Finite Group Databasebeta

← #14651586

Subgroups — #14651586

Order 2816.

610 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 97 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#13070971C211yesmaximal, characteristic
3#13068716C211yesmaximal, characteristic
4#13068713C211yesmaximal, characteristic
5#13066945C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic
7C11×#1284C211yesmaximal, characteristic
8C2×#66979C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C11×#407C2211yescharacteristic
12C11×#381C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622563—21no—
17#10622556—21no—
18C22⋊C4×Dic11—21no—
19C4×Dic11⋊C4—22no—
20#10622274C412yescomplemented
21#10622272C412yescomplemented
22#10622266—22no—
23#10622262—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—22no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4C2×C412yes—
49C2×Dic11⋊C4D412yes—
50C2×C4×Dic11—22no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—22no—
53C2×C4×Dic11D412yes—
54C2×#4318—21no—
55#66930—28no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95C2×C412yes—
61C11⋊#95—22no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9478—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—42no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—24no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—22no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—42no—
88C22×Dic11C22⋊C412yes—
89C22×Dic11C22⋊C412yes—
90C11×M16—42no—
91C2×C8×C11—41no—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—42no—
94C42×C11—42no—
95C22⋊Dic11—24no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—44no—
103Dic11⋊C4—28no—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108C4×Dic11—28no—
109C4×Dic11—42no—
110C4×Dic11—41no—
111C4×Dic11—41no—
112C4×Dic11—82no—
113#4318—42no—
114C2×C11⋊C8—41no—
115#2484—111no—
116#2274—111no—
117#1826—111no—
118#1826—111no—
119#1463—111no—
120#1284—111no—
121#1284D1111yescharacteristic
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#12011yescharacteristic
127C23×C11#12311yescharacteristic
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—24no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—24no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—81no—
160C2×Dic11#10414yes—
161C8×C11—81no—
162C11⋊C8—81no—
163C2×#117—111no—
164C2×#117—221no—
165C22×C4⋊C4—111no—
166#407—111no—
167#407C2×D1111yescharacteristic
168#400—112no—
169#398—112no—
170#387—222no—
171#385—221no—
172#381—221no—
173#381C2×D1111yescharacteristic
174C4×C4⋊C4—222no—
175C4×C4⋊C4—222no—
176C4×C22⋊C4—111no—
177C4×C22⋊C4—221no—
178C4×C22⋊C4C2×D1111yescharacteristic
179#339—222no—
180#339—222no—
181#324—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—44no—
190C22×C11#38611yescharacteristic
191C22×C11C2×#10412yes—
192C22×C11#45812yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—44no—
198C4×C11—82no—
199Dic11—24no—
200Dic11—44no—
201Dic11—42no—
202Dic11—81no—
203Dic11—81no—
204C23×C4—111no—
205C23×C4—111no—
206C23×C4C22×D1111yescharacteristic
207C2×M16—21no—
208C2×M16—221no—
209#117—228no—
210#117—221no—
211#117—221no—
212#117—221no—
213#117—221no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—222no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C42—112no—
229C2×C42—222no—
230C2×C42—221no—
231C2×C42—222no—
232C2×C42D4412yes—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237#95—21no—
238#95—21no—
239#95—222no—
240#95—222no—
241#95—222no—
242#95—222no—
243#95—221no—
244#95C4×D1112yes—
245C2×C11—22no—
246C2×C11—22no—
247C2×C11—41no—
248C2×C11#189011yescharacteristic
249C2×C11#189611yescharacteristic
250C2×C11#191211yescharacteristic
251C24D4×D1111yescharacteristic
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—42no—
255C22×C4—112no—
256C22×C4—112no—
257C22×C4—224no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—222no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—442no—
266C22×C4C2×C4×D1111yescharacteristic
267C22×C4C2×D4411yescharacteristic
268C22×C4#433911yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4#434311yescharacteristic
272M16—42no—
273M16—442no—
274C2×C8—41no—
275C2×C8—441no—
276C4⋊C4—228no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—444no—
286C22⋊C4—24no—
287C22⋊C4—42no—
288C22⋊C4—224no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C42—42no—
292C42—228no—
293C42—442no—
294C42—441no—
295C42—441no—
296C42—882no—
297C11#947811yescharacteristic, complemented, Sylow
298C23—22no—
299C23—22no—
300C23—41no—
301C23C22⋊C4×D1111yescharacteristic
302C23#6693511yescharacteristic
303C23#6694711yescharacteristic
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—114no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—224no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—224no—
323C2×C4—222no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4—881no—
333C2×C4C4×D4411yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6694611yescharacteristic
336C2×C4#6694811yescharacteristic
337C8—81no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#1062227811yescharacteristic
348C22#1062235512yes—
349C22D11×#10412yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—44no—
355C4—82no—
356C4—224no—
357C4—444no—
358C4—442no—
359C4—881no—
360C4—881no—
361C2—22no—
362C2—22no—
363C2—41no—
364C2#1306902811yescharacteristic
365C2#1306905811yescharacteristic
366C2#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#9478
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
297. C11#9478semidirect

Maximal subgroups

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

subgroupindex
#130729052
#130709712
#130687162
#130687132
#130669452
#130664682
C11×#12842
#947811