Finite Group Databasebeta

← #14647331

Subgroups — #14647331

Order 2816.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071556C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066494C212yesmaximal, complemented
4#13066483C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C11×#99—21no—
8C11×#380C2212yes—
9#10622833—21no—
10#10622825C2211yescharacteristic
11#10622824C411yescharacteristic, complemented
12C4×C22⋊Dic11C411yescharacteristic, complemented
13C2×C11⋊#95C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622594—21no—
16#10622564—21no—
17C22⋊C4×Dic11—21no—
18#10622550C411yescharacteristic, complemented
19#10622545C411yescharacteristic, complemented
20C11×#342—21no—
21#10622166—21no—
22#10622163—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11—21no—
41C22×C11⋊C8—22no—
42C11×#99—42no—
43C11×#95—22no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95C2×C411yescharacteristic
50C11⋊#95C2×C411yescharacteristic
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—22no—
55#8763—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—81no—
66C22×C4×C11—81no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4112yes—
73C22×C4×C11#4112yes—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C22×Dic11—81no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—82no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—42no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—81no—
93C4⋊Dic11—81no—
94C4×Dic11—42no—
95C4×Dic11—81no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—82no—
98#2353—111no—
99#1799D1111yescharacteristic
100#1459—111no—
101#1294—112no—
102#1289—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11#12312yes—
112C23×C11#13512yes—
113C23×C11AGL(1,ℤ/8)11yescharacteristic
114C23×C11#13711yescharacteristic
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11#11711yescharacteristic
134C2×C4×C11#11711yescharacteristic
135C2×C4×C11#12312yes—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
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—84no—
149C11⋊C8—82no—
150C2×C4×D4C2×D1111yescharacteristic
151C2×#99—21no—
152C2×C22⋊C8—112no—
153#388—221no—
154#387—221no—
155#386—221no—
156#383—111no—
157#381—111no—
158#380—111no—
159#380C2×D1112yes—
160C4×C22⋊C4—111no—
161C4×C22⋊C4—221no—
162#376—111no—
163C2×#95—111no—
164#342—21no—
165#324—221no—
166#323—221no—
167C22×C11—21no—
168C22×C11—22no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—42no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11#38111yescharacteristic
180C22×C11#41611yescharacteristic
181C22×C11#41711yescharacteristic
182C22×C11#48212yes—
183C22×C11#48512yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—22no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—162no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C22×D4C22⋊D1111yescharacteristic
196C23×C4—221no—
197C23×C4C4×D1111yescharacteristic
198C23×C4C22×D1111yescharacteristic
199C22×C8—222no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4D4411yescharacteristic
205C2×C22⋊C4—22no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4D4411yescharacteristic
210C2×C22⋊C4C22⋊D1111yescharacteristic
211C2×C42—221no—
212C2×C42—221no—
213C2×C42C4×D1111yescharacteristic
214#99—42no—
215C22⋊C8—222no—
216C22⋊C8—222no—
217#95—22no—
218#95—111no—
219#95—111no—
220#95—111no—
221#95—111no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11—22no—
230C2×C11—22no—
231C2×C11—81no—
232C2×C11#182511yescharacteristic
233C2×C11#182711yescharacteristic
234C2×C11#182811yescharacteristic
235C24(C2×D11)⋊C411yescharacteristic
236C24C2×C22⋊D1111yescharacteristic
237C2×D4—21no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4—881no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4C2×D4411yescharacteristic
258C22×C4#434112yes—
259C22×C4#434112yes—
260C2×C8—442no—
261C2×C8—882no—
262C4⋊C4—22no—
263C4⋊C4—82no—
264C4⋊C4—881no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—442no—
270C22⋊C4—441no—
271C22⋊C4—441no—
272C22⋊C4—881no—
273C42—21no—
274C42—21no—
275C42—442no—
276C42—881no—
277C11#876311yescharacteristic, complemented, Sylow
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23C2×(C2×D11)⋊C411yescharacteristic
286C23#6698511yescharacteristic
287C23#6698812yes—
288C23#6699511yescharacteristic
289C23#6700312yes—
290D4—42no—
291D4—42no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—222no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—884no—
321C2×C4#6693011yescharacteristic
322C2×C4#6693011yescharacteristic
323C2×C4#6693912yes—
324C8—882no—
325C22—21no—
326C22—22no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22—81no—
337C22#1062255611yescharacteristic
338C22#1062257911yescharacteristic
339C22#1062261511yescharacteristic
340C22#1062264812yes—
341C22#1062265812yes—
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—162no—
349C4—442no—
350C4—881no—
351C4—881no—
352C4—881no—
353C2—22no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—81no—
358C2#1306870811yescharacteristic
359C2#1306871711yescharacteristic
360C2#1306872211yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#8763
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13066494C2semidirect
4. #13066483C2semidirect
11. #10622824C4semidirect
12. C4×C22⋊Dic11C4semidirect
18. #10622550C4semidirect
19. #10622545C4semidirect
277. C11#8763semidirect

Maximal subgroups

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

subgroupindex
#130715562
#130669342
#130664942
#130664832
C11×#17992
#876311