Finite Group Databasebeta

← #14655448

Subgroups — #14655448

Order 2816.

506 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079603C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067226C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic, complemented
6#13066515C211yesmaximal, characteristic, complemented
7C2×C11×#489C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#489—22no—
12C11×#489—22no—
13C2×C11×#103—21no—
14C2×C11×#102—21no—
15C2×C11×#97C2211yescharacteristic
16#10622840—21no—
17#10622840—22no—
18#10622830—21no—
19#10622698—21no—
20#10622696—22no—
21#10622694—21no—
22#10622671—21no—
23#10622670—22no—
24#10622668—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622185—22no—
29#10622163—22no—
30#10622102—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×#4339—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C11×#124—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—22no—
50C2×#4325—24no—
51C2×#4323—22no—
52#66983—21no—
53#66983—21no—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#103—24no—
60C11×#102—24no—
61C11×#97—21no—
62C11×#97D412yes—
63#66899—22no—
64#66899—24no—
65#66896—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10136—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—42no—
81C2×Q8×C11—41no—
82C2×Q8×C11—82no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92#4339—82no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—21no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112#4325—84no—
113#4325—82no—
114#4323—82no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3213—111no—
123#3206—111no—
124C2×#489D1111yescharacteristic, complemented
125#1556—111no—
126#1530—111no—
127#1469—111no—
128#1302—111no—
129C23×C11—41no—
130C23×C11—42no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11#12111yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—82no—
139D4×C11—42no—
140D4×C11—42no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C22⋊D11—82no—
155C2×Dic11—41no—
156D44—42no—
157D44—42no—
158D44—81no—
159C4×D11—82no—
160Dic22—81no—
161C8×C11—42no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165#532—111no—
166C2×C4⋊Q8C2×D1111yescharacteristic
167C2×#124C2×D1111yescharacteristic
168#496—221no—
169#492—221no—
170#489—22no—
171#489—22no—
172#489—221no—
173#487—221no—
174#463—222no—
175#461—222no—
176#448—222no—
177#448—221no—
178#447—221no—
179#432—111no—
180#432—111no—
181#431—111no—
182C2×#103—21no—
183C2×#102—21no—
184C2×#97C2×D1111yescharacteristic
185#332—222no—
186#329—222no—
187#323—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—162no—
194C22×C11#39211yescharacteristic
195C22×C11#47112yes—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11#45512yes—
207Dic11—81no—
208C2×#41—221no—
209C22×Q8—21no—
210C22×Q8C22⋊D1111yescharacteristic
211C22×D4C22⋊D1111yescharacteristic
212C2×SD16—224no—
213C2×SD16—222no—
214C2×D8—222no—
215C22×C8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—111no—
220C4⋊Q8C22⋊D1112yes—
221#127—111no—
222#124—21no—
223#124—21no—
224#124—21no—
225#124—21no—
226#124—221no—
227#121—221no—
228#121—221no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—112no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239#103—24no—
240#103—224no—
241#103—222no—
242#102—24no—
243#102—222no—
244C22⋊C8—112no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#97—21no—
248#97—221no—
249#97—221no—
250#97C22⋊D1112yes—
251C4×C8—221no—
252C2×C11—22no—
253C2×C11—161no—
254C2×C11#200411yescharacteristic
255C2×C11#200811yescharacteristic
256C2×C11#201911yescharacteristic
257D11—161no—
258C24—21no—
259#41—882no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—42no—
264C2×Q8—41no—
265C2×Q8—82no—
266C2×Q8—221no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—42no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—441no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278C22×C4#434111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280SD16—884no—
281SD16—882no—
282D8—882no—
283C2×C8—22no—
284C2×C8—42no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—441no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C2×C22⋊D1111yescharacteristic
304C11#1013611yescharacteristic, complemented, Sylow
305C23—41no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—441no—
310C23#6699211yescharacteristic
311Q8—44no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315Q8—881no—
316D4—42no—
317D4—42no—
318D4—442no—
319D4—442no—
320D4—881no—
321D4—882no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—81no—
329C2×C4—441no—
330C2×C4—882no—
331C2×C4#6699011yescharacteristic
332C2×C4#6699011yescharacteristic
333C2×C4#6699111yescharacteristic
334C2×C4#6699211yescharacteristic
335C2×C4#6699311yescharacteristic
336C2×C4#6700611yescharacteristic
337C8—42no—
338C8—442no—
339C8—442no—
340C8—881no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—162no—
347C22—881no—
348C22—881no—
349C22—881no—
350C22#1062281612yes—
351C22#1062283611yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—82no—
359C4—881no—
360C4#1062267412yes—
361C2—22no—
362C2—161no—
363C2—1761no—
364C2#1306964511yescharacteristic
365C2#1306966711yescharacteristic
366C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#489C2
socleC22×C11#392
prime radical#13079603C2
hypercenterC2×#489D11
hypocenterC11#10136
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. #13079541C2semidirect
3. #13067333C2semidirect
4. #13067226C2semidirect
5. #13066968C2semidirect
6. #13066515C2semidirect
7. C2×C11×#489C2semidirect
124. C2×#489D11semidirect
304. C11#10136semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130795412
#130673332
#130672262
#130669682
#130665152
C2×C11×#4892
#1013611