Finite Group Databasebeta

← #14666033

Subgroups — #14666033

Order 2816.

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

normal subgroups only

This group has 398 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#13076599C211yesmaximal, characteristic, complemented
2#13069663C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066643C211yesmaximal, characteristic, complemented
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1616C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#67004—21no—
10C11×#481—21no—
11C11×#400C2211yescharacteristic
12C2×#66901—21no—
13#10622647—21no—
14#10622599C2211yescharacteristic
15#10622597—21no—
16#10622587C2211yescharacteristic
17#10622270—21no—
18#10622266—21no—
19#10622265—21no—
20#10622260—21no—
21#10622259—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Dic22D411yescharacteristic
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35#67004—42no—
36#67004—42no—
37C2×#4326—41no—
38C2×#4324—41no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48C11×#106—41no—
49C11×#102—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54#66901—42no—
55#66896—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66872—41no—
65#12131—111nomaximal, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
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—21no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22SD1612yes—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96#4326—44no—
97#4324—44no—
98C4⋊Dic11—41no—
99C4⋊Dic11—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104C4×Dic11—41no—
105C4×Dic11—81no—
106#4318—22no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2809—111no—
111#2007—111no—
112#1616—111no—
113#1616D1111yescharacteristic
114#1353—111no—
115#1353—111no—
116#1319—111no—
117C23×C11—41no—
118C23×C11#12011yescharacteristic
119Q8×C11—41no—
120Q8×C11—41no—
121D4×C11—41no—
122D4×C11—41no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
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×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—22no—
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—
155C2×Dic11—41no—
156Dic22—42no—
157Dic22—81no—
158C8×C11—81no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×#137—221no—
162#537C2×D1111yescharacteristic
163#481—21no—
164#481—221no—
165C2×#104—221no—
166#400—111no—
167#400C2×D1111yescharacteristic
168#398—221no—
169#398—221no—
170#391—111no—
171#391—221no—
172#389—221no—
173#387—221no—
174#387—221no—
175#343—111no—
176#327—21no—
177#327—221no—
178#324—111no—
179#324C2×D1111yescharacteristic
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#44811yescharacteristic
186C22×C11#45311yescharacteristic
187C22×C11B(4,𝔽2)11yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—42no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199C2×#41—21no—
200C22×Q8—111no—
201#137—442no—
202#137—442no—
203C2×Q16—441no—
204C2×SD16—441no—
205C2×M16—221no—
206C22⋊Q8—41no—
207#121—21no—
208#121—21no—
209#121—41no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C4⋊C4C22×D1111yescharacteristic
218C2×C42—111no—
219C2×C42—221no—
220#106—41no—
221#106—441no—
222#104—442no—
223#102—41no—
224#102—441no—
225C22⋊C8—21no—
226C22⋊C8—221no—
227#95—21no—
228#95—21no—
229#95—111no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95C22⋊D1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—161no—
240C2×C11#159611yescharacteristic
241C2×C11#220111yescharacteristic
242C2×C11#220411yescharacteristic
243#41—41no—
244#41—41no—
245#41—41no—
246#41—41no—
247C2×Q8—21no—
248C2×Q8—112no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266Q16—444no—
267SD16—444no—
268M16—222no—
269M16—441no—
270C2×C8—41no—
271C2×C8—441no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—881no—
282C4⋊C4—881no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42—441no—
286C42—881no—
287C11#1213111yescharacteristic, complemented, Sylow
288C23—41no—
289C23#6699011yescharacteristic
290Q8—41no—
291Q8—41no—
292Q8—442no—
293Q8—881no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298D4—81no—
299D4—81no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—222no—
316C2×C4—222no—
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—
327C2×C4SD16×D1111yescharacteristic
328C2×C4#6696811yescharacteristic
329C8—81no—
330C8—442no—
331C8—881no—
332C22—21no—
333C22—21no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22#1062264511yescharacteristic
338C22#1062278311yescharacteristic
339C22#1062281111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—442no—
348C4—442no—
349C4—881no—
350C4—881no—
351C2—21no—
352C2—21no—
353C2—161no—
354C2#1306753711yescharacteristic
355C2#1307062711yescharacteristic
356C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1616C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1616D11
hypocenterC11#12131
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1616

Complements

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

NH ≅ G/Ntype
1. #13076599C2semidirect
4. #13066644C2semidirect
5. #13066643C2semidirect
6. #13066549C2semidirect
287. C11#12131semidirect

Maximal subgroups

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

subgroupindex
#130765992
#130696632
#130676532
#130666442
#130666432
#130665492
C11×#16162
#1213111