Finite Group Databasebeta

← #14673461

Subgroups — #14673461

Order 2816.

384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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#13076602C211yesmaximal, characteristic
2#13068831C211yesmaximal, characteristic
3#13068831C211yesmaximal, characteristic
4#13066743C211yesmaximal, characteristic
5#13066742C211yesmaximal, characteristic
6#13066742C211yesmaximal, characteristic
7C11×#1857C211yesmaximal, characteristic
8C11×#519C2211yescharacteristic
9C11×#428—21no—
10C2×C11×#101C2211yescharacteristic
11C11×#391C2211yescharacteristic
12#10622843C2211yescharacteristic
13#10622843C2211yescharacteristic
14C2×#66900C2211yescharacteristic
15C2×#66900C2211yescharacteristic
16#10622608—21no—
17#10622608—21no—
18#10622597—21no—
19#10622546—21no—
20#10622273—21no—
21#10622270—21no—
22#10622267—21no—
23#10622260—21no—
24C11×#339—21no—
25#10622170—21no—
26#10622170—21no—
27C22×Q8×C11C2311yescharacteristic
28C2×C11×M16—21no—
29C4×Q8×C11—41no—
30C4×Q8×C11—41no—
31C11×#117—21no—
32C11×#117—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47C11×#107—41no—
48C11×#106—41no—
49C11×#101—21no—
50C11×#101Q812yes—
51C11×#95—21no—
52C11×#95—21no—
53#66900—21no—
54#66900—21no—
55#66900Q812yes—
56#66900Q812yes—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64#66872—41no—
65#66872—41no—
66#66871—41no—
67#66871—41no—
68#13465—111nomaximal, Sylow
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11C2×Q811yescharacteristic
72C2×Q8×C11C2×Q811yescharacteristic
73C2×Q8×C11C2×Q811yescharacteristic
74C2×Q8×C11#4111yescharacteristic
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C11×M16—22no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108#4318—22no—
109#4318—22no—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2809—111no—
115#1857—111no—
116#1857—111no—
117#1857D1111yescharacteristic
118#1394—111no—
119#1394—111no—
120#1394—111no—
121C23×C11#12011yescharacteristic
122Q8×C11—41no—
123Q8×C11—41no—
124Q8×C11—41no—
125Q8×C11—41no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
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×C11C22⋊Q811yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11C4⋊Q811yescharacteristic
144C2×C4×C11C4⋊Q811yescharacteristic
145C2×C4×C11C4⋊Q811yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C8×C11—42no—
158C11⋊C8—42no—
159C11⋊C8—42no—
160#519C2×D1111yescharacteristic
161#428—21no—
162#428—221no—
163#428—221no—
164C2×#101—111no—
165C2×#101—111no—
166C2×#101C2×D1111yescharacteristic
167#400—221no—
168#398—221no—
169#398—221no—
170#391—111no—
171#391—111no—
172#391C2×D1111yescharacteristic
173#389—221no—
174#387—221no—
175#387—221no—
176#339—21no—
177#339—221no—
178#339—221no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39511yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C22×C11#45811yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194Dic11—42no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8C22×D1111yescharacteristic
199C2×M16—21no—
200C2×M16—221no—
201C2×M16—221no—
202C4×Q8—41no—
203C4×Q8—41no—
204#117—21no—
205#117—21no—
206#117—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C42—111no—
216C2×C42—111no—
217C2×C42C22⋊D1111yescharacteristic
218#107—41no—
219#107—441no—
220#107—441no—
221#106—41no—
222#106—441no—
223#106—441no—
224#101—21no—
225#101—112no—
226#101—112no—
227#101—221no—
228#101—221no—
229#101Dic2212yes—
230#95—21no—
231#95—21no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11#206211yescharacteristic
242C2×C11#220311yescharacteristic
243C2×C11#220411yescharacteristic
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C2×Dic2211yescharacteristic
247C2×Q8#433911yescharacteristic
248C2×Q8Q8×D1111yescharacteristic
249C2×Q8Q8×D1111yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—22no—
260M16—41no—
261M16—222no—
262M16—222no—
263M16—441no—
264M16—441no—
265C2×C8—41no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—881no—
281C4⋊C4—881no—
282C22⋊C4—41no—
283C42—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—441no—
288C42—441no—
289C11#1346511yescharacteristic, complemented, Sylow
290C23#6699011yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—41no—
294Q8—41no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—222no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4#6694111yescharacteristic
321C2×C4#6694111yescharacteristic
322C2×C4#6694911yescharacteristic
323C2×C4#6694911yescharacteristic
324C2×C4#6697711yescharacteristic
325C2×C4#6699711yescharacteristic
326C8—42no—
327C8—442no—
328C8—442no—
329C22—21no—
330C22—21no—
331C22#1062259211yescharacteristic
332C22#1062264511yescharacteristic
333C22#1062266611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—442no—
345C4—881no—
346C4—881no—
347C4—881no—
348C2—21no—
349C2—21no—
350C2#1306996911yescharacteristic
351C2#1307063511yescharacteristic
352C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1857C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1857D11
hypocenterC11#13465
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
289. C11#13465semidirect

Maximal subgroups

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

subgroupindex
#130766022
#130688312
#130667432
#130667422
C11×#18572
#1346511