Finite Group Databasebeta

← #14666958

Subgroups — #14666958

Order 2816.

362 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076763C211yesmaximal, characteristic
2#13069769C211yesmaximal, characteristic
3#13067590C211yesmaximal, characteristic, complemented
4#13066647C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic
7C11×#1611C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C11×#483—21no—
10C11×#398C2211yescharacteristic
11#10622663—21no—
12#10622614—21no—
13#10622607—21no—
14#10622604—21no—
15#10622601C2211yescharacteristic
16#10622594—21no—
17#10622592C2211yescharacteristic
18#10622288—21no—
19#10622287—21no—
20#10622286—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C11×C4⋊Q8—41no—
30C11×#125—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×#4326—41no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48C11×#106—41no—
49C11×#103—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95D411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66874—41no—
60#66873—41no—
61#66873—41no—
62#12276—111nomaximal, Sylow
63C23×D11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—41no—
78C2×Dic22—41no—
79C2×Dic22—81no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93#4326—82no—
94(C2×D11)⋊C4—81no—
95(C2×D11)⋊C4—81no—
96(C2×D11)⋊C4—81no—
97(C2×D11)⋊C4—81no—
98(C2×D11)⋊C4—81no—
99(C2×D11)⋊C4—81no—
100C4⋊Dic11—81no—
101Dic11⋊C4—81no—
102C4×Dic11—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2830—111no—
108#2027—111no—
109#1611D1111yescharacteristic, complemented
110#1605—111no—
111#1354—111no—
112#1346—111no—
113#1318—111no—
114C23×C11#12011yescharacteristic
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149D44—42no—
150D44—81no—
151Dic22—42no—
152Dic22—81no—
153C8×C11—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#544C2×D1111yescharacteristic
157#483—21no—
158#451—221no—
159#418—221no—
160#398C2×D1111yescharacteristic
161#397—221no—
162#397—221no—
163#396—221no—
164#395—111no—
165#394—221no—
166#393—221no—
167#390—111no—
168#387—221no—
169#343—111no—
170#339—221no—
171#328—21no—
172#328—221no—
173#324—111no—
174#324C2×D1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#45211yescharacteristic
178C22×C11#45511yescharacteristic
179C22×C11B(4,𝔽2)11yescharacteristic
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—111no—
199C22×D4—111no—
200C2×Q16—441no—
201C2×M16—221no—
202C4⋊Q8—41no—
203#125—41no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206#117—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C42—111no—
219#106—41no—
220#103—41no—
221#103—441no—
222#102—441no—
223#102—441no—
224C22⋊C8—21no—
225C22⋊C8—221no—
226#95—21no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95C22⋊D1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11#160611yescharacteristic
236C2×C11#220011yescharacteristic
237C2×C11#220311yescharacteristic
238D11—161no—
239C24—221no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—441no—
243C2×Q8—881no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—441no—
247C2×D4—441no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256Q16—882no—
257M16—441no—
258M16—441no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C22⋊C4—41no—
275C22⋊C4—881no—
276C22⋊C4—881no—
277C22⋊C4—881no—
278C22⋊C4—881no—
279C22⋊C4—881no—
280C22⋊C4—881no—
281C42—41no—
282C42—441no—
283C11#1227611yescharacteristic, complemented, Sylow
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23#6699011yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—442no—
295Q8—881no—
296D4—442no—
297D4—881no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4#6696811yescharacteristic
322C2×C4#6696911yescharacteristic
323C8—81no—
324C8—881no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—881no—
332C22—881no—
333C22—881no—
334C22—881no—
335C22#1062264511yescharacteristic
336C22#1062278611yescharacteristic
337C22#1062281511yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—881no—
347C4—881no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—1761no—
352C2#1306759311yescharacteristic
353C2#1307062011yescharacteristic
354C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1611C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#1611D11
hypocenterC11#12276
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
3. #13067590C2semidirect
4. #13066647C2semidirect
5. #13066622C2semidirect
7. C11×#1611C2semidirect
109. #1611D11semidirect
283. C11#12276semidirect

Maximal subgroups

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

subgroupindex
#130767632
#130697692
#130675902
#130666472
#130666222
#130665472
C11×#16112
#1227611