Finite Group Databasebeta

← #14664527

Subgroups — #14664527

Order 2816.

368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074439C211yesmaximal, characteristic
2#13068698C211yesmaximal, characteristic
3#13066949C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066646C211yesmaximal, characteristic, complemented
6#13066645C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#66997C411yescharacteristic
9C2×#66945C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622844C411yescharacteristic
12#10622739—21no—
13#10622605—21no—
14#10622592C2211yescharacteristic
15#10622585—21no—
16#10622332—21no—
17#10622286C411yescharacteristic
18#10622280—21no—
19#10622273—21no—
20#10622263C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33#66997—41no—
34#66997—41no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4C2×C411yescharacteristic
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47#66945—41no—
48#66945—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58(C2×D11)⋊C8—41no—
59(C2×D11)⋊C8—41no—
60#66879—41no—
61Dic11⋊C8—41no—
62#11819—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C2×Q8×C11—41no—
65C2×Q8×C11—81no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—41no—
81C2×Dic22—41no—
82C2×Dic22—81no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—81no—
92(C2×D11)⋊C4—81no—
93C4⋊Dic11—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2628—111no—
108#1822—111no—
109#1464—111no—
110#1354—111no—
111#1354—111no—
112#1354—111no—
113#1354D1111yescharacteristic, complemented
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—41no—
119C22×D11—41no—
120Q8×C11—82no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11#9911yescharacteristic
148C2×Dic11#9911yescharacteristic
149C4×D11—41no—
150C4×D11—41no—
151C4×D11—41no—
152C4×D11—41no—
153Dic22—82no—
154C8×C11—81no—
155C8×C11—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158C2×C4⋊Q8—111no—
159C2×#117—111no—
160#432—221no—
161#407—221no—
162#400—221no—
163#399—221no—
164#395—111no—
165#395C2×D1111yescharacteristic
166#393—111no—
167#393—111no—
168#389—221no—
169#382—111no—
170#380—221no—
171#343—111no—
172#343—221no—
173#343C2×D1111yescharacteristic
174#324—111no—
175#324C2×D1111yescharacteristic
176#323—221no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11C2×#9911yescharacteristic
180C22×C11#41911yescharacteristic
181C22×C11#42111yescharacteristic
182C2×D11—42no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—81no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—21no—
194Dic11—21no—
195Dic11—41no—
196Dic11—41no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—111no—
200C22×Q8C4×D1111yescharacteristic
201C23×C4—111no—
202C2×M16—21no—
203C2×M16—221no—
204C4⋊Q8—441no—
205C4⋊Q8—441no—
206#117—441no—
207#117—441no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C42—111no—
220C2×C42—111no—
221C4⋊C8—441no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C22⋊C8—441no—
225C22⋊C8—441no—
226#97—441no—
227#95—21no—
228#95—111no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95C4×D1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#151111yescharacteristic
237C2×C11#212211yescharacteristic
238C2×C11#213511yescharacteristic
239D11—81no—
240C24—111no—
241C2×Q8—41no—
242C2×Q8—81no—
243C2×Q8—441no—
244C2×Q8—881no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—441no—
257C22×C4C2×C4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260M16—41no—
261M16—41no—
262M16—441no—
263M16—441no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—881no—
276C22⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—881no—
279C22⋊C4—881no—
280C42—221no—
281C42—221no—
282C42—221no—
283C42—221no—
284C11#1181911yescharacteristic, complemented, Sylow
285C23—221no—
286C23—221no—
287C23—221no—
288C23—441no—
289C23—441no—
290C23C22⋊C4×D1111yescharacteristic
291Q8—82no—
292Q8—882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—111no—
306C2×C4—111no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4#6696811yescharacteristic
324C2×C4#6697111yescharacteristic
325C8—81no—
326C8—81no—
327C8—881no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—442no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22—881no—
336C22D11×#9911yescharacteristic
337C22#1062241511yescharacteristic
338C22#1062243411yescharacteristic
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—221no—
346C4—221no—
347C4—441no—
348C4—441no—
349C4—881no—
350C4—881no—
351C2—21no—
352C2—21no—
353C2—881no—
354C2#1306714711yescharacteristic
355C2#1307026411yescharacteristic
356C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11819
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #13066647C2semidirect
5. #13066646C2semidirect
6. #13066645C2semidirect
7. C11×#1354C2semidirect
113. #1354D11semidirect
284. C11#11819semidirect

Maximal subgroups

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

subgroupindex
#130744392
#130686982
#130669492
#130666472
#130666462
#130666452
C11×#13542
#1181911