Finite Group Databasebeta

← #14666751

Subgroups — #14666751

Order 2816.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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#13075522C211yesmaximal, characteristic
2#13067607C211yesmaximal, characteristic
3#13067607C211yesmaximal, characteristic
4#13066615C211yesmaximal, characteristic
5#13066615C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic
7C11×#2062C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C2×#66932—21no—
10C11×#385—21no—
11C11×#385C2211yescharacteristic
12#10622825—21no—
13#10622656—21no—
14#10622656—21no—
15#10622598—21no—
16#10622596—21no—
17#10622566C2211yescharacteristic
18#10622566C2211yescharacteristic
19#10622274—21no—
20#10622266—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×C22⋊Q8—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—41no—
31C11×C22⋊Q8—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48#66932—42no—
49#66932—42no—
50C11×#95—21no—
51C11×#95—41no—
52#66899—41no—
53#66899—41no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66872—41no—
63#66872—41no—
64#12244—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—82no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4SD1612yes—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101C4⋊Dic11—42no—
102C4⋊Dic11—81no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105C4×Dic11—42no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2722—111no—
109#2062D1111yescharacteristic
110#1608—111no—
111#1608—111no—
112#1344—111no—
113#1344—111no—
114#1326—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#12011yescharacteristic
120C23×C11C2×SD1611yescharacteristic
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×Dic11—41no—
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—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157#543C2×D1111yescharacteristic
158C2×#126—221no—
159#483—221no—
160#483—221no—
161#398—221no—
162#398—221no—
163#397—111no—
164#397—111no—
165#389—221no—
166#387—221no—
167#385—21no—
168#385C2×D1111yescharacteristic
169#380—221no—
170#342—21no—
171#342C2×D1111yescharacteristic
172#328—221no—
173#328—221no—
174#323—111no—
175#323—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—81no—
185C22×C11#45011yescharacteristic
186C22×C11#45611yescharacteristic
187C22×C11B(4,𝔽2)11yescharacteristic
188C4×C11—42no—
189C4×C11—42no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—82no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C23×C4C22⋊D1111yescharacteristic
200#126—442no—
201#126—442no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C22⋊Q8—41no—
205C22⋊Q8—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42—221no—
222#106—441no—
223#106—441no—
224#103—441no—
225#103—441no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#95—21no—
229#95—41no—
230#95—111no—
231#95—111no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—41no—
239C2×C11—41no—
240C2×C11#160411yescharacteristic
241C2×C11#219711yescharacteristic
242C2×C11#220111yescharacteristic
243C24C2×C22⋊D1111yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—82no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—881no—
274C22⋊C4—21no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4#432512yes—
285C42—442no—
286C11#1224411yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#6699011yescharacteristic
292C23C2×#432511yescharacteristic
293C23#6700211yescharacteristic
294Q8—81no—
295Q8—81no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C8—881no—
328C8—881no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22#1062264511yescharacteristic
339C22#1062265911yescharacteristic
340C22#1062270811yescharacteristic
341C4—42no—
342C4—41no—
343C4—42no—
344C4—41no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—881no—
349C4—881no—
350C4—881no—
351C4—881no—
352C2—21no—
353C2—21no—
354C2—41no—
355C2—41no—
356C2#1306758411yescharacteristic
357C2#1307060411yescharacteristic
358C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2062C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#2062D11
hypocenterC11#12244
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
286. C11#12244semidirect

Maximal subgroups

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

subgroupindex
#130755222
#130676072
#130666152
#130665642
C11×#20622
#1224411