Finite Group Databasebeta

← #14650693

Subgroups — #14650693

Order 2816.

492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078711C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13069561C211yesmaximal, characteristic, complemented
4#13067058C211yesmaximal, characteristic
5#13066509C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622700C412yescomplemented
13#10622696C412yescomplemented
14#10622659—21no—
15#10622657—21no—
16#10622639—22no—
17#10622552—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19#10622541—21no—
20#10622539C2211yescharacteristic
21C4×#4318C2211yescharacteristic
22#10622282—22no—
23#10622280—21no—
24#10622277—21no—
25C11×#328—21no—
26C11×#328—21no—
27#10622170—22no—
28#10622121—22no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117—21no—
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4325—22no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4—22no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—22no—
48C2×C4×Dic11D412yes—
49C2×#4318—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44C2×C412yes—
53C4×D44D412yes—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#95—21no—
58C11×#95D411yescharacteristic
59C11×#95D411yescharacteristic
60#66899—22no—
61C11⋊#95—22no—
62C11⋊#95—21no—
63C22⋊(C11⋊C8)—21no—
64#66873—22no—
65#66871—22no—
66C4⋊(C11⋊C8)C2×C412yes—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70#9327—111nomaximal, Sylow
71C23×D11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—22no—
81C2×D44—21no—
82C2×D44—42no—
83C2×D44C22⋊C412yes—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—82no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—42no—
96C42×C11—41no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101#4325—44no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—82no—
105(C2×D11)⋊C4—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—42no—
108C4⋊Dic11C22⋊C412yes—
109Dic11⋊C4—82no—
110C4×Dic11—42no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#3110—111no—
116#2319—111no—
117#1986—111no—
118#1506D1111yescharacteristic, complemented
119#1490—111no—
120#1300—111no—
121#1285—111no—
122C23×C11#12011yescharacteristic
123C22×D11—22no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11—41no—
127C22×D11—41no—
128Q8×C11—42no—
129Q8×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×Dic11—22no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153D44—22no—
154D44—22no—
155D44—42no—
156C4×D11—82no—
157C4×D11—82no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161#533C2×D1111yescharacteristic
162C2×C4×D4—111no—
163#484—221no—
164#474—112no—
165#461—112no—
166#450—221no—
167#440—222no—
168#432—111no—
169#432C2×D1111yescharacteristic
170C4×M16—111no—
171#390—221no—
172#389—221no—
173#388—222no—
174#381—221no—
175#380—221no—
176C4×C4⋊C4—111no—
177#376C2×D1111yescharacteristic
178#339—222no—
179#328—21no—
180#328—21no—
181D4⋊C8—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#38611yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11#45611yescharacteristic
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—42no—
190C2×D11—82no—
191C2×D11—82no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11#42112yes—
202Dic11—42no—
203Dic11—82no—
204C22×D4—111no—
205C23×C4—221no—
206C2×SD16—222no—
207C2×M16—221no—
208C4⋊Q8C4×D1111yescharacteristic
209C4⋊Q8C4×D1111yescharacteristic
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—112no—
216C4×D4—112no—
217C4×D4—221no—
218C4×D4—221no—
219#117—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—222no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—222no—
225C2×C22⋊C4—222no—
226C2×C42—21no—
227C2×C42—112no—
228C2×C42C22×D1111yescharacteristic
229#107—222no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232#103—222no—
233#102—222no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236#97—21no—
237#97—221no—
238#97—221no—
239C4×C8—221no—
240#95—21no—
241#95—222no—
242#95—221no—
243#95C22⋊D1111yescharacteristic
244#95C22⋊D1111yescharacteristic
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#188211yescharacteristic
248C2×C11#189711yescharacteristic
249C2×C11#190411yescharacteristic
250D11—82no—
251C24—221no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—112no—
255C2×D4—221no—
256C2×D4—442no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—221no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—882no—
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—444no—
268M16—222no—
269M16—441no—
270C2×C8—41no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—112no—
280C4⋊C4—221no—
281C4⋊C4—442no—
282C4⋊C4—882no—
283C22⋊C4—41no—
284C22⋊C4—222no—
285C22⋊C4—222no—
286C22⋊C4—882no—
287C22⋊C4—882no—
288C42—42no—
289C42—41no—
290C42—442no—
291C42C2×C4×D1111yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42#434111yescharacteristic
295C11#932711yescharacteristic, complemented, Sylow
296C23—222no—
297C23—442no—
298C23—442no—
299C23—441no—
300C23—441no—
301C23#6699011yescharacteristic
302Q8—42no—
303Q8—81no—
304D4—222no—
305D4—222no—
306D4—442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—222no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—882no—
325C2×C4—882no—
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4#6693611yescharacteristic
329C2×C4#6693711yescharacteristic
330C2×C4C4×C22⋊D1111yescharacteristic
331C2×C4#6699111yescharacteristic
332C8—81no—
333C8—442no—
334C8—442no—
335C22—21no—
336C22—21no—
337C22—442no—
338C22—442no—
339C22—442no—
340C22—882no—
341C22—882no—
342C22#1062256911yescharacteristic
343C22#1062281511yescharacteristic
344C22#1062281811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—442no—
355C4—882no—
356C4#1062243412yes—
357C2—21no—
358C2—21no—
359C2—882no—
360C2#1306898211yescharacteristic
361C2#1306906111yescharacteristic
362C2#1306910611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9327
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
3. #13069561C2semidirect
5. #13066509C2semidirect
6. #13066471C2semidirect
7. C11×#1506C2semidirect
12. #10622700C4semidirect
13. #10622696C4semidirect
118. #1506D11semidirect
295. C11#9327semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130712602
#130695612
#130670582
#130665092
#130664712
C11×#15062
#932711