Finite Group Databasebeta

← #14651127

Subgroups — #14651127

Order 2816.

538 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 117 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#13077639C211yesmaximal, characteristic
2#13073785C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic, complemented
5#13067296C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66887—21no—
14#10622600—22no—
15#10622552—21no—
16#10622549—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622447—22no—
20D11×C22⋊C8—22no—
21C8×D44—22no—
22#10622286C414yes—
23#10622192—21no—
24#10622119—22no—
25#10622119—22no—
26C22×D44D411yescharacteristic
27C22×C4×D11D412yes—
28C22×Dic22C2×C412yes—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—24no—
34C2×(C2×D11)⋊C4C2×C412yes—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×#4318—21no—
39C2×C8×D11—24no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43C4×D44—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C11×#95C2×C412yes—
54C11⋊#95—24no—
55C22⋊(C11⋊C8)—21no—
56#66887—42no—
57(C2×D11)⋊C8—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62#9391—111nomaximal, Sylow
63C23×D11C22⋊C412yes—
64C22×C4×C11—22no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11C22⋊C412yes—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44SD1612yes—
75C2×D44Q1612yes—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—44no—
79C2×Dic22—22no—
80C2×Dic22—22no—
81C2×Dic22—82no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C11×C4⋊C4—42no—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—84no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C8×D11—84no—
107#2972—111no—
108#2563—111no—
109#1800—111no—
110#1548—111no—
111#1548—111no—
112#1303—111no—
113#1303D1111yescharacteristic, complemented
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—22no—
116C22×D11—22no—
117C22×D11—42no—
118C22×D11—42no—
119C22×D11#10314yes—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×Q1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—42no—
137C2×Dic11—44no—
138C2×Dic11—42no—
139D44—22no—
140D44—22no—
141D44—22no—
142D44—22no—
143C4×D11—44no—
144C4×D11—82no—
145Dic22—82no—
146Dic22—82no—
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—42no—
150C11⋊C8—81no—
151C2×C4⋊Q8—111no—
152C2×C4×D4—111no—
153C8×D4—222no—
154C8×D4—222no—
155#431—111no—
156#431C2×D1111yescharacteristic
157#423—111no—
158#423C2×D1111yescharacteristic
159C2×#100—221no—
160C2×C22⋊C8—222no—
161#393—114no—
162#390—221no—
163#382—221no—
164#380—222no—
165C4×C4⋊C4C2×D1111yescharacteristic
166#343—221no—
167#333—222no—
168#333—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#38611yescharacteristic
172C22×C11C2×#10311yescharacteristic
173C22×C11#41611yescharacteristic
174C2×D11—24no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—44no—
178C2×D11—82no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—82no—
183C4×C11#45512yes—
184C4×C11#46511yescharacteristic
185C4×C11#46511yescharacteristic
186C4×C11#46711yescharacteristic
187C4×C11#46711yescharacteristic
188Dic11—42no—
189Dic11—82no—
190C22×Q8—112no—
191C22×D4—111no—
192C23×C4—112no—
193C2×M16—21no—
194C2×M16—221no—
195C22×C8—224no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4×D4—221no—
201C4×D4—221no—
202C4×D4—221no—
203C4×D4—221no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—224no—
210C2×C42—21no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8D4412yes—
218#100—442no—
219C22⋊C8—21no—
220C22⋊C8—224no—
221C22⋊C8—221no—
222C4×C8—21no—
223C4×C8—221no—
224#95—224no—
225#95C4×D1112yes—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#188511yescharacteristic
229C2×C11#189211yescharacteristic
230C2×C11#191411yescharacteristic
231D11—44no—
232C24—112no—
233C2×Q8—222no—
234C2×Q8—222no—
235C2×Q8—882no—
236C2×D4—112no—
237C2×D4—112no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C22×C4—22no—
243C22×C4—112no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—444no—
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251M16—41no—
252M16—41no—
253M16—441no—
254M16—441no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—441no—
259C2×C8—884no—
260C4⋊C4—42no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C22⋊C4—222no—
268C22⋊C4—222no—
269C22⋊C4—884no—
270C42—41no—
271C42—41no—
272C42C2×D4411yescharacteristic
273C42#433911yescharacteristic
274C42D4×D1111yescharacteristic
275C42#434311yescharacteristic
276C11#939111yescharacteristic, complemented, Sylow
277C23—114no—
278C23—222no—
279C23—222no—
280C23—442no—
281C23—442no—
282C23C22⋊C4×D1111yescharacteristic
283Q8—882no—
284Q8—882no—
285D4—222no—
286D4—222no—
287D4—222no—
288D4—222no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—222no—
295C2×C4—444no—
296C2×C4—442no—
297C2×C4—444no—
298C2×C4—442no—
299C2×C4—882no—
300C2×C4C4×D4411yescharacteristic
301C2×C4#6693511yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4#6694611yescharacteristic
304C2×C4#6694711yescharacteristic
305C2×C4#6694811yescharacteristic
306C2×C4#6696511yescharacteristic
307C2×C4SD16×D1111yescharacteristic
308C2×C4#6696911yescharacteristic
309C2×C4Q16×D1111yescharacteristic
310C8—42no—
311C8—81no—
312C8—442no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—224no—
317C22—444no—
318C22—442no—
319C22—442no—
320C22—882no—
321C22#1062227811yescharacteristic
322C22#1062238511yescharacteristic
323C22D11×#10311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—442no—
329C4—882no—
330C4#1062239111yescharacteristic
331C4#1062242611yescharacteristic
332C4#1062243812yes—
333C4#1062247711yescharacteristic
334C4#1062250011yescharacteristic
335C2—21no—
336C2—21no—
337C2—444no—
338C2#1306900311yescharacteristic
339C2#1306903811yescharacteristic
340C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9391
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. #13067298C2semidirect
5. #13067296C2semidirect
6. #13066519C2semidirect
7. C11×#1303C2semidirect
113. #1303D11semidirect
276. C11#9391semidirect

Maximal subgroups

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

subgroupindex
#130776392
#130737852
#130686052
#130672982
#130672962
#130665192
C11×#13032
#939111