Finite Group Databasebeta

← #14655777

Subgroups — #14655777

Order 2816.

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

normal subgroups only

This group has 476 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×#10622704C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic
4#13067019C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#3209C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#494—21no—
12C11×#487—21no—
13C11×#462—22no—
14C11×#451—22no—
15C11×#431C2211yescharacteristic
16#10622707—21no—
17#10622704—22no—
18#10622704—21no—
19#10622704—22no—
20#10622676—22no—
21#10622617—21no—
22#10622608—21no—
23C2×#66874—21no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622185—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622107—22no—
31C22×Q8×C11—21no—
32C22×Dic22D411yescharacteristic
33C2×C11×Q16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
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—22no—
67#66871—24no—
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#10183—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
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×Dic22Q1612yescomplemented
93C11×Q16—84no—
94C2×C8×C11—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#3209D1111yescharacteristic
125#3078—111no—
126C2×#477—111no—
127#1549—111no—
128#1481—111no—
129#1461—111no—
130#1301—111no—
131C23×C11#12111yescharacteristic
132Q8×C11—42no—
133Q8×C11—44no—
134Q8×C11—42no—
135Q8×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—81no—
157Dic22—22no—
158Dic22—22no—
159Dic22—41no—
160Dic22—41no—
161C8×C11—42no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165#533C2×D1111yescharacteristic
166C2×C4⋊Q8C2×D1111yescharacteristic
167C2×C4×Q8—111no—
168#494—21no—
169#487—21no—
170#479—222no—
171#477—222no—
172#477—222no—
173#477—221no—
174#475—221no—
175#462—22no—
176#451—22no—
177#431—111no—
178#431C2×D1111yescharacteristic
179#428—221no—
180C2×#107—221no—
181#423—111no—
182C2×C4⋊C8—111no—
183#419—221no—
184C2×#103—221no—
185#332—222no—
186Q8⋊C8—222no—
187#324—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#39211yescharacteristic
191C22×C11#46711yescharacteristic
192C22×C11#47011yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#45111yescharacteristic
200C4×C11#45111yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#45211yescharacteristic
203C4×C11#47312yes—
204Dic11—42no—
205Dic11—81no—
206C22×Q8—21no—
207C22×Q8—111no—
208C2×Q16—24no—
209C2×M16—221no—
210C22×C8—221no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8C22⋊D1112yes—
215C4⋊Q8C22⋊D1111yescharacteristic
216C4⋊Q8C22⋊D1111yescharacteristic
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—221no—
223C4×Q8—221no—
224C4×Q8—221no—
225C4×Q8—221no—
226#117—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233#107—224no—
234#107—222no—
235#106—222no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242#103—24no—
243#103—224no—
244#103—222no—
245#103—222no—
246C22⋊C8—221no—
247C22⋊C8C22⋊D1112yes—
248C4×C8—21no—
249C4×C8—221no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#200111yescharacteristic
253C2×C11#200811yescharacteristic
254C2×C11#202011yescharacteristic
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—21no—
258C2×Q8—41no—
259C2×Q8—82no—
260C2×Q8—112no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—221no—
266C22×C4—41no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4D4×D1111yescharacteristic
270C22×C4#434111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—84no—
273M16—441no—
274M16—441no—
275C2×C8—22no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C22⋊C4—41no—
296C42—41no—
297C42—441no—
298C42—441no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1018311yescharacteristic, complemented, Sylow
304C23#6699111yescharacteristic
305Q8—42no—
306Q8—44no—
307Q8—42no—
308Q8—82no—
309Q8—222no—
310Q8—222no—
311Q8—441no—
312Q8—441no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—222no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4Q16×D1111yescharacteristic
325C2×C4#6697111yescharacteristic
326C2×C4#6697111yescharacteristic
327C2×C4#6697211yescharacteristic
328C2×C4#6699011yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6699311yescharacteristic
333C2×C4#6700611yescharacteristic
334C8—42no—
335C8—442no—
336C8—442no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22#1062280111yescharacteristic
341C22#1062280211yescharacteristic
342C22#1062283611yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—82no—
347C4—81no—
348C4—81no—
349C4—442no—
350C4—881no—
351C4#1062279911yescharacteristic
352C4#1062279911yescharacteristic
353C4#1062280011yescharacteristic
354C4#1062280011yescharacteristic
355C4#1062281712yes—
356C2—21no—
357C2—21no—
358C2#1306962311yescharacteristic
359C2#1306966911yescharacteristic
360C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3209C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3209D11
hypocenterC11#10183
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
92. C2×Dic22Q16semidirect
303. C11#10183semidirect

Maximal subgroups

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

subgroupindex
#130784172
C2×#106227042
#130673012
#130670192
#130669392
#130665122
C11×#32092
#1018311