Finite Group Databasebeta

← #14646755

Subgroups — #14646755

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068654C211yesmaximal, characteristic, complemented
2#13068645C211yesmaximal, characteristic, complemented
3#13067159C212yesmaximal
4#13066521C212yesmaximal, complemented
5C11×#2929C211yesmaximal, characteristic
6C2×C11×#131C411yescharacteristic, complemented
7C23×C8×C11C2211yescharacteristic
8C11×#525C2211yescharacteristic
9C11×#435—21no—
10C11×#435—21no—
11C8×D4×C11—21no—
12C8×D4×C11—21no—
13C11×#424C411yescharacteristic, complemented
14C11×#408C411yescharacteristic, complemented
15C11×#407C2211yescharacteristic
16C11×#405C411yescharacteristic, complemented
17#10622825C2212yes—
18#10622820C2212yes—
19C2×#66883—21no—
20C2×#66882—21no—
21#10622190—21no—
22#10622189—21no—
23#10622176—22no—
24#10622175—22no—
25C2×C11×#41C2×C411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C11×#131—42no—
28C2×C11×M16—21no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16C2×C411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—42no—
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11C2×C411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C11×#123—21no—
40C11×C22⋊Q8D411yescharacteristic
41C11×C22⋊Q8Q811yescharacteristic
42C11×#121D411yescharacteristic
43C11×#121Q811yescharacteristic
44C11×#120—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C11×#117C2×C411yescharacteristic
48C2×C22⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×#4318—22no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62#66883—42no—
63#66882—42no—
64#8628—111nomaximal, Sylow
65C24×C11#4111yescharacteristic
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11C4⋊C411yescharacteristic
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11C4⋊C411yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×Q811yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—42no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—42no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C2×C8×C11C22⋊C411yescharacteristic
96C2×C8×C11C22⋊C411yescharacteristic
97C2×C8×C11C22⋊C411yescharacteristic
98C2×C8×C11C22⋊C411yescharacteristic
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4C4⋊C411yescharacteristic
102C11×C4⋊C4C4⋊C411yescharacteristic
103C11×C22⋊C4—21no—
104C11×C22⋊C4—21no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C42×C11—21no—
109C22⋊Dic11—82no—
110C4⋊Dic11—42no—
111C4⋊Dic11—42no—
112#4318—42no—
113#4318—42no—
114C2×C11⋊C8—42no—
115#2929D1111yescharacteristic
116#1810—111no—
117#1808—111no—
118#1513—112no—
119#1305—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#11711yescharacteristic
126C23×C11#12111yescharacteristic
127C23×C11C22⋊Q811yescharacteristic
128Q8×C11—41no—
129D4×C11—41no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—41no—
133D4×C11—41no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C2×C4⋊C411yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11C22⋊Q811yescharacteristic
152C2×Dic11—82no—
153C2×Dic11—82no—
154C2×Dic11—82no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C8×C11—41no—
159C8×C11—41no—
160C8×C11#9912yes—
161C11⋊C8—82no—
162C2×#131Dic1111yescharacteristic, complemented
163C23×C8C2×D1111yescharacteristic
164#525C2×D1111yescharacteristic
165#435—21no—
166#435—21no—
167C8×D4—21no—
168C8×D4—21no—
169C2×#108—221no—
170C2×#107—221no—
171#424Dic1111yescharacteristic, complemented
172#408Dic1111yescharacteristic, complemented
173#407—112no—
174#407C2×D1111yescharacteristic
175#405Dic1111yescharacteristic, complemented
176#380—112no—
177#341—221no—
178#340—221no—
179#328—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#38011yescharacteristic
195C22×C11#47211yescharacteristic
196C22×C11#47311yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11C2×#9911yescharacteristic
204C4×C11#41011yescharacteristic
205Dic11—162no—
206C2×#41C2×Dic1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208#131—42no—
209C2×M16—21no—
210C2×M16—222no—
211C2×M16C2×Dic1111yescharacteristic
212C2×M16C2×Dic1111yescharacteristic
213C22×C8—21no—
214C22×C8—42no—
215C22×C8C2×Dic1111yescharacteristic
216C22×C8C2×Dic1111yescharacteristic
217C22×C8C22⋊D1111yescharacteristic
218C22×C8C22⋊D1111yescharacteristic
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22⋊D1111yescharacteristic
221#123—21no—
222C22⋊Q8Dic2211yescharacteristic
223C22⋊Q8D4411yescharacteristic
224#121Dic2211yescharacteristic
225#121D4411yescharacteristic
226#120—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117C2×Dic1111yescharacteristic
230C2×C4⋊C4—222no—
231C2×C22⋊C4—222no—
232#108—442no—
233#107—442no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C22⋊C8—222no—
241C22⋊C8—222no—
242#97—21no—
243C4×C8—21no—
244#95—222no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—41no—
248C2×C11—41no—
249C2×C11—81no—
250C2×C11#179911yescharacteristic
251C2×C11#181411yescharacteristic
252C2×C11#181611yescharacteristic
253C24#433911yescharacteristic
254#41—41no—
255#41—41no—
256C2×Q8C4⋊Dic1111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C4⋊Dic1111yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—442no—
265C22×C4C2×Dic2211yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4#433911yescharacteristic
268C22×C4C22×Dic1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—42no—
272M16—41no—
273M16—41no—
274M16—442no—
275M16—442no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—442no—
286C2×C8C22⋊Dic1111yescharacteristic
287C2×C8C22⋊Dic1111yescharacteristic
288C2×C8C22⋊Dic1111yescharacteristic
289C2×C8C22⋊Dic1111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C4⋊C4C4⋊Dic1111yescharacteristic
295C4⋊C4C4⋊Dic1111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—882no—
302C42—21no—
303C11#862811yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23#6697711yescharacteristic
310C23#6697911yescharacteristic
311C23#6698311yescharacteristic
312Q8—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4#6697711yescharacteristic
336C2×C4C2×C4⋊Dic1111yescharacteristic
337C2×C4#6698311yescharacteristic
338C2×C4C2×C22⋊Dic1111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—41no—
343C8—41no—
344C8—882no—
345C8#6689812yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22#1062275511yescharacteristic
360C22#1062275611yescharacteristic
361C22#1062282511yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—1762no—
369C4C2×#6689811yescharacteristic
370C4#1062285311yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—81no—
376C2#1306860411yescharacteristic
377C2#1306867011yescharacteristic
378C2#1306868011yescharacteristic
subgroupG/H
centerC22#10622825
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2929C2
socleC22×C11#380
prime radicalC11×#525C22
cosocleC23×C4×C11C23
hypercenter#2929D11
hypocenterC11#8628
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13068654C2semidirect
2. #13068645C2semidirect
4. #13066521C2semidirect
6. C2×C11×#131C4semidirect
13. C11×#424C4semidirect
14. C11×#408C4semidirect
16. C11×#405C4semidirect
162. C2×#131Dic11semidirect
171. #424Dic11semidirect
172. #408Dic11semidirect
175. #405Dic11semidirect
303. C11#8628semidirect

Maximal subgroups

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

subgroupindex
#130686542
#130686452
#130671592
#130665212
C11×#29292
#862811