Finite Group Databasebeta

← #14642271

Subgroups — #14642271

Order 2816.

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

normal subgroups only

This group has 530 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#13076925C211yesmaximal, characteristic
2#13068377C211yesmaximal, characteristic
3D11×#336C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D11—21no—
9C2×#66943C411yescharacteristic
10C2×C42×D11C2211yescharacteristic
11C11×#389C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×#66879—21no—
14#10622602—21no—
15#10622600C411yescharacteristic
16#10622600C411yescharacteristic
17#10622594—21no—
18#10622590C411yescharacteristic
19#10622541C2211yescharacteristic
20#10622281—21no—
21#10622265—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—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×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C2×C8×D11—24no—
49C2×C8×D11—42no—
50C2×C8×D11—42no—
51#66943—42no—
52C42×D11—42no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59(C2×D11)⋊C8—24no—
60#66879—42no—
61#7691—111nomaximal, Sylow
62C23×D11C22⋊C411yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—41no—
102C4⋊Dic11—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C8×D11—48no—
116#2851—111no—
117#1749—111no—
118C2×#336—111no—
119#1271—111no—
120#1271—111no—
121#1271—111no—
122#1271D1111yescharacteristic, complemented
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11#10112yes—
129C22×D11#10412yes—
130C22×D11#10412yes—
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—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#13111yescharacteristic
144C2×C4×C11#13111yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11#9912yes—
164C4×D11—24no—
165C4×D11—24no—
166C4×D11—42no—
167C4×D11—42no—
168C4×D11—42no—
169C4×D11—42no—
170C8×C11—42no—
171C8×C11—42no—
172C11⋊C8—42no—
173C11⋊C8—42no—
174C23×C8—221no—
175C2×#125—111no—
176C22×C42—111no—
177C2×C22⋊C8—221no—
178C2×#97—221no—
179#389—111no—
180#389C2×D1111yescharacteristic
181#387—221no—
182#387—221no—
183#385—221no—
184#385—221no—
185#382—111no—
186#380—111no—
187#380—111no—
188#336—111no—
189#336—111no—
190#336—221no—
191#336C2×D1111yescharacteristic
192#336C2×D1111yescharacteristic
193C22×C11#40811yescharacteristic
194C22×C11C2×#9911yescharacteristic
195C22×C11C2×#10111yescharacteristic
196C22×C11#41611yescharacteristic
197C22×C11#41711yescharacteristic
198C22×C11C2×#10411yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—22no—
206C2×D11#33014yes—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—81no—
214C4×C11—81no—
215Dic11—22no—
216Dic11—41no—
217Dic11—41no—
218Dic11—81no—
219Dic11—81no—
220C23×C4—111no—
221C23×C4—111no—
222C23×C4—111no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—224no—
226C22×C8—221no—
227C22×C8—221no—
228C22×C8—442no—
229C22×C8—442no—
230#125—442no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4C4×D1111yescharacteristic
238C2×C4⋊C4C4×D1111yescharacteristic
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C42—111no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—442no—
245C2×C42C22×D1111yescharacteristic
246C22⋊C8—224no—
247#97—442no—
248#95—21no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11#147211yescharacteristic
255C2×C11#148311yescharacteristic
256C2×C11#149411yescharacteristic
257C2×C11#150111yescharacteristic
258C2×C11#150411yescharacteristic
259C2×C11C2×#33011yescharacteristic
260C2×C11#155211yescharacteristic
261D11—24no—
262C24—111no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—222no—
269C22×C4—222no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—448no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—441no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C42—41no—
313C42—222no—
314C42—222no—
315C42—441no—
316C11#769111yescharacteristic, complemented, Sylow
317C23—112no—
318C23—112no—
319C23—112no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23C22⋊C4×D1111yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—112no—
338C2×C4—224no—
339C2×C4—224no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4#6695411yescharacteristic
359C2×C4#6696011yescharacteristic
360C2×C4#6696511yescharacteristic
361C2×C4#6696711yescharacteristic
362C2×C4#6696911yescharacteristic
363C2×C4#6697111yescharacteristic
364C8—42no—
365C8—42no—
366C8—442no—
367C8—442no—
368C22—114no—
369C22—222no—
370C22—222no—
371C22—222no—
372C22—222no—
373C22—222no—
374C22—222no—
375C22#1062234011yescharacteristic
376C22D11×#9911yescharacteristic
377C22D11×#10111yescharacteristic
378C22#1062238511yescharacteristic
379C22#1062241611yescharacteristic
380C22D11×#10411yescharacteristic
381C22D11×#10411yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—222no—
391C4—441no—
392C4—441no—
393C4—881no—
394C4—881no—
395C2—224no—
396C2#1306697811yescharacteristic
397C2#1306702811yescharacteristic
398C2#1306707311yescharacteristic
399C2#1306710411yescharacteristic
400C2#1306711911yescharacteristic
401C2D11×#33011yescharacteristic
402C2#1306731311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7691
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13066440C2semidirect
5. #13066439C2semidirect
6. #13066438C2semidirect
7. C11×#1271C2semidirect
122. #1271D11semidirect
316. C11#7691semidirect

Maximal subgroups

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

subgroupindex
#130769252
#130683772
D11×#3362
#130664402
#130664392
#130664382
C11×#12712
#769111