Finite Group Databasebeta

← #14672443

Subgroups — #14672443

Order 2816.

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

normal subgroups only

This group has 556 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#13073569C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066740C214yesmaximal
4C4×C11×#99C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66977—21no—
7C2×#66977—21no—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×#99C2212yes—
10C4×C11×C22⋊C4—21no—
11#10622834C2212yes—
12C2×#66898C2212yes—
13#10622825—21no—
14#10622589C412yescomplemented
15#10622562—21no—
16#10622562—21no—
17C4×C4⋊Dic11C411yescharacteristic, complemented
18C11×#342—21no—
19#10622164—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C42×C11—41no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—41no—
38C2×C4⋊Dic11C2×C412yes—
39#66977—44no—
40#66977—44no—
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—22no—
43C2×C4×Dic11C2×C412yes—
44#66922—41no—
45#66922—41no—
46C11×#99—22no—
47C11×#99Q814yescomplemented
48C11×#95—41no—
49#66898—24no—
50C11⋊#95—21no—
51C11⋊#95—41no—
52#13298—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
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×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—42no—
74C2×Dic22—42no—
75C2×Dic22—42no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—24no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—42no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—82no—
86C22⋊Dic11—42no—
87C22⋊Dic11—44no—
88C22⋊Dic11—44no—
89C22⋊Dic11—42no—
90C4⋊Dic11—24no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—82no—
94Dic11⋊C4—44no—
95Dic11⋊C4—44no—
96C4×Dic11—42no—
97#2542—111no—
98#1799—111no—
99C4×#99D1111yescharacteristic
100#1393—114no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11C22⋊Q812yes—
111C23×C11#12411yescharacteristic
112C23×C11C4⋊Q811yescharacteristic
113D4×C11—42no—
114D4×C11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—44no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—82no—
130C2×C4×C11—82no—
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11C4×Q812yes—
134C2×Dic11—24no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—82no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143Dic22—82no—
144Dic22—82no—
145C2×C4⋊Q8—111no—
146C2×C22⋊Q8—221no—
147C2×C22⋊Q8—221no—
148C2×C4×D4C2×D1111yescharacteristic
149C2×#99—112no—
150C2×#99C2×D1112yes—
151#399—221no—
152#399—221no—
153#390—112no—
154#384—112no—
155#380—221no—
156C4×C4⋊C4—111no—
157C4×C22⋊C4—21no—
158#342—21no—
159#342—221no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11#39111yescharacteristic
175C22×C11C2×#9911yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—84no—
183C4×C11#35312yes—
184Dic11—44no—
185Dic11—82no—
186Dic11—162no—
187C22×Q8—221no—
188C22×D4C22×D1111yescharacteristic
189C23×C4D4411yescharacteristic
190C23×C4C22⋊D1111yescharacteristic
191C4⋊Q8—441no—
192C4⋊Q8—441no—
193C22⋊Q8—444no—
194C22⋊Q8—444no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—441no—
203C2×C4⋊C4C4×D1111yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4—222no—
207C2×C22⋊C4—222no—
208C2×C22⋊C4D4411yescharacteristic
209C2×C22⋊C4C22⋊D1111yescharacteristic
210C2×C42—41no—
211C2×C42—112no—
212C2×C42C4×D1111yescharacteristic
213#99—22no—
214#99—224no—
215#99Dic2214yescomplemented
216#95—41no—
217#95—221no—
218#95—441no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—41no—
222C2×C11—42no—
223C2×C11—41no—
224C2×C11#199611yescharacteristic
225C2×C11C2×#35311yescharacteristic
226C2×C11#212911yescharacteristic
227C24C2×D4411yescharacteristic
228C24C2×C22⋊D1111yescharacteristic
229C2×Q8—442no—
230C2×Q8—442no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4C2×Dic2212yes—
236C2×D4#433912yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4—442no—
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4C2×C4×D1111yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—224no—
254C4⋊C4—442no—
255C4⋊C4—442no—
256C4⋊C4—444no—
257C4⋊C4—444no—
258C4⋊C4—882no—
259C22⋊C4—24no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—444no—
264C22⋊C4—444no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C42—21no—
268C42—21no—
269C42—82no—
270C42—442no—
271C11#1329811yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#6692211yescharacteristic
281C23#6692811yescharacteristic
282C23#6697712yes—
283C23C2×(C2×D11)⋊C411yescharacteristic
284Q8—882no—
285Q8—882no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—44no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—224no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—882no—
311C2×C4—882no—
312C2×C4—882no—
313C2×C4#6687011yescharacteristic
314C2×C4#6687011yescharacteristic
315C2×C4C4×Dic2212yes—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22—81no—
330C22#1062254211yescharacteristic
331C22C2×#6687011yescharacteristic
332C22#1062261911yescharacteristic
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—84no—
339C4—444no—
340C4—882no—
341C4—1762no—
342C4#1062211212yes—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—41no—
347C2—41no—
348C2#1306960111yescharacteristic
349C2C2×#1062211211yescharacteristic
350C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13298
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
8. C2×#66922C4semidirect
14. #10622589C4semidirect
17. C4×C4⋊Dic11C4semidirect
47. C11×#99Q8semidirect
215. #99Dic22semidirect
271. C11#13298semidirect

Maximal subgroups

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

subgroupindex
#130735692
#130686042
#130667402
C4×C11×#992
#1329811