Finite Group Databasebeta

← #14666183

Subgroups — #14666183

Order 2816.

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

normal subgroups only

This group has 424 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#13073985C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic
3#13067619C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#66940—21no—
10C11×#480—21no—
11C11×#398C2211yescharacteristic
12C2×#66901—21no—
13#10622845—21no—
14#10622646—21no—
15#10622597—21no—
16#10622596C2211yescharacteristic
17#10622589C2211yescharacteristic
18#10622585—21no—
19#10622260—21no—
20#10622259—21no—
21#10622259—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⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47#66940—42no—
48#66940—42no—
49C11×#107—41no—
50C11×#102—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54#66901—42no—
55#66899—41no—
56#66896—41no—
57#66896—41no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66871—41no—
65#12153—111nomaximal, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—24no—
86C2×Dic22—42no—
87C2×Dic22—42no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99Dic11⋊C4—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—81no—
105C4×Dic11—21no—
106C4×Dic11—42no—
107C4×Dic11—42no—
108C4×Dic11D812yes—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2582—111no—
114#2039—111no—
115#1610—111no—
116#1610D1111yescharacteristic
117#1346—111no—
118#1346—111no—
119#1325—111no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122Q8×C11—41no—
123Q8×C11—41no—
124D4×C11—41no—
125D4×C11—41no—
126D4×C11—81no—
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
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×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159Dic22—48no—
160C8×C11—81no—
161C11⋊C8—81no—
162C11⋊C8—81no—
163#537C2×D1111yescharacteristic
164C2×C4×Q8—221no—
165#480—21no—
166#480—221no—
167C2×#104—221no—
168#417—221no—
169#398—111no—
170#398—221no—
171#398C2×D1111yescharacteristic
172#391—221no—
173#391—221no—
174#389—221no—
175#389—221no—
176#384—111no—
177#343—111no—
178#327—21no—
179#327—221no—
180#324—111no—
181#324C2×D1111yescharacteristic
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#44711yescharacteristic
188C22×C11#45411yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—42no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—24no—
198Dic11—42no—
199Dic11—81no—
200Dic11—81no—
201C2×#41—21no—
202C22×Q8—221no—
203C2×M16—221no—
204C22⋊Q8—41no—
205#121—21no—
206#121—21no—
207#121—41no—
208C4×Q8—442no—
209C4×Q8—442no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4C22⋊D1111yescharacteristic
219C2×C4⋊C4C22×D1111yescharacteristic
220C2×C42—111no—
221C2×C42—221no—
222C2×C42—221no—
223#107—41no—
224#107—441no—
225#104—442no—
226#103—441no—
227#102—41no—
228#102—441no—
229#102—441no—
230C22⋊C8—21no—
231C22⋊C8—221no—
232#95—21no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95C22⋊D1111yescharacteristic
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—161no—
242C2×C11#159811yescharacteristic
243C2×C11#219811yescharacteristic
244C2×C11#220511yescharacteristic
245#41—41no—
246#41—41no—
247#41—41no—
248#41—41no—
249C2×Q8—21no—
250C2×Q8—224no—
251C2×Q8—442no—
252C2×Q8—442no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267M16—441no—
268M16—441no—
269C2×C8—41no—
270C2×C8—441no—
271C2×C8—441no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—881no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C42—112no—
289C42—221no—
290C42—442no—
291C42—442no—
292C11#1215311yescharacteristic, complemented, Sylow
293C23—41no—
294C23#6699011yescharacteristic
295Q8—41no—
296Q8—41no—
297Q8—448no—
298D4—41no—
299D4—41no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4D8×D1111yescharacteristic
332C2×C4#6696411yescharacteristic
333C8—81no—
334C8—881no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1062264511yescharacteristic
342C22#1062276911yescharacteristic
343C22#1062281411yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—224no—
352C4—442no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1306754911yescharacteristic
359C2#1307061011yescharacteristic
360C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1610D11
hypocenterC11#12153
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13073985C2semidirect
4. #13066623C2semidirect
5. #13066622C2semidirect
6. #13066561C2semidirect
292. C11#12153semidirect

Maximal subgroups

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

subgroupindex
#130739852
#130698372
#130676192
#130666232
#130666222
#130665612
C11×#16102
#1215311