Finite Group Databasebeta

← #14655476

Subgroups — #14655476

Order 2816.

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

normal subgroups only

This group has 494 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#13079737C211yesmaximal, characteristic, complemented
2#13079603C211yesmaximal, characteristic
3#13067342C211yesmaximal, 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#10622830—21no—
18#10622701—21no—
19#10622700—22no—
20#10622691—21no—
21#10622671—21no—
22#10622670—22no—
23#10622668—21no—
24#10622580—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622184—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×#4323—22no—
51#66983—21no—
52#66983—21no—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922D411yescharacteristic
58C11×#103—24no—
59C11×#102—24no—
60C11×#97—21no—
61C11×#97D412yes—
62#66899—22no—
63#66896—22no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)D412yes—
67#66873—24no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10140—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
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—82no—
113#4323—82no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3226—111no—
122#3213—111no—
123C2×#489D1111yescharacteristic, complemented
124#1558—111no—
125#1530—111no—
126#1469—111no—
127#1302—111no—
128C23×C11—41no—
129C23×C11—42no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11#12111yescharacteristic
133C22×D11—41no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—82no—
137Q8×C11—82no—
138D4×C11—42no—
139D4×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C22⋊D11—82no—
154C2×Dic11—41no—
155D44—42no—
156D44—42no—
157D44—81no—
158C4×D11—82no—
159Dic22—81no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#532—111no—
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#124C2×D1111yescharacteristic
167#500—221no—
168#496—221no—
169#489—22no—
170#489—22no—
171#489—221no—
172#486—221no—
173#480—222no—
174#474—222no—
175#463—222no—
176#448—221no—
177#447—221no—
178#432—111no—
179#432—111no—
180#431—111no—
181C2×#103—21no—
182C2×#102—21no—
183C2×#97C2×D1111yescharacteristic
184#333—222no—
185#329—222no—
186#323—222no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—162no—
193C22×C11#39211yescharacteristic
194C22×C11#47212yes—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11#45512yes—
206Dic11—81no—
207C2×#41—221no—
208C22×Q8—21no—
209C22×Q8C22⋊D1111yescharacteristic
210C22×D4C22⋊D1111yescharacteristic
211C2×SD16—222no—
212C2×D8—222no—
213C22×C8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—111no—
218C4⋊Q8C22⋊D1112yes—
219#127—111no—
220#124—21no—
221#124—21no—
222#124—21no—
223#124—21no—
224#124—221no—
225#121—221no—
226#121—221no—
227C4×D4—221no—
228C4×D4—221no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42C22×D1111yescharacteristic
234#107—224no—
235C4⋊C8—112no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238#103—24no—
239#103—222no—
240#102—24no—
241#102—224no—
242#102—222no—
243C22⋊C8—112no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#97—21no—
247#97—221no—
248#97—221no—
249#97C22⋊D1112yes—
250C4×C8—221no—
251C2×C11—22no—
252C2×C11—161no—
253C2×C11#200411yescharacteristic
254C2×C11#200911yescharacteristic
255C2×C11#201811yescharacteristic
256D11—161no—
257C24—21no—
258#41—882no—
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—42no—
263C2×Q8—41no—
264C2×Q8—82no—
265C2×Q8—221no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—42no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—441no—
276C22×C4D4×D1111yescharacteristic
277C22×C4#434111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279SD16—882no—
280D8—882no—
281C2×C8—22no—
282C2×C8—42no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—441no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42D4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C11#1014011yescharacteristic, complemented, Sylow
303C23—41no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—441no—
308C23#6699211yescharacteristic
309Q8—42no—
310Q8—42no—
311Q8—82no—
312Q8—82no—
313Q8—881no—
314D4—42no—
315D4—42no—
316D4—442no—
317D4—442no—
318D4—881no—
319D4—882no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—441no—
328C2×C4—882no—
329C2×C4#6699011yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699111yescharacteristic
332C2×C4#6699211yescharacteristic
333C2×C4#6699311yescharacteristic
334C2×C4#6700611yescharacteristic
335C8—42no—
336C8—442no—
337C8—442no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—162no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22#1062281212yes—
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—82no—
357C4—881no—
358C4#1062267412yes—
359C2—22no—
360C2—161no—
361C2—1761no—
362C2#1306964511yescharacteristic
363C2#1306967411yescharacteristic
364C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#489C2
socleC22×C11#392
prime radical#13079603C2
hypercenterC2×#489D11
hypocenterC11#10140
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
1. #13079737C2semidirect
3. #13067342C2semidirect
4. #13067226C2semidirect
5. #13066968C2semidirect
6. #13066515C2semidirect
7. C2×C11×#489C2semidirect
123. C2×#489D11semidirect
302. C11#10140semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130796032
#130673422
#130672262
#130669682
#130665152
C2×C11×#4892
#1014011