Finite Group Databasebeta

← #14666608

Subgroups — #14666608

Order 2816.

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

normal subgroups only

This group has 394 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#13076317C211yesmaximal, characteristic
2#13067658C211yesmaximal, characteristic, complemented
3#13067590C211yesmaximal, characteristic, complemented
4#13066645C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic
7C11×#2027C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#418—21no—
10C11×#390C2211yescharacteristic
11#10622833—21no—
12#10622663—21no—
13#10622657—21no—
14#10622599C2211yescharacteristic
15#10622592C2211yescharacteristic
16#10622561—21no—
17#10622560—21no—
18#10622559—21no—
19#10622555—21no—
20#10622546—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C23×Dic11—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C11×C4⋊Q8—41no—
32C11×#125—41no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×#4326—41no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C11×#102—41no—
49C11×#102—41no—
50#66899—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66871—41no—
62#12223—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11Q1612yescomplemented
70C22×C4×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—42no—
79C22×Dic11—81no—
80C22×Dic11—81no—
81C2×Dic22—41no—
82C2×Dic22—81no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C42×C11—41no—
97C42×C11—41no—
98C22⋊Dic11—42no—
99C22⋊Dic11—81no—
100C22⋊Dic11—81no—
101#4326—82no—
102C4⋊Dic11—41no—
103Dic11⋊C4—42no—
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2784—111no—
109#2027D1111yescharacteristic
110#1617—111no—
111#1605—111no—
112#1354—111no—
113#1353—111no—
114#1318—111no—
115C23×C11—22no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123Q8×C11—81no—
124Q8×C11—81no—
125D4×C11—42no—
126D4×C11—81no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
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×C11C2×Q1611yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—22no—
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—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—84no—
153Dic22—42no—
154Dic22—81no—
155C8×C11—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158#544C2×D1111yescharacteristic
159#484—221no—
160#451—221no—
161#418—21no—
162#400—111no—
163#396—221no—
164#395—111no—
165#393—221no—
166#390C2×D1111yescharacteristic
167#387—221no—
168#386—221no—
169#385—221no—
170#380—221no—
171#343C2×D1111yescharacteristic
172#339—21no—
173#328—221no—
174#328—221no—
175#324—111no—
176#324—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#45111yescharacteristic
187C22×C11#45511yescharacteristic
188C22×C11B(4,𝔽2)11yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×Q8—111no—
201C22×D4C22⋊D1111yescharacteristic
202C23×C4—221no—
203C2×Q16—441no—
204C2×M16—21no—
205C4⋊Q8—41no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C42C22⋊D1111yescharacteristic
221#107—441no—
222#103—441no—
223#103—441no—
224#102—41no—
225#102—41no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228#95—111no—
229#95—111no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—82no—
238C2×C11#160211yescharacteristic
239C2×C11#220011yescharacteristic
240C2×C11#220411yescharacteristic
241C24—21no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—441no—
245C2×Q8—881no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4#432612yescomplemented
250C22×C4—21no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—442no—
256C22×C4—881no—
257C22×C4—881no—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261Q16—882no—
262M16—41no—
263M16—41no—
264C2×C8—41no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—881no—
277C4⋊C4—881no—
278C22⋊C4—41no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4—442no—
282C22⋊C4—881no—
283C22⋊C4—881no—
284C42—41no—
285C42—41no—
286C11#1222311yescharacteristic, complemented, Sylow
287C23—22no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#6699011yescharacteristic
295Q8—81no—
296Q8—81no—
297Q8—442no—
298Q8—881no—
299D4—42no—
300D4—81no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—222no—
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—441no—
323C2×C4—441no—
324C2×C4—884no—
325C2×C4C2×#432611yescharacteristic
326C2×C4#6700411yescharacteristic
327C8—81no—
328C8—881no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22#1062264511yescharacteristic
340C22#1062266311yescharacteristic
341C22#1062267411yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—442no—
350C4—881no—
351C4—881no—
352C4—881no—
353C2—21no—
354C2—21no—
355C2—82no—
356C2#1306757211yescharacteristic
357C2#1307062211yescharacteristic
358C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2027C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#2027D11
hypocenterC11#12223
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2027

Complements

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

NH ≅ G/Ntype
2. #13067658C2semidirect
3. #13067590C2semidirect
4. #13066645C2semidirect
5. #13066642C2semidirect
69. C2×D4×C11Q16semidirect
249. C2×D4#4326semidirect
286. C11#12223semidirect

Maximal subgroups

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

subgroupindex
#130763172
#130676582
#130675902
#130666452
#130666422
#130665482
C11×#20272
#1222311