Finite Group Databasebeta

← #14667054

Subgroups — #14667054

Order 2816.

354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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#13079922C211yesmaximal, characteristic
2#13070802C211yesmaximal, characteristic, complemented
3#13070799C211yesmaximal, characteristic, complemented
4#13070111C211yesmaximal, characteristic, complemented
5#13066624C211yesmaximal, characteristic, complemented
6#13066555C211yesmaximal, characteristic, complemented
7C11×#1347C211yesmaximal, characteristic, complemented
8#10623127—21no—
9C11×#466C2211yescharacteristic
10#10622763—21no—
11#10622728C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13C2×Dic11⋊C8C2211yescharacteristic
14#10622651—21no—
15#10622598—21no—
16#10622503—21no—
17#10622399—21no—
18#10622372—21no—
19C11×C22⋊C16C2211yescharacteristic
20C11×#340C2211yescharacteristic
21#10622200—21no—
22C22⋊(C11⋊C16)C2211yescharacteristic
23#10622167—21no—
24#10622147—21no—
25#10622143—21no—
26#10622128—21no—
27C2×#4341—41no—
28C2×C11×D8D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×#121—21no—
31C2×C11×C4⋊C4—21no—
32#66993—21no—
33#66992—41no—
34D4×Dic11—21no—
35C2×#4323—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—41no—
39C2×C4×Dic11D411yescharacteristic
40C22×C11⋊C8D411yescharacteristic
41C2×D88D411yescharacteristic
42#66946—21no—
43#66941—21no—
44#66938—41no—
45(C22⋊D11)⋊C4—41no—
46C2×C11×C16—21no—
47C11×#107D411yescharacteristic
48C11×#102—21no—
49#66896—21no—
50C11⋊#95—41no—
51#66885—21no—
52#66882—21no—
53#66882—21no—
54#66882D411yescharacteristic
55Dic11⋊C8—21no—
56Dic11⋊C8—21no—
57C2×C11⋊C16—21no—
58#66873—21no—
59#66871—21no—
60#12291—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C2×C22⋊D11—41no—
68C22×Dic11—41no—
69C22×Dic11—41no—
70C22×Dic11D811yescharacteristic
71C22×Dic11D811yescharacteristic
72#4341—82no—
73#4341—82no—
74C2×D44—21no—
75C2×C4×D11—41no—
76C2×Dic22—41no—
77C11×D8—41no—
78C2×C8×C11—41no—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—22no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C22⋊Dic11—41no—
86#4323—81no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—82no—
93Dic11⋊C4—41no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—41no—
98D88—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3245—111no—
102#2233—111no—
103#2233—111no—
104#2087—111no—
105#1347—111no—
106#1347D1111yescharacteristic, complemented
107#1322—111no—
108C23×C11—41no—
109C23×C11C2×D811yescharacteristic
110C22×D11—41no—
111D4×C11—41no—
112D4×C11—41no—
113D4×C11—81no—
114D4×C11—81no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C22⋊D11—82no—
124C22⋊D11—82no—
125C22⋊D11—81no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—82no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11SD3212yes—
137D44—41no—
138D44—41no—
139C4×D11—82no—
140Dic22—82no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—41no—
144#532—221no—
145#474—221no—
146#474—221no—
147#466—111no—
148#466—221no—
149#466C2×D1111yescharacteristic
150#459—221no—
151#459—221no—
152C2×#107—111no—
153C2×C4⋊C8—111no—
154#389—221no—
155#367—221no—
156#367—221no—
157#357—221no—
158#357—221no—
159C22⋊C16—111no—
160C22⋊C16C2×D1111yescharacteristic
161#340—221no—
162#340C2×D1111yescharacteristic
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#44711yescharacteristic
169C22×C11C2×SD3211yescharacteristic
170C22×C11#50911yescharacteristic
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11—81no—
177C4×C11#45611yescharacteristic
178C4×C11#45811yescharacteristic
179Dic11—22no—
180Dic11—41no—
181Dic11—81no—
182Dic11—161no—
183C2×#41—441no—
184C2×D8—111no—
185C2×D8—221no—
186C2×D8D4411yescharacteristic
187C22×C8—111no—
188C22×C8C22×D1111yescharacteristic
189C4⋊Q8—221no—
190#127—221no—
191#124—441no—
192#121—21no—
193#121—221no—
194#121—441no—
195C4×D4—221no—
196C4×D4—221no—
197C4×D4—441no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—441no—
201C2×C42—111no—
202C2×C16—21no—
203C2×C16—221no—
204#107—111no—
205#107—221no—
206#107—221no—
207#107—221no—
208#107D4411yescharacteristic
209C4⋊C8—221no—
210C4⋊C8—221no—
211#102—21no—
212#102—221no—
213#102—221no—
214#102—221no—
215#95—441no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11—161no—
219C2×C11#161011yescharacteristic
220C2×C11#218711yescharacteristic
221C2×C11#219011yescharacteristic
222D11—161no—
223#41—882no—
224#41—882no—
225C2×Q8—441no—
226C2×D4—21no—
227C2×D4—41no—
228C2×D4—221no—
229C2×D4—441no—
230C2×D4—441no—
231C2×D4—441no—
232C22×C4—41no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—441no—
236C22×C4—441no—
237C22×C4—441no—
238C22×C4D4×D1111yescharacteristic
239D8—41no—
240D8—441no—
241D8—881no—
242C2×C8—41no—
243C2×C8—221no—
244C2×C8—441no—
245C2×C8C2×D4411yescharacteristic
246C2×C8D4×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—221no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—882no—
255C22⋊C4—41no—
256C22⋊C4—441no—
257C22⋊C4—441no—
258C22⋊C4—441no—
259C42—221no—
260C42—221no—
261C16—41no—
262C16—441no—
263C11#1229111yescharacteristic, complemented, Sylow
264C23—41no—
265C23—441no—
266C23D8×D1111yescharacteristic
267Q8—882no—
268D4—41no—
269D4—41no—
270D4—81no—
271D4—81no—
272D4—441no—
273D4—441no—
274D4—882no—
275D4—882no—
276D4—881no—
277D4—881no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—112no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—882no—
291C2×C4—882no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4#6693511yescharacteristic
296C2×C4#6696711yescharacteristic
297C8—21no—
298C8—21no—
299C8—441no—
300C22—21no—
301C22—21no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—881no—
306C22—881no—
307C22—881no—
308C22#1062238611yescharacteristic
309C22#1062252411yescharacteristic
310C22D11×SD3211yescharacteristic
311C4—21no—
312C4—82no—
313C4—81no—
314C4—222no—
315C4—441no—
316C4—881no—
317C4—1761no—
318C4#1062235511yescharacteristic
319C4#1062243911yescharacteristic
320C2—21no—
321C2—21no—
322C2—161no—
323C2—1761no—
324C2#1306762011yescharacteristic
325C2#1307054611yescharacteristic
326C2#1307056311yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1347C2
socleC22×C11#447
prime radical#13079922C2
hypercenter#1347D11
hypocenterC11#12291
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13070802C2semidirect
3. #13070799C2semidirect
4. #13070111C2semidirect
5. #13066624C2semidirect
6. #13066555C2semidirect
7. C11×#1347C2semidirect
106. #1347D11semidirect
263. C11#12291semidirect

Maximal subgroups

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

subgroupindex
#130799222
#130708022
#130707992
#130701112
#130666242
#130665552
C11×#13472
#1229111