Finite Group Databasebeta

← #14672421

Subgroups — #14672421

Order 2816.

612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071981C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066735C214yesmaximal
4C4×C11×#100C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×#100C2212yes—
9C4×C11×M16—21no—
10#10622833C2212yes—
11C2×#66898C2212yes—
12#10622825—21no—
13#10622825C411yescharacteristic, complemented
14#10622592—21no—
15#10622560—21no—
16#10622559C412yescomplemented
17#10622542—21no—
18C11×#343—21no—
19#10622164—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C22×Dic22—21no—
25C22×Dic22—21no—
26C22×Dic22—44no—
27C22×Dic22—41no—
28C22×Dic22—41no—
29C2×C11×M16—22no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11C2×C412yes—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—41no—
41#66977—44no—
42C2×Dic11⋊C4—22no—
43C11×#100—22no—
44C11×#100Q814yescomplemented
45C11×#97—41no—
46C4×C8×C11—41no—
47#66898—24no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C11⋊#95—22no—
51C11⋊#95—41no—
52#13293—111nomaximal, Sylow
53C24×C11C22×C411yescharacteristic
54C24×C11C2×D411yescharacteristic
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11C2×Q812yes—
58C2×D4×C11#4112yes—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—44no—
75C2×Dic22—24no—
76C2×Dic22—42no—
77C2×Dic22—42no—
78C2×Dic22—44no—
79C2×Dic22—48no—
80C2×Dic22—44no—
81C2×Dic22—44no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C11×M16—24no—
85C11×M16—42no—
86C2×C8×C11—42no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—21no—
91C42×C11—21no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—44no—
95C22⋊Dic11—42no—
96C4⋊Dic11—42no—
97C4⋊Dic11—82no—
98Dic11⋊C4—44no—
99#2409—111no—
100#1799—111no—
101C4×#100D1111yescharacteristic
102#1390—114no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11C4×Q812yes—
113C23×C11#12411yescharacteristic
114C23×C11C4⋊Q811yescharacteristic
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11C22⋊Q812yes—
133C2×Dic11—24no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136C2×Dic11—42no—
137C2×Dic11—44no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144Dic22—44no—
145Dic22—48no—
146Dic22—44no—
147C8×C11—44no—
148C23×Q8—111no—
149C2×C22⋊Q8—221no—
150C2×C4×D4C2×D1111yescharacteristic
151C2×#100C2×D1112yes—
152C2×#99—112no—
153C4×M16—21no—
154#395—221no—
155#393—221no—
156#391—221no—
157#386—112no—
158#385—112no—
159#380—111no—
160#380—221no—
161#343—21no—
162#342—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—42no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—81no—
177C22×C11#39111yescharacteristic
178C22×C11C2×#9911yescharacteristic
179C22×C11#41011yescharacteristic
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11AΣL(1,𝔽16)12yes—
186Dic11—44no—
187Dic11—82no—
188Dic11—162no—
189C22×Q8—221no—
190C22×Q8—221no—
191C22×Q8—441no—
192C22×Q8—441no—
193C22×Q8—444no—
194C22×D4C22×D1111yescharacteristic
195C23×C4—112no—
196C23×C4C4×D1111yescharacteristic
197C23×C4D4411yescharacteristic
198C2×M16—22no—
199C22⋊Q8—444no—
200C4×D4—41no—
201C4×D4—41no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—441no—
205C2×C4⋊C4C22⋊D1111yescharacteristic
206C2×C22⋊C4—112no—
207C2×C22⋊C4—222no—
208C2×C22⋊C4—222no—
209C2×C22⋊C4C4×D1111yescharacteristic
210C2×C22⋊C4D4411yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212#100—22no—
213#100Dic2214yescomplemented
214#99—224no—
215#97—41no—
216C4×C8—41no—
217#95—221no—
218#95—222no—
219#95—222no—
220#95—441no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—41no—
224C2×C11—42no—
225C2×C11—41no—
226C2×C11#199611yescharacteristic
227C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
228C2×C11#212311yescharacteristic
229C24C2×C4×D1111yescharacteristic
230C24C2×D4411yescharacteristic
231C2×Q8—224no—
232C2×Q8—442no—
233C2×Q8—442no—
234C2×Q8—444no—
235C2×Q8—444no—
236C2×Q8—448no—
237C2×Q8—444no—
238C2×Q8—441no—
239C2×Q8—441no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4C2×Dic2212yes—
243C2×D4#433912yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—444no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260M16—24no—
261M16—42no—
262C2×C8—42no—
263C4⋊C4—41no—
264C4⋊C4—442no—
265C4⋊C4—444no—
266C4⋊C4—882no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—444no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C42—21no—
274C42—21no—
275C11#1329311yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23C4×Dic2212yes—
285C23#6692211yescharacteristic
286C23#6692811yescharacteristic
287C23C2×(C2×D11)⋊C411yescharacteristic
288Q8—444no—
289Q8—448no—
290Q8—444no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—224no—
307C2×C4—442no—
308C2×C4—444no—
309C2×C4—442no—
310C2×C4—444no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—882no—
315C2×C4—882no—
316C2×C4—882no—
317C2×C4#6687011yescharacteristic
318C2×C4#6687011yescharacteristic
319C2×C4#6697712yes—
320C8—44no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—22no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22#1062254211yescharacteristic
336C22C2×#6687011yescharacteristic
337C22#1062261911yescharacteristic
338C4—22no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—444no—
344C4—882no—
345C4—1762no—
346C4#1062211312yes—
347C2—21no—
348C2—21no—
349C2—41no—
350C2—42no—
351C2—41no—
352C2#1306960111yescharacteristic
353C2C2×#1062211311yescharacteristic
354C2#1307027111yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#100C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC4×#100D11
hypocenterC11#13293
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
5. C23×Dic22C4semidirect
13. #10622825C4semidirect
16. #10622559C4semidirect
44. C11×#100Q8semidirect
213. #100Dic22semidirect
275. C11#13293semidirect

Maximal subgroups

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

subgroupindex
#130719812
#130686042
#130667352
C4×C11×#1002
#1329311