Finite Group Databasebeta

← #14658233

Subgroups — #14658233

Order 2816.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073855C211yesmaximal, characteristic
2#13069375C211yesmaximal, characteristic
3#13069374C211yesmaximal, characteristic
4#13068773C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C4×C11×C4⋊C4C2211yescharacteristic
11C2×#66882—21no—
12C2×#66881—22no—
13#10622590—21no—
14#10622586—21no—
15C2×#66871—21no—
16#10622549—21no—
17#10622548C2211yescharacteristic
18#10622548C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20#10622541—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622273—22no—
23#10622189—21no—
24#10622167—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D412yes—
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11—21no—
41C22×C11⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8Q812yes—
44C4×C8×C11—21no—
45C4×C8×C11Q812yes—
46C11×#95—21no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51#66882—42no—
52#66881—44no—
53#66871—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)Q812yes—
56#10577—111nomaximal, Sylow
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C22×Dic11—22no—
65C22×Dic11—41no—
66C2×C8×C11—22no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C42×C11—41no—
77C42×C11—41no—
78C42×C11C2×Q811yescharacteristic
79C42×C11C2×Q811yescharacteristic
80C42×C11C2×Q811yescharacteristic
81C42×C11#4111yescharacteristic
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—82no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#2571—111no—
103#1947—111no—
104#1947—111no—
105#1844—111no—
106#1296—111no—
107#1279—111no—
108#1279D1111yescharacteristic
109C23×C11#12011yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11C22⋊Q811yescharacteristic
121C2×C4×C11C4⋊Q811yescharacteristic
122C2×C4×C11C4⋊Q811yescharacteristic
123C2×C4×C11C4⋊Q811yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—41no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C8×C11—24no—
145C8×C11—42no—
146C11⋊C8—42no—
147C2×#107—221no—
148C2×#107—221no—
149C2×#106—222no—
150C2×C4⋊C8—111no—
151C2×C4⋊C8C2×D1111yescharacteristic
152C2×C4×C8C2×D1111yescharacteristic
153#400—222no—
154#389—221no—
155#389—221no—
156#384—111no—
157#384—111no—
158#382—221no—
159#382—221no—
160C4×C4⋊C4—111no—
161C4×C4⋊C4C2×D1111yescharacteristic
162#340—221no—
163#340—221no—
164C22×C11#39511yescharacteristic
165C22×C11#44911yescharacteristic
166C22×C11#44911yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45211yescharacteristic
169C22×C11#45311yescharacteristic
170C22×C11#45611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11#47811yescharacteristic
176C4×C11#47811yescharacteristic
177C4×C11#47911yescharacteristic
178C4×C11#47911yescharacteristic
179C4×C11#49911yescharacteristic
180C4×C11#49911yescharacteristic
181C4×C11#50111yescharacteristic
182C4×C11#50111yescharacteristic
183Dic11—81no—
184Dic11—82no—
185Dic11—81no—
186Dic11—161no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—221no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4D4411yescharacteristic
200C2×C4⋊C4D4411yescharacteristic
201C2×C42—21no—
202C2×C42—221no—
203C2×C42C22×D1111yescharacteristic
204#107—442no—
205#107—442no—
206#106—444no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8Dic2212yes—
211C4×C8—21no—
212C4×C8Dic2212yes—
213#95—21no—
214#95—222no—
215#95—222no—
216#95—222no—
217#95—221no—
218C2×C11#162411yescharacteristic
219C2×C11#163011yescharacteristic
220C2×C11#165211yescharacteristic
221C2×C11#165211yescharacteristic
222C2×C11#205911yescharacteristic
223C2×C11#205911yescharacteristic
224C2×C11#206011yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—222no—
230C22×C4—441no—
231C22×C4C2×D4411yescharacteristic
232C22×C4D4×D1111yescharacteristic
233C22×C4D4×D1111yescharacteristic
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—222no—
241C2×C8—441no—
242C2×C8—441no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—882no—
262C42—41no—
263C42—41no—
264C42—441no—
265C42—441no—
266C42C2×Dic2211yescharacteristic
267C42C2×Dic2211yescharacteristic
268C42#434111yescharacteristic
269C42Q8×D1111yescharacteristic
270C11#1057711yescharacteristic, complemented, Sylow
271C23#6693511yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—442no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—442no—
286C2×C4—442no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6692211yescharacteristic
293C2×C4#6693111yescharacteristic
294C2×C4#6693111yescharacteristic
295C2×C4#6694111yescharacteristic
296C2×C4#6694111yescharacteristic
297C2×C4#6695011yescharacteristic
298C2×C4#6695711yescharacteristic
299C2×C4#6695711yescharacteristic
300C2×C4#6696111yescharacteristic
301C2×C4#6696211yescharacteristic
302C2×C4#6696411yescharacteristic
303C2×C4#6696911yescharacteristic
304C2×C4#6696911yescharacteristic
305C2×C4#6697111yescharacteristic
306C8—24no—
307C8—42no—
308C8—442no—
309C22#1062226911yescharacteristic
310C22#1062234611yescharacteristic
311C22#1062234711yescharacteristic
312C22#1062239411yescharacteristic
313C22#1062242311yescharacteristic
314C22#1062243511yescharacteristic
315C22#1062243911yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—881no—
321C4—881no—
322C4—882no—
323C4—1761no—
324C4#1062229611yescharacteristic
325C4#1062231511yescharacteristic
326C4#1062237611yescharacteristic
327C4#1062241211yescharacteristic
328C4#1062244211yescharacteristic
329C4#1062246011yescharacteristic
330C4#1062247111yescharacteristic
331C4#1062248911yescharacteristic
332C2#1306770111yescharacteristic
333C2#1306773911yescharacteristic
334C2#1306788811yescharacteristic
335C2#1306788911yescharacteristic
336C2#1306995311yescharacteristic
337C2#1306995511yescharacteristic
338C2#1306996011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socle, prime radicalC23×C11#120
hypercenter#1279D11
hypocenterC11#10577
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
270. C11#10577semidirect

Maximal subgroups

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

subgroupindex
#130738552
#130693752
#130693742
#130687732
#130665002
#130664562
C11×#12792
#1057711