Finite Group Databasebeta

← #29696153

Subgroups — #29696153

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840439C211yesmaximal, characteristic
2#21448671C211yesmaximal, characteristic, complemented
3#21448665C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446276C211yesmaximal, characteristic, complemented
6#21446276C211yesmaximal, characteristic, complemented
7#21446271C211yesmaximal, characteristic
8#21446271C211yesmaximal, characteristic
9#21445895C211yesmaximal, characteristic, complemented
10#21445892C211yesmaximal, characteristic, complemented
11#21445804C211yesmaximal, characteristic, complemented
12C4×#14519691C211yesmaximal, characteristic, complemented
13#21445550C211yesmaximal, characteristic, complemented
14#342×D61C211yesmaximal, characteristic, complemented
15C61×#1996C211yesmaximal, characteristic, complemented
16#16840439—21no—
17#16840439—21no—
18#16840439—21no—
19#16840439—21no—
20#16840439—21no—
21#16840439—21no—
22#16840439—21no—
23#16840439—21no—
24C2×#14519772C411yescharacteristic, complemented
25C2×#14519772C411yescharacteristic, complemented
26C2×#14519766C411yescharacteristic, complemented
27C2×#14519762C411yescharacteristic, complemented
28C2×#14519762C411yescharacteristic, complemented
29C2×#14519761C2211yescharacteristic
30C2×#14519753C411yescharacteristic, complemented
31C2×#14519747C2211yescharacteristic
32C2×#14519739C411yescharacteristic, complemented
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519735C411yescharacteristic, complemented
35C2×#14519733C2211yescharacteristic
36C2×#14519733C2211yescharacteristic
37C2×#14519733C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C2×C22⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61C2211yescharacteristic
41C2×C22⋊C4×D61C2211yescharacteristic
42C2×#14519691C2211yescharacteristic
43C2×#14519691C2211yescharacteristic
44C2×#14519691C2211yescharacteristic
45C2×#14519691C2211yescharacteristic
46#16839654—21no—
47#16839653—21no—
48#16839652—21no—
49#16839651—21no—
50#16839636—21no—
51#16839633—21no—
52#16839623C2211yescharacteristic
53#16839623C2211yescharacteristic
54#16839622C2211yescharacteristic
55#16839617C2211yescharacteristic
56#16839617C2211yescharacteristic
57C4×#11758198—21no—
58C4×C22⋊Dic61C2211yescharacteristic
59#16839609—21no—
60#16839529C2211yescharacteristic
61#16839529C2211yescharacteristic
62#16839529C2211yescharacteristic
63#16839529C2211yescharacteristic
64#16839528C2211yescharacteristic
65#16839528C2211yescharacteristic
66#16839528C2211yescharacteristic
67#16839528C2211yescharacteristic
68C2×C22⋊Q8×C61C2211yescharacteristic
69C61×#380C2211yescharacteristic
70C4×C22⋊C4×C61C2211yescharacteristic
71C61×#342C2211yescharacteristic
72C61×#342C2211yescharacteristic
73C61×#342C2211yescharacteristic
74C61×#342C2211yescharacteristic
75C24×D61C2311yescharacteristic
76C22×D244C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2×C411yescharacteristic, complemented
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519766—21no—
94#14519766—21no—
95#14519766—21no—
96#14519766—21no—
97#14519762—21no—
98#14519762—21no—
99#14519762—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519761—21no—
106#14519761—21no—
107#14519761—21no—
108#14519761—21no—
109#14519753—21no—
110#14519753—21no—
111#14519753—21no—
112#14519753—21no—
113#14519747—21no—
114#14519747—21no—
115#14519747—21no—
116#14519747—21no—
117#14519739—21no—
118#14519739—21no—
119#14519739—21no—
120#14519739—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125#14519735—21no—
126#14519735—21no—
127#14519735—21no—
128#14519735—21no—
129#14519733—21no—
130#14519733—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—22no—
134#14519733—22no—
135#14519733—41no—
136#14519733—41no—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61C2×C411yescharacteristic, complemented
139C2×C4⋊Dic61C2×C411yescharacteristic, complemented
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196C2×C411yescharacteristic, complemented
143C2×#11758196C2×C411yescharacteristic, complemented
144C2×#11758196C2×C411yescharacteristic, complemented
145C2×C22⋊Dic61C2311yescharacteristic
146C2×C22⋊Dic61C2311yescharacteristic
147C2×C22⋊Dic61C2311yescharacteristic
148C2×C22⋊Dic61C2311yescharacteristic
149C2×C22⋊Dic61C2311yescharacteristic
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic, complemented
165C2×#11758198C2×C411yescharacteristic, complemented
166C2×#11758198C2×C411yescharacteristic, complemented
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C2×#11758198D411yescharacteristic
172C2×#11758198D411yescharacteristic
173C2×#11758198D411yescharacteristic
174C2×#11758198D411yescharacteristic
175C22⋊C4×D61—21no—
176C22⋊C4×D61—21no—
177C22⋊C4×D61—21no—
178C22⋊C4×D61—21no—
179C22⋊C4×D61—22no—
180C22⋊C4×D61—22no—
181C22⋊C4×D61—41no—
182C22⋊C4×D61—41no—
183C2×C4×Dic61—21no—
184C2×C4×Dic61—21no—
185C2×C4×Dic61—21no—
186C2×C4×Dic61C2×C411yescharacteristic, complemented
187C2×C4×Dic61C2×C411yescharacteristic, complemented
188C2×C4×Dic61C2×C411yescharacteristic, complemented
189#14519691—22no—
190#14519691—22no—
191#14519691—41no—
192#14519691—41no—
193#14519684—21no—
194#14519684—21no—
195#14519684—21no—
196#14519684—21no—
197#14519684—21no—
198#14519684—21no—
199C22×Q8×C61C2×C411yescharacteristic, complemented
200C23×C4×C61C2311yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203C22⋊Q8×C61—21no—
204C22⋊Q8×C61—21no—
205C2×C4⋊C4×C61—21no—
206C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
207C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
208C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
209C2×C22⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61C2311yescharacteristic
212C2×C22⋊C4×C61C2311yescharacteristic
213C2×C22⋊C4×C61C2311yescharacteristic
214C2×C22⋊C4×C61C2311yescharacteristic
215C2×C42×C61—21no—
216#95×C61—21no—
217#95×C61—21no—
218C24×C61C2411yescharacteristic
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—42no—
224C23×D61—81no—
225C23×D61C22×C411yescharacteristic
226C23×D61C22×C411yescharacteristic
227C23×D61C22×C411yescharacteristic
228C23×D61C2×D411yescharacteristic
229C23×D61C2×D411yescharacteristic
230C23×D61C2×D411yescharacteristic
231C23×D61C2×D411yescharacteristic
232C2×Q8×C61—21no—
233C2×Q8×C61—21no—
234C2×Q8×C61—81no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—81no—
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C22×C411yescharacteristic
245C22×C4×C61C22×C411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C2×C22⋊D61—21no—
251C2×C22⋊D61—21no—
252C2×C22⋊D61—21no—
253C2×C22⋊D61—21no—
254C2×C22⋊D61—21no—
255C2×C22⋊D61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61C22×C411yescharacteristic
265C22×Dic61C22×C411yescharacteristic
266C22×Dic61C22×C411yescharacteristic
267C22×Dic61C22×C411yescharacteristic
268C22×Dic61C22×C411yescharacteristic
269C22×Dic61C2×D411yescharacteristic
270C22×Dic61C2×D411yescharacteristic
271C22×Dic61C2×D411yescharacteristic
272C22×Dic61C2×D411yescharacteristic
273C2×D244—21no—
274C2×D244—21no—
275C2×D244—21no—
276C2×D244—21no—
277C2×D244—42no—
278C2×D244—81no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—42no—
286C2×C4×D61—42no—
287C2×C4×D61—42no—
288C2×C4×D61—42no—
289C2×C4×D61—42no—
290C2×C4×D61—81no—
291C2×C4×D61—81no—
292C2×C4×D61—81no—
293C2×C4×D61—81no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61—21no—
299C4⋊C4×C61—21no—
300C4⋊C4×C61—81no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61#4112yes—
313C42×C61—81no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61#4112yes—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—42no—
339#11758198—42no—
340#11758198—42no—
341#11758198—42no—
342#11758198—81no—
343#11758198—81no—
344#11758198C22⋊C411yescharacteristic
345#11758198C22⋊C411yescharacteristic
346#11758198C22⋊C411yescharacteristic
347#11758198C22⋊C411yescharacteristic
348#11758198C22⋊C411yescharacteristic
349#11758198C22⋊C411yescharacteristic
350#11758198C22⋊C411yescharacteristic
351#11758198C22⋊C411yescharacteristic
352#11758198C22⋊C411yescharacteristic
353#11758198C22⋊C411yescharacteristic
354#11758198C22⋊C411yescharacteristic
355#11758198C22⋊C411yescharacteristic
356#11758198C22⋊C411yescharacteristic
357#11758198C22⋊C411yescharacteristic
358#11758198C22⋊C411yescharacteristic
359#11758198C22⋊C411yescharacteristic
360C4⋊Dic61—21no—
361C4⋊Dic61—21no—
362C4⋊Dic61—21no—
363C4⋊Dic61—21no—
364C4⋊Dic61—81no—
365#11758196—21no—
366#11758196—21no—
367#11758196—21no—
368#11758196—21no—
369#11758196—21no—
370#11758196—21no—
371#11758196—42no—
372#11758196—42no—
373C4×Dic61—21no—
374C4×Dic61—21no—
375C4×Dic61—21no—
376C4×Dic61—21no—
377C4×Dic61—21no—
378C4×Dic61—21no—
379C4×Dic61—42no—
380C4×Dic61—42no—
381C4×Dic61—81no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61C23×C411yescharacteristic
385C23×C61C22×D411yescharacteristic
386C23×C61C22×D411yescharacteristic
387C23×C61C2×#4111yescharacteristic
388C23×C61C2×#4111yescharacteristic
389C23×C61H(5,𝔽2)11yescharacteristic
390C23×C612−1+411yescharacteristic
391C22×D61—21no—
392C22×D61—21no—
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—21no—
396C22×D61—21no—
397C22×D61—21no—
398C22×D61—21no—
399C22×D61—21no—
400C22×D61—21no—
401C22×D61—21no—
402C22×D61—21no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—21no—
407C22×D61—21no—
408C22×D61—21no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—82no—
421C22×D61—82no—
422C22×D61—82no—
423C22×D61—82no—
424C22×D61C2×C22⋊C411yescharacteristic
425C22×D61C2×C22⋊C411yescharacteristic
426C22×D61C2×C22⋊C411yescharacteristic
427C22×D61C2×C22⋊C411yescharacteristic
428Q8×C61—81no—
429Q8×C61—81no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—22no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61C2×C22⋊C411yescharacteristic
457C2×C4×C61C2×C22⋊C411yescharacteristic
458C2×C4×C61C2×C22⋊C411yescharacteristic
459C2×C4×C61C2×C22⋊C411yescharacteristic
460C22⋊D61—41no—
461C22⋊D61—41no—
462C22⋊D61—41no—
463C22⋊D61—41no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—21no—
478C2×Dic61—21no—
479C2×Dic61—21no—
480C2×Dic61—21no—
481C2×Dic61—22no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61C2×C22⋊C411yescharacteristic
496C2×Dic61C2×C22⋊C411yescharacteristic
497C2×Dic61C2×C22⋊C411yescharacteristic
498C2×Dic61C2×C22⋊C411yescharacteristic
499D244—42no—
500D244—42no—
501D244—81no—
502D244—81no—
503C4×D61—42no—
504C4×D61—42no—
505C4×D61—81no—
506C4×D61—81no—
507C4×D61—81no—
508C4×D61—81no—
509C4×D61—84no—
510C4×D61—84no—
511#22477—611nomaximal, Sylow
512C22×C61—21no—
513C22×C61—21no—
514C22×C61—21no—
515C22×C61—21no—
516C22×C61—21no—
517C22×C61—21no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61—41no—
522C22×C61C22×C22⋊C411yescharacteristic
523C22×C61C4×#4111yescharacteristic
524C22×C61#52011yescharacteristic
525C22×C61#54611yescharacteristic
526C22×C61#54611yescharacteristic
527C22×C61#54711yescharacteristic
528C22×C61#54711yescharacteristic
529C2×D61—21no—
530C2×D61—21no—
531C2×D61—21no—
532C2×D61—21no—
533C2×D61—21no—
534C2×D61—21no—
535C2×D61—21no—
536C2×D61—21no—
537C2×D61—21no—
538C2×D61—21no—
539C2×D61—21no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—41no—
547C2×D61—41no—
548C2×D61—41no—
549C2×D61—81no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61#41012yes—
558C4×C61—21no—
559C4×C61—21no—
560C4×C61—21no—
561C4×C61—21no—
562C4×C61—42no—
563C4×C61—41no—
564C4×C61—41no—
565C4×C61—41no—
566C4×C61—41no—
567C4×C61—81no—
568C4×C61—81no—
569C4×C61—81no—
570Dic61—21no—
571Dic61—21no—
572Dic61—21no—
573Dic61—21no—
574Dic61—42no—
575Dic61—41no—
576Dic61—41no—
577Dic61—41no—
578Dic61—81no—
579Dic61—81no—
580Dic61—81no—
581C2×#551—611no—
582#2342—611no—
583#2342—611no—
584#1996—611no—
585#1996D6111yescharacteristic, complemented
586#1899—611no—
587#1899—611no—
588#1898—611no—
589#1898—611no—
590#1820—611no—
591#1819—611no—
592#1799—611no—
593C4×#99—611no—
594#1740—611no—
595C2×#342—611no—
596C2×C61—21no—
597C2×C61—21no—
598C2×C61—21no—
599C2×C61—21no—
600C2×C61—21no—
601C2×C61—21no—
602C2×C61#233911yescharacteristic
603C2×C61C2×#41011yescharacteristic
604C2×C61#288311yescharacteristic
605D61—22no—
606D61—41no—
607D61—41no—
608D61—41no—
609D61—81no—
610#551—1221no—
611#551—1221no—
612#551—1221no—
613#551—1221no—
614#551—1221no—
615#551—1221no—
616#551—1221no—
617#551—1221no—
618C2×#126—611no—
619C2×#126—611no—
620C2×#124—611no—
621C2×#123—611no—
622C2×#123—611no—
623C2×#123—611no—
624C2×C22⋊Q8—611no—
625C2×C22⋊Q8C2×D6111yescharacteristic
626C2×#120—611no—
627C2×C4×D4—611no—
628C2×C4×D4—611no—
629C2×#117—611no—
630C2×#117—611no—
631C2×#117—611no—
632C2×#117—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C2×#99—611no—
638C2×#99—611no—
639C2×#99—611no—
640C2×#99—611no—
641#388—1221no—
642#388—1221no—
643#388—1221no—
644#388—1221no—
645#385—1221no—
646#385—1221no—
647#381—611no—
648#381—611no—
649#380—611no—
650#380C2×D6111yescharacteristic
651#379—611no—
652#379—611no—
653C4×C22⋊C4—611no—
654C4×C22⋊C4—1221no—
655C4×C22⋊C4—1221no—
656C4×C22⋊C4C2×D6111yescharacteristic
657#342—611no—
658#342—611no—
659#342—611no—
660#342—611no—
661#342—611no—
662#342—611no—
663#342—611no—
664#342—611no—
665#342C2×D6111yescharacteristic
666#342C2×D6111yescharacteristic
667#342C2×D6111yescharacteristic
668#342C2×D6111yescharacteristic
669C61#2247711yescharacteristic, complemented, Sylow
670C25—611no—
671C22×Q8C4×D6111yescharacteristic, complemented
672C22×D4—611no—
673C22×D4—611no—
674C22×D4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—1221no—
680C23×C4—1221no—
681C23×C4C22×D6111yescharacteristic
682#126—1221no—
683#126—1221no—
684#126—1221no—
685#126—1221no—
686#126—1221no—
687#126—1221no—
688#126—1221no—
689#126—1221no—
690#124—1221no—
691#124—1221no—
692#124—1221no—
693#124—1221no—
694#123—1221no—
695#123—1221no—
696#123—1221no—
697#123—1221no—
698#123—1221no—
699#123—1221no—
700#123—1221no—
701#123—1221no—
702#123—1221no—
703#123—1221no—
704#123—1221no—
705#123—1221no—
706C22⋊Q8—21no—
707C22⋊Q8—21no—
708C22⋊Q8—21no—
709C22⋊Q8—21no—
710C22⋊Q8—1221no—
711C22⋊Q8—1221no—
712C22⋊Q8—1221no—
713C22⋊Q8—1221no—
714#120—1221no—
715#120—1221no—
716#120—1221no—
717#120—1221no—
718C4×D4—1221no—
719C4×D4—1221no—
720C4×D4—1221no—
721C4×D4—1221no—
722C4×D4—1221no—
723C4×D4—1221no—
724C4×D4—1221no—
725C4×D4—1221no—
726#117—1221no—
727#117—1221no—
728#117—1221no—
729#117—1221no—
730#117—1221no—
731#117—1221no—
732#117—1221no—
733#117—1221no—
734#117—1222no—
735#117—1222no—
736#117—2441no—
737#117—2441no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—611no—
740C2×C4⋊C4—611no—
741C2×C4⋊C4—611no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—1221no—
745C2×C4⋊C4—1221no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4C4×D6111yescharacteristic, complemented
748C2×C4⋊C4C4×D6111yescharacteristic, complemented
749C2×C4⋊C4C4×D6111yescharacteristic, complemented
750C2×C22⋊C4—611no—
751C2×C22⋊C4—611no—
752C2×C22⋊C4—611no—
753C2×C22⋊C4—611no—
754C2×C22⋊C4—611no—
755C2×C22⋊C4—611no—
756C2×C22⋊C4—611no—
757C2×C22⋊C4—611no—
758C2×C22⋊C4—611no—
759C2×C22⋊C4—611no—
760C2×C22⋊C4—611no—
761C2×C22⋊C4—611no—
762C2×C22⋊C4—611no—
763C2×C22⋊C4—611no—
764C2×C22⋊C4—611no—
765C2×C22⋊C4—611no—
766C2×C22⋊C4—611no—
767C2×C22⋊C4—611no—
768C2×C22⋊C4—611no—
769C2×C22⋊C4—611no—
770C2×C22⋊C4—611no—
771C2×C22⋊C4—611no—
772C2×C22⋊C4—611no—
773C2×C22⋊C4—611no—
774C2×C22⋊C4—1222no—
775C2×C22⋊C4—1221no—
776C2×C22⋊C4—1221no—
777C2×C22⋊C4—1221no—
778C2×C22⋊C4—1221no—
779C2×C22⋊C4—1222no—
780C2×C22⋊C4—1221no—
781C2×C22⋊C4—1221no—
782C2×C22⋊C4—1221no—
783C2×C22⋊C4—1221no—
784C2×C22⋊C4—1221no—
785C2×C22⋊C4—1221no—
786C2×C22⋊C4—2441no—
787C2×C22⋊C4—2441no—
788C2×C22⋊C4C22×D6111yescharacteristic
789C2×C22⋊C4C22×D6111yescharacteristic
790C2×C22⋊C4C22×D6111yescharacteristic
791C2×C22⋊C4C22×D6111yescharacteristic
792C2×C22⋊C4C22×D6111yescharacteristic
793C2×C22⋊C4C22×D6111yescharacteristic
794C2×C42—21no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—611no—
798C2×C42—1221no—
799C2×C42—1221no—
800C2×C42—1221no—
801#99—1222no—
802#99—1222no—
803#99—2441no—
804#99—2441no—
805#95—21no—
806#95—21no—
807#95—1221no—
808#95—1221no—
809#95—1221no—
810#95—1221no—
811#95—1221no—
812#95—1221no—
813C24—611no—
814C24—611no—
815C24—611no—
816C24—611no—
817C24—611no—
818C24—611no—
819C24—611no—
820C24—1221no—
821C24—1221no—
822C24—1221no—
823C24—1221no—
824C24—4881no—
825C24—2442no—
826C24C23×D6111yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—81no—
830C2×D4—1221no—
831C2×D4—1221no—
832C2×D4—1221no—
833C2×D4—1221no—
834C2×D4—1221no—
835C2×D4—1221no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—4881no—
841C2×D4—2442no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—81no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—4881no—
871C22×C4—4881no—
872C22×C4—4881no—
873C22×C4—4881no—
874C22×C4—2442no—
875C22×C4—2442no—
876C22×C4—2442no—
877C22×C4—2442no—
878C22×C4—2442no—
879C22×C4C2×C4×D6111yescharacteristic
880C22×C4C2×C4×D6111yescharacteristic
881C22×C4C2×C4×D6111yescharacteristic
882C22×C4C2×C4×D6111yescharacteristic
883C22×C4C2×C4×D6111yescharacteristic
884C22×C4C2×C4×D6111yescharacteristic
885C22×C4D4×D6111yescharacteristic
886C22×C4D4×D6111yescharacteristic
887C22×C4D4×D6111yescharacteristic
888C22×C4D4×D6111yescharacteristic
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—81no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—1221no—
901C4⋊C4—1221no—
902C4⋊C4—1221no—
903C4⋊C4—1221no—
904C4⋊C4—1221no—
905C4⋊C4—1221no—
906C4⋊C4—4881no—
907C4⋊C4—2442no—
908C4⋊C4—2442no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—21no—
920C22⋊C4—611no—
921C22⋊C4—611no—
922C22⋊C4—611no—
923C22⋊C4—611no—
924C22⋊C4—611no—
925C22⋊C4—611no—
926C22⋊C4—611no—
927C22⋊C4—611no—
928C22⋊C4—611no—
929C22⋊C4—611no—
930C22⋊C4—611no—
931C22⋊C4—611no—
932C22⋊C4—611no—
933C22⋊C4—611no—
934C22⋊C4—611no—
935C22⋊C4—611no—
936C22⋊C4—612no—
937C22⋊C4—1221no—
938C22⋊C4—1221no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—1221no—
942C22⋊C4—1221no—
943C22⋊C4—1221no—
944C22⋊C4—1221no—
945C22⋊C4—1221no—
946C22⋊C4—1221no—
947C22⋊C4—1221no—
948C22⋊C4—1221no—
949C22⋊C4—1221no—
950C22⋊C4—1221no—
951C22⋊C4—1221no—
952C22⋊C4—1221no—
953C22⋊C4—1221no—
954C22⋊C4—1221no—
955C22⋊C4—1221no—
956C22⋊C4—1221no—
957C22⋊C4—1221no—
958C22⋊C4—1221no—
959C22⋊C4—1221no—
960C22⋊C4—4881no—
961C22⋊C4—4881no—
962C22⋊C4—2442no—
963C22⋊C4—2442no—
964C22⋊C4—2442no—
965C22⋊C4—2442no—
966C22⋊C4#1175822612yes—
967C42—81no—
968C42—1221no—
969C42—1221no—
970C42—1221no—
971C42—1221no—
972C42—1221no—
973C42—1221no—
974C42—4881no—
975C42—2442no—
976C42—2442no—
977C23—41no—
978C23—41no—
979C23—611no—
980C23—611no—
981C23—611no—
982C23—611no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1221no—
987C23—1221no—
988C23—1221no—
989C23—1221no—
990C23—1221no—
991C23—1221no—
992C23—1221no—
993C23—1221no—
994C23—1221no—
995C23—1221no—
996C23—1221no—
997C23—1221no—
998C23—1221no—
999C23—1221no—
1000C23—1221no—
1001C23—4882no—
1002C23—4882no—
1003C23—4882no—
1004C23—4882no—
1005C23—2441no—
1006C23—2441no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23C22×C4×D6111yescharacteristic
1017C23C2×D4×D6111yescharacteristic
1018C23C2×D4×D6111yescharacteristic
1019C23#41×D6111yescharacteristic
1020C23C2×#1175822611yescharacteristic
1021C23#1451982311yescharacteristic
1022C23#1451982511yescharacteristic
1023Q8—81no—
1024Q8—81no—
1025D4—4881no—
1026D4—4881no—
1027D4—2442no—
1028D4—2442no—
1029D4—2441no—
1030D4—2441no—
1031D4—2441no—
1032D4—2441no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—611no—
1060C2×C4—611no—
1061C2×C4—611no—
1062C2×C4—611no—
1063C2×C4—1221no—
1064C2×C4—1221no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1221no—
1070C2×C4—1221no—
1071C2×C4—1221no—
1072C2×C4—1221no—
1073C2×C4—1221no—
1074C2×C4—1221no—
1075C2×C4—1221no—
1076C2×C4—1221no—
1077C2×C4—1221no—
1078C2×C4—1221no—
1079C2×C4—1221no—
1080C2×C4—1222no—
1081C2×C4—4881no—
1082C2×C4—4881no—
1083C2×C4—4884no—
1084C2×C4—4881no—
1085C2×C4—4881no—
1086C2×C4—4884no—
1087C2×C4—2442no—
1088C2×C4—2442no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4C22⋊C4×D6111yescharacteristic
1103C2×C4C22⋊C4×D6111yescharacteristic
1104C2×C4C22⋊C4×D6111yescharacteristic
1105C2×C4C22⋊C4×D6111yescharacteristic
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—612no—
1117C22—1221no—
1118C22—1221no—
1119C22—1221no—
1120C22—1221no—
1121C22—1221no—
1122C22—1221no—
1123C22—1221no—
1124C22—1221no—
1125C22—1221no—
1126C22—1221no—
1127C22—1221no—
1128C22—4881no—
1129C22—4881no—
1130C22—4881no—
1131C22—4881no—
1132C22—4881no—
1133C22—4881no—
1134C22—4881no—
1135C22—4881no—
1136C22—2442no—
1137C22—2442no—
1138C22—2442no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2441no—
1143C22—2441no—
1144C22—2441no—
1145C22C2×C22⋊C4×D6111yescharacteristic
1146C22C4×#1175822611yescharacteristic
1147C22#1684024411yescharacteristic
1148C22#1684040311yescharacteristic
1149C22#1684040511yescharacteristic
1150C22#1684041411yescharacteristic
1151C22#1684041511yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—1221no—
1165C4—1221no—
1166C4—1221no—
1167C4—1221no—
1168C4—4881no—
1169C4—4881no—
1170C4—4881no—
1171C4—2442no—
1172C4—2441no—
1173C4—2441no—
1174C4—2441no—
1175C2—21no—
1176C2—21no—
1177C2—21no—
1178C2—21no—
1179C2—21no—
1180C2—21no—
1181C2—1222no—
1182C2—4881no—
1183C2—2441no—
1184C2—2441no—
1185C2—2441no—
1186C2#2144864811yescharacteristic
1187C2#410×D6111yescharacteristic
1188C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C22
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448671C2semidirect
3. #21448665C2semidirect
4. #21446805C2semidirect
5. #21446276C2semidirect
6. #21446276C2semidirect
9. #21445895C2semidirect
10. #21445892C2semidirect
11. #21445804C2semidirect
12. C4×#14519691C2semidirect
13. #21445550C2semidirect
14. #342×D61C2semidirect
15. C61×#1996C2semidirect
24. C2×#14519772C4semidirect
25. C2×#14519772C4semidirect
26. C2×#14519766C4semidirect
27. C2×#14519762C4semidirect
28. C2×#14519762C4semidirect
30. C2×#14519753C4semidirect
32. C2×#14519739C4semidirect
34. C2×#14519735C4semidirect
84. C22×C4×D61C2×C4semidirect
138. C2×C4⋊Dic61C2×C4semidirect
139. C2×C4⋊Dic61C2×C4semidirect
142. C2×#11758196C2×C4semidirect
143. C2×#11758196C2×C4semidirect
144. C2×#11758196C2×C4semidirect
164. C2×#11758198C2×C4semidirect
165. C2×#11758198C2×C4semidirect
166. C2×#11758198C2×C4semidirect
186. C2×C4×Dic61C2×C4semidirect
187. C2×C4×Dic61C2×C4semidirect
188. C2×C4×Dic61C2×C4semidirect
199. C22×Q8×C61C2×C4semidirect
206. C2×C4⋊C4×C61C2×C4semidirect
207. C2×C4⋊C4×C61C2×C4semidirect
208. C2×C4⋊C4×C61C2×C4semidirect
585. #1996D61semidirect
669. C61#22477semidirect
671. C22×Q8C4×D61semidirect
747. C2×C4⋊C4C4×D61semidirect
748. C2×C4⋊C4C4×D61semidirect
749. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404392
#214486712
#214486652
#214468052
#214462762
#214462712
#214458952
#214458922
#214458042
C4×#145196912
#214455502
#342×D612
C61×#19962
#2247761