Finite Group Databasebeta

← #14651187

Subgroups — #14651187

Order 2816.

570 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077656C211yesmaximal, characteristic
2#13073565C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic, complemented
5#13067300C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×#66950—22no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14C2×#66887—21no—
15#10622552—21no—
16#10622548—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622451—22no—
20#10622339—22no—
21#10622301—22no—
22#10622290C414yes—
23#10622192—21no—
24#10622124—22no—
25#10622120—22no—
26C22×D44D411yescharacteristic
27C22×C4×D11D412yes—
28C22×Dic22—21no—
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—24no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11D411yescharacteristic
39C2×#4318—21no—
40C2×#4313—24no—
41#66950—48no—
42C4×D44—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D412yes—
53C11×C22⋊C8—21no—
54C4×C8×C11—21no—
55C11×#95C2×C412yes—
56C22⋊(C11⋊C8)—21no—
57#66887—42no—
58(C2×D11)⋊C8—24no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62C4×C11⋊C8—21no—
63#9403—111nomaximal, Sylow
64C23×D11C22⋊C412yes—
65C22×C4×C11—22no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—22no—
70C22×Dic11C22⋊C412yes—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—44no—
80C2×Dic22—44no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C11×C4⋊C4—24no—
88C42×C11—41no—
89C42×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—48no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—48no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108#4313—84no—
109#2975—111no—
110#2542—111no—
111#1800—111no—
112#1549—111no—
113#1549—111no—
114#1303—111no—
115#1303D1111yescharacteristic, complemented
116C23×C11C2×C22⋊C411yescharacteristic
117C22×D11—22no—
118C22×D11—22no—
119C22×D11—22no—
120C22×D11—42no—
121C22×D11—42no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—22no—
138C2×Dic11—42no—
139C2×Dic11—44no—
140C2×Dic11—42no—
141D44—41no—
142D44—41no—
143D44—41no—
144D44—41no—
145C4×D11—44no—
146C4×D11—82no—
147Dic22—82no—
148Dic22—82no—
149C8×C11—42no—
150C8×C11—81no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C2×C4⋊Q8—111no—
154C2×C22⋊Q8—222no—
155C2×C4×D4—111no—
156#436—222no—
157#436—222no—
158#431—111no—
159#431C2×D1111yescharacteristic
160#423—111no—
161#423C2×D1111yescharacteristic
162C2×#100—221no—
163#407—222no—
164#399—114no—
165#390—221no—
166#384—221no—
167C4×C4⋊C4C2×D1111yescharacteristic
168#343—221no—
169#332—222no—
170#332—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#38611yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11#41911yescharacteristic
176C2×D11—44no—
177C2×D11—42no—
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—82no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—44no—
185C4×C11#45312yes—
186C4×C11#46811yescharacteristic
187C4×C11#46811yescharacteristic
188C4×C11#47011yescharacteristic
189C4×C11#47011yescharacteristic
190Dic11—42no—
191Dic11—82no—
192C22×Q8—221no—
193C22×D4—111no—
194C23×C4—112no—
195C2×M16—21no—
196C2×M16—224no—
197C2×M16—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C22⋊Q8—448no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—221no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—224no—
211C2×C4⋊C4—221no—
212C2×C22⋊C4—112no—
213C2×C22⋊C4—224no—
214C2×C42—21no—
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—112no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8D4412yes—
222#100—442no—
223C22⋊C8—21no—
224C22⋊C8—224no—
225C22⋊C8—221no—
226C4×C8—21no—
227C4×C8—221no—
228#95C4×D1112yes—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11#188711yescharacteristic
232C2×C11#189411yescharacteristic
233C2×C11#191511yescharacteristic
234D11—82no—
235C24—112no—
236C2×Q8—444no—
237C2×Q8—441no—
238C2×Q8—441no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C22×C4—22no—
246C22×C4—112no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—444no—
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254M16—41no—
255M16—41no—
256M16—441no—
257M16—441no—
258M16—884no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—441no—
263C4⋊C4—24no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—448no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—222no—
272C22⋊C4—222no—
273C22⋊C4—448no—
274C42—41no—
275C42—41no—
276C42C2×D4411yescharacteristic
277C42#433911yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434311yescharacteristic
280C11#940311yescharacteristic, complemented, Sylow
281C23—222no—
282C23—222no—
283C23—222no—
284C23—442no—
285C23—442no—
286C23C22⋊C4×D1111yescharacteristic
287Q8—882no—
288Q8—882no—
289D4—441no—
290D4—441no—
291D4—441no—
292D4—441no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—222no—
299C2×C4—444no—
300C2×C4—442no—
301C2×C4—444no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4C4×D4411yescharacteristic
305C2×C4#6693511yescharacteristic
306C2×C4#6693711yescharacteristic
307C2×C4#6694611yescharacteristic
308C2×C4#6694711yescharacteristic
309C2×C4#6694811yescharacteristic
310C2×C4#6696411yescharacteristic
311C2×C4#6696811yescharacteristic
312C2×C4#6696811yescharacteristic
313C2×C4#6697111yescharacteristic
314C8—42no—
315C8—81no—
316C8—442no—
317C8—881no—
318C22—21no—
319C22—21no—
320C22—444no—
321C22—442no—
322C22—442no—
323C22—442no—
324C22—882no—
325C22#1062227811yescharacteristic
326C22#1062238411yescharacteristic
327C22#1062241511yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—442no—
333C4—882no—
334C4#1062239311yescharacteristic
335C4#1062242911yescharacteristic
336C4#1062243512yes—
337C4#1062248111yescharacteristic
338C4#1062249911yescharacteristic
339C2—21no—
340C2—21no—
341C2—882no—
342C2#1306901311yescharacteristic
343C2#1306904811yescharacteristic
344C2#1306916711yescharacteristic
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#9403
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. #13067302C2semidirect
5. #13067300C2semidirect
6. #13066519C2semidirect
7. C11×#1303C2semidirect
115. #1303D11semidirect
280. C11#9403semidirect

Maximal subgroups

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

subgroupindex
#130776562
#130735652
#130686052
#130673022
#130673002
#130665192
C11×#13032
#940311