Finite Group Databasebeta

← #14664397

Subgroups — #14664397

Order 2816.

462 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 83 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#13073792C211yesmaximal, characteristic
2#13066957C211yesmaximal, characteristic
3#13066639C212yesmaximal, complemented
4#13066636C212yesmaximal, complemented
5C4×C11×#99C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C4×C11×C22⋊C4—21no—
10#10622833—21no—
11#10622823—21no—
12C2×C11⋊#95C411yescharacteristic, complemented
13#10622599C411yescharacteristic, complemented
14#10622592C411yescharacteristic, complemented
15#10622562C2211yescharacteristic
16#10622560C2211yescharacteristic
17#10622555—21no—
18#10622546—21no—
19#10622539—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C22×Dic22C2×C411yescharacteristic
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11—41no—
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—41no—
41#66977—41no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C11×#99—24no—
46C11×#95—41no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56#66867—41no—
57#11789—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—42no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—42no—
80C22×Dic11—42no—
81C22×Dic11—81no—
82C2×Dic22—41no—
83C2×Dic22—81no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—24no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—82no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—81no—
95C4⋊Dic11—41no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—81no—
100C2×C11⋊C8—42no—
101#2564—111no—
102C4×#99D1111yescharacteristic
103#1466—111no—
104#1352—112no—
105#1351—112no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11#10412yes—
115C23×C11C2×C22⋊C411yescharacteristic
116C23×C11#13712yes—
117D4×C11—44no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—44no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—82no—
134C2×C4×C11—82no—
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#9911yescharacteristic
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—84no—
150Dic22—82no—
151C11⋊C8—82no—
152C2×C22⋊Q8—111no—
153C2×C4×D4C2×D1111yescharacteristic
154#432—221no—
155C2×#99—21no—
156#400—111no—
157#399—111no—
158#395—111no—
159#393—111no—
160#387—221no—
161#386—221no—
162#385—221no—
163#380—221no—
164C4×C22⋊C4—21no—
165C2×#95—111no—
166#342C2×D1112yes—
167#323—112no—
168#323—221no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—81no—
181C22×C11C2×#9911yescharacteristic
182C22×C11#41911yescharacteristic
183C22×C11C2×#10411yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—84no—
191Dic11—42no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—111no—
196C22×D4C22⋊D1111yescharacteristic
197C23×C4—221no—
198C23×C4C4×D1111yescharacteristic
199C23×C4C22⋊D1111yescharacteristic
200C22⋊Q8—441no—
201C22⋊Q8—441no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C4×D1111yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4D4411yescharacteristic
214C2×C22⋊C4C22×D1111yescharacteristic
215C2×C42—41no—
216C2×C42D4411yescharacteristic
217C4⋊C8—441no—
218#99—24no—
219C22⋊C8—222no—
220#97—441no—
221#95—41no—
222#95—111no—
223#95—111no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—42no—
232C2×C11—42no—
233C2×C11#150811yescharacteristic
234C2×C11#212111yescharacteristic
235C2×C11#212611yescharacteristic
236C24(C2×D11)⋊C411yescharacteristic
237C24C2×C22⋊D1111yescharacteristic
238C2×Q8—441no—
239C2×Q8—881no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—881no—
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C2×C8—442no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—881no—
269C22⋊C4—24no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—881no—
276C42—21no—
277C42—21no—
278C42—82no—
279C11#1178911yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#6686912yes—
289C23C2×(C2×D11)⋊C411yescharacteristic
290C23#6700412yes—
291Q8—882no—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—222no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—884no—
323C2×C4#6687011yescharacteristic
324C2×C4#6687011yescharacteristic
325C8—882no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#6686911yescharacteristic
339C22C2×#6687011yescharacteristic
340C22#1062261711yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—84no—
348C4—442no—
349C4—881no—
350C4—881no—
351C4—881no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#1306713511yescharacteristic
357C2#1307026011yescharacteristic
358C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11789
LCSG ▷ C22×C4×C11 ▷ C23×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
3. #13066639C2semidirect
4. #13066636C2semidirect
7. C2×#66977C4semidirect
12. C2×C11⋊#95C4semidirect
13. #10622599C4semidirect
14. #10622592C4semidirect
279. C11#11789semidirect

Maximal subgroups

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

subgroupindex
#130737922
#130669572
#130666392
#130666362
C4×C11×#992
#1178911