Finite Group Databasebeta

← #14672918

Subgroups — #14672918

Order 2816.

572 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 75 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#13076609C211yesmaximal, characteristic, complemented
2#13068575C212yesmaximal
3#13066743C211yesmaximal, characteristic, complemented
4#13066742C212yesmaximal, complemented
5C11×#1793C211yesmaximal, characteristic
6C2×C11×2−1+4C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C2×C11×#101C2211yescharacteristic
10C11×#391C2211yescharacteristic
11C2×#66901—22no—
12#10622845—22no—
13#10622843C2212yes—
14C2×#66900C2212yes—
15#10622592—21no—
16#10622542—21no—
17#10622269—22no—
18#10622259—22no—
19C11×2−1+4—21no—
20C11×2−1+4—22no—
21C11×2−1+4—42no—
22C11×2−1+4Q812yescomplemented
23C2×C11×#41—22no—
24C2×C11×#41—21no—
25C2×C11×#41—41no—
26C22×Q8×C11—41no—
27C22×Q8×C11C2311yescharacteristic
28C22×Dic22—21no—
29C22×Dic22—21no—
30C2×C11×M16—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11D412yes—
37C2×#4318—22no—
38C11×#104—42no—
39C11×#103—41no—
40C11×#102—41no—
41C11×#101—22no—
42C11×#95—22no—
43#66901—44no—
44#66900—22no—
45#66900—22no—
46#66899—42no—
47#66896—42no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52#13378—111nomaximal, Sylow
53C11×#41—24no—
54C11×#41—22no—
55C11×#41—24no—
56C11×#41—22no—
57C11×#41—42no—
58C11×#41—41no—
59C11×#41—42no—
60C11×#41—42no—
61C11×#41—44no—
62C11×#41—42no—
63C11×#41—41no—
64C2×Q8×C11—22no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×Q811yescharacteristic
72C2×Q8×C11#4111yescharacteristic
73C2×Q8×C11#4112yes—
74C2×D4×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—42no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C2×Dic22—24no—
86C2×Dic22—81no—
87C2×Dic22—81no—
88C2×Dic22—82no—
89C2×Dic22—81no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C42×C11—41no—
95C4⋊Dic11—42no—
96C4⋊Dic11—81no—
97Dic11⋊C4—82no—
98C4×Dic11—42no—
99#4318—42no—
100#4318—42no—
101C2×C11⋊C8—42no—
102#2811—111no—
103#1793—112no—
104#1793D1111yescharacteristic
105#1394—112no—
106#1394—111no—
107C23×C11—41no—
108C23×C11#12011yescharacteristic
109Q8×C11—24no—
110Q8×C11—22no—
111Q8×C11—41no—
112Q8×C11—41no—
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—41no—
116D4×C11—24no—
117D4×C11—22no—
118D4×C11—42no—
119D4×C11—41no—
120D4×C11—42no—
121D4×C11—42no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11C22⋊Q812yes—
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11#12412yes—
139C2×C4×C11#12411yescharacteristic
140C2×Dic11—24no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146Dic22—84no—
147Dic22—84no—
148C8×C11—81no—
149C11⋊C8—82no—
150C2×2−1+4C2×D1111yescharacteristic
151C2×#104—21no—
152C2×#104—222no—
153#417—21no—
154#417—222no—
155C2×#101—112no—
156C2×#101C2×D1111yescharacteristic
157#395—222no—
158#395—221no—
159#391—112no—
160#391—222no—
161#391—221no—
162#391C2×D1111yescharacteristic
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—42no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#39311yescharacteristic
169C22×C11B(4,𝔽2)11yescharacteristic
170C22×C11B(4,𝔽2)11yescharacteristic
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—22no—
174C4×C11—21no—
175C4×C11—42no—
176C4×C11—42no—
177C4×C11—81no—
178Dic11—44no—
179Dic11—82no—
1802−1+4—21no—
1812−1+4—22no—
1822−1+4—42no—
1832−1+4Dic2212yescomplemented
184C2×#41—22no—
185C2×#41—21no—
186C2×#41—41no—
187C22×Q8—41no—
188C22×Q8—221no—
189C22×Q8—221no—
190C22×Q8C22×D1111yescharacteristic
191C2×M16—21no—
192C2×M16—222no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4C22⋊D1111yescharacteristic
197C2×C42—112no—
198C2×C42C22⋊D1111yescharacteristic
199#104—42no—
200#104—444no—
201#103—41no—
202#103—442no—
203#102—41no—
204#102—442no—
205#101—22no—
206#101—222no—
207#101—222no—
208#95—22no—
209#95—222no—
210#95—221no—
211#95—222no—
212#95—222no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—82no—
216C2×C11#202911yescharacteristic
217C2×C11#220211yescharacteristic
218C2×C11#220511yescharacteristic
219#41—22no—
220#41—24no—
221#41—24no—
222#41—22no—
223#41—41no—
224#41—42no—
225#41—42no—
226#41—42no—
227#41—44no—
228#41—42no—
229#41—41no—
230C2×Q8—21no—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—44no—
237C2×Q8—224no—
238C2×Q8—881no—
239C2×Q8—881no—
240C2×Q8—882no—
241C2×Q8—881no—
242C2×Q8C2×Dic2211yescharacteristic
243C2×Q8#433911yescharacteristic
244C2×Q8#434112yes—
245C2×D4—21no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4D4×D1112yes—
255C22×C4C2×C22⋊D1111yescharacteristic
256M16—41no—
257M16—41no—
258M16—442no—
259M16—442no—
260C2×C8—41no—
261C2×C8—442no—
262C4⋊C4—41no—
263C4⋊C4—442no—
264C4⋊C4—882no—
265C4⋊C4—881no—
266C42—41no—
267C42—442no—
268C11#1337811yescharacteristic, complemented, Sylow
269C23—41no—
270C23#6699011yescharacteristic
271Q8—24no—
272Q8—22no—
273Q8—41no—
274Q8—41no—
275Q8—42no—
276Q8—41no—
277Q8—42no—
278Q8—884no—
279Q8—884no—
280D4—24no—
281D4—22no—
282D4—41no—
283D4—42no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—224no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4#6693112yes—
307C2×C4#6693812yes—
308C2×C4#6697711yescharacteristic
309C2×C4#6698911yescharacteristic
310C8—81no—
311C8—882no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—81no—
316C22—81no—
317C22#1062256011yescharacteristic
318C22#1062264511yescharacteristic
319C22#1062264511yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—444no—
328C4—882no—
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1306978011yescharacteristic
333C2#1307063211yescharacteristic
334C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1793C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×2−1+4C22
hypercenter#1793D11
hypocenterC11#13378
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1793

Complements

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

NH ≅ G/Ntype
1. #13076609C2semidirect
3. #13066743C2semidirect
4. #13066742C2semidirect
22. C11×2−1+4Q8semidirect
183. 2−1+4Dic22semidirect
268. C11#13378semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130685752
#130667432
#130667422
C11×#17932
#1337811