Finite Group Databasebeta

← #14663402

Subgroups — #14663402

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#13073599C211yesmaximal, characteristic
2#13066958C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066550C211yesmaximal, characteristic, complemented
5#13066547C211yesmaximal, characteristic
6#13066547C211yesmaximal, characteristic
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic
9C2×#66997C411yescharacteristic
10C2×#66940C2211yescharacteristic
11C2×#66928C411yescharacteristic
12C11×#391C2211yescharacteristic
13#10622601C2211yescharacteristic
14C4×Dic11⋊C4C411yescharacteristic
15#10622332—21no—
16#10622331—21no—
17#10622289—21no—
18#10622289—21no—
19#10622282—21no—
20#10622282—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32#67000—41no—
33#67000—41no—
34#66997—42no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—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#66928—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
65C23×D11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—41no—
83C2×D44—41no—
84C2×Dic22—22no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C42×C11—41no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
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#1319D1111yescharacteristic, complemented
118#1318—111no—
119#1318—111no—
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128Q8×C11—81no—
129Q8×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#13111yescharacteristic
143C2×C4×C11#13111yescharacteristic
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—22no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11#9911yescharacteristic
156C2×Dic11#9911yescharacteristic
157C2×Dic11#10012yes—
158D44—81no—
159D44—81no—
160Dic22—42no—
161Dic22—42no—
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#391C2×D1111yescharacteristic
175#390—111no—
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#40811yescharacteristic
188C22×C11C2×#9911yescharacteristic
189C22×C11C2×#10011yescharacteristic
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—81no—
202C4×C11—81no—
203Dic11—21no—
204Dic11—21no—
205Dic11—22no—
206Dic11—42no—
207Dic11—41no—
208Dic11—41no—
209C22×Q8—111no—
210C22×Q8C4×D1111yescharacteristic
211C22×D4—111no—
212C4⋊Q8—442no—
213#124—442no—
214#124—441no—
215#124—441no—
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—221no—
225C2×C22⋊C4—221no—
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—21no—
244#95—21no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11#147111yescharacteristic
249C2×C11#212611yescharacteristic
250C2×C11#213311yescharacteristic
251D11—161no—
252C24—221no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—222no—
258C2×Q8—221no—
259C2×Q8—221no—
260C2×Q8—441no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—441no—
264C2×D4—441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—111no—
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—441no—
286C22⋊C4—441no—
287C22⋊C4—442no—
288C22⋊C4—442no—
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—441no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23C22⋊C4×D1111yescharacteristic
309Q8—81no—
310Q8—81no—
311Q8—442no—
312Q8—442no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—111no—
328C2×C4—111no—
329C2×C4—112no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—222no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
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—881no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22#1062234011yescharacteristic
357C22D11×#9911yescharacteristic
358C22D11×#10011yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—222no—
366C4—221no—
367C4—221no—
368C4—442no—
369C4—441no—
370C4—441no—
371C2—21no—
372C2—21no—
373C2—1761no—
374C2#1306697411yescharacteristic
375C2#1307028011yescharacteristic
376C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1319D11
hypocenterC11#11565
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
2. #13066958C2semidirect
3. #13066938C2semidirect
4. #13066550C2semidirect
7. C11×#1319C2semidirect
117. #1319D11semidirect
300. C11#11565semidirect

Maximal subgroups

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

subgroupindex
#130735992
#130669582
#130669382
#130665502
#130665472
C11×#13192
#1156511