Finite Group Databasebeta

← #14655833

Subgroups — #14655833

Order 2816.

464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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#13078417C211yesmaximal, characteristic
2C2×#10622707C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067019C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#3230C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16#10622707—22no—
17#10622707—21no—
18#10622707—22no—
19#10622704—21no—
20#10622676—22no—
21#10622617—21no—
22#10622608—21no—
23C2×#66874—21no—
24C2×#66872—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622184—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622107—22no—
31C22×Q8×C11—21no—
32C22×Dic22D411yescharacteristic
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×#4318—21no—
52C22×C11⋊C8—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×#107—24no—
58C11×C4⋊C8—21no—
59C11×#103—24no—
60C11×C22⋊C8D412yes—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64#66874—22no—
65#66874—22no—
66#66872—24no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10191—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22Q1612yes—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114C4×Dic11—41no—
115C4×Dic11—41no—
116#4318—41no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#3230D1111yescharacteristic
124#3078—111no—
125C2×#475—111no—
126#1548—111no—
127#1481—111no—
128#1461—111no—
129#1301—111no—
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—82no—
134Q8×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×C4×C11C2×Q1611yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156Dic22—22no—
157Dic22—22no—
158Dic22—41no—
159Dic22—41no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#533C2×D1111yescharacteristic
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×C4×Q8—111no—
167#500—21no—
168#487—21no—
169#484—22no—
170#479—222no—
171#477—22no—
172#477—221no—
173#475—222no—
174#475—222no—
175#475—221no—
176#431—111no—
177#431C2×D1111yescharacteristic
178#428—221no—
179C2×#106—221no—
180#423—111no—
181C2×C4⋊C8—111no—
182#419—221no—
183C2×#103—221no—
184#333—222no—
185Q8⋊C8—222no—
186#324—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#39211yescharacteristic
190C22×C11#46711yescharacteristic
191C22×C11#47011yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11#45111yescharacteristic
199C4×C11#45111yescharacteristic
200C4×C11#45211yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#47112yes—
203Dic11—42no—
204Dic11—81no—
205C22×Q8—21no—
206C22×Q8—111no—
207C2×M16—221no—
208C22×C8—221no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8C22⋊D1112yes—
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215#125—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×Q8—221no—
224#117—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231#107—24no—
232#107—222no—
233#106—224no—
234#106—222no—
235C4⋊C8—21no—
236C4⋊C8—112no—
237C4⋊C8—112no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#103—24no—
242#103—224no—
243#103—222no—
244#103—222no—
245C22⋊C8—221no—
246C22⋊C8C22⋊D1112yes—
247C4×C8—21no—
248C4×C8—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#200111yescharacteristic
252C2×C11#200911yescharacteristic
253C2×C11#201911yescharacteristic
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—82no—
259C2×Q8—112no—
260C2×Q8—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C22×C4—41no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4D4×D1111yescharacteristic
269C22×C4#434111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—441no—
272M16—441no—
273C2×C8—22no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—41no—
294C42—41no—
295C42—441no—
296C42—441no—
297C42D4×D1111yescharacteristic
298C42D4×D1111yescharacteristic
299C42C2×C22⋊D1111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C11#1019111yescharacteristic, complemented, Sylow
302C23#6699111yescharacteristic
303Q8—42no—
304Q8—42no—
305Q8—82no—
306Q8—82no—
307Q8—222no—
308Q8—222no—
309Q8—441no—
310Q8—441no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—82no—
317C2×C4—222no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4Q16×D1111yescharacteristic
323C2×C4#6697111yescharacteristic
324C2×C4#6697111yescharacteristic
325C2×C4#6697211yescharacteristic
326C2×C4#6699011yescharacteristic
327C2×C4#6699011yescharacteristic
328C2×C4#6699211yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6699311yescharacteristic
331C2×C4#6700611yescharacteristic
332C8—42no—
333C8—442no—
334C8—442no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22#1062280111yescharacteristic
339C22#1062280211yescharacteristic
340C22#1062283611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—81no—
345C4—82no—
346C4—81no—
347C4—442no—
348C4—881no—
349C4#1062279911yescharacteristic
350C4#1062279911yescharacteristic
351C4#1062280011yescharacteristic
352C4#1062280011yescharacteristic
353C4#1062281312yes—
354C2—21no—
355C2—21no—
356C2#1306962311yescharacteristic
357C2#1306967611yescharacteristic
358C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3230D11
hypocenterC11#10191
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
301. C11#10191semidirect

Maximal subgroups

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

subgroupindex
#130784172
C2×#106227072
#130672972
#130670192
#130669392
#130665122
C11×#32302
#1019111