Finite Group Databasebeta

← #14655806

Subgroups — #14655806

Order 2816.

496 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079760C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic
4#13067018C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic
6#13066513C211yesmaximal, characteristic
7C2×C11×#462C211yesmaximal, characteristic
8C22×C11×Q16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#462—22no—
13C11×#462—22no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×#103—21no—
16#10622838—21no—
17#10622707—22no—
18#10622706—21no—
19#10622692—21no—
20#10622635—22no—
21#10622634—21no—
22#10622633—21no—
23#10622584—22no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29#10622166—22no—
30#10622122—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×C11×Q16—24no—
34C2×C11×Q16—42no—
35C2×C11×Q16—42no—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51#66979—21no—
52#66977—21no—
53#66977—21no—
54C2×#4318—21no—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63#66899—22no—
64#66899—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)D412yes—
67#66874—24no—
68#66872—22no—
69#66872—24no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10187—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11SD1612yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×Dic22—21no—
97C2×Dic22—21no—
98C11×Q16—48no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129#3229—111no—
130#3078—111no—
131C2×#462D1111yescharacteristic
132#1546—111no—
133#1481—111no—
134#1461—111no—
135#1301—111no—
136C23×C11#12111yescharacteristic
137Q8×C11—22no—
138Q8×C11—22no—
139Q8×C11—41no—
140Q8×C11—41no—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—81no—
144Q8×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C2×C4×C11C2×SD1611yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C2×Dic11—41no—
166C2×Dic11—41no—
167Dic22—42no—
168Dic22—42no—
169C8×C11—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C22×Q16—21no—
174#533—111no—
175C2×C4⋊Q8C2×D1111yescharacteristic
176C2×C4×Q8C2×D1111yescharacteristic
177#498—221no—
178#487—221no—
179#483—222no—
180#479—222no—
181#477—221no—
182#475—221no—
183#475—222no—
184#462—22no—
185#462—22no—
186#431—111no—
187#431—111no—
188#428—221no—
189#423—111no—
190C2×C4⋊C8C2×D1111yescharacteristic
191#419—221no—
192C2×#103—21no—
193#332—222no—
194Q8⋊C8—222no—
195#324—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#39211yescharacteristic
199C22×C11#46511yescharacteristic
200C22×C11#46811yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11#44811yescharacteristic
208C4×C11#44911yescharacteristic
209C4×C11#45011yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#47312yes—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—21no—
215C22×Q8C22⋊D1111yescharacteristic
216C2×Q16—24no—
217C2×Q16—42no—
218C2×Q16—42no—
219C2×M16—221no—
220C22×C8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—111no—
225C4⋊Q8—111no—
226C4⋊Q8C22⋊D1112yes—
227#125—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—221no—
235C4×Q8—221no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C22⋊D1111yescharacteristic
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—222no—
244#106—222no—
245#106—224no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8C22⋊D1112yes—
252#103—24no—
253#103—224no—
254#103—222no—
255#103—222no—
256C22⋊C8—112no—
257C22⋊C8—221no—
258C4×C8—221no—
259C4×C8—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#200011yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#202011yescharacteristic
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8#432412yes—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—48no—
286M16—441no—
287M16—441no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—441no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—441no—
309C42—41no—
310C42—41no—
311C42—441no—
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#1018711yescharacteristic, complemented, Sylow
317C23#6699211yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322Q8—42no—
323Q8—42no—
324Q8—81no—
325Q8—81no—
326Q8—442no—
327Q8—442no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4#6698511yescharacteristic
341C2×C4C2×#432411yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699111yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699311yescharacteristic
347C2×C4#6700311yescharacteristic
348C2×C4#6700411yescharacteristic
349C2×C4#6700611yescharacteristic
350C8—42no—
351C8—442no—
352C8—442no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22#1062265411yescharacteristic
357C22#1062265511yescharacteristic
358C22#1062283611yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—881no—
366C4—881no—
367C4#1062265011yescharacteristic
368C4#1062265311yescharacteristic
369C4#1062280512yes—
370C4#1062283111yescharacteristic
371C4#1062285211yescharacteristic
372C2—21no—
373C2—21no—
374C2#1306961911yescharacteristic
375C2#1306967411yescharacteristic
376C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#462C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenterC2×#462D11
hypocenterC11#10187
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
316. C11#10187semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130784212
#130672882
#130670182
#130669402
#130665132
C2×C11×#4622
#1018711