Finite Group Databasebeta

← #14664283

Subgroups — #14664283

Order 2816.

446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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
2D11×#343C211yesmaximal, characteristic
3#13066944C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066623C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66945C411yescharacteristic
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#400C2211yescharacteristic
12#10622596C2211yescharacteristic
13#10622595C411yescharacteristic
14#10622339—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—
43M16×D11—24no—
44M16×D11—42no—
45C2×#4313—41no—
46C2×#4313—41no—
47C2×C8×D11—41no—
48#66945—41no—
49#66945—41no—
50C4⋊C4×D11—41no—
51C4⋊C4×D11—41no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11764—111nomaximal, Sylow
65C23×D11C22⋊C411yescharacteristic
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—22no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—42no—
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#4313—44no—
109#4313—82no—
110C8×D11—44no—
111#2484—111no—
112C2×#343—111no—
113#1463—111no—
114#1353—111no—
115#1353D1111yescharacteristic, complemented
116#1346—111no—
117#1346—111no—
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—22no—
122C22×D11—41no—
123C22×D11#9911yescharacteristic
124C22×D11#9911yescharacteristic
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11#10412yes—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—22no—
155C4×D11—42no—
156C4×D11—42no—
157C4×D11—42no—
158C4×D11—81no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C22×M16—221no—
164C2×#117—111no—
165C22×C4⋊C4—111no—
166#407—221no—
167#400—111no—
168#400C2×D1111yescharacteristic
169#398—111no—
170#398—111no—
171#387—221no—
172#387—221no—
173#385—221no—
174#381—111no—
175#381—221no—
176#343—111no—
177#343—221no—
178#343C2×D1111yescharacteristic
179#324—111no—
180#324—221no—
181#324C2×D1111yescharacteristic
182C22×C11—21no—
183C22×C11—21no—
184C22×C11C2×#9911yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—42no—
193C2×D11—42no—
194C2×D11#35212yes—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—81no—
200C4×C11—81no—
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204Dic11—81no—
205Dic11—81no—
206C23×C4—111no—
207C23×C4—111no—
208C23×C4—111no—
209C2×M16—21no—
210C2×M16—224no—
211C2×M16—221no—
212C2×M16—441no—
213C2×M16—441no—
214C2×M16—442no—
215C22×C8—441no—
216#117—441no—
217#117—441no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—441no—
225C2×C4⋊C4—441no—
226C2×C4⋊C4C4×D1111yescharacteristic
227C2×C4⋊C4C22×D1111yescharacteristic
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—221no—
231C22⋊C8—21no—
232C22⋊C8—221no—
233C22⋊C8—441no—
234#95—21no—
235#95—21no—
236#95—111no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95C4×D1111yescharacteristic
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#150411yescharacteristic
246C2×C11C2×#35211yescharacteristic
247C2×C11#213311yescharacteristic
248D11—22no—
249D11—41no—
250C24—111no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—222no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272M16—22no—
273M16—41no—
274M16—222no—
275M16—444no—
276M16—441no—
277M16—882no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—444no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—442no—
295C42—442no—
296C11#1176411yescharacteristic, complemented, Sylow
297C23—111no—
298C23—111no—
299C23—222no—
300C23—221no—
301C23—221no—
302C23—441no—
303C23C22⋊C4×D1111yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—112no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4#6696711yescharacteristic
337C2×C4#6697111yescharacteristic
338C8—42no—
339C8—81no—
340C8—442no—
341C8—881no—
342C22—21no—
343C22—21no—
344C22—112no—
345C22—221no—
346C22—221no—
347C22—221no—
348C22—221no—
349C22—221no—
350C22—442no—
351C22—442no—
352C22D11×#9911yescharacteristic
353C22#1062241611yescharacteristic
354C22D11×#10411yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—222no—
362C4—441no—
363C4—441no—
364C4—881no—
365C4—881no—
366C2—21no—
367C2—21no—
368C2—222no—
369C2—441no—
370C2#1306711911yescharacteristic
371C2D11×#35211yescharacteristic
372C2#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#11764
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
115. #1353D11semidirect
296. C11#11764semidirect

Maximal subgroups

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

subgroupindex
#130729042
D11×#3432
#130669442
#130666432
#130666232
#130666212
C11×#13532
#1176411