Finite Group Databasebeta

← #14657002

Subgroups — #14657002

Order 2816.

602 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068561C212yesmaximal
2#13068533C211yesmaximal, characteristic
3#13066524C211yesmaximal, characteristic, complemented
4#13066469C212yesmaximal, complemented
5C11×#2607C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C11×#399—21no—
8C11×#393—21no—
9C11×#391—22no—
10C11×#387—22no—
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2212yes—
13#10622824C2211yescharacteristic
14#10622820C2212yes—
15C2×#66870—21no—
16C2×#66870—21no—
17C2×#66869—22no—
18C2×#66869—22no—
19C22×Q8×C11—21no—
20C23×C4×C11C2311yescharacteristic
21C22×C22⋊D11—21no—
22C2×#4339—22no—
23C2×#4339—22no—
24C2×#4339—42no—
25C2×#4339—42no—
26C22×D44Q811yescharacteristic, complemented
27C22×C4×D11—21no—
28C22×Dic22Q811yescharacteristic, complemented
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D412yes—
35C2×C42×C11D412yes—
36C2×C22⋊Dic11—21no—
37C2×#4318—22no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—21no—
41C11×#95—22no—
42C11×#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46#66870—42no—
47#66870—42no—
48#66869—44no—
49#66869—44no—
50#10386—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C23×D11—21no—
53C2×Q8×C11—44no—
54C2×Q8×C11—81no—
55C22×C4×C11—22no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×Q811yescharacteristic
63C22×C4×C11#4112yes—
64C22×C4×C11#4111yescharacteristic
65C2×C22⋊D11—22no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—41no—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73#4339—24no—
74#4339—24no—
75#4339—42no—
76#4339—42no—
77#4339—44no—
78#4339—44no—
79C2×D44—22no—
80C2×D44—42no—
81C2×C4×D11—42no—
82C2×C4×D11—42no—
83C2×C4×D11—42no—
84C2×Dic22—22no—
85C2×Dic22—42no—
86C11×C4⋊C4—44no—
87C11×C4⋊C4—81no—
88C11×C22⋊C4—44no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—42no—
92C42×C11—42no—
93C22⋊Dic11—41no—
94C22⋊Dic11—41no—
95#4318—42no—
96#4318—42no—
97C2×C11⋊C8—42no—
98#2607D1111yescharacteristic, complemented
99#1789—112no—
100#1782—111no—
101#1306—111no—
102#1284—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—42no—
106C23×C11#12011yescharacteristic
107C23×C11C22⋊Q811yescharacteristic
108C23×C11#12411yescharacteristic
109C22×D11—22no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—82no—
113Q8×C11—84no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—24no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11C22⋊Q812yes—
130C2×C4×C11#12412yes—
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C2×Dic11—22no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—81no—
139C2×Dic11—82no—
140D44—24no—
141D44—42no—
142C4×D11—44no—
143C4×D11—44no—
144Dic22—24no—
145Dic22—42no—
146C11⋊C8—82no—
147C22×#41—111no—
148C2×#104—222no—
149C2×#104—222no—
150C2×#99—221no—
151C2×#99—221no—
152#407—112no—
153#399—21no—
154#393—21no—
155#391—22no—
156#387—22no—
157#381—111no—
158#381C2×D1111yescharacteristic
159C4×C22⋊C4C2×D1112yes—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11#39311yescharacteristic
168C22×C11B(4,𝔽2)11yescharacteristic
169C22×C11B(4,𝔽2)11yescharacteristic
170C2×D11—42no—
171C2×D11—82no—
172C2×D11—82no—
173C2×D11—82no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—44no—
177C4×C11—82no—
178C4×C11—81no—
179C4×C11—81no—
180Dic11—42no—
181Dic11—161no—
182C2×#41—222no—
183C2×#41—222no—
184C2×#41—442no—
185C2×#41—442no—
186C22×Q8—21no—
187C22×Q8—111no—
188C22×D4—111no—
189C22×D4—221no—
190C23×C4—221no—
191C23×C4C22×D1111yescharacteristic
192C2×M16—222no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—221no—
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4C22⋊D1111yescharacteristic
199C2×C42C22⋊D1112yes—
200C2×C42C22⋊D1112yes—
201#104—444no—
202#104—444no—
203#99—442no—
204#99—442no—
205C22⋊C8—222no—
206C22⋊C8—222no—
207#95—21no—
208#95—22no—
209#95—21no—
210#95—22no—
211#95—22no—
212#95—222no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—41no—
216C2×C11—41no—
217C2×C11#202911yescharacteristic
218C2×C11#203112yes—
219D11—82no—
220C24—221no—
221C24C2×C22⋊D1111yescharacteristic
222#41—224no—
223#41—224no—
224#41—442no—
225#41—442no—
226#41—444no—
227#41—444no—
228C2×Q8—44no—
229C2×Q8—81no—
230C2×Q8—222no—
231C2×Q8—442no—
232C2×D4—222no—
233C2×D4—222no—
234C2×D4—222no—
235C2×D4—442no—
236C2×D4—441no—
237C2×D4—441no—
238C2×D4—441no—
239C2×D4—441no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—221no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4—442no—
250C22×C4—441no—
251C22×C4Q8×D1111yescharacteristic
252C22×C4#434312yes—
253C22×C4#434311yescharacteristic
254C22×C4C2×C22⋊D1112yes—
255M16—442no—
256M16—442no—
257C2×C8—442no—
258C4⋊C4—44no—
259C4⋊C4—81no—
260C22⋊C4—44no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C42—42no—
266C42—42no—
267C11#1038611yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—42no—
271C23—222no—
272C23—441no—
273C23—441no—
274C23—882no—
275C23#6699911yescharacteristic
276C23#6700011yescharacteristic
277C23#6700611yescharacteristic
278Q8—84no—
279Q8—224no—
280Q8—442no—
281D4—224no—
282D4—442no—
283D4—442no—
284D4—442no—
285D4—442no—
286D4—442no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—222no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—881no—
308C2×C4—882no—
309C2×C4#6699912yes—
310C2×C4#6700012yes—
311C8—882no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—81no—
318C22—81no—
319C22—442no—
320C22—882no—
321C22—882no—
322C22—882no—
323C22#1062284411yescharacteristic
324C22#1062285711yescharacteristic
325C22#1062285711yescharacteristic
326C4—22no—
327C4—22no—
328C4—44no—
329C4—81no—
330C4—82no—
331C4—81no—
332C4—442no—
333C4—1761no—
334C2—21no—
335C2—21no—
336C2—41no—
337C2—41no—
338C2—882no—
339C2#1306977911yescharacteristic
340C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2607C2
socleC22×C11#393
prime radicalC22×#4339C22
hypercenter#2607D11
hypocenterC11#10386
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
3. #13066524C2semidirect
4. #13066469C2semidirect
5. C11×#2607C2semidirect
26. C22×D44Q8semidirect
28. C22×Dic22Q8semidirect
98. #2607D11semidirect
267. C11#10386semidirect

Maximal subgroups

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

subgroupindex
#130685612
#130685332
#130665242
#130664692
C11×#26072
#1038611