Finite Group Databasebeta

← #14666371

Subgroups — #14666371

Order 2816.

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

normal subgroups only

This group has 360 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#13076889C211yesmaximal, characteristic, complemented
2#13069842C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066643C211yesmaximal, characteristic, complemented
6#13066559C211yesmaximal, characteristic, complemented
7C11×#1616C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#481—21no—
10C11×#400C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622647—21no—
14#10622599C2211yescharacteristic
15#10622592—21no—
16#10622590C2211yescharacteristic
17#10622272—21no—
18#10622271—21no—
19#10622269—21no—
20#10622269—21no—
21#10622263—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11D411yescharacteristic
42C2×#4318—21no—
43C11×#106—41no—
44C11×#102—41no—
45C11×C22⋊C8—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95D411yescharacteristic
49#66901—42no—
50#66899—41no—
51#66896—41no—
52#66896—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66872—41no—
63#12185—111nomaximal, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×Dic22—81no—
84C2×Dic22—81no—
85C2×Dic22—81no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—81no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C4×Dic11—21no—
100C4×Dic11SD1612yes—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2844—111no—
106#2040—111no—
107#1616—111no—
108#1616D1111yescharacteristic
109#1353—111no—
110#1353—111no—
111#1324—111no—
112C23×C11—41no—
113C23×C11#12011yescharacteristic
114Q8×C11—41no—
115Q8×C11—41no—
116D4×C11—41no—
117D4×C11—41no—
118D4×C11—81no—
119D4×C11—81no—
120D4×C11—81no—
121D4×C11—81no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
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—81no—
136C2×C4×C11—81no—
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—22no—
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—
149C2×Dic11—41no—
150C2×Dic11—41no—
151Dic22—84no—
152C8×C11—81no—
153C11⋊C8—81no—
154C11⋊C8—81no—
155#537C2×D1111yescharacteristic
156#481—21no—
157#481—221no—
158C2×#104—221no—
159#417—221no—
160#400—111no—
161#400—221no—
162#400—221no—
163#400C2×D1111yescharacteristic
164#395—221no—
165#395—221no—
166#395—221no—
167#382—111no—
168#382—221no—
169#343—111no—
170#327—21no—
171#327—221no—
172#324—111no—
173#324C2×D1111yescharacteristic
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11#44811yescharacteristic
180C22×C11#45411yescharacteristic
181C22×C11B(4,𝔽2)11yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—81no—
189Dic11—42no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193C2×#41—21no—
194C22×Q8—221no—
195C2×M16—221no—
196C22⋊Q8—41no—
197#121—21no—
198#121—21no—
199#121—41no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4C22⋊D1111yescharacteristic
207C2×C4⋊C4C22×D1111yescharacteristic
208C2×C42—111no—
209#106—41no—
210#106—441no—
211#104—442no—
212#103—441no—
213#102—41no—
214#102—441no—
215#102—441no—
216C22⋊C8—21no—
217C22⋊C8—221no—
218#95—21no—
219#95—21no—
220#95—111no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95C22⋊D1111yescharacteristic
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—161no—
232C2×C11#159911yescharacteristic
233C2×C11#220111yescharacteristic
234C2×C11#220211yescharacteristic
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×Q8—881no—
241C2×Q8—881no—
242C2×Q8—881no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257M16—441no—
258M16—441no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—881no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—112no—
275C42—221no—
276C11#1218511yescharacteristic, complemented, Sylow
277C23—41no—
278C23#6699011yescharacteristic
279Q8—41no—
280Q8—41no—
281Q8—884no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286D4—81no—
287D4—81no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—222no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4SD16×D1111yescharacteristic
316C2×C4#6696811yescharacteristic
317C8—81no—
318C8—881no—
319C8—881no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#1062264511yescharacteristic
326C22#1062278311yescharacteristic
327C22#1062281411yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C4—442no—
336C4—881no—
337C4—881no—
338C4—881no—
339C2—21no—
340C2—21no—
341C2—161no—
342C2#1306755411yescharacteristic
343C2#1307062711yescharacteristic
344C2#1307063211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1616C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1616D11
hypocenterC11#12185
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1616

Complements

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

NH ≅ G/Ntype
1. #13076889C2semidirect
4. #13066644C2semidirect
5. #13066643C2semidirect
6. #13066559C2semidirect
276. C11#12185semidirect

Maximal subgroups

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

subgroupindex
#130768892
#130698422
#130676532
#130666442
#130666432
#130665592
C11×#16162
#1218511