Finite Group Databasebeta

← #14663986

Subgroups — #14663986

Order 2816.

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

normal subgroups only

This group has 452 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#13074384C211yesmaximal, characteristic
2#13068353C211yesmaximal, characteristic
3#13066929C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066621C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66949—21no—
10C2×#66945C2211yescharacteristic
11C2×#66941C411yescharacteristic
12C11×#398C2211yescharacteristic
13#10622606C411yescharacteristic
14#10622597—21no—
15#10622596C2211yescharacteristic
16#10622331—21no—
17#10622288—21no—
18#10622287C411yescharacteristic
19#10622263C411yescharacteristic
20#10622259—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×C4×D11D411yescharacteristic
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4C2×C411yescharacteristic
36C2×(C2×D11)⋊C4D411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45M16×D11—24no—
46M16×D11—42no—
47C2×#4313—41no—
48C2×C8×D11—41no—
49#66949—42no—
50#66949—42no—
51#66945—41no—
52#66945—41no—
53#66941—41no—
54#66941—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95C2×C411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64Dic11⋊C8—41no—
65C8×Dic11—41no—
66#11700—111nomaximal, Sylow
67C23×D11C22⋊C411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—22no—
81C2×C4×D11D812yes—
82C2×C4×D11SD1612yes—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—42no—
86C2×Dic22—42no—
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109#4318—22no—
110#4318—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#4313—44no—
114C8×D11—44no—
115#2621—111no—
116#1742—111no—
117#1458—111no—
118#1346—111no—
119#1346—111no—
120#1346—111no—
121#1346D1111yescharacteristic, complemented
122C23×C11C2×C22⋊C411yescharacteristic
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11#10212yes—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×SD1611yescharacteristic
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11#9911yescharacteristic
153C2×Dic11#9911yescharacteristic
154C2×Dic11#10212yes—
155C2×Dic11#10412yes—
156C4×D11—22no—
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—22no—
160Dic22—82no—
161Dic22—82no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C22×M16—221no—
167C2×C4⋊Q8—111no—
168C2×C22⋊Q8—221no—
169C2×#117—111no—
170#431—221no—
171#398—111no—
172#398—221no—
173#398C2×D1111yescharacteristic
174#397—111no—
175#397—111no—
176#397—221no—
177#391—221no—
178#382—111no—
179#343—111no—
180#343—221no—
181#343C2×D1111yescharacteristic
182#324—111no—
183#324C2×D1111yescharacteristic
184#323—221no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11C2×#9911yescharacteristic
188C22×C11C2×#10211yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C2×D11—22no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—42no—
194C2×D11—81no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—81no—
200C4×C11—81no—
201Dic11—41no—
202Dic11—41no—
203Dic11—81no—
204Dic11—81no—
205Dic11#32712yes—
206Dic11#32712yes—
207C22×Q8—221no—
208C23×C4—111no—
209C2×M16—21no—
210C2×M16—224no—
211C2×M16—221no—
212C2×M16—441no—
213C2×M16—442no—
214C22×C8—441no—
215C4⋊Q8—441no—
216C4⋊Q8—441no—
217C22⋊Q8—442no—
218C22⋊Q8—442no—
219#117—441no—
220#117—441no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4C4×D1111yescharacteristic
228C2×C4⋊C4C22×D1111yescharacteristic
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C42—111no—
234C2×C42—111no—
235C4⋊C8—441no—
236C22⋊C8—21no—
237C22⋊C8—221no—
238C4×C8—441no—
239#95—21no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95C4×D1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11C2×#32711yescharacteristic
249C2×C11#212311yescharacteristic
250C2×C11#213511yescharacteristic
251D11—42no—
252C24—111no—
253C2×Q8—442no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—442no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—111no—
260C22×C4—112no—
261C22×C4—112no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—222no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272M16—22no—
273M16—41no—
274M16—222no—
275M16—444no—
276M16—441no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—444no—
280C2×C8—441no—
281C2×C8—441no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—221no—
300C11#1170011yescharacteristic, complemented, Sylow
301C23—112no—
302C23—221no—
303C23—221no—
304C23—441no—
305C23—441no—
306C23C22⋊C4×D1111yescharacteristic
307Q8—882no—
308Q8—882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—112no—
324C2×C4—112no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4D8×D1111yescharacteristic
340C2×C4SD16×D1111yescharacteristic
341C8—42no—
342C8—81no—
343C8—442no—
344C8—881no—
345C22—21no—
346C22—21no—
347C22—222no—
348C22—442no—
349C22—441no—
350C22—441no—
351C22—881no—
352C22D11×#9911yescharacteristic
353C22D11×#10211yescharacteristic
354C22D11×#10411yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—112no—
362C4—112no—
363C4—441no—
364C4—441no—
365C4—881no—
366C4—881no—
367C2—21no—
368C2—21no—
369C2—442no—
370C2D11×#32711yescharacteristic
371C2#1307026811yescharacteristic
372C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11700
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
4. #13066623C2semidirect
5. #13066622C2semidirect
6. #13066621C2semidirect
7. C11×#1346C2semidirect
121. #1346D11semidirect
300. C11#11700semidirect

Maximal subgroups

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

subgroupindex
#130743842
#130683532
#130669292
#130666232
#130666222
#130666212
C11×#13462
#1170011