Finite Group Databasebeta

← #14657270

Subgroups — #14657270

Order 2816.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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#13076683C211yesmaximal, characteristic
2#13069584C211yesmaximal, characteristic
3#13068782C211yesmaximal, characteristic
4C2×#10622181C211yesmaximal, characteristic
5C2×#10622103C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1992C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622599—21no—
13#10622597—21no—
14#10622597—21no—
15#10622596—21no—
16#10622595—21no—
17#10622593—21no—
18C2×#66872—21no—
19C2×#66871—21no—
20#10622549C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C11×#340—21no—
24C11×#340—21no—
25#10622181—22no—
26#10622167—21no—
27#10622167—21no—
28#10622103—22no—
29C22×C8×C11—21no—
30C11×#125—21no—
31C11×#125—21no—
32C11×#125—21no—
33C11×#125—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52#66923—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56C11×#97—21no—
57C11×#97—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66#66872—42no—
67#66871—42no—
68#66867—21no—
69#66867—21no—
70#66867—21no—
71#66867D412yes—
72#10429—111nomaximal, Sylow
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—81no—
113Dic11⋊C4—81no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2822—111no—
121#1992—111no—
122#1992D1111yescharacteristic
123#1847—111no—
124C2×#330—111no—
125C2×#330—111no—
126#1295—111no—
127C23×C11#12011yescharacteristic
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12411yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C8×C11—42no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164C2×#125—111no—
165C2×#125C2×D1111yescharacteristic
166C2×#107—221no—
167C2×#106—221no—
168C2×#97—111no—
169C2×#97—111no—
170C2×#97C2×D1111yescharacteristic
171#400—221no—
172#400—221no—
173#398—221no—
174#398—221no—
175#398—221no—
176#398—221no—
177#384C2×D1111yescharacteristic
178#382—111no—
179#340—21no—
180#340—21no—
181#340—221no—
182#340—221no—
183#330—222no—
184#330—222no—
185C22×C11#39411yescharacteristic
186C22×C11#45311yescharacteristic
187C22×C11#45411yescharacteristic
188C22×C11#45411yescharacteristic
189C22×C11#45611yescharacteristic
190C22×C11#45611yescharacteristic
191C22×C11#45611yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—161no—
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204Dic11—81no—
205C22×C8—21no—
206C22×C8—221no—
207C22×C8—221no—
208#125—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#125—221no—
213#125—221no—
214#125—221no—
215#125—221no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C42C22×D1111yescharacteristic
232#107—442no—
233#106—442no—
234#97—21no—
235#97—21no—
236#97—112no—
237#97—221no—
238#97—221no—
239#97—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11#165711yescharacteristic
249C2×C11#166011yescharacteristic
250C2×C11#166311yescharacteristic
251C2×C11#166311yescharacteristic
252C2×C11#203811yescharacteristic
253C2×C11#203811yescharacteristic
254C2×C11#203911yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C2×C8—22no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C2×C8—441no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—881no—
297C4⋊C4—881no—
298C42#433911yescharacteristic
299C42#433911yescharacteristic
300C42D4×D1111yescharacteristic
301C42#434111yescharacteristic
302C11#1042911yescharacteristic, complemented, Sylow
303C23#6699011yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4#6693611yescharacteristic
332C2×C4#6693711yescharacteristic
333C2×C4#6693711yescharacteristic
334C2×C4#6693811yescharacteristic
335C2×C4#6698211yescharacteristic
336C2×C4#6699211yescharacteristic
337C8—42no—
338C8—224no—
339C8—442no—
340C22#1062257211yescharacteristic
341C22#1062267511yescharacteristic
342C22#1062270811yescharacteristic
343C22#1062281111yescharacteristic
344C22#1062281411yescharacteristic
345C22#1062281811yescharacteristic
346C22#1062281811yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—81no—
354C4—81no—
355C4—161no—
356C4—881no—
357C4—881no—
358C4—881no—
359C4—881no—
360C2#1306791311yescharacteristic
361C2#1306792611yescharacteristic
362C2#1306794211yescharacteristic
363C2#1306794311yescharacteristic
364C2#1306983111yescharacteristic
365C2#1306983311yescharacteristic
366C2#1306983811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1992C2
socle, prime radicalC23×C11#120
hypercenter#1992D11
hypocenterC11#10429
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
302. C11#10429semidirect

Maximal subgroups

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

subgroupindex
#130766832
#130695842
#130687822
C2×#106221812
C2×#106221032
#130664982
C11×#19922
#1042911