented
9#21446631C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446073C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445829C211yesmaximal, characteristic, complemented
15C2×C61×#559C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16839974—24no—
21C4×#11758199—24no—
22C2×#14519710C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839697—21no—
36#16839673—21no—
37#16839664C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839633—21no—
42#16839633—21no—
43#16839628C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#559—24no—
51C61×#559—24no—
52C2×#127×C61C2211yescharacteristic
53C2×#124×C61—21no—
54C2×#124×C61C2211yescharacteristic
55C2×#124×C61C2211yescharacteristic
56C2×#123×C61—21no—
57C2×#123×C61—21no—
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×Q8×C61C2211yescharacteristic
60C2×C4×D4×C61—21no—
61C2×C4×D4×C61C2211yescharacteristic
62C2×C4×D4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—41no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90#14519710—22no—
91C4⋊#92418—22no—
92#14519701—22no—
93#14519701—22no—
94#14519701—41no—
95#14519698—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—41no—
99#14519698—41no—
100#14519698—41no—
101#14519697—22no—
102C4×#92418—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61D411yescharacteristic
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61—21no—
111C22×D4×C61C2311yescharacteristic
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61—21no—
115#127×C61—22no—
116#127×C61—22no—
117#124×C61—28no—
118#124×C61—22no—
119#124×C61—22no—
120#124×C61—22no—
121#124×C61D414yes—
122#123×C61—28no—
123#123×C61—28no—
124C4×Q8×C61—22no—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C4×Q8×C61—22no—
128C4×D4×C61—28no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61D414yes—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C24×C61—21no—
149C24×C61—21no—
150C23×D61—21no—
151C2×Q8×C61—22no—
152C2×Q8×C61—22no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—41no—
159C2×Q8×C61C2×D412yes—
160C2×D4×C61—24no—
161C2×D4×C61—24no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61C2×D412yes—
177C2×D4×C61C2×D412yes—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—24no—
181C22×C4×C61—24no—
182C22×C4×C61—81no—
183C22×C4×C61—81no—
184C22×C4×C61—81no—
185C22×C4×C61—81no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
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×D244#4112yes—
202C2×C4×D61—42no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—24no—
213C22⋊C4×C61—24no—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—24no—
217C42×C61—24no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61C2×D412yes—
223C42×C61C2×D412yes—
224#11758201—44no—
225#11758199—28no—
226#11758199—44no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230#11758198—81no—
231#11758198—81no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238#11758196—81no—
239#11758196—81no—
240C2×#92418—21no—
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×#92418#4112yes—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—44no—
277Q8×C61—41no—
278Q8×C61—41no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—48no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—84no—
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—22no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—84no—
311C2×C4×C61—84no—
312C2×C4×C61#12012yes—
313C2×C4×C61#12012yes—
314C2×C4×C61#13512yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C612−1+411yescharacteristic
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330D244—22no—
331D244—22no—
332D244—41no—
333D244—41no—
334C4×D61—84no—
335#92418—22no—
336#92418—41no—
337#92418—41no—
338#92418—41no—
339#24192—611nomaximal, Sylow
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61C2×#12011yescharacteristic
355C22×C61#54811yescharacteristic
356C22×C61#55011yescharacteristic
357C22×C61C2×#13511yescharacteristic
358C22×C61#57511yescharacteristic
359C22×C61#57611yescharacteristic
360C22×C61#57611yescharacteristic
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61#52511yescharacteristic
377C4×C61#53711yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#54711yescharacteristic
380Dic61—81no—
381Dic61—81no—
382Dic61—81no—
383C2×#559D6111yescharacteristic, complemented
384C2×#463—611no—
385C2×C4×D8—611no—
386#2580—611no—
387#2042—611no—
388#2041—611no—
389#2012—611no—
390#2011—611no—
391#1984—611no—
392#1958—611no—
393#1880—611no—
394#1879—611no—
395#1863—611no—
396#1862—611no—
397#1804—611no—
398C2×C61—82no—
399C2×C61—82no—
400C2×C61#240711yescharacteristic
401C2×C61#300211yescharacteristic
402C2×C61#300811yescharacteristic
403C2×C61#336111yescharacteristic
404C2×C61#337011yescharacteristic
405C2×C61#339611yescharacteristic
406C2×C61#340311yescharacteristic
407D61—82no—
408C22×SD16—611no—
409C22×D8—611no—
410C22×D8—611no—
411#559—24no—
412#559—24no—
413C2×#127C2×D6111yescharacteristic
414C2×#124—21no—
415C2×#124C2×D6111yescharacteristic
416C2×#124C2×D6111yescharacteristic
417C2×#123—21no—
418C2×#123—21no—
419C2×C4×Q8C2×D6111yescharacteristic
420C2×C4×Q8C2×D6111yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4—611no—
423C2×C4×D4C2×D6111yescharacteristic
424C2×C4×D4C2×D6111yescharacteristic
425#463—1224no—
426C4×D8—1224no—
427C2×#107—611no—
428C2×C4⋊C8—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C4×C8—611no—
440#399—1221no—
441#393—1221no—
442#390—611no—
443#390—611no—
444#389—611no—
445#389—611no—
446#385—1221no—
447#385—1221no—
448#382—611no—
449#340—611no—
450#340—611no—
451#336—611no—
452#336—611no—
453#336—611no—
454#336—611no—
455C61#2419211yescharacteristic, complemented, Sylow
456C22×Q8C22⋊D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—611no—
461C22×D4C22×D6111yescharacteristic
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—1221no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—2441no—
469C2×D8—1222no—
470C2×D8—1222no—
471C2×D8—1222no—
472C2×D8—1222no—
473C2×D8—1222no—
474C2×D8—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479#127—22no—
480#127—22no—
481#124—28no—
482#124—22no—
483#124—22no—
484#124—22no—
485#124C22⋊D6114yes—
486#123—28no—
487#123—28no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4C22⋊D6114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22⋊D6111yescharacteristic
506C2×C4⋊C4C22⋊D6111yescharacteristic
507C2×C4⋊C4C22⋊D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C42—21no—
521C2×C42C22×D6111yescharacteristic
522C2×C42C22×D6111yescharacteristic
523C2×C42C22×D6111yescharacteristic
524#107—1222no—
525C4⋊C8—1222no—
526#103—1222no—
527#103—1222no—
528#103—2441no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—2441no—
534#102—2441no—
535#102—2441no—
536C4×C8—1222no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541C24—21no—
542C24—21no—
543C24—1221no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8C2×C22⋊D6112yes—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—612no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4C2×C22⋊D6112yes—
576C2×D4C2×C22⋊D6112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—2442no—
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598SD16—2444no—
599D8—1228no—
600D8—2444no—
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—
612C2×C8—1221no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—4881no—
625C4⋊C4—4881no—
626C4⋊C4C2×C22⋊D6112yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C22⋊C4—2442no—
638C42—24no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×C22⋊D6112yes—
644C42C2×C22⋊D6112yes—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—1222no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23C22×C22⋊D6111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—44no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—48no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—1222no—
683D4—1222no—
684D4—2441no—
685D4—2441no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—4884no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4#1451974612yes—
720C2×C4#1451974612yes—
721C2×C4#1451979712yes—
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C22×C22⋊D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#41×D6111yescharacteristic
726C2×C4#1451982311yescharacteristic
727C2×C4#1451982411yescharacteristic
728C8—1222no—
729C8—2441no—
730C8—2441no—
731C8—2441no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—4881no—
747C22—4881no—
748C22—4881no—
749C22—4881no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22C2×#1451974611yescharacteristic
754C22#1684041911yescharacteristic
755C22#1684043111yescharacteristic
756C22C2×#1451979711yescharacteristic
757C22#1684056011yescharacteristic
758C22#1684056511yescharacteristic
759C22#1684056511yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—4881no—
769C4—4881no—
770C4—4881no—
771C4#1684026911yescharacteristic
772C4#1684034011yescharacteristic
773C4#1684040011yescharacteristic
774C4#1684041111yescharacteristic
775C2—82no—
776C2—82no—
777C2—4882no—
778C2#2144915811yescharacteristic
779C2#2145503711yescharacteristic
780C2#2145508711yescharacteristic
781C2#2145847511yescharacteristic
782C2#2145856611yescharacteristic
783C2#2145882711yescharacteristic
784C2#2145890311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#559C2
socleC23×C61C22×D4
prime radical#21446890C2
hypercenterC2×#559D61
hypocenterC61#24192
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16839974C2semidirect
2. C2×C4×#11758199C2semidirect
3. #21451177C2semidirect
4. #21447055C2semidirect
5. #21447050C2semidirect
6. #21446896C2semidirect
8. #21446756C2semidirect
9. #21446631C2semidirect
10. #21446174C2semidirect
11. #21446167C2semidirect
12. #21446073C2semidirect
13. #21446066C2semidirect
14. #21445829C2semidirect
15. C2×C61×#559C2semidirect
383. C2×#559D61semidirect
455. C61#24192semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×C4×#117581992
#214511772
#214470552
#214470502
#214468962
#214468902
#214467562
#214466312
#214461742
#214461672
#214460732
#214460662
#214458292
C2×C61×#5592
#2419261