Finite Group Databasebeta

← #14765802

Subgroups — #14765802

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C211yesmaximal, characteristic, complemented
2C2×#10622333C211yesmaximal, characteristic
3#13071890C211yesmaximal, characteristic
4#13069550C211yesmaximal, characteristic, complemented
5#13069337C211yesmaximal, characteristic, complemented
6#13069333C211yesmaximal, characteristic, complemented
7#13069331C211yesmaximal, characteristic, complemented
8#13069231C211yesmaximal, characteristic
9#13069219C211yesmaximal, characteristic
10#13069219C211yesmaximal, characteristic
11#13069180C211yesmaximal, characteristic, complemented
12#13069174C211yesmaximal, characteristic, complemented
13#13068598C211yesmaximal, characteristic
14#13068489C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C2×#66979C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622562C411yescharacteristic
37#10622561C411yescharacteristic
38#10622561C411yescharacteristic
39#10622560C411yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622333—24no—
46#10622314—24no—
47#10622274C411yescharacteristic
48#10622273C411yescharacteristic
49#10622270C411yescharacteristic
50#10622269C411yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2×C411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75#66979—22no—
76#66979—22no—
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×C4⋊C8—41no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—41no—
101C11×#97—22no—
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—41no—
114#66879D414yes—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—41no—
121C8×Dic11—22no—
122C8×Dic11—22no—
123C8×Dic11—41no—
124C4⋊(C11⋊C8)—22no—
125#66867—41no—
126#22109—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—41no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C2×D412yes—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C22⋊Dic11—22no—
170C22⋊Dic11—22no—
171C22⋊Dic11—22no—
172C22⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—41no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11C2×D412yes—
191C4×Dic11#4112yes—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C2×D412yes—
204C2×#446—111no—
205C2×#433—111no—
206#2396—111no—
207#1984—111no—
208#1940—111no—
209#1939—111no—
210#1939—111no—
211#1924—111no—
212#1924D1111yescharacteristic
213#1923—111no—
214#1923—111no—
215#1917—111no—
216#1916—111no—
217#1798—111no—
218#1771—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11C23×C411yescharacteristic
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11C4×D412yes—
273C2×Dic11C4×D412yes—
274C2×Dic11#13112yes—
275C2×Dic11#13112yes—
276Dic22—44no—
277C8×C11—22no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C4×Q8—111no—
286C2×#117—111no—
287#446—224no—
288#433—224no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×C22⋊C8—111no—
299C2×C22⋊C8C2×D1111yescharacteristic
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×#97—111no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306C2×C4×C8—111no—
307#400—111no—
308#399—111no—
309#398—111no—
310#398—111no—
311#396—111no—
312#396—111no—
313#395—111no—
314#393—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C22⋊C4—111no—
319C4×C22⋊C4C2×D1111yescharacteristic
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336C2×D1111yescharacteristic
329#336C2×D1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#51911yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11C2×#13111yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C22×C11#56811yescharacteristic
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11#53611yescharacteristic
350C4×C11#53711yescharacteristic
351C4×C11#54111yescharacteristic
352C4×C11#54211yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—22no—
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361C22×Q8—111no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4×Q8—222no—
372C4×Q8—222no—
373#117—222no—
374#117—222no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C22⋊C4—111no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C22⋊C4—111no—
390C2×C22⋊C4C4×D1111yescharacteristic
391C2×C22⋊C4C4×D1111yescharacteristic
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42C22×D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—41no—
399C4⋊C8—222no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402C4⋊C8—222no—
403C4⋊C8—222no—
404C4⋊C8—222no—
405C4⋊C8—441no—
406C22⋊C8—22no—
407C22⋊C8—41no—
408C22⋊C8—222no—
409C22⋊C8—441no—
410#97—22no—
411#97—114no—
412#97—441no—
413C4×C8—222no—
414C4×C8—222no—
415C4×C8—441no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95C4×D1111yescharacteristic
425#95C4×D1111yescharacteristic
426C2×C11—81no—
427C2×C11#232311yescharacteristic
428C2×C11#293311yescharacteristic
429C2×C11#293511yescharacteristic
430C2×C11#298611yescharacteristic
431C2×C11#298711yescharacteristic
432C2×C11#299211yescharacteristic
433C2×C11#299311yescharacteristic
434C24C2×C4×D1111yescharacteristic
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—441no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8D4×D1112yes—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—112no—
504C42—112no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C11#2210911yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C22×C4×D1111yescharacteristic
520Q8—444no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4#6703711yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704311yescharacteristic
568C2×C4#6704311yescharacteristic
569C2×C4#6704311yescharacteristic
570C8—22no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—222no—
575C8—441no—
576C8—441no—
577C8—441no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22#1062304711yescharacteristic
586C22C4×D4×D1111yescharacteristic
587C22#1062307711yescharacteristic
588C22#1062327611yescharacteristic
589C22#1062327611yescharacteristic
590C22D11×#13111yescharacteristic
591C22D11×#13111yescharacteristic
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—222no—
598C4—222no—
599C4—222no—
600C4—222no—
601C4—441no—
602C4—441no—
603C4—441no—
604C4—441no—
605C4#1062313911yescharacteristic
606C4#1062317911yescharacteristic
607C4#1062320011yescharacteristic
608C4#1062323211yescharacteristic
609C2—81no—
610C2#1307129511yescharacteristic
611C2#1307734511yescharacteristic
612C2#1307735711yescharacteristic
613C2#1307771511yescharacteristic
614C2#1307772111yescharacteristic
615C2#1307775111yescharacteristic
616C2#1307775811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#22109
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#10622314C2semidirect
4. #13069550C2semidirect
5. #13069337C2semidirect
6. #13069333C2semidirect
7. #13069331C2semidirect
11. #13069180C2semidirect
12. #13069174C2semidirect
14. #13068489C2semidirect
511. C11#22109semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C2×#106223332
#130718902
#130695502
#130693372
#130693332
#130693312
#130692312
#130692192
#130691802
#130691742
#130685982
#130684892
C11×#19242
#2210911