Finite Group Databasebeta

← #14779903

Subgroups — #14779903

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66988C211yesmaximal, characteristic
2#13069336C211yesmaximal, characteristic, complemented
3#13069331C211yesmaximal, characteristic, complemented
4#13069232C211yesmaximal, characteristic, complemented
5#13069226C211yesmaximal, characteristic, complemented
6#13069225C211yesmaximal, characteristic, complemented
7#13069219C211yesmaximal, characteristic, complemented
8#13069180C211yesmaximal, characteristic, complemented
9#13069180C211yesmaximal, characteristic, complemented
10#13068909C211yesmaximal, characteristic
11#13068793C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068594C211yesmaximal, characteristic, complemented
14#13068594C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66988C411yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26#10622833C411yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622591C411yescharacteristic
42#10622591C411yescharacteristic
43#10622559C411yescharacteristic
44#10622557C411yescharacteristic
45#10622557C411yescharacteristic
46#10622556C411yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2×C411yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80#66988—24no—
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×C4×Dic11—41no—
86C2×C4×Dic11—41no—
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8—41no—
94C22×C11⋊C8—41no—
95C22×C11⋊C8—41no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C11×C4⋊C8—41no—
101C11×C22⋊C8—41no—
102C11×C22⋊C8—41no—
103C11×C22⋊C8—41no—
104C11×C22⋊C8—41no—
105C11×#97—41no—
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C11⋊#95C2×C411yescharacteristic
116C22⋊(C11⋊C8)—41no—
117C22⋊(C11⋊C8)—41no—
118C22⋊(C11⋊C8)—41no—
119#66879—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124Dic11⋊C8—41no—
125Dic11⋊C8—41no—
126C8×Dic11—41no—
127#23318—111nomaximal, Sylow
128C24×C11C22×C411yescharacteristic
129C24×C11C22×C411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—41no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—22no—
182C22⋊Dic11—22no—
183C22⋊Dic11—22no—
184C22⋊Dic11—22no—
185C22⋊Dic11—41no—
186C22⋊Dic11M1614yes—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—41no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—41no—
200C4×Dic11—41no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—44no—
214C4×#123—111no—
215#1955D1111yescharacteristic
216#1940—111no—
217#1939—111no—
218#1924—111no—
219#1924—111no—
220#1923—111no—
221#1923—111no—
222#1917—111no—
223#1917—111no—
224#1869—111no—
225#1850—111no—
226#1850—111no—
227#1797—111no—
228#1797—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11C2×M1612yes—
242C23×C11#13112yes—
243C23×C11C23×C411yescharacteristic
244D4×C11—44no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—44no—
293C2×Dic11—44no—
294C2×Dic11C2×M1612yes—
295C2×Dic11C2×M1612yes—
296C2×Dic11#13112yes—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C23×C8—111no—
306C2×#123—111no—
307C2×C4×D4C2×D1111yescharacteristic
308C22×C42—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8C2×D1111yescharacteristic
320C2×C22⋊C8C2×D1111yescharacteristic
321C2×C22⋊C8C2×D1111yescharacteristic
322C2×C22⋊C8C2×D1111yescharacteristic
323C2×#97—111no—
324C2×#97C2×D1111yescharacteristic
325C2×C4×C8—111no—
326#388—111no—
327#388—111no—
328#387—111no—
329#387—111no—
330#386—111no—
331#385—111no—
332#381—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—111no—
336C4×C22⋊C4—111no—
337C4×C22⋊C4—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11#51811yescharacteristic
363C22×C11#52011yescharacteristic
364C22×C11#52011yescharacteristic
365C22×C11C22×M1611yescharacteristic
366C22×C11C2×#13111yescharacteristic
367C22×C11C2×#13111yescharacteristic
368C22×C11#56811yescharacteristic
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11#56011yescharacteristic
374C4×C11#56211yescharacteristic
375C4×C11#56211yescharacteristic
376C4×C11#56311yescharacteristic
377Dic11—22no—
378Dic11—22no—
379Dic11—22no—
380Dic11—41no—
381Dic11—41no—
382Dic11—41no—
383Dic11—41no—
384Dic11—41no—
385C22×D4C4×D1111yescharacteristic
386C23×C4—111no—
387C23×C4—111no—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—441no—
395C22×C8—441no—
396C22×C8—441no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401#123—224no—
402C4×D4—41no—
403C4×D4—41no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4C4×D1111yescharacteristic
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—111no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4C4×D1111yescharacteristic
416C2×C22⋊C4C4×D1111yescharacteristic
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—441no—
424C2×C42—441no—
425C2×C42C22×D1111yescharacteristic
426C4⋊C8—41no—
427C4⋊C8—441no—
428C4⋊C8—441no—
429C4⋊C8—441no—
430C4⋊C8—441no—
431C4⋊C8—441no—
432C4⋊C8—441no—
433C22⋊C8—41no—
434C22⋊C8—41no—
435C22⋊C8—41no—
436C22⋊C8—41no—
437C22⋊C8—441no—
438C22⋊C8—441no—
439C22⋊C8—441no—
440#97—41no—
441#97—441no—
442C4×C8—441no—
443#95—111no—
444#95—111no—
445#95—111no—
446#95—111no—
447#95—111no—
448#95—111no—
449#95—111no—
450#95—111no—
451#95—111no—
452#95—111no—
453C2×C11—42no—
454C2×C11—42no—
455C2×C11#237611yescharacteristic
456C2×C11#297411yescharacteristic
457C2×C11#297611yescharacteristic
458C2×C11#298911yescharacteristic
459C2×C11#299011yescharacteristic
460C2×C11#299211yescharacteristic
461C2×C11#299411yescharacteristic
462C24C2×C4×D1111yescharacteristic
463C24C2×C4×D1111yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—441no—
491C22×C4—441no—
492C22×C4—441no—
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—444no—
523C4⋊C4—41no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—441no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—114no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—441no—
536C42—21no—
537C42—21no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—441no—
547C42—441no—
548C11#2331811yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23M16×D1112yes—
562C23#6696012yes—
563C23C22×C4×D1111yescharacteristic
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—444no—
610C2×C4—444no—
611C2×C4#6703711yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#6703711yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#6704311yescharacteristic
616C2×C4#6704311yescharacteristic
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22#1062301711yescharacteristic
640C22#1062307711yescharacteristic
641C22#1062307711yescharacteristic
642C22C2×M16×D1111yescharacteristic
643C22C2×#6696011yescharacteristic
644C22D11×#13111yescharacteristic
645C22#1062328111yescharacteristic
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—222no—
651C4—222no—
652C4—222no—
653C4—441no—
654C4—441no—
655C4—441no—
656C4—441no—
657C4—441no—
658C4#1062315211yescharacteristic
659C4#1062315211yescharacteristic
660C4#1062320311yescharacteristic
661C4#1062325111yescharacteristic
662C2—42no—
663C2—42no—
664C2#1307176611yescharacteristic
665C2#1307765211yescharacteristic
666C2#1307765911yescharacteristic
667C2#1307772811yescharacteristic
668C2#1307773611yescharacteristic
669C2#1307775611yescharacteristic
670C2#1307776911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#23318
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13069336C2semidirect
3. #13069331C2semidirect
4. #13069232C2semidirect
5. #13069226C2semidirect
6. #13069225C2semidirect
7. #13069219C2semidirect
8. #13069180C2semidirect
9. #13069180C2semidirect
11. #13068793C2semidirect
12. #13068793C2semidirect
13. #13068594C2semidirect
14. #13068594C2semidirect
548. C11#23318semidirect

Maximal subgroups

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

subgroupindex
C4×#669882
#130693362
#130693312
#130692322
#130692262
#130692252
#130692192
#130691802
#130689092
#130687932
#130685942
C11×#19552
#2331811