Finite Group Databasebeta

← #30622504

Subgroups — #30622504

Order 15616.

1076 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840790C211yesmaximal, characteristic, complemented
2C2×#16840789C211yesmaximal, characteristic, complemented
3#21461890C211yesmaximal, characteristic, complemented
4#21461888C211yesmaximal, characteristic, complemented
5#21461874C211yesmaximal, characteristic, complemented
6#21461873C211yesmaximal, characteristic, complemented
7#21461795C211yesmaximal, characteristic, complemented
8#21461794C211yesmaximal, characteristic, complemented
9#21461793C211yesmaximal, characteristic, complemented
10#21461793C211yesmaximal, characteristic, complemented
11#21461553C211yesmaximal, characteristic, complemented
12C22⋊C4×#92420C211yesmaximal, characteristic, complemented
13C4×#14519834C211yesmaximal, characteristic, complemented
14#21461480C211yesmaximal, characteristic, complemented
15#21448331C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840790—24no—
21#16840789—24no—
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C4×#92420C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519750C411yescharacteristic
47C2×#14519739C2211yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839662C411yescharacteristic
52#16839657C411yescharacteristic
53#16839653C411yescharacteristic
54#16839640C411yescharacteristic
55#16839638C411yescharacteristic
56#16839621C411yescharacteristic
57#16839613C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#388C411yescharacteristic
61C2×D61⋊C8—22no—
62C2×D61⋊C8—22no—
63C2×D61⋊C8—22no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—41no—
68C2×D61⋊C8—41no—
69C2×D61⋊C8—41no—
70C22×#92420—22no—
71C22×#92420—22no—
72C22×#92420—41no—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82C4⋊#92420—22no—
83#14519834—22no—
84#14519834—22no—
85#14519834—22no—
86#14519834—41no—
87#14519834D414yescomplemented
88C22⋊#92420—22no—
89C22⋊#92420—22no—
90C22⋊#92420—41no—
91C4×#92420—22no—
92C4×#92420—22no—
93C4×#92420—41no—
94C4×#92420—41no—
95C22×D244C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C23×Dic61C2311yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2311yescharacteristic
103#14519750C818yescomplemented
104#14519739—22no—
105#14519739—22no—
106#14519737—22no—
107#14519737—22no—
108#14519737—41no—
109#14519737—41no—
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×C4×Dic61C2×C411yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2311yescharacteristic
126C42×D61—41no—
127C42×D61—41no—
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C42×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138#95×C61C2×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61C2×C814yescomplemented
153C2×C22⋊D61C2×C814yescomplemented
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C2411yescharacteristic
166C2×D244—22no—
167C2×D244—22no—
168C2×D244C2×C814yescomplemented
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—41no—
182C2×C4×D61—41no—
183C2×C4×D61—41no—
184C2×C4×D61C2×C814yescomplemented
185C2×C4×D61C2×D412yes—
186C2×C4×D61#4112yes—
187C2×#92420—21no—
188C2×#92420—21no—
189C2×#92420—21no—
190C2×#92420—21no—
191C2×#92420—21no—
192C2×#92420—21no—
193C2×#92420—21no—
194C2×#92420—21no—
195C2×#92420—21no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—21no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—44no—
208C2×#92420C2×D412yes—
209C2×#92420C2×D412yes—
210C2×#92420#4112yes—
211C2×#92420#4112yes—
212D61⋊C8—44no—
213D61⋊C8—44no—
214D61⋊C8—44no—
215C4⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—41no—
218C22⋊C4×C61C2×C814yescomplemented
219C42×C61—41no—
220C22⋊Dic61—22no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—41no—
226#11758198C2×C814yescomplemented
227#11758196—22no—
228#11758196—41no—
229#11758196—41no—
230#11758196C2×C814yescomplemented
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—41no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61C22×C812yes—
247C23×C61C23×C411yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61C4×D412yes—
259C22×D61C22×C812yes—
260C22×D61C22×C812yes—
261C22×D61#13112yes—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61C4×D412yes—
278C2×C4×C61C22×C812yes—
279C2×C4×C61C22×C812yes—
280C22⋊D61—28no—
281C22⋊D61—44no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61C22×C812yes—
299C2×Dic61C22×C812yes—
300C2×Dic61#13112yes—
301C2×Dic61C22×D411yescharacteristic
302C2×Dic61C2×#4111yescharacteristic
303C2×Dic61C2×#4111yescharacteristic
304C2×Dic61C2×#4111yescharacteristic
305C2×Dic61H(5,𝔽2)11yescharacteristic
306C2×Dic61H(5,𝔽2)11yescharacteristic
307D244—28no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—44no—
313C4×D61—44no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318#92420—22no—
319#92420—22no—
320#92420—22no—
321#92420—22no—
322#92420—41no—
323#92420—41no—
324#92420—41no—
325#92420—41no—
326#23116—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61C2×C4×D411yescharacteristic
335C22×C61C4×#4111yescharacteristic
336C22×C61#51811yescharacteristic
337C22×C61C23×C811yescharacteristic
338C22×C61C2×#13111yescharacteristic
339C22×C61C2×#13111yescharacteristic
340C22×C61#56811yescharacteristic
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61C8×D414yes—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361Dic61—22no—
362Dic61—22no—
363Dic61—22no—
364Dic61—41no—
365Dic61—41no—
366Dic61#54611yescharacteristic
367Dic61#54611yescharacteristic
368Dic61#55311yescharacteristic
369Dic61#55311yescharacteristic
370C2×C8×D4—611no—
371C2×C8×D4—611no—
372C4×#121—611no—
373#1923—611no—
374#1923—611no—
375#1916—611no—
376#1916—611no—
377#1869—611no—
378#1869—611no—
379#1869—611no—
380#1869—611no—
381C8×C22⋊C4—611no—
382C8×C22⋊C4—611no—
383C4×C22⋊C8—611no—
384C2×#336—611no—
385C2×C61—42no—
386C2×C61#236411yescharacteristic
387C2×C61C2×C8×D411yescharacteristic
388C2×C61#293511yescharacteristic
389C2×C61C8×#4111yescharacteristic
390C2×C61#296811yescharacteristic
391C2×C61#297211yescharacteristic
392C2×C61#297711yescharacteristic
393D61—24no—
394D61—42no—
395C23×C8—611no—
396C23×C8—611no—
397C23×C8—611no—
398C23×C8—611no—
399C2×#121—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403C22×C42—611no—
404C8×D4—1224no—
405C8×D4—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C4×C8—611no—
417C2×C4×C8—611no—
418C2×C4×C8—611no—
419C2×C4×C8—611no—
420#390—611no—
421#389—611no—
422#388—611no—
423#388#692311yescharacteristic
424#386—611no—
425#386—611no—
426#380—611no—
427C4×C4⋊C4—611no—
428C4×C22⋊C4—611no—
429C4×C22⋊C4—611no—
430#336—611no—
431#336—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440C61#2311611yescharacteristic, complemented, Sylow
441C22×D4—611no—
442C22×D4—611no—
443C22×D4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—1222no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8—1222no—
465C22×C8—2441no—
466C22×C8—2441no—
467C22×C8—2441no—
468C22×C8—2441no—
469#121—618no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2441no—
475C4×D4—2441no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4C2×#692311yescharacteristic
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4C2×#692311yescharacteristic
489C2×C22⋊C4C2×#692311yescharacteristic
490C2×C22⋊C4C2×#692311yescharacteristic
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—2441no—
497C2×C42—2441no—
498C2×C42C2×#692311yescharacteristic
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C22⋊C8—614no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—2441no—
508C22⋊C8—2441no—
509C4×C8—1222no—
510C4×C8—1222no—
511C4×C8—2441no—
512C4×C8—2441no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95C2×#692311yescharacteristic
518#95C2×#692311yescharacteristic
519C24—611no—
520C24—611no—
521C24C22×#692311yescharacteristic
522C2×D4—614no—
523C2×D4—614no—
524C2×D4—614no—
525C2×D4—1222no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—2441no—
530C2×D4—2441no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—614no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4—2441no—
561C22×C4C22×#692311yescharacteristic
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565C22×C4C22×#692311yescharacteristic
566C22×C4C22×#692311yescharacteristic
567C2×C8—612no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—612no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—2444no—
592C2×C8—2444no—
593C2×C8—2444no—
594C2×C8—2444no—
595C4⋊C4—22no—
596C4⋊C4—614no—
597C4⋊C4—1222no—
598C4⋊C4—2441no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—614no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—2441no—
609C22⋊C4D61⋊C814yescomplemented
610C42—41no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—2441no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—612no—
627C23—612no—
628C23—612no—
629C23—612no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23C2×D61⋊C812yes—
641C23C23×#692311yescharacteristic
642D4—1228no—
643D4—1228no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—2444no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2444no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4D4×#692312yes—
696C2×C4C2×D61⋊C812yes—
697C2×C4C2×D61⋊C812yes—
698C8—1222no—
699C8—1222no—
700C8—1222no—
701C8—1222no—
702C8—2441no—
703C8—2441no—
704C8—2441no—
705C8—2441no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—614no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—1222no—
718C22—1222no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22C2×D4×#692311yescharacteristic
728C22#41×#692311yescharacteristic
729C22#1684082911yescharacteristic
730C22C22×D61⋊C811yescharacteristic
731C22D61⋊#13111yescharacteristic
732C22D61⋊#13111yescharacteristic
733C22#1684084111yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—611no—
741C4—611no—
742C4—611no—
743C4—611no—
744C4—1222no—
745C4—1222no—
746C4—1222no—
747C4—2441no—
748C4—2441no—
749C2—42no—
750C2—1224no—
751C2—2442no—
752C2#2146234711yescharacteristic
753C2D4×D61⋊C811yescharacteristic
754C2#2146256411yescharacteristic
755C2#2146262311yescharacteristic
756C2#2146264911yescharacteristic
757C2#2146266711yescharacteristic
758C2#2146269311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C23×C8
FittingC61×#388C4
socleC23×C61C23×C4
prime radicalC2×#14519750C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61#23116
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840790C2semidirect
2. C2×#16840789C2semidirect
3. #21461890C2semidirect
4. #21461888C2semidirect
5. #21461874C2semidirect
6. #21461873C2semidirect
7. #21461795C2semidirect
8. #21461794C2semidirect
9. #21461793C2semidirect
10. #21461793C2semidirect
11. #21461553C2semidirect
12. C22⋊C4×#92420C2semidirect
13. C4×#14519834C2semidirect
14. #21461480C2semidirect
87. #14519834D4semidirect
103. #14519750C8semidirect
152. C2×C22⋊D61C2×C8semidirect
153. C2×C22⋊D61C2×C8semidirect
168. C2×D244C2×C8semidirect
184. C2×C4×D61C2×C8semidirect
218. C22⋊C4×C61C2×C8semidirect
226. #11758198C2×C8semidirect
230. #11758196C2×C8semidirect
440. C61#23116semidirect
609. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#168407902
C2×#168407892
#214618902
#214618882
#214618742
#214618732
#214617952
#214617942
#214617932
#214615532
C22⋊C4×#924202
C4×#145198342
#214614802
#214483312
#2311661