Finite Group Databasebeta

← #14642002

Subgroups — #14642002

Order 2816.

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

normal subgroups only

This group has 510 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
1#13071080C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic, complemented
3#13066438C212yesmaximal, complemented
4#13066436C212yesmaximal
5C11×#1767C211yesmaximal, characteristic, complemented
6C2×C4×D44C411yescharacteristic
7C2×#66925—21no—
8C2×C11×C4⋊C8—21no—
9C2×C11×#97—21no—
10C43×C11C2211yescharacteristic
11#10622553—21no—
12#10622553—21no—
13#10622552C411yescharacteristic
14#10622552C2211yescharacteristic
15C4×(C2×D11)⋊C4—21no—
16C4×C4⋊Dic11C411yescharacteristic
17#10622541C411yescharacteristic
18#10622541C2211yescharacteristic
19C2×#66867—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C22×D44C2×C411yescharacteristic
24C22×C4×D11—21no—
25C22×C8×C11—22no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11C2×C411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—22no—
45C4×D44—22no—
46C4×D44—22no—
47#66925—44no—
48C11×C4⋊C8—24no—
49C11×#97—42no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53#66867—24no—
54#7628—111nomaximal, Sylow
55C23×D11—21no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×D44—21no—
67C2×D44—41no—
68C2×D44—41no—
69C2×D44M1612yes—
70C2×C4×D11—24no—
71C2×C4×D11—42no—
72C2×C4×D11—42no—
73C2×C8×C11—24no—
74C2×C8×C11—42no—
75C2×C8×C11—42no—
76C42×C11—22no—
77C42×C11—22no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—22no—
82C42×C11—21no—
83C42×C11—41no—
84C42×C11—41no—
85(C2×D11)⋊C4—24no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11M1612yes—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97C4×Dic11—42no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101#2293—111no—
102#1767D1111yescharacteristic, complemented
103#1745—111no—
104#1271—112no—
105#1270—112no—
106C23×C11C2×C22⋊C411yescharacteristic
107C22×D11—22no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C2×C4×C11—21no—
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—21no—
130C2×C4×C11#10412yes—
131C2×C4×C11#10412yes—
132C2×C4×C11C2×M1611yescharacteristic
133C2×C4×C11C2×M1611yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)12yes—
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146D44—42no—
147D44—42no—
148C4×D11—48no—
149C8×C11—44no—
150C11⋊C8—44no—
151C2×C4×D4—111no—
152C2×#117—221no—
153C2×C4⋊C8—21no—
154C2×#97—21no—
155C2×#97—221no—
156#390—111no—
157#390—111no—
158#389—111no—
159#389—111no—
160#388—221no—
161#388—221no—
162C4×C4⋊C4—111no—
163C4×C22⋊C4—221no—
164C43C2×D1111yescharacteristic
165#336—112no—
166#336—221no—
167#336C2×D1112yes—
168C22×C11#40711yescharacteristic
169C22×C11#41011yescharacteristic
170C22×C11#41311yescharacteristic
171C22×C11#41711yescharacteristic
172C22×C11#41811yescharacteristic
173C22×C11C2×#10411yescharacteristic
174C22×C11C2×#10411yescharacteristic
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—22no—
189C4×C11—41no—
190C4×C11—41no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194C22×D4—111no—
195C23×C4—221no—
196C22×C8—22no—
197C22×C8—222no—
198C4×D4—222no—
199C4×D4—222no—
200#117—444no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—221no—
211C2×C42—221no—
212C2×C42C4×D1111yescharacteristic
213C2×C42C4×D1111yescharacteristic
214C2×C42D4411yescharacteristic
215C2×C42D4411yescharacteristic
216C2×C42C22⋊D1111yescharacteristic
217C2×C42C22⋊D1111yescharacteristic
218C2×C42C22×D1111yescharacteristic
219C4⋊C8—24no—
220#97—42no—
221#97—224no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11#146411yescharacteristic
226C2×C11#148911yescharacteristic
227C2×C11#149011yescharacteristic
228C2×C11#150511yescharacteristic
229C2×C11#150911yescharacteristic
230C2×C11#152411yescharacteristic
231C2×C11#155711yescharacteristic
232D11—82no—
233C24—221no—
234C2×D4—112no—
235C2×D4—221no—
236C2×D4—441no—
237C2×D4—441no—
238C22×C4—224no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—442no—
243C22×C4—442no—
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4C2×D4411yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251C2×C8—24no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—224no—
255C2×C8—442no—
256C2×C8—442no—
257C4⋊C4—112no—
258C4⋊C4—221no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—442no—
262C4⋊C4—442no—
263C22⋊C4—224no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C22⋊C4—441no—
268C22⋊C4—441no—
269C42—22no—
270C42—22no—
271C42—21no—
272C42—21no—
273C42—22no—
274C42—21no—
275C42—21no—
276C42—41no—
277C42—41no—
278C42—442no—
279C11#762811yescharacteristic, complemented, Sylow
280C23—222no—
281C23—441no—
282C23—441no—
283C23—441no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23C2×(C2×D11)⋊C411yescharacteristic
288D4—442no—
289D4—442no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
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—222no—
307C2×C4—448no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4#6686912yes—
317C2×C4#6688912yes—
318C2×C4M16×D1111yescharacteristic
319C2×C4M16×D1111yescharacteristic
320C2×C4#6696112yes—
321C2×C4#6698511yescharacteristic
322C2×C4#6699511yescharacteristic
323C8—44no—
324C8—444no—
325C22—442no—
326C22—442no—
327C22—442no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—881no—
332C22C2×#6686911yescharacteristic
333C22#1062257911yescharacteristic
334C22#1062261911yescharacteristic
335C22#1062273911yescharacteristic
336C22#1062274411yescharacteristic
337C22#1062274511yescharacteristic
338C22C2×#6688911yescharacteristic
339C4—22no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—442no—
349C4—881no—
350C4—881no—
351C2—882no—
352C2#1306694811yescharacteristic
353C2#1306705311yescharacteristic
354C2#1306706011yescharacteristic
355C2#1306712511yescharacteristic
356C2#1306713911yescharacteristic
357C2#1306720211yescharacteristic
358C2#1306733611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#7628
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #13068365C2semidirect
3. #13066438C2semidirect
5. C11×#1767C2semidirect
102. #1767D11semidirect
279. C11#7628semidirect

Maximal subgroups

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

subgroupindex
#130710802
#130683652
#130664382
#130664362
C11×#17672
#762811