Finite Group Databasebeta

← #14647892

Subgroups — #14647892

Order 2816.

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

normal subgroups only

This group has 380 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#13077757C211yesmaximal, characteristic
2#13068770C211yesmaximal, characteristic, complemented
3#13067402C211yesmaximal, characteristic, complemented
4#13067100C211yesmaximal, characteristic
5#13067030C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8#10623010C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622538C2211yescharacteristic
13C2×C4⋊(C11⋊C8)—21no—
14C2×C4⋊(C11⋊C8)—21no—
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622453—21no—
18#10622452—21no—
19#10622343—21no—
20(C22⋊D11)⋊C8—21no—
21#10622319—21no—
22#10622314—21no—
23#10622118—21no—
24#10622117—21no—
25#10622097—21no—
26#10622094—21no—
27#10622090C411yescharacteristic
28#10622090C411yescharacteristic
29#10622089C411yescharacteristic
30#10622089C411yescharacteristic
31C2×C11×M16—21no—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34#66983C2×C411yescharacteristic
35#66982—21no—
36C4×C22⋊D11—21no—
37#66977C2×C411yescharacteristic
38C22×C11⋊C8—21no—
39C22×C11⋊C8D411yescharacteristic
40C22×C11⋊C8D411yescharacteristic
41C2×#4313—21no—
42C2×C8×D11—21no—
43#66929—21no—
44#66928Q811yescharacteristic
45C4×D44D411yescharacteristic
46#66925—21no—
47#66923Q811yescharacteristic
48C4×Dic22D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×C4⋊C8D411yescharacteristic
51C11×C22⋊C8—21no—
52C11×#97—21no—
53C11×#97—21no—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11×#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)C2×C411yescharacteristic
59C22⋊(C11⋊C8)C2×C411yescharacteristic
60(C2×D11)⋊C8—21no—
61(C2×D11)⋊C8—21no—
62#66879—21no—
63Dic11⋊C8—21no—
64Dic11⋊C8—21no—
65C8×Dic11—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—42no—
72C4⋊(C11⋊C8)—42no—
73C4×C11⋊C8—21no—
74#8876—111nomaximal, Sylow
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—21no—
81C2×D44C4⋊C411yescharacteristic
82C2×C4×D11—21no—
83C2×Dic22C4⋊C411yescharacteristic
84C11×M16—22no—
85C11×M16—41no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—41no—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×Q811yescharacteristic
94C42×C11#4111yescharacteristic
95C22⋊Dic11—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11C4⋊C411yescharacteristic
101C4⋊Dic11C4⋊C411yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#4313—81no—
117C8×D11—81no—
118#2992—111no—
119#1843—111no—
120#1573—111no—
121#1500—111no—
122#1483—111no—
123#1300D1111yescharacteristic, complemented
124#1283—111no—
125C23×C11C4×D411yescharacteristic
126C22×D11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
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×C11C2×C4⋊C411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C22⋊D11—41no—
145C22⋊D11—41no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149D44—41no—
150C4×D11—41no—
151C4×D11—41no—
152Dic22—41no—
153C8×C11—42no—
154C8×C11—41no—
155C8×C11—41no—
156C11⋊C8—41no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—41no—
160C11⋊C8—81no—
161#529—111no—
162#446—221no—
163#435—221no—
164#435—221no—
165C8×D4—221no—
166#433—221no—
167#432C2×D1111yescharacteristic
168#431—111no—
169#424—221no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8—221no—
173C2×C4⋊C8—221no—
174C4×M16C2×D1111yescharacteristic
175#376C2×D1111yescharacteristic
176#335—221no—
177#334—221no—
178#328—111no—
179#328—111no—
180#327—111no—
181#327—111no—
182Q8⋊C8—221no—
183D4⋊C8—221no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11#38511yescharacteristic
187C22×C11#44311yescharacteristic
188C22×C11#44411yescharacteristic
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—42no—
199C4×C11#45311yescharacteristic
200C4×C11#45611yescharacteristic
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204C2×M16—21no—
205C2×M16—221no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8—221no—
209C22×C8—221no—
210#126—221no—
211#125—111no—
212#124—111no—
213#123—221no—
214C22⋊Q8—111no—
215#121—111no—
216C4×Q8—111no—
217C4×D4—111no—
218C4×D4—221no—
219#117—221no—
220C2×C42—21no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229C4⋊C8—442no—
230C4⋊C8—442no—
231C4⋊C8D4411yescharacteristic
232C4⋊C8D4411yescharacteristic
233C22⋊C8—21no—
234C22⋊C8—111no—
235C22⋊C8—111no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238#97—21no—
239#97—21no—
240#97—221no—
241C4×C8—21no—
242C4×C8—221no—
243C4×C8—221no—
244#95—21no—
245#95C4×D1111yescharacteristic
246#95C4×D1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#185911yescharacteristic
250C2×C11#186611yescharacteristic
251C2×C11#186811yescharacteristic
252D11—81no—
253C2×Q8—111no—
254C2×D4—111no—
255C2×D4—221no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4C2×C4×D1111yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262M16—22no—
263M16—41no—
264M16—881no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—41no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—221no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—881no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C42—22no—
290C42—22no—
291C42—221no—
292C42C2×D4411yescharacteristic
293C42#433911yescharacteristic
294C42D4×D1111yescharacteristic
295C42Q8×D1111yescharacteristic
296C11#887611yescharacteristic, complemented, Sylow
297C23—221no—
298C23(C22⋊D11)⋊C411yescharacteristic
299Q8—441no—
300D4—441no—
301D4—441no—
302D4—441no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4C4×D4411yescharacteristic
320C2×C4#6693511yescharacteristic
321C2×C4#6693611yescharacteristic
322C2×C4C4⋊C4×D1111yescharacteristic
323C2×C4#6694911yescharacteristic
324C2×C4#6695011yescharacteristic
325C8—42no—
326C8—41no—
327C8—41no—
328C8—441no—
329C8—441no—
330C8—441no—
331C8—441no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—441no—
336C22—441no—
337C22—441no—
338C22#1062228111yescharacteristic
339C22#1062243611yescharacteristic
340C22#1062243711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—441no—
349C4—441no—
350C4—441no—
351C4#1062243511yescharacteristic
352C4#1062243911yescharacteristic
353C2—21no—
354C2—21no—
355C2—881no—
356C2#1306884311yescharacteristic
357C2#1306889211yescharacteristic
358C2#1306890311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1300C2
socleC22×C11#385
prime radical#66983C2×C4
cosocleC2×C42×C11C23
hypercenter#1300D11
hypocenterC11#8876
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
2. #13068770C2semidirect
3. #13067402C2semidirect
6. #13066467C2semidirect
7. C11×#1300C2semidirect
123. #1300D11semidirect
296. C11#8876semidirect

Maximal subgroups

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

subgroupindex
#130777572
#130687702
#130674022
#130671002
#130670302
#130664672
C11×#13002
#887611