Finite Group Databasebeta

← #14664879

Subgroups — #14664879

Order 2816.

394 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 77 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#13078199C211yesmaximal, characteristic
2#13070225C211yesmaximal, characteristic, complemented
3#13068653C211yesmaximal, characteristic, complemented
4#13066634C211yesmaximal, characteristic, complemented
5#13066632C211yesmaximal, characteristic, complemented
6#13066630C211yesmaximal, characteristic, complemented
7C11×#1350C211yesmaximal, characteristic, complemented
8C2×#66972C411yescharacteristic
9C22×C8×D11C2211yescharacteristic
10#10623158—21no—
11C11×#467C2211yescharacteristic
12#10622801C411yescharacteristic
13#10622739—21no—
14C2×#66886—21no—
15#10622728C2211yescharacteristic
16#10622661—21no—
17C2×#66862—21no—
18#10622496C411yescharacteristic
19#10622493C411yescharacteristic
20#10622420—21no—
21#10622417—21no—
22C11×C22⋊C16C2211yescharacteristic
23C11×#341C2211yescharacteristic
24#10622190C2211yescharacteristic
25C22⋊(C11⋊C16)C2211yescharacteristic
26(C2×D11)⋊C16—21no—
27C2×#4343—21no—
28C22×C4×D11D411yescharacteristic
29C2×C11×Q16C2×C411yescharacteristic
30C2×C11×M16—21no—
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—21no—
33#66999—21no—
34C2×#4325—21no—
35#66983—21no—
36C2×#4318—21no—
37C22×C11⋊C8D411yescharacteristic
38#66972—42no—
39C2×D88C2×C411yescharacteristic
40C2×C8×D11—42no—
41C2×C8×D11C2×C411yescharacteristic
42C2×C8×D11C2×C411yescharacteristic
43C2×C8×D11D411yescharacteristic
44C2×C8×D11D411yescharacteristic
45#66948—21no—
46#66947—41no—
47#66946—41no—
48#66945—21no—
49#66935—41no—
50(C22⋊D11)⋊C4—41no—
51C2×C11×C16—21no—
52C11×#107C2×C411yescharacteristic
53C11×#103—21no—
54#66899—21no—
55#66886—42no—
56#66885—21no—
57(C2×D11)⋊C8—41no—
58(C2×D11)⋊C8—41no—
59#66882C2×C411yescharacteristic
60C2×C11⋊C16—21no—
61#66873—21no—
62#66872—21no—
63#66862—42no—
64#11894—111nomaximal, Sylow
65C23×D11SD1611yescharacteristic
66C2×Q8×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C2×C22⋊D11—41no—
69C22×Dic11SD1611yescharacteristic
70#4343—42no—
71#4343—42no—
72C2×D44—21no—
73C2×D44—41no—
74C2×D44—41no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C2×C4×D11C22⋊C411yescharacteristic
79C2×C4×D11C22⋊C411yescharacteristic
80C2×C4×D11D811yescharacteristic
81C2×C4×D11D811yescharacteristic
82C11×Q16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11C22×C411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92#4325—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97C4⋊Dic11—21no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8C22⋊C411yescharacteristic
105C2×C11⋊C8C22⋊C411yescharacteristic
106D88—41no—
107C8×D11—22no—
108C8×D11—22no—
109C8×D11—41no—
110C8×D11—41no—
111C11×C16—41no—
112C11⋊C16—41no—
113#3050—111no—
114#2112—111no—
115#1810—111no—
116#1350—111no—
117#1350D1111yescharacteristic, complemented
118#1349—111no—
119#1349—111no—
120C23×C11C2×SD1611yescharacteristic
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11#10211yescharacteristic
126C22×D11#10211yescharacteristic
127Q8×C11—41no—
128Q8×C11—41no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C22⋊D11—82no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11#10211yescharacteristic
139C2×Dic11#10211yescharacteristic
140D44—41no—
141D44—41no—
142D44—82no—
143D44—82no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—82no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—81no—
154C11⋊C8—21no—
155C11⋊C8—81no—
156C11⋊C8#9912yes—
157C2×#135—111no—
158C23×C8—111no—
159#525—221no—
160C2×M32—221no—
161#467—111no—
162#467C2×D1111yescharacteristic
163#466—111no—
164#466—111no—
165#465—221no—
166#465—221no—
167C2×#108—221no—
168#427—111no—
169#416—221no—
170#407—221no—
171C22⋊C16—111no—
172C22⋊C16—221no—
173C22⋊C16C2×D1111yescharacteristic
174#341—111no—
175#341C2×D1111yescharacteristic
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11C2×#10211yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—44no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11C2×#9911yescharacteristic
194C4×C11#42111yescharacteristic
195Dic11—21no—
196Dic11—21no—
197Dic11—81no—
198C2×#41—221no—
199C23×C4—111no—
200#135—442no—
201C2×Q16C4×D1111yescharacteristic
202C2×SD16—221no—
203C2×D8—111no—
204C2×M16—21no—
205C2×M16—221no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8—111no—
209C22×C8—111no—
210C22×C8—111no—
211C22×C8—442no—
212C22×C8C22×D1111yescharacteristic
213#123—441no—
214C22⋊Q8—21no—
215C22⋊Q8—221no—
216#121—221no—
217#121—221no—
218#120—441no—
219C4×D4—441no—
220C4×D4—441no—
221#117—221no—
222M32—442no—
223C2×C16—21no—
224C2×C16—221no—
225#108—442no—
226#107—111no—
227#107C4×D1111yescharacteristic
228#106—221no—
229#103—21no—
230#103—221no—
231#102—221no—
232#102—221no—
233C22⋊C8—441no—
234C22⋊C8—441no—
235C2×C11—41no—
236C2×C11#151911yescharacteristic
237C2×C11#214311yescharacteristic
238C2×C11#214811yescharacteristic
239D11—41no—
240D11—41no—
241D11—161no—
242C24—111no—
243#41—442no—
244#41—442no—
245C2×Q8—21no—
246C2×D4—221no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4D4×D1111yescharacteristic
259Q16—41no—
260SD16—442no—
261D8—441no—
262M16—41no—
263M16—41no—
264M16—441no—
265M16—441no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8C2×C4×D1111yescharacteristic
277C2×C8D4×D1111yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C22⋊C4—41no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42—441no—
288C16—41no—
289C16—441no—
290C11#1189411yescharacteristic, complemented, Sylow
291C23—111no—
292C23—111no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23SD16×D1111yescharacteristic
298Q8—41no—
299Q8—41no—
300D4—441no—
301D4—441no—
302D4—882no—
303D4—882no—
304D4—882no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—882no—
320C2×C4C22⋊C4×D1111yescharacteristic
321C2×C4D8×D1111yescharacteristic
322C8—21no—
323C8—21no—
324C8—81no—
325C8—112no—
326C8—221no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—221no—
335C22—221no—
336C22—221no—
337C22—444no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22D11×#10211yescharacteristic
342C4—21no—
343C4—81no—
344C4—81no—
345C4—221no—
346C4—221no—
347C4—881no—
348C4D11×#9911yescharacteristic
349C4#1062243411yescharacteristic
350C2—41no—
351C2—441no—
352C2—441no—
353C2—1761no—
354C2#1306718211yescharacteristic
355C2#1307034211yescharacteristic
356C2#1307036411yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1350C2
socleC22×C11C2×#102
prime radical#13078199C2
cosocleC22×C8×C11C23
hypercenter#1350D11
hypocenterC11#11894
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
2. #13070225C2semidirect
3. #13068653C2semidirect
4. #13066634C2semidirect
5. #13066632C2semidirect
6. #13066630C2semidirect
7. C11×#1350C2semidirect
117. #1350D11semidirect
290. C11#11894semidirect

Maximal subgroups

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

subgroupindex
#130781992
#130702252
#130686532
#130666342
#130666322
#130666302
C11×#13502
#1189411