Finite Group Databasebeta

← #14666366

Subgroups — #14666366

Order 2816.

372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076887C211yesmaximal, characteristic, complemented
2#13069842C211yesmaximal, characteristic
3#13067585C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic, complemented
5#13066646C211yesmaximal, characteristic, complemented
6#13066559C211yesmaximal, characteristic, complemented
7C11×#1604C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#448—21no—
10C11×#395C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622842—21no—
14#10622653—21no—
15#10622595—21no—
16#10622592—21no—
17#10622592C2211yescharacteristic
18#10622590C2211yescharacteristic
19#10622273—21no—
20#10622271—21no—
21#10622263—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C2×C11×SD16—41no—
31C11×C22⋊Q8—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×#4324—41no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11D411yescharacteristic
44C2×#4318—21no—
45C11×#103—41no—
46C11×C22⋊C8—21no—
47C11×#95—21no—
48C11×#95D411yescharacteristic
49#66901—42no—
50#66899—41no—
51#66896—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66874—41no—
63#12184—111nomaximal, Sylow
64C11×#41—41no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—81no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—41no—
86C2×Dic22—81no—
87C11×SD16—82no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—81no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95#4324—82no—
96C4⋊Dic11—41no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101C4×Dic11—21no—
102C4×Dic11SD1612yescomplemented
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2844—111no—
108#2040—111no—
109#1604—111no—
110#1604D1111yescharacteristic
111#1354—111no—
112#1354—111no—
113#1324—111no—
114C23×C11—41no—
115C23×C11#12011yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118Q8×C11—42no—
119Q8×C11—81no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
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×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154Dic22—42no—
155Dic22—81no—
156C8×C11—81no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159#537C2×D1111yescharacteristic
160#448—21no—
161#448—221no—
162C2×#104—221no—
163#417—221no—
164#400—221no—
165#400—221no—
166#400—221no—
167#395—111no—
168#395—221no—
169#395—221no—
170#395C2×D1111yescharacteristic
171#382—111no—
172#382—221no—
173#343—111no—
174#327—21no—
175#327—221no—
176#324—111no—
177#324C2×D1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11#44811yescharacteristic
184C22×C11#45411yescharacteristic
185C22×C11B(4,𝔽2)11yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—42no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197C2×#41—21no—
198C22×Q8—111no—
199C22×Q8C22⋊D1111yescharacteristic
200C2×SD16—41no—
201C2×SD16—441no—
202C2×M16—221no—
203C22⋊Q8—41no—
204#121—21no—
205#121—21no—
206#121—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22×D1111yescharacteristic
214C2×C42—111no—
215#104—442no—
216#103—41no—
217#103—441no—
218#103—441no—
219#102—441no—
220C22⋊C8—21no—
221C22⋊C8—221no—
222#95—21no—
223#95—111no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95C22⋊D1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—161no—
236C2×C11#159911yescharacteristic
237C2×C11#219911yescharacteristic
238C2×C11#220311yescharacteristic
239#41—41no—
240#41—41no—
241#41—41no—
242#41—41no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—81no—
246C2×Q8—441no—
247C2×Q8—881no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4D4×D1111yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262SD16—82no—
263SD16—882no—
264M16—441no—
265M16—441no—
266C2×C8—41no—
267C2×C8—441no—
268C2×C8—441no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—81no—
273C4⋊C4—441no—
274C4⋊C4—881no—
275C4⋊C4—881no—
276C4⋊C4—881no—
277C4⋊C4—881no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42—112no—
281C42—221no—
282C11#1218411yescharacteristic, complemented, Sylow
283C23—41no—
284C23#6699011yescharacteristic
285Q8—41no—
286Q8—41no—
287Q8—42no—
288Q8—81no—
289Q8—442no—
290Q8—881no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295D4—81no—
296D4—81no—
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—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—222no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4SD16×D1111yescharacteristic
324C2×C4#6696811yescharacteristic
325C8—81no—
326C8—881no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1062264511yescharacteristic
334C22#1062278311yescharacteristic
335C22#1062281411yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—442no—
344C4—881no—
345C4—881no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#1306755411yescharacteristic
351C2#1307061511yescharacteristic
352C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1604C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1604D11
hypocenterC11#12184
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1604

Complements

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

NH ≅ G/Ntype
1. #13076887C2semidirect
4. #13066647C2semidirect
5. #13066646C2semidirect
6. #13066559C2semidirect
102. C4×Dic11SD16semidirect
282. C11#12184semidirect

Maximal subgroups

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

subgroupindex
#130768872
#130698422
#130675852
#130666472
#130666462
#130665592
C11×#16042
#1218411