Finite Group Databasebeta

← #14666959

Subgroups — #14666959

Order 2816.

362 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076759C211yesmaximal, characteristic
2#13067624C211yesmaximal, characteristic, complemented
3#13067590C211yesmaximal, characteristic, complemented
4#13066645C211yesmaximal, characteristic, complemented
5#13066621C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic
7C11×#2027C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C11×#418—21no—
10C11×#390C2211yescharacteristic
11#10622835—21no—
12#10622663—21no—
13#10622656—21no—
14#10622596C2211yescharacteristic
15#10622592C2211yescharacteristic
16#10622565—21no—
17#10622565—21no—
18#10622561—21no—
19#10622560—21no—
20#10622546—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C11×C4⋊Q8—41no—
31C11×#125—41no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×#117—21no—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—21no—
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#66872—41no—
62#12276—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
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—
78C2×Dic22—41no—
79C2×Dic22—81no—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—81no—
92C11×C22⋊C4—81no—
93C42×C11—41no—
94C42×C11—41no—
95C22⋊Dic11—81no—
96C22⋊Dic11—81no—
97C22⋊Dic11—81no—
98C22⋊Dic11—81no—
99#4326—82no—
100C4⋊Dic11—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—81no—
104Dic11⋊C4—81no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2830—111no—
108#2027D1111yescharacteristic
109#1611—111no—
110#1605—111no—
111#1354—111no—
112#1346—111no—
113#1318—111no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122Q8×C11—81no—
123Q8×C11—81no—
124D4×C11—42no—
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#13511yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
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—
151Dic22—42no—
152Dic22—81no—
153C8×C11—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#544C2×D1111yescharacteristic
157#483—221no—
158#451—221no—
159#418—21no—
160#398—111no—
161#397—221no—
162#397—221no—
163#396—221no—
164#395—111no—
165#394—221no—
166#393—221no—
167#390C2×D1111yescharacteristic
168#387—221no—
169#343C2×D1111yescharacteristic
170#339—21no—
171#328—221no—
172#328—221no—
173#324—111no—
174#324—111no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#45211yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11B(4,𝔽2)11yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—111no—
199C22×D4C22⋊D1111yescharacteristic
200C2×Q16—441no—
201C2×M16—21no—
202C4⋊Q8—41no—
203#125—41no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206#117—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C42C22⋊D1111yescharacteristic
219#106—441no—
220#103—441no—
221#103—441no—
222#102—41no—
223#102—41no—
224C22⋊C8—221no—
225C22⋊C8—221no—
226#95—111no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—161no—
236C2×C11#160611yescharacteristic
237C2×C11#220011yescharacteristic
238C2×C11#220311yescharacteristic
239C24—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—441no—
243C2×Q8—881no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256Q16—882no—
257M16—41no—
258M16—41no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C22⋊C4—41no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C22⋊C4—881no—
278C22⋊C4—881no—
279C22⋊C4—881no—
280C22⋊C4—881no—
281C42—41no—
282C42—41no—
283C11#1227611yescharacteristic, complemented, Sylow
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#6699011yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—442no—
295Q8—881no—
296D4—42no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
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#6699511yescharacteristic
322C2×C4#6700311yescharacteristic
323C8—81no—
324C8—881no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062264511yescharacteristic
336C22#1062266011yescharacteristic
337C22#1062267411yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—881no—
346C4—881no—
347C4—881no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1306759411yescharacteristic
353C2#1307062211yescharacteristic
354C2#1307063611yescharacteristic
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#12276
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. #13067624C2semidirect
3. #13067590C2semidirect
4. #13066645C2semidirect
5. #13066621C2semidirect
283. C11#12276semidirect

Maximal subgroups

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

subgroupindex
#130767592
#130676242
#130675902
#130666452
#130666212
#130665482
C11×#20272
#1227611