Finite Group Databasebeta

← #14666607

Subgroups — #14666607

Order 2816.

394 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076319C211yesmaximal, characteristic
2#13069769C211yesmaximal, characteristic
3#13067658C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066644C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic
7C11×#1605C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C11×#451—21no—
10C11×#395C2211yescharacteristic
11#10622844—21no—
12#10622657—21no—
13#10622614—21no—
14#10622607—21no—
15#10622601C2211yescharacteristic
16#10622600—21no—
17#10622599C2211yescharacteristic
18#10622281—21no—
19#10622278—21no—
20#10622268—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×Q16—41no—
31C11×C4⋊Q8—41no—
32C11×#125—41no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2311yescharacteristic
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×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48C11×#103—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52#66899—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66873—41no—
60#66873—41no—
61#66871—41no—
62#12223—111nomaximal, Sylow
63C23×D11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—21no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44Q1612yescomplemented
80C2×C4×D11—42no—
81C2×C4×D11—81no—
82C2×C4×D11—81no—
83C11×Q16—82no—
84C2×C8×C11—41no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—81no—
97(C2×D11)⋊C4—81no—
98(C2×D11)⋊C4—81no—
99(C2×D11)⋊C4—81no—
100C4⋊Dic11—41no—
101C4⋊Dic11—81no—
102Dic11⋊C4—42no—
103C4×Dic11—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2784—111no—
109#2027—111no—
110#1617—111no—
111#1605D1111yescharacteristic, complemented
112#1354—111no—
113#1353—111no—
114#1318—111no—
115C23×C11#12011yescharacteristic
116C22×D11—22no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
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—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152D44—42no—
153D44—81no—
154C4×D11—84no—
155C8×C11—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158#544C2×D1111yescharacteristic
159#484—221no—
160#451—21no—
161#418—221no—
162#400—111no—
163#396—221no—
164#395C2×D1111yescharacteristic
165#393—221no—
166#390—111no—
167#387—221no—
168#386—221no—
169#385—221no—
170#380—221no—
171#343—111no—
172#339—221no—
173#328—21no—
174#328—221no—
175#324—111no—
176#324C2×D1111yescharacteristic
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#45111yescharacteristic
180C22×C11#45511yescharacteristic
181C22×C11B(4,𝔽2)11yescharacteristic
182C2×D11—42no—
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×Q8C22⋊D1111yescharacteristic
201C22×D4—111no—
202C23×C4—221no—
203C2×Q16—41no—
204C2×M16—221no—
205C4⋊Q8—41no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C42—111no—
221#107—441no—
222#103—41no—
223#103—441no—
224#102—441no—
225#102—441no—
226C22⋊C8—21no—
227C22⋊C8—221no—
228#95—21no—
229#95—111no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95C22⋊D1111yescharacteristic
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#160211yescharacteristic
238C2×C11#220011yescharacteristic
239C2×C11#220411yescharacteristic
240D11—82no—
241C24—221no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—81no—
246C2×D4—112no—
247C2×D4—221no—
248C2×D4—441no—
249C2×D4—441no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—442no—
256C22×C4—881no—
257C22×C4—881no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261Q16—82no—
262M16—441no—
263M16—441no—
264C2×C8—41no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4—881no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—881no—
281C22⋊C4—881no—
282C22⋊C4—881no—
283C22⋊C4—881no—
284C42—41no—
285C42—441no—
286C11#1222311yescharacteristic, complemented, Sylow
287C23—222no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23#6699011yescharacteristic
295Q8—42no—
296Q8—81no—
297Q8—81no—
298Q8—81no—
299D4—442no—
300D4—881no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—884no—
325C2×C4Q16×D1111yescharacteristic
326C2×C4#6697111yescharacteristic
327C8—81no—
328C8—881no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—442no—
333C22—442no—
334C22—442no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22#1062264511yescharacteristic
340C22#1062279911yescharacteristic
341C22#1062281511yescharacteristic
342C4—21no—
343C4—21no—
344C4—42no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—881no—
351C4—881no—
352C4—881no—
353C2—21no—
354C2—21no—
355C2—882no—
356C2#1306757111yescharacteristic
357C2#1307062111yescharacteristic
358C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1605C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#1605D11
hypocenterC11#12223
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1605

Complements

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

NH ≅ G/Ntype
3. #13067658C2semidirect
4. #13066646C2semidirect
5. #13066644C2semidirect
7. C11×#1605C2semidirect
79. C2×D44Q16semidirect
111. #1605D11semidirect
286. C11#12223semidirect

Maximal subgroups

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

subgroupindex
#130763192
#130697692
#130676582
#130666462
#130666442
#130665472
C11×#16052
#1222311