Finite Group Databasebeta

← #14651606

Subgroups — #14651606

Order 2816.

518 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 93 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#13072905C211yesmaximal, characteristic
2#13071216C211yesmaximal, characteristic
3#13068716C211yesmaximal, characteristic
4#13068713C211yesmaximal, characteristic
5#13066945C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic
7C11×#1284C211yesmaximal, characteristic
8C2×#66979C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622563—21no—
16#10622556—21no—
17#10622556—21no—
18#10622555—21no—
19#10622546—22no—
20#10622274C412yescomplemented
21#10622272C412yescomplemented
22#10622266—22no—
23#10622265—22no—
24#10622193—22no—
25#10622161—22no—
26#10622107—22no—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11D412yes—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36#66979—21no—
37#66979—21no—
38#66979—21no—
39#66979—21no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4C2×C412yes—
49C2×Dic11⋊C4D412yes—
50C2×C4×Dic11—21no—
51C2×C4×Dic11D412yes—
52C2×#4318—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95C2×C412yes—
58C11⋊#95—22no—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#9482—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—42no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—22no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—42no—
85C22×Dic11—42no—
86C22×Dic11C22⋊C412yes—
87C22×Dic11C22⋊C412yes—
88C11×M16—42no—
89C2×C8×C11—41no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4—42no—
92C42×C11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—44no—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103Dic11⋊C4—22no—
104Dic11⋊C4—22no—
105Dic11⋊C4—82no—
106C4×Dic11—42no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109#4318—42no—
110C2×C11⋊C8—41no—
111#2484—111no—
112#2313—111no—
113#1826—111no—
114#1826—111no—
115#1463—111no—
116#1284—111no—
117#1284D1111yescharacteristic
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—41no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11#12011yescharacteristic
123C23×C11#12311yescharacteristic
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—81no—
156C8×C11—81no—
157C11⋊C8—81no—
158C2×#117—111no—
159C22×C4⋊C4—111no—
160#407—111no—
161#407C2×D1111yescharacteristic
162#400—112no—
163#398—112no—
164#387—222no—
165#387—222no—
166#387—222no—
167#385—221no—
168#381—221no—
169#381—221no—
170#381C2×D1111yescharacteristic
171#380—221no—
172C4×C22⋊C4—111no—
173C4×C22⋊C4C2×D1111yescharacteristic
174#339—222no—
175#339—222no—
176#324—222no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—44no—
185C22×C11#38611yescharacteristic
186C22×C11#42112yes—
187C22×C11#45812yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—82no—
193C4×C11—82no—
194Dic11—42no—
195Dic11—42no—
196Dic11—82no—
197Dic11—81no—
198Dic11—81no—
199C23×C4—111no—
200C23×C4—111no—
201C23×C4C22×D1111yescharacteristic
202C2×M16—21no—
203C2×M16—221no—
204#117—221no—
205#117—221no—
206#117—221no—
207#117—221no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—222no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—112no—
223C2×C42—221no—
224C2×C42D4412yes—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—221no—
228C22⋊C8—221no—
229#95—21no—
230#95—21no—
231#95—222no—
232#95—222no—
233#95—222no—
234#95—222no—
235#95—224no—
236#95—221no—
237#95C4×D1112yes—
238C2×C11—22no—
239C2×C11—22no—
240C2×C11—41no—
241C2×C11#189011yescharacteristic
242C2×C11#189711yescharacteristic
243C2×C11#191211yescharacteristic
244C24D4×D1111yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—112no—
249C22×C4—112no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—222no—
257C22×C4—442no—
258C22×C4—442no—
259C22×C4C2×C4×D1111yescharacteristic
260C22×C4C2×D4411yescharacteristic
261C22×C4#433911yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4#434311yescharacteristic
265M16—42no—
266M16—442no—
267C2×C8—41no—
268C2×C8—441no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—444no—
278C4⋊C4—882no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—442no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C42—42no—
285C42—442no—
286C42—441no—
287C42—441no—
288C11#948211yescharacteristic, complemented, Sylow
289C23—22no—
290C23—22no—
291C23—41no—
292C23C22⋊C4×D1111yescharacteristic
293C23#6693511yescharacteristic
294C23#6694711yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—881no—
323C2×C4C4×D4411yescharacteristic
324C2×C4#6693711yescharacteristic
325C2×C4#6694611yescharacteristic
326C2×C4#6694811yescharacteristic
327C8—81no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1062227811yescharacteristic
338C22#1062235512yes—
339C22#1062243412yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—82no—
346C4—442no—
347C4—442no—
348C4—882no—
349C4—881no—
350C4—881no—
351C2—22no—
352C2—22no—
353C2—41no—
354C2#1306902811yescharacteristic
355C2#1306906311yescharacteristic
356C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9482
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
20. #10622274C4semidirect
21. #10622272C4semidirect
288. C11#9482semidirect

Maximal subgroups

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

subgroupindex
#130729052
#130712162
#130687162
#130687132
#130669452
#130664682
C11×#12842
#948211