Finite Group Databasebeta

← #14656904

Subgroups — #14656904

Order 2816.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#13071910C211yesmaximal, characteristic
2#13069598C211yesmaximal, characteristic
3#13067115C211yesmaximal, characteristic
4#13066519C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1503C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Dic22—21no—
10C11×#431C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622597—21no—
13#10622592—21no—
14C4×C4⋊Dic11C2211yescharacteristic
15#10622545C2211yescharacteristic
16C4×Dic11⋊C4—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622270—21no—
20#10622269—21no—
21C11×#328—21no—
22C11×#328—21no—
23#10622176—21no—
24#10622176—21no—
25#10622170—21no—
26#10622170—21no—
27C22×Dic22—21no—
28C11×C4⋊Q8Q811yescharacteristic, complemented
29C11×C4⋊Q8Q811yescharacteristic, complemented
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C4×Dic22—42no—
50C4×Dic22—42no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67#10371—111nomaximal, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11C2×Q811yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108C4×Dic11SD1612yes—
109C4×Dic11Q1612yes—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2399—111no—
115#1995—111no—
116#1503—111no—
117#1503D1111yescharacteristic
118#1303—111no—
119#1303—111no—
120#1274—111no—
121C23×C11#12011yescharacteristic
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—22no—
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—41no—
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11#12411yescharacteristic
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
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—41no—
156Dic22—48no—
157C8×C11—81no—
158C11⋊C8—81no—
159C11⋊C8—81no—
160#533C2×D1111yescharacteristic
161C2×C4×Q8—221no—
162#431—111no—
163#431C2×D1111yescharacteristic
164#423—111no—
165#398—221no—
166#398—221no—
167#395—221no—
168#395—221no—
169C4×C4⋊C4—111no—
170C4×C4⋊C4—221no—
171C4×C4⋊C4C2×D1111yescharacteristic
172#376—111no—
173#339—221no—
174#339—221no—
175#328—21no—
176#328—21no—
177#328—221no—
178#328—221no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39311yescharacteristic
182C22×C11#45011yescharacteristic
183C22×C11#45111yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11#47511yescharacteristic
193C4×C11#47711yescharacteristic
194C4×C11#48711yescharacteristic
195C4×C11#48911yescharacteristic
196Dic11—42no—
197Dic11—42no—
198Dic11—42no—
199Dic11—81no—
200C22×Q8—221no—
201C2×M16—221no—
202C4⋊Q8Dic2211yescharacteristic, complemented
203C4⋊Q8Dic2211yescharacteristic, complemented
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—442no—
210C4×Q8—442no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C42—21no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8—221no—
228C22⋊C8—21no—
229C22⋊C8—221no—
230C4×C8—21no—
231C4×C8—221no—
232#95—111no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95C22⋊D1111yescharacteristic
239#95C22⋊D1111yescharacteristic
240C2×C11—21no—
241C2×C11—21no—
242C2×C11#202411yescharacteristic
243C2×C11#203111yescharacteristic
244C2×C11#203111yescharacteristic
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—442no—
248C2×Q8—442no—
249C2×Q8—442no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—441no—
260M16—441no—
261C2×C8—41no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C22⋊C4—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C42—112no—
282C42—112no—
283C42—221no—
284C42—221no—
285C42—441no—
286C42—441no—
287C42C2×Dic2211yescharacteristic
288C42#433911yescharacteristic
289C42#434111yescharacteristic
290C42#434111yescharacteristic
291C11#1037111yescharacteristic, complemented, Sylow
292C23#6699011yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—448no—
296C2×C4—22no—
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—41no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4#6693111yescharacteristic
319C2×C4#6693111yescharacteristic
320C2×C4#6693811yescharacteristic
321C2×C4#6693811yescharacteristic
322C2×C4SD16×D1111yescharacteristic
323C2×C4#6696711yescharacteristic
324C2×C4Q16×D1111yescharacteristic
325C2×C4#6697111yescharacteristic
326C2×C4#6697711yescharacteristic
327C2×C4#6698911yescharacteristic
328C8—81no—
329C8—881no—
330C8—881no—
331C22—21no—
332C22—21no—
333C22#1062256011yescharacteristic
334C22#1062278211yescharacteristic
335C22#1062279911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—442no—
345C4—442no—
346C4—442no—
347C4—881no—
348C4#1062240411yescharacteristic
349C4#1062240511yescharacteristic
350C4#1062240711yescharacteristic
351C4#1062240811yescharacteristic
352C2—21no—
353C2—21no—
354C2#1306975511yescharacteristic
355C2#1306978811yescharacteristic
356C2#1306979011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1503D11
hypocenterC11#10371
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
28. C11×C4⋊Q8Q8semidirect
29. C11×C4⋊Q8Q8semidirect
202. C4⋊Q8Dic22semidirect
203. C4⋊Q8Dic22semidirect
291. C11#10371semidirect

Maximal subgroups

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

subgroupindex
#130719102
#130695982
#130671152
#130665192
#130665182
#130664442
C11×#15032
#1037111