Finite Group Databasebeta

← #14667366

Subgroups — #14667366

Order 2816.

346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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#13080963C211yesmaximal, characteristic, complemented
2#13070841C211yesmaximal, characteristic, complemented
3#13070652C211yesmaximal, characteristic, complemented
4#13067972C211yesmaximal, characteristic, complemented
5#13066576C211yesmaximal, characteristic, complemented
6#13066570C211yesmaximal, characteristic, complemented
7C11×#1364C211yesmaximal, characteristic, complemented
8#10623257—21no—
9C11×#500C2211yescharacteristic
10#10622700—21no—
11C2×D176—21no—
12#10622496—21no—
13#10622495—22no—
14D11×#107—21no—
15#10622456—21no—
16#10622308C2211yescharacteristic
17C4×D88C2211yescharacteristic
18C8×D44C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#335C2211yescharacteristic
21#10622147—21no—
22#10622129—22no—
23#10622123—21no—
24C4×C11⋊C16C2211yescharacteristic
25C2×#4343—41no—
26C11×C4⋊Q8—21no—
27#66999—41no—
28C2×D88—21no—
29C2×D88—21no—
30C2×D88—41no—
31C2×D88D411yescharacteristic
32C2×C8×D11—21no—
33#66948—22no—
34#66947—42no—
35C4⋊C4×D11—22no—
36#66927—21no—
37C4×D44—21no—
38C4×D44D411yescharacteristic
39C2×C11×C16—21no—
40C11×#107—21no—
41C11×#107D412yes—
42C11×C4⋊C8—21no—
43C4×C8×C11C2311yescharacteristic
44#66885—21no—
45#66885—41no—
46(C2×D11)⋊C8—21no—
47#66882D411yescharacteristic
48C2×C11⋊C16—21no—
49#66873—22no—
50#66871—22no—
51C4⋊(C11⋊C8)D411yescharacteristic
52D176—42no—
53#12340—111nomaximal, Sylow
54C2×Q8×C11—41no—
55#4343—82no—
56#4343—82no—
57C2×D44—21no—
58C2×D44—42no—
59C2×D44—41no—
60C2×D44—41no—
61C2×D44—41no—
62C2×D44D811yescharacteristic
63C2×C4×D11—21no—
64C2×C4×D11—42no—
65C2×C4×D11—41no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—22no—
70C11×C4⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72(C2×D11)⋊C4—21no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11D811yescharacteristic
77Dic11⋊C4—42no—
78C2×C11⋊C8—21no—
79D88—21no—
80D88—21no—
81D88—42no—
82D88—41no—
83D88—41no—
84D88—82no—
85C8×D11—41no—
86C8×D11—41no—
87C11×C16—41no—
88C11⋊C16—41no—
89#3334—111no—
90#2240—111no—
91#2206—111no—
92#1667—111no—
93#1364D1111yescharacteristic, complemented
94#1331—111no—
95D4⋊C16—111no—
96C22×D11—21no—
97C22×D11—41no—
98C22×D11—81no—
99Q8×C11—81no—
100Q8×C11—81no—
101C2×C4×C11—42no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—21no—
106C2×Dic11—41no—
107D44—21no—
108D44—41no—
109D44—41no—
110D44—84no—
111D44—81no—
112D44—81no—
113D44—81no—
114D44—81no—
115D44—161no—
116D44D1612yescomplemented
117C4×D11—41no—
118C4×D11—41no—
119C4×D11—84no—
120C4×D11—81no—
121C4×D11—81no—
122C8×C11—21no—
123C8×C11—81no—
124C8×C11#13511yescharacteristic
125C8×C11AGL(1,ℤ/8)11yescharacteristic
126C11⋊C8—41no—
127#547—221no—
128C2×D16—221no—
129#500C2×D1111yescharacteristic
130#493—111no—
131#480—222no—
132#474—221no—
133#466—221no—
134#459—221no—
135C4×D8—111no—
136C8×D4—111no—
137C2×#107—221no—
138C4⋊C16C2×D1111yescharacteristic
139#357—221no—
140#357—222no—
141C4×C16—111no—
142#335C2×D1111yescharacteristic
143#331—221no—
144C22×C11#44711yescharacteristic
145C2×D11—22no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—81no—
149C2×D11—81no—
150C2×D11—81no—
151C2×D11—161no—
152C2×D11—161no—
153C2×D11—161no—
154C4×C11—21no—
155C4×C11—82no—
156C4×C11#44911yescharacteristic
157C4×C11#45411yescharacteristic
158C4×C11C2×D1611yescharacteristic
159C4×C11#50911yescharacteristic
160Dic11—41no—
161Dic11—81no—
162C2×#41—441no—
163C2×D8—111no—
164C2×D8—221no—
165C2×D8—221no—
166C2×D8—441no—
167C22×C8—221no—
168C4⋊Q8—21no—
169#127—221no—
170#123—442no—
171C22⋊Q8—441no—
172#121—222no—
173C4×D4—111no—
174C4×D4—221no—
175C2×C4⋊C4—222no—
176D16—442no—
177C2×C16—21no—
178C2×C16—221no—
179#107—21no—
180#107—111no—
181#107—222no—
182#107D4412yes—
183C4⋊C8—21no—
184C4⋊C8—111no—
185#102—222no—
186#102—221no—
187#102—441no—
188C22⋊C8—221no—
189C4×C8C22×D1111yescharacteristic
190C2×C11#162511yescharacteristic
191C2×C11#218411yescharacteristic
192C2×C11#219311yescharacteristic
193D11—42no—
194D11—161no—
195D11—321no—
196#41—882no—
197#41—882no—
198C2×Q8—41no—
199C2×D4—111no—
200C2×D4—221no—
201C2×D4—442no—
202C2×D4—441no—
203C2×D4—441no—
204C2×D4—441no—
205C22×C4—221no—
206C22×C4—442no—
207C22×C4—441no—
208D8—221no—
209D8—221no—
210D8—442no—
211D8—441no—
212D8—441no—
213D8—882no—
214C2×C8—41no—
215C2×C8—221no—
216C2×C8—441no—
217C2×C8—441no—
218C2×C8C2×D4411yescharacteristic
219C2×C8D4×D1111yescharacteristic
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—111no—
223C4⋊C4—221no—
224C4⋊C4—442no—
225C22⋊C4—221no—
226C22⋊C4—442no—
227C22⋊C4—441no—
228C42D4×D1111yescharacteristic
229C16—41no—
230C16—441no—
231C11#1234011yescharacteristic, complemented, Sylow
232C23—221no—
233C23—441no—
234C23—881no—
235Q8—81no—
236Q8—81no—
237D4—112no—
238D4—221no—
239D4—441no—
240D4—441no—
241D4—884no—
242D4—881no—
243D4—881no—
244D4—881no—
245D4—881no—
246D4—1761no—
247C2×C4—42no—
248C2×C4—221no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—884no—
253C2×C4—881no—
254C2×C4—881no—
255C2×C4#6693511yescharacteristic
256C2×C4D8×D1111yescharacteristic
257C2×C4#6696711yescharacteristic
258C8—21no—
259C8—81no—
260C8—441no—
261C8#6696711yescharacteristic
262C8#6697211yescharacteristic
263C22—222no—
264C22—441no—
265C22—441no—
266C22—881no—
267C22—881no—
268C22—881no—
269C22—1761no—
270C22—1761no—
271C22—1761no—
272C22#1062238611yescharacteristic
273C4—21no—
274C4—82no—
275C4—441no—
276C4—881no—
277C4#1062236611yescharacteristic
278C4#1062242411yescharacteristic
279C4D11×D1611yescharacteristic
280C4#1062252711yescharacteristic
281C2—442no—
282C2—3521no—
283C2—1761no—
284C2#1306770611yescharacteristic
285C2#1307052911yescharacteristic
286C2#1307058311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1364C2
socleC22×C11#447
hypercenter#1364D11
hypocenterC11#12340
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #13080963C2semidirect
2. #13070841C2semidirect
3. #13070652C2semidirect
4. #13067972C2semidirect
5. #13066576C2semidirect
6. #13066570C2semidirect
7. C11×#1364C2semidirect
93. #1364D11semidirect
116. D44D16semidirect
231. C11#12340semidirect

Maximal subgroups

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

subgroupindex
#130809632
#130708412
#130706522
#130679722
#130665762
#130665702
C11×#13642
#1234011