Finite Group Databasebeta

← #14664685

Subgroups — #14664685

Order 2816.

396 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 71 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#13072904C211yesmaximal, characteristic
2#13068695C211yesmaximal, characteristic
3D11×#324C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066623C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×#66945C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#400C2211yescharacteristic
11#10622739—21no—
12#10622596C2211yescharacteristic
13#10622595C411yescharacteristic
14D11×C22⋊C8—21no—
15#10622281—21no—
16#10622277—21no—
17#10622277C411yescharacteristic
18#10622274C411yescharacteristic
19#10622268—21no—
20#10622267—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4C2×C411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×#4318—21no—
43C2×C8×D11—41no—
44#66945—41no—
45#66945—41no—
46C4⋊C4×D11—41no—
47C4⋊C4×D11—41no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—41no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11850—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—41no—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—42no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C8×D11—82no—
107#2484—111no—
108#1821—111no—
109C2×#324—111no—
110#1353—111no—
111#1353D1111yescharacteristic, complemented
112#1346—111no—
113#1346—111no—
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—22no—
118C22×D11—41no—
119C22×D11#9911yescharacteristic
120C22×D11#9911yescharacteristic
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—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×Dic11—21no—
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—
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—41no—
151C4×D11—42no—
152C4×D11—42no—
153C4×D11—42no—
154C4×D11—81no—
155C8×C11—81no—
156C8×C11—81no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159C2×#117—111no—
160C22×C4⋊C4—111no—
161#407—221no—
162C2×C22⋊C8—221no—
163#400—111no—
164#400C2×D1111yescharacteristic
165#398—111no—
166#398—111no—
167#387—221no—
168#387—221no—
169#385—221no—
170#381—111no—
171#381—221no—
172#343—111no—
173#343—221no—
174#343C2×D1111yescharacteristic
175#324—111no—
176#324—221no—
177#324C2×D1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41611yescharacteristic
182C22×C11#42111yescharacteristic
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—42no—
189C2×D11—42no—
190C2×D11#35212yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11—81no—
201Dic11—81no—
202C23×C4—111no—
203C23×C4—111no—
204C23×C4—111no—
205C2×M16—21no—
206C2×M16—221no—
207C22×C8—441no—
208#117—441no—
209#117—441no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—441no—
217C2×C4⋊C4—441no—
218C2×C4⋊C4C4×D1111yescharacteristic
219C2×C4⋊C4C22×D1111yescharacteristic
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—221no—
223C22⋊C8—21no—
224C22⋊C8—221no—
225C22⋊C8—441no—
226C22⋊C8—441no—
227C22⋊C8—441no—
228#95—21no—
229#95—21no—
230#95—111no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95C4×D1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11#151611yescharacteristic
240C2×C11C2×#35211yescharacteristic
241C2×C11#213311yescharacteristic
242D11—22no—
243D11—41no—
244C24—111no—
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—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—441no—
261C22×C4—442no—
262C22×C4—442no—
263C22×C4C2×C4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266M16—41no—
267M16—41no—
268M16—441no—
269M16—441no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—882no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—442no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—442no—
287C42—442no—
288C11#1185011yescharacteristic, complemented, Sylow
289C23—111no—
290C23—111no—
291C23—222no—
292C23—221no—
293C23—221no—
294C23—441no—
295C23C22⋊C4×D1111yescharacteristic
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—881no—
328C2×C4#6696911yescharacteristic
329C2×C4#6697211yescharacteristic
330C8—81no—
331C8—81no—
332C8—881no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—112no—
337C22—221no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22—221no—
342C22—442no—
343C22—442no—
344C22D11×#9911yescharacteristic
345C22#1062241711yescharacteristic
346C22#1062243411yescharacteristic
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—441no—
354C4—441no—
355C4—441no—
356C4—881no—
357C4—881no—
358C2—21no—
359C2—21no—
360C2—222no—
361C2—441no—
362C2#1306717111yescharacteristic
363C2D11×#35211yescharacteristic
364C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11850
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #13066643C2semidirect
5. #13066623C2semidirect
6. #13066621C2semidirect
7. C11×#1353C2semidirect
111. #1353D11semidirect
288. C11#11850semidirect

Maximal subgroups

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

subgroupindex
#130729042
#130686952
D11×#3242
#130666432
#130666232
#130666212
C11×#13532
#1185011