Finite Group Databasebeta

← #14654337

Subgroups — #14654337

Order 2816.

772 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#10622647C212yesmaximal, complemented
2C2×#10622175C212yesmaximal, complemented
3#13066885C211yesmaximal, characteristic, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#2656C211yesmaximal, characteristic
6C2×C11×#121—22no—
7C2×C11×#121C2212yes—
8C22×C4⋊Dic11C2211yescharacteristic
9C11×#399—22no—
10C11×#392—22no—
11C2×C11×#95C2211yescharacteristic
12C2×#66896—22no—
13C2×C11⋊#95—22no—
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622647—24no—
17#10622647—24no—
18C2×#66872—22no—
19#10622175—24no—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×D4×C11D412yes—
23C23×C4×C11D412yes—
24C23×C4×C11C2311yescharacteristic
25C23×Dic11—21no—
26C23×Dic11—21no—
27C11×#121—22no—
28C11×#121—22no—
29C11×#121—22no—
30C11×#121—22no—
31C11×#121—44no—
32C11×#121—44no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4D412yes—
35C2×C11×C22⋊C4—24no—
36C2×C11×C22⋊C4—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D412yescomplemented
41C22×C11⋊C8—22no—
42C11×#95—22no—
43#66896—28no—
44C11⋊#95—22no—
45C11⋊#95—44no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)D414yescomplemented
48#66872—28no—
49#9968—111nomaximal, Sylow
50C24×C11—22no—
51C24×C11C2×D411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—44no—
55C2×D4×C11—44no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—44no—
59C2×D4×C11—44no—
60C2×D4×C11—82no—
61C2×D4×C11—82no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11SD1614yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C22×Dic11—42no—
76C22×Dic11—41no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—42no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—44no—
86C11×C22⋊C4—48no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—42no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—44no—
93C2×#481—112no—
94#2656D1111yescharacteristic
95C2×#327—112no—
96#1445—111no—
97#1280—111no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—44no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—44no—
106C23×C11#12011yescharacteristic
107C23×C11#12111yescharacteristic
108C23×C11#12711yescharacteristic
109C23×C11C2×SD1612yes—
110C23×C11AGL(1,ℤ/8)12yes—
111D4×C11—44no—
112D4×C11—82no—
113D4×C11—88no—
114D4×C11—84no—
115D4×C11—82no—
116D4×C11—82no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—82no—
128C2×C4×C11#12012yes—
129C2×C4×C11#12112yes—
130C2×Dic11—44no—
131C2×Dic11—42no—
132C2×Dic11—44no—
133C2×Dic11—42no—
134C2×Dic11—82no—
135C2×Dic11—81no—
136C2×Dic11—82no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C11⋊C8—44no—
141C2×#121—22no—
142C2×#121C2×D1112yes—
143C22×C4⋊C4—111no—
144#481—224no—
145#481—224no—
146C2×#106—222no—
147C2×#102—222no—
148C2×C22⋊C8—112no—
149#399—22no—
150#392—22no—
151C2×#95—111no—
152C2×#95—222no—
153C2×#95C2×D1111yescharacteristic
154#327—224no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—84no—
164C22×C11—84no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11#39211yescharacteristic
169C22×C11#45012yes—
170C22×C11#45311yescharacteristic
171C22×C11#45411yescharacteristic
172C22×C11#45812yes—
173C22×C11#46012yes—
174C22×C11#49211yescharacteristic
175C22×C11#49611yescharacteristic
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—44no—
179C4×C11—82no—
180Dic11—82no—
181Dic11—82no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4C22⋊D1112yes—
185C23×C4—221no—
186C23×C4—221no—
187C23×C4C22⋊D1112yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8—222no—
190#121—22no—
191#121—22no—
192#121—22no—
193#121—22no—
194#121—44no—
195#121—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4C22⋊D1112yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204#106—228no—
205#102—228no—
206C22⋊C8—114no—
207C22⋊C8—222no—
208#95—22no—
209#95—222no—
210#95—444no—
211C2×C11—21no—
212C2×C11—22no—
213C2×C11—21no—
214C2×C11—162no—
215C2×C11#161312yes—
216C2×C11#161612yes—
217C2×C11#200611yescharacteristic
218C2×C11#201411yescharacteristic
219C2×C11#202211yescharacteristic
220C24—22no—
221C24C2×C22⋊D1111yescharacteristic
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—44no—
227C2×D4—44no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4—82no—
231C2×D4—82no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—222no—
239C22×C4—222no—
240C22×C4—442no—
241C22×C4—442no—
242C22×C4—441no—
243C22×C4—442no—
244C22×C4—442no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—441no—
248C22×C4#432414yes—
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1112yes—
251C22×C4#434111yescharacteristic
252C22×C4C2×C22⋊D1112yes—
253C2×C8—224no—
254C2×C8—444no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—44no—
258C4⋊C4—224no—
259C4⋊C4—442no—
260C22⋊C4—48no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C11#996811yescharacteristic, complemented, Sylow
264C23—21no—
265C23—22no—
266C23—21no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—44no—
271C23—42no—
272C23#6698512yes—
273C23C2×#432412yes—
274C23#6699111yescharacteristic
275C23#6699311yescharacteristic
276C23#6700611yescharacteristic
277D4—44no—
278D4—82no—
279D4—88no—
280D4—82no—
281D4—84no—
282D4—82no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—442no—
295C2×C4—444no—
296C2×C4—444no—
297C2×C4—442no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4—882no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4#6699012yes—
305C2×C4#6699212yes—
306C8—444no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—82no—
316C22—84no—
317C22—84no—
318C22—82no—
319C22—82no—
320C22#1062268711yescharacteristic
321C22#1062268812yes—
322C22#1062268911yescharacteristic
323C22#1062283112yes—
324C22#1062283611yescharacteristic
325C22#1062285411yescharacteristic
326C22#1062285612yes—
327C22#1062285811yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—882no—
333C4—882no—
334C2—21no—
335C2—22no—
336C2—21no—
337C2—162no—
338C2#1306763612yes—
339C2#1306765312yes—
340C2#1306965811yescharacteristic
341C2#1306970411yescharacteristic
342C2#1306974511yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#2656C2
socleC23×C11#120
hypercenter#2656D11
hypocenterC11#9968
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#10622647C2semidirect
2. C2×#10622175C2semidirect
3. #13066885C2semidirect
4. #13066459C2semidirect
40. C2×C4⋊Dic11D4semidirect
47. C22⋊(C11⋊C8)D4semidirect
263. C11#9968semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
C2×#106221752
#130668852
#130664592
C11×#26562
#996811