Finite Group Databasebeta

← #14642248

Subgroups — #14642248

Order 2816.

464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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#13076980C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic, complemented
3#13068464C211yesmaximal, characteristic, complemented
4#13066440C211yesmaximal, characteristic, complemented
5#13066438C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#1270C211yesmaximal, characteristic
8C2×#66932—21no—
9C11×#390C2211yescharacteristic
10#10622834C411yescharacteristic
11#10622834C411yescharacteristic
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14C2×Dic11⋊C8—21no—
15C2×C8×Dic11—21no—
16#10622598C411yescharacteristic
17#10622586C411yescharacteristic
18#10622564—21no—
19#10622558—21no—
20#10622557—21no—
21C42×Dic11C2211yescharacteristic
22#10622541C2211yescharacteristic
23C11×#336C2211yescharacteristic
24C11×#336C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66932—42no—
52#66932—42no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66879—42no—
57Dic11⋊C8—24no—
58Dic11⋊C8—24no—
59C8×Dic11—42no—
60#7686—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—41no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—22no—
100C4×Dic11—22no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—41no—
106C4×Dic11D812yes—
107C4×Dic11SD1612yes—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2860—111no—
115#1767—111no—
116C4×C4⋊C8—111no—
117#1271—111no—
118#1271—111no—
119#1270—111no—
120#1270D1111yescharacteristic
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C2×C22⋊C411yescharacteristic
129D4×C11—81no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11#13111yescharacteristic
141C2×C4×C11#13111yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11#10212yes—
161C2×Dic11#10212yes—
162C2×Dic11#10412yes—
163C2×Dic11#10412yes—
164C8×C11—42no—
165C8×C11—42no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C2×#126—221no—
169C2×C4⋊C8—221no—
170C2×C4⋊C8—221no—
171C2×#97—221no—
172C2×C4×C8—221no—
173#390—111no—
174#390—111no—
175#390C2×D1111yescharacteristic
176#389—111no—
177#389—111no—
178#389—111no—
179#388—221no—
180#388—221no—
181#388—221no—
182C43—111no—
183#336—111no—
184#336—111no—
185#336C2×D1111yescharacteristic
186#336C2×D1111yescharacteristic
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#40811yescharacteristic
195C22×C11#41011yescharacteristic
196C22×C11#41311yescharacteristic
197C22×C11C2×#10211yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—81no—
208Dic11—22no—
209Dic11—22no—
210Dic11—22no—
211Dic11—22no—
212Dic11—81no—
213Dic11—81no—
214C22×D4C4×D1111yescharacteristic
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—221no—
218C22×C8—221no—
219#126—442no—
220#126—442no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4C4×D1111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—224no—
241C4⋊C8—224no—
242#97—442no—
243C4×C8—442no—
244#95—221no—
245#95—221no—
246#95—221no—
247C2×C11—161no—
248C2×C11#147311yescharacteristic
249C2×C11#148311yescharacteristic
250C2×C11#149211yescharacteristic
251C2×C11#150211yescharacteristic
252C2×C11#150911yescharacteristic
253C2×C11#152411yescharacteristic
254C2×C11#154711yescharacteristic
255C24—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C2×C8—441no—
282C4⋊C4—41no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C42—41no—
299C42—112no—
300C42—112no—
301C42—222no—
302C42—222no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42—221no—
307C42—441no—
308C11#768611yescharacteristic, complemented, Sylow
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23C22⋊C4×D1111yescharacteristic
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—112no—
329C2×C4—112no—
330C2×C4—112no—
331C2×C4—112no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4#6695411yescharacteristic
347C2×C4#6696011yescharacteristic
348C2×C4D8×D1111yescharacteristic
349C2×C4#6696411yescharacteristic
350C2×C4SD16×D1111yescharacteristic
351C2×C4#6696811yescharacteristic
352C8—42no—
353C8—42no—
354C8—442no—
355C8—442no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22#1062234011yescharacteristic
364C22#1062235311yescharacteristic
365C22#1062235811yescharacteristic
366C22D11×#10211yescharacteristic
367C22#1062238411yescharacteristic
368C22D11×#10411yescharacteristic
369C22D11×#10411yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—222no—
378C4—222no—
379C4—222no—
380C4—222no—
381C4—881no—
382C4—881no—
383C2—161no—
384C2#1306698211yescharacteristic
385C2#1306702611yescharacteristic
386C2#1306706511yescharacteristic
387C2#1306710911yescharacteristic
388C2#1306713811yescharacteristic
389C2#1306720111yescharacteristic
390C2#1306729011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1270D11
hypocenterC11#7686
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13068468C2semidirect
3. #13068464C2semidirect
4. #13066440C2semidirect
5. #13066438C2semidirect
308. C11#7686semidirect

Maximal subgroups

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

subgroupindex
#130769802
#130684682
#130684642
#130664402
#130664382
#130664372
C11×#12702
#768611