Finite Group Databasebeta

← #14664897

Subgroups — #14664897

Order 2816.

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

normal subgroups only

This group has 580 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#13068604C211yesmaximal, characteristic
2#13066937C211yesmaximal, characteristic
3#13066637C214yesmaximal, complemented
4C11×#2409C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#395C412yescomplemented
9C11×#393C2212yes—
10C11×#391—21no—
11C11×#386—21no—
12C11×#385—21no—
13C11×#380C411yescharacteristic, complemented
14C2×#66898—21no—
15#10622825—21no—
16#10622538—21no—
17#10622164C2212yes—
18#10622163—21no—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C22×Q8×C11—41no—
22C22×Q8×C11—41no—
23C22×Q8×C11—44no—
24C22×Q8×C11C2×C412yes—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C11×C22⋊Q8—44no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—22no—
41C2×C4⋊Dic11—41no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95C2×C412yes—
45#66898—42no—
46C11⋊#95—41no—
47C22⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—41no—
49C4×C11⋊C8—41no—
50#11898—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—24no—
54C2×Q8×C11—42no—
55C2×Q8×C11—44no—
56C2×Q8×C11—42no—
57C2×Q8×C11—48no—
58C2×Q8×C11—44no—
59C2×Q8×C11—44no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11SD1612yes—
65C2×D4×C11Q1612yes—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—44no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—44no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—44no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C4⋊Dic11—82no—
94C2×C11⋊C8—42no—
95#2409D1111yescharacteristic
96#1799—111no—
97#1460—111no—
98#1351—114no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10312yes—
108C23×C11C2×C22⋊C411yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110C23×C11C2×Q1611yescharacteristic
111Q8×C11—44no—
112Q8×C11—44no—
113Q8×C11—44no—
114Q8×C11—44no—
115D4×C11—42no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—24no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—48no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—81no—
137C2×C4×C11#9911yescharacteristic
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#10312yes—
140C2×Dic11—82no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C11⋊C8—82no—
144C23×Q8Dic1111yescharacteristic, complemented
145C2×C22⋊Q8—21no—
146C2×C4×D4C2×D1111yescharacteristic
147#431—221no—
148C2×#99—221no—
149#395Dic1112yescomplemented
150#393C2×D1112yes—
151#391—21no—
152#386—21no—
153#385—21no—
154#380—221no—
155#380Dic1111yescharacteristic, complemented
156#342—112no—
157#323—112no—
158#323—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—42no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—81no—
173C22×C11C2×#9911yescharacteristic
174C22×C11C2×#10311yescharacteristic
175C22×C11#42111yescharacteristic
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—44no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—82no—
183C4×C11AΣL(1,𝔽16)12yes—
184Dic11—162no—
185C22×Q8—21no—
186C22×Q8—41no—
187C22×Q8—41no—
188C22×Q8—44no—
189C22×Q8C2×Dic1112yes—
190C22×D4C22⋊D1111yescharacteristic
191C23×C4—21no—
192C23×C4C2×Dic1111yescharacteristic
193C23×C4C22⋊D1111yescharacteristic
194C22⋊Q8—44no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—441no—
200C2×C4⋊C4C2×Dic1111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—222no—
204C2×C22⋊C4C22⋊D1111yescharacteristic
205C2×C22⋊C4C22×D1111yescharacteristic
206C2×C42C22⋊D1111yescharacteristic
207C4⋊C8—441no—
208#99—442no—
209C22⋊C8—222no—
210C4×C8—441no—
211#95—22no—
212#95—22no—
213#95—441no—
214#95C2×Dic1112yes—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—41no—
218C2×C11—42no—
219C2×C11—41no—
220C2×C11#152011yescharacteristic
221C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
222C2×C11#212911yescharacteristic
223C24C22⋊Dic1111yescharacteristic
224C24C2×C22⋊D1111yescharacteristic
225C2×Q8—24no—
226C2×Q8—44no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—44no—
230C2×Q8—48no—
231C2×Q8—44no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4#432512yes—
237C2×D4#432612yes—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—44no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—442no—
249C22×C4C22⋊Dic1111yescharacteristic
250C22×C4C22⋊Dic1111yescharacteristic
251C22×C4C22⋊Dic1111yescharacteristic
252C22×C4C22×Dic1111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254C2×C8—442no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—44no—
258C4⋊C4—882no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—44no—
262C22⋊C4—42no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C42—21no—
266C42—21no—
267C11#1189811yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23#6689912yes—
277C23C2×#432511yescharacteristic
278C23C2×#432611yescharacteristic
279C23C2×C22⋊Dic1111yescharacteristic
280Q8—44no—
281Q8—44no—
282Q8—44no—
283Q8—44no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—48no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—81no—
306C2×C4—882no—
307C2×C4—882no—
308C2×C4—882no—
309C2×C4#6689811yescharacteristic
310C2×C4#6689811yescharacteristic
311C2×C4#6689912yes—
312C8—882no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22C2×#6689811yescharacteristic
328C22C2×#6689911yescharacteristic
329C22#1062284911yescharacteristic
330C4—21no—
331C4—22no—
332C4—44no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—82no—
337C4—1762no—
338C4#1062217412yes—
339C2—21no—
340C2—21no—
341C2—41no—
342C2—42no—
343C2—41no—
344C2#1306718811yescharacteristic
345C2C2×#1062217411yescharacteristic
346C2#1307029111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2409C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2409D11
hypocenterC11#11898
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
3. #13066637C2semidirect
5. C23×Q8×C11C4semidirect
8. C11×#395C4semidirect
13. C11×#380C4semidirect
144. C23×Q8Dic11semidirect
149. #395Dic11semidirect
155. #380Dic11semidirect
267. C11#11898semidirect

Maximal subgroups

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

subgroupindex
#130686042
#130669372
#130666372
C11×#24092
#1189811