Finite Group Databasebeta

← #14655477

Subgroups — #14655477

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#13079599C211yesmaximal, characteristic
2C2×#10622702C211yesmaximal, characteristic, complemented
3#13067342C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic, complemented
5#13066967C211yesmaximal, characteristic, complemented
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3226C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66928C2211yescharacteristic
11C11×#500—21no—
12C11×#486—21no—
13C11×#480—22no—
14C11×#474—22no—
15C11×#431C2211yescharacteristic
16#10622702—21no—
17#10622702—22no—
18#10622702—22no—
19#10622687—21no—
20#10622653—21no—
21#10622649—21no—
22#10622629—22no—
23C2×#66874—21no—
24C2×#66873—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622184—22no—
29#10622178—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4324—22no—
50C2×#4323—22no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C22×C11⋊C8—21no—
54#66928—21no—
55#66928—21no—
56#66928—21no—
57#66928—21no—
58C11×#107—24no—
59C11×C4⋊C8—21no—
60C11×#102—24no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66874—22no—
67#66873—24no—
68#66873—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10140—111nomaximal, Sylow
76C23×D11—21no—
77C11×#41—82no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—42no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—42no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111#4324—82no—
112#4323—82no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—41no—
121#3226D1111yescharacteristic, complemented
122#3213—111no—
123C2×#489—111no—
124#1558—111no—
125#1530—111no—
126#1469—111no—
127#1302—111no—
128C23×C11—41no—
129C23×C11#12111yescharacteristic
130C22×D11—41no—
131C22×D11—42no—
132C22×D11—81no—
133C22×D11—81no—
134Q8×C11—82no—
135Q8×C11—81no—
136Q8×C11—82no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—81no—
140D4×C11—82no—
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—82no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×Dic11—41no—
155C2×Dic11—81no—
156D44—42no—
157D44—42no—
158Dic22—42no—
159Dic22—42no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#532C2×D1111yescharacteristic
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#124—111no—
167#500—21no—
168#496—221no—
169#489—222no—
170#489—222no—
171#489—221no—
172#486—21no—
173#480—22no—
174#474—22no—
175#463—222no—
176#448—221no—
177#447—221no—
178#432—111no—
179#432—111no—
180#431C2×D1111yescharacteristic
181C2×#103—221no—
182C2×#102—221no—
183C2×#97—111no—
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#39211yescharacteristic
193C22×C11#47212yes—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—162no—
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—21no—
208C22×Q8—21no—
209C22×Q8—111no—
210C22×D4—111no—
211C2×SD16—222no—
212C2×D8—222no—
213C22×C8—221no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8C22⋊D1112yes—
218C4⋊Q8C22⋊D1111yescharacteristic
219#127C22⋊D1111yescharacteristic
220#124—21no—
221#124—221no—
222#124—221no—
223#124—221no—
224#124—221no—
225#121—21no—
226#121—21no—
227C4×D4—21no—
228C4×D4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C42C22×D1111yescharacteristic
234#107—24no—
235C4⋊C8—21no—
236C4⋊C8—112no—
237C4⋊C8—221no—
238#103—224no—
239#103—222no—
240#102—24no—
241#102—224no—
242#102—222no—
243C22⋊C8—221no—
244C22⋊C8—221no—
245C22⋊C8C22⋊D1112yes—
246#97—112no—
247#97—221no—
248#97—221no—
249#97—221no—
250C4×C8—21no—
251C2×C11—22no—
252C2×C11—161no—
253C2×C11#200411yescharacteristic
254C2×C11#200911yescharacteristic
255C2×C11#201811yescharacteristic
256D11—161no—
257C24—221no—
258#41—82no—
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—82no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—442no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—442no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4D4×D1111yescharacteristic
277C22×C4#434111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279SD16—882no—
280D8—882no—
281C2×C8—22no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—442no—
285C2×C8—441no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42D4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C11#1014011yescharacteristic, complemented, Sylow
303C23—41no—
304C23—441no—
305C23—442no—
306C23—881no—
307C23—881no—
308C23#6699111yescharacteristic
309Q8—82no—
310Q8—81no—
311Q8—82no—
312Q8—442no—
313Q8—442no—
314D4—42no—
315D4—42no—
316D4—81no—
317D4—82no—
318D4—442no—
319D4—442no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—441no—
328C2×C4—881no—
329C2×C4#6699011yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699211yescharacteristic
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—881no—
345C22—881no—
346C22—881no—
347C22—1762no—
348C22#1062277312yes—
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—82no—
357C4—881no—
358C4#1062281512yes—
359C2—22no—
360C2—161no—
361C2—1761no—
362C2#1306964211yescharacteristic
363C2#1306967611yescharacteristic
364C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3226C2
socleC22×C11#392
prime radical#13079599C2
hypercenter#3226D11
hypocenterC11#10140
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. C2×#10622702C2semidirect
3. #13067342C2semidirect
4. #13067227C2semidirect
5. #13066967C2semidirect
6. #13066516C2semidirect
7. C11×#3226C2semidirect
121. #3226D11semidirect
302. C11#10140semidirect

Maximal subgroups

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

subgroupindex
#130795992
C2×#106227022
#130673422
#130672272
#130669672
#130665162
C11×#32262
#1014011