Finite Group Databasebeta

← #14663400

Subgroups — #14663400

Order 2816.

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

normal subgroups only

This group has 412 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#13073598C211yesmaximal, characteristic
2#13066958C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066549C211yesmaximal, characteristic, complemented
5#13066549C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic
7C11×#1318C211yesmaximal, characteristic
8C2×#66989C411yescharacteristic
9C2×#66989C411yescharacteristic
10C2×#66940C2211yescharacteristic
11C2×#66922C411yescharacteristic
12C11×#390C2211yescharacteristic
13#10622587C2211yescharacteristic
14#10622564—21no—
15#10622564—21no—
16#10622561—21no—
17#10622561—21no—
18C4×Dic11⋊C4C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66989—41no—
39#66989—41no—
40#66989—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4D411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50#66940—41no—
51#66940—41no—
52#66922—42no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66879—41no—
61Dic11⋊C8—41no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#11565—111nomaximal, Sylow
65C24×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×Dic22—22no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C42×C11—41no—
94C22⋊Dic11—42no—
95C22⋊Dic11—42no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—42no—
99C4⋊Dic11—42no—
100C4⋊Dic11—42no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—42no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2545—111no—
114#1467—111no—
115#1461—111no—
116#1319—111no—
117#1319—111no—
118#1318—111no—
119#1318D1111yescharacteristic
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11C2×C22⋊C411yescharacteristic
128D4×C11—81no—
129D4×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11#13111yescharacteristic
140C2×C4×C11#13111yescharacteristic
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11#9911yescharacteristic
156C2×Dic11#9911yescharacteristic
157C2×Dic11#10012yes—
158Dic22—42no—
159Dic22—42no—
160Dic22—81no—
161Dic22—81no—
162C8×C11—81no—
163C8×C11—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166C2×C4⋊Q8—111no—
167C2×#124—111no—
168C2×#124—111no—
169C2×C4×Q8—111no—
170#432—221no—
171#431—221no—
172#396—221no—
173#396—221no—
174#391—111no—
175#390C2×D1111yescharacteristic
176#388—221no—
177#388—221no—
178C4×C4⋊C4—111no—
179#324—111no—
180#324—111no—
181#324—221no—
182#324—221no—
183#324C2×D1111yescharacteristic
184#324C2×D1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#40811yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C22×C11C2×#10011yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—41no—
201C4×C11—41no—
202Dic11—21no—
203Dic11—21no—
204Dic11—22no—
205Dic11—41no—
206Dic11—41no—
207Dic11—81no—
208Dic11—81no—
209C22×Q8—111no—
210C22×Q8—111no—
211C22×D4C4×D1111yescharacteristic
212C4⋊Q8—442no—
213#124—441no—
214#124—441no—
215#124—442no—
216C4×Q8—441no—
217C4×Q8—441no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4C22×D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—111no—
231C2×C42—111no—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42C4×D1111yescharacteristic
235C4⋊C8—441no—
236C4⋊C8—441no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—221no—
240C22⋊C8—221no—
241#97—441no—
242C4×C8—441no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—161no—
249C2×C11#147111yescharacteristic
250C2×C11#212611yescharacteristic
251C2×C11#213311yescharacteristic
252C24—21no—
253C2×Q8—222no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×Q8—441no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—41no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C42—41no—
293C42—221no—
294C42—221no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—441no—
300C11#1156511yescharacteristic, complemented, Sylow
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23C22⋊C4×D1111yescharacteristic
309Q8—442no—
310Q8—442no—
311Q8—881no—
312Q8—881no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—112no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4#6695411yescharacteristic
342C2×C4#6696011yescharacteristic
343C8—81no—
344C8—81no—
345C8—881no—
346C8—881no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1062234011yescharacteristic
357C22D11×#9911yescharacteristic
358C22D11×#10011yescharacteristic
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—222no—
365C4—221no—
366C4—221no—
367C4—441no—
368C4—441no—
369C4—881no—
370C4—881no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1306697411yescharacteristic
375C2#1307027811yescharacteristic
376C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11565
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066958C2semidirect
3. #13066938C2semidirect
4. #13066549C2semidirect
5. #13066549C2semidirect
300. C11#11565semidirect

Maximal subgroups

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

subgroupindex
#130735982
#130669582
#130669382
#130665492
#130665482
C11×#13182
#1156511