Finite Group Databasebeta

← #14670575

Subgroups — #14670575

Order 2816.

580 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071791C211yesmaximal, characteristic
2C2×#10622112C211yesmaximal, characteristic
3#13069014C211yesmaximal, characteristic
4#13068897C211yesmaximal, characteristic, complemented
5#13066734C211yesmaximal, characteristic, complemented
6#13066733C211yesmaximal, characteristic, complemented
7C11×#1867C211yesmaximal, characteristic, complemented
8C11×#518C2211yescharacteristic
9C2×#66993C2211yescharacteristic
10C2×C11×#99C2211yescharacteristic
11C11×#386C2211yescharacteristic
12C11×#385—21no—
13#10622833C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66897C2211yescharacteristic
16#10622826—21no—
17#10622614—21no—
18#10622571—21no—
19#10622569—21no—
20#10622569—21no—
21#10622559—21no—
22#10622278—21no—
23#10622264—21no—
24C11×#342—21no—
25#10622170—21no—
26#10622164—21no—
27#10622112C414yescomplemented
28C22×D4×C11C2311yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C22×C22⋊D11—21no—
32C23×Dic11D411yescharacteristic
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C4×D4×C11—41no—
36C4×D4×C11—41no—
37C11×#117—21no—
38C2×C11×C4⋊C4—41no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D411yescharacteristic
47#66993—21no—
48#66993—21no—
49#66993C2×C412yes—
50#66993Q812yes—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×Dic11⋊C4—41no—
55C2×C4×Dic11D411yescharacteristic
56C2×#4318—21no—
57C11×#99—21no—
58C11×#99C2×C412yescomplemented
59C11×#95—21no—
60C11×#95—41no—
61#66898—21no—
62#66898C2×C412yescomplemented
63#66897—21no—
64#66897—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—41no—
71#66873—41no—
72#66873—41no—
73#12966—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11C22×C411yescharacteristic
80C2×D4×C11C2×Q811yescharacteristic
81C2×D4×C11#4111yescharacteristic
82C2×D4×C11#4111yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—81no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—22no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—22no—
96C2×C22⋊D11—22no—
97C2×C22⋊D11—81no—
98C2×C22⋊D11—81no—
99C2×C22⋊D11—81no—
100C2×C22⋊D11—81no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—81no—
107C2×D44—21no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44C4⋊C412yescomplemented
111C2×C4×D11—81no—
112C2×C4×D11—81no—
113C2×C4×D11—81no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—82no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—81no—
124C42×C11—41no—
125C22⋊Dic11—22no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—81no—
129(C2×D11)⋊C4—81no—
130(C2×D11)⋊C4—81no—
131(C2×D11)⋊C4—81no—
132Dic11⋊C4—82no—
133C4×Dic11—21no—
134C4×Dic11C4⋊C412yescomplemented
135#4318—41no—
136#4318—41no—
137C2×C11⋊C8—41no—
138#2380—111no—
139C2×#353—111no—
140#1887—111no—
141#1867—111no—
142#1867D1111yescharacteristic, complemented
143#1390—111no—
144#1390—111no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11C4×D411yescharacteristic
154C23×C11C4×D411yescharacteristic
155C23×C11#12011yescharacteristic
156C23×C11C22⋊Q811yescharacteristic
157C23×C11C22⋊Q811yescharacteristic
158C22×D11—22no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11C2×C4⋊C411yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C22⋊D11—82no—
191C22⋊D11—82no—
192C22⋊D11—82no—
193C22⋊D11—82no—
194C2×Dic11—22no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208D44—42no—
209D44—81no—
210C4×D11—84no—
211C11⋊C8—81no—
212C2×#127—111no—
213#518C2×D1111yescharacteristic
214#418—221no—
215C2×#100—111no—
216C2×#99—111no—
217C2×#99C2×D1111yescharacteristic
218#386—111no—
219#386—221no—
220#386—221no—
221#386—221no—
222#386—221no—
223#386—221no—
224#386C2×D1111yescharacteristic
225#385—21no—
226#385—221no—
227#383—221no—
228#353—114no—
229#342—21no—
230#342—221no—
231#339—221no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11#38511yescharacteristic
249C22×C11B(4,𝔽2)11yescharacteristic
250C22×C11#45811yescharacteristic
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11—81no—
265Dic11—42no—
266Dic11—81no—
267Dic11—82no—
268Dic11—81no—
269C22×D4—111no—
270C22×D4—221no—
271C22×D4—221no—
272C22×D4C22×D1111yescharacteristic
273C23×C4—111no—
274C23×C4—221no—
275C23×C4C22⋊D1111yescharacteristic
276C2×M16—221no—
277#127—112no—
278#127—112no—
279#127—221no—
280#127—221no—
281C4×D4—41no—
282C4×D4—41no—
283#117—21no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—441no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4C22⋊D1111yescharacteristic
297C2×C42—111no—
298#102—441no—
299#102—441no—
300#100—221no—
301#100—221no—
302#99—21no—
303#99—112no—
304#99—221no—
305#99C4×D1112yescomplemented
306#95—21no—
307#95—41no—
308#95—221no—
309#95—221no—
310#95—221no—
311#95—221no—
312#95—221no—
313#95—441no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—41no—
317C2×C11—41no—
318C2×C11—41no—
319C2×C11—41no—
320C2×C11#186711yescharacteristic
321C2×C11#220011yescharacteristic
322C2×C11#220011yescharacteristic
323D11—82no—
324C24—221no—
325C24D4×D1111yescharacteristic
326C24C2×C22⋊D1111yescharacteristic
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—112no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—881no—
338C2×D4—881no—
339C2×D4—881no—
340C2×D4—881no—
341C2×D4C2×C4×D1111yescharacteristic
342C2×D4#433911yescharacteristic
343C2×D4Q8×D1111yescharacteristic
344C2×D4#434311yescharacteristic
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—81no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—881no—
360C22×C4—881no—
361C22×C4—881no—
362C22×C4—881no—
363C22×C4D4×D1111yescharacteristic
364M16—441no—
365M16—441no—
366C2×C8—441no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—82no—
370C4⋊C4—882no—
371C22⋊C4—22no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—81no—
378C22⋊C4—222no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—881no—
382C22⋊C4—881no—
383C22⋊C4—881no—
384C22⋊C4—881no—
385C42—41no—
386C42—112no—
387C42—221no—
388C11#1296611yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—222no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23#6694611yescharacteristic
405C23#6694911yescharacteristic
406C23C4×C22⋊D1111yescharacteristic
407C23#6699011yescharacteristic
408C23#6699911yescharacteristic
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—442no—
414D4—881no—
415D4—882no—
416D4—882no—
417D4—882no—
418D4—882no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—222no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—884no—
450C2×C4—881no—
451C2×C4—881no—
452C2×C4—881no—
453C2×C4C4⋊C4×D1111yescharacteristic
454C2×C4#6694711yescharacteristic
455C8—881no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—81no—
471C22—81no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22—881no—
479C22#1062260211yescharacteristic
480C22#1062264511yescharacteristic
481C22#1062266611yescharacteristic
482C4—21no—
483C4—21no—
484C4—81no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—442no—
490C4—881no—
491C4—882no—
492C4—881no—
493C2—21no—
494C2—21no—
495C2—41no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—882no—
500C2#1306889511yescharacteristic
501C2#1307062011yescharacteristic
502C2#1307062111yescharacteristic
subgroupG/H
centerC22#10622645
commutatorC2×D4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1867C2
socleC22×C11B(4,𝔽2)
prime radicalC2×#66993C22
cosocleC22×D4×C11C23
hypercenter#1867D11
hypocenterC11#12966
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1867

Complements

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

NH ≅ G/Ntype
4. #13068897C2semidirect
5. #13066734C2semidirect
6. #13066733C2semidirect
7. C11×#1867C2semidirect
27. #10622112C4semidirect
58. C11×#99C2×C4semidirect
62. #66898C2×C4semidirect
110. C2×D44C4⋊C4semidirect
134. C4×Dic11C4⋊C4semidirect
142. #1867D11semidirect
305. #99C4×D11semidirect
388. C11#12966semidirect

Maximal subgroups

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

subgroupindex
#130717912
C2×#106221122
#130690142
#130688972
#130667342
#130667332
C11×#18672
#1296611