Finite Group Databasebeta

← #14641982

Subgroups — #14641982

Order 2816.

506 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C4×#66977C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066441C212yesmaximal, complemented
4#13066440C212yesmaximal, complemented
5C11×#1749C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C2×C4×Dic22C411yescharacteristic
9C2×C11×C22⋊C8—21no—
10C2×C11×#97—21no—
11#10622825C411yescharacteristic
12#10622823—21no—
13C4×C22⋊Dic11—21no—
14C2×C22⋊(C11⋊C8)—21no—
15C4×C4⋊Dic11C411yescharacteristic
16#10622546—21no—
17C4×Dic11⋊C4—21no—
18#10622542C2211yescharacteristic
19#10622541C2211yescharacteristic
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—22no—
28C2×C42×C11—42no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38#66977—22no—
39#66977—22no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—22no—
46C4×Dic22—42no—
47C11×C22⋊C8—24no—
48C11×#97—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—42no—
55#7623—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×Dic22—21no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22M1612yes—
81C2×C8×C11—24no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C42×C11—22no—
85C42×C11—22no—
86C42×C11—41no—
87C42×C11—41no—
88C22⋊Dic11—24no—
89C22⋊Dic11—42no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11M1612yes—
94Dic11⋊C4—24no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97C4×Dic11—42no—
98C4×Dic11—42no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—42no—
102C4×C22⋊Q8—111no—
103#1817—111no—
104#1749D1111yescharacteristic
105#1272—112no—
106#1271—112no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11#10412yes—
114C23×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11#9912yes—
134C2×C4×C11C2×M1611yescharacteristic
135C2×C4×C11C2×M1611yescharacteristic
136C2×C4×C11#13512yes—
137C2×C4×C11#13712yes—
138C2×Dic11—22no—
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150Dic22—42no—
151Dic22—42no—
152C8×C11—44no—
153C11⋊C8—82no—
154C2×C22⋊Q8—111no—
155C2×C4×Q8—111no—
156C22×C42C2×D1111yescharacteristic
157C2×C22⋊C8—21no—
158C2×C22⋊C8—221no—
159C2×#97—21no—
160#391—111no—
161#389—111no—
162#387—221no—
163#385—221no—
164#380—111no—
165C4×C4⋊C4—111no—
166C4×C4⋊C4—221no—
167C4×C22⋊C4—221no—
168#336—112no—
169#336—221no—
170#336C2×D1112yes—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11#40711yescharacteristic
179C22×C11C2×#9911yescharacteristic
180C22×C11#41311yescharacteristic
181C22×C11#41611yescharacteristic
182C22×C11#41911yescharacteristic
183C22×C11C2×#10411yescharacteristic
184C22×C11#42111yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—42no—
193Dic11—42no—
194Dic11—81no—
195Dic11—81no—
196C22×Q8—111no—
197C23×C4C4×D1111yescharacteristic
198C23×C4D4411yescharacteristic
199C23×C4C22⋊D1111yescharacteristic
200C22×C8—22no—
201C22×C8—222no—
202C22⋊Q8—222no—
203C22⋊Q8—222no—
204C4×Q8—442no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C42—42no—
214C2×C42—221no—
215C2×C42—221no—
216C2×C42C4×D1111yescharacteristic
217C2×C42D4411yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C22⋊C8—24no—
221C22⋊C8—442no—
222#97—42no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11—42no—
229C2×C11#146511yescharacteristic
230C2×C11#148811yescharacteristic
231C2×C11#149111yescharacteristic
232C2×C11#150111yescharacteristic
233C2×C11#151111yescharacteristic
234C2×C11#153211yescharacteristic
235C2×C11#155411yescharacteristic
236C24(C2×D11)⋊C411yescharacteristic
237C2×Q8—112no—
238C2×Q8—221no—
239C2×Q8—441no—
240C2×Q8—441no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4C2×C4×D1111yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C2×C8—24no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—442no—
265C2×C8—442no—
266C2×C8—442no—
267C4⋊C4—112no—
268C4⋊C4—224no—
269C4⋊C4—221no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C22⋊C4—224no—
275C22⋊C4—442no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—41no—
280C42—442no—
281C42—442no—
282C11#762311yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#6686912yes—
290C23C2×(C2×D11)⋊C411yescharacteristic
291Q8—442no—
292Q8—442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4#6687012yes—
324C2×C4M16×D1111yescharacteristic
325C2×C4M16×D1111yescharacteristic
326C2×C4#6696212yes—
327C2×C4#6700312yes—
328C8—44no—
329C8—882no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×#6686911yescharacteristic
338C22C2×#6687011yescharacteristic
339C22#1062261511yescharacteristic
340C22#1062273311yescharacteristic
341C22#1062273911yescharacteristic
342C22#1062274511yescharacteristic
343C22#1062275211yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—442no—
352C4—442no—
353C4—881no—
354C4—881no—
355C2—42no—
356C2#1306695211yescharacteristic
357C2#1306704811yescharacteristic
358C2#1306706411yescharacteristic
359C2#1306710511yescharacteristic
360C2#1306715011yescharacteristic
361C2#1306723411yescharacteristic
362C2#1306732711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#7623
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13066441C2semidirect
4. #13066440C2semidirect
282. C11#7623semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130686842
#130664412
#130664402
C11×#17492
#762311