Finite Group Databasebeta

← #14650441

Subgroups — #14650441

Order 2816.

494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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
2#13077333C211yesmaximal, characteristic
3#13069437C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66960—21no—
10#10623008C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66899—21no—
14C2×#66899—21no—
15#10622742—21no—
16#10622701C412yescomplemented
17#10622700—22no—
18#10622691C412yescomplemented
19#10622580—22no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622449—22no—
24#10622449—22no—
25C11×#332—22no—
26#10622108—22no—
27C22×Q8×C11—21no—
28C2×#4339—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8C2×C412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37#66983—21no—
38#66983D412yes—
39C2×C4⋊Dic11—21no—
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42#66960—42no—
43#66960—42no—
44C2×#4313—22no—
45C2×C8×D11—22no—
46#66928—21no—
47#66927C2×C411yescharacteristic
48C4×D44—21no—
49C4×D44D412yes—
50#66922C2×C411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8D412yes—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56#66899—42no—
57#66899—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—24no—
62#66873—24no—
63#66871—24no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66#66867—21no—
67C4×C11⋊C8C2×C412yes—
68#9291—111nomaximal, Sylow
69C2×Q8×C11—22no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—22no—
80C22×Dic11—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44C22⋊C412yes—
88C2×C4×D11—22no—
89C2×Dic22—21no—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C22×C411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11C22⋊C412yes—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8D812yes—
115#4313—44no—
116C8×D11—44no—
117#3226—111no—
118#2932—111no—
119#1960—111no—
120#1546D1111yescharacteristic, complemented
121#1517—111no—
122#1286—111no—
123#1275—111no—
124C23×C11#12111yescharacteristic
125C22×D11—22no—
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—81no—
129Q8×C11—81no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C22⋊D11—42no—
146C22⋊D11—42no—
147C2×Dic11—22no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151D44—42no—
152D44—41no—
153D44—41no—
154D44—81no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—22no—
162C11⋊C8—42no—
163C11⋊C8—41no—
164C2×#131—221no—
165#532—111no—
166C2×C4⋊Q8C2×D1111yescharacteristic
167#500—112no—
168#486—112no—
169#480—222no—
170#474—222no—
171#435—222no—
172#435—222no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#423C2×D1111yescharacteristic
176C2×#103—221no—
177C2×#103—221no—
178#408—221no—
179C2×#97—111no—
180#382—111no—
181#332—22no—
182#327—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#38611yescharacteristic
186C22×C11#45911yescharacteristic
187C22×C11#46311yescharacteristic
188C2×D11—42no—
189C2×D11—42no—
190C2×D11—42no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11C4×D811yescharacteristic
197C4×C11#44211yescharacteristic
198C4×C11#44711yescharacteristic
199C4×C11#44911yescharacteristic
200Dic11—42no—
201Dic11—161no—
202C2×#41—221no—
203C22×Q8—21no—
204#131—442no—
205#131—442no—
206C2×M16—21no—
207C2×M16—222no—
208C22×C8—111no—
209C22×C8—111no—
210C22×C8—222no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—111no—
215C4⋊Q8C4×D1112yes—
216#127—111no—
217#124—221no—
218#121—112no—
219#121—221no—
220C4×D4—112no—
221C4×D4—221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—221no—
225C2×C42C22×D1111yescharacteristic
226#107—224no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—221no—
230C4⋊C8C22⋊D1112yes—
231#103—442no—
232#103—442no—
233#102—224no—
234C22⋊C8—21no—
235C22⋊C8—224no—
236C22⋊C8—221no—
237#97—221no—
238#97—221no—
239C4×C8—21no—
240C4×C8—112no—
241#95—221no—
242#95—221no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#187911yescharacteristic
246C2×C11#190211yescharacteristic
247C2×C11#190911yescharacteristic
248D11—82no—
249#41—441no—
250#41—441no—
251#41—441no—
252#41—441no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—221no—
260C2×D4—112no—
261C2×D4—222no—
262C2×D4—221no—
263C2×D4—221no—
264C22×C4—41no—
265C22×C4—222no—
266C22×C4—441no—
267C22×C4#433911yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270M16—41no—
271M16—41no—
272M16—444no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—112no—
276C2×C8—221no—
277C2×C8—221no—
278C2×C8—222no—
279C2×C8—221no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—444no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—112no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C42C2×C4×D1111yescharacteristic
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C11#929111yescharacteristic, complemented, Sylow
298C23—222no—
299C23#6693711yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304Q8—441no—
305Q8—441no—
306D4—442no—
307D4—442no—
308D4—442no—
309D4—441no—
310D4—441no—
311D4—881no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—222no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4C22⋊C4×D1111yescharacteristic
324C2×C4(C22⋊D11)⋊C411yescharacteristic
325C2×C4#6693611yescharacteristic
326C2×C4D8×D1111yescharacteristic
327C2×C4#6696411yescharacteristic
328C2×C4#6696711yescharacteristic
329C2×C4#6696911yescharacteristic
330C2×C4C4×C22⋊D1111yescharacteristic
331C2×C4#6699011yescharacteristic
332C2×C4#6699111yescharacteristic
333C8—42no—
334C8—81no—
335C8—222no—
336C8—442no—
337C8—441no—
338C22—21no—
339C22—21no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22#1062239911yescharacteristic
344C22#1062240011yescharacteristic
345C22#1062256911yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—82no—
351C4—442no—
352C4—1761no—
353C4#1062236911yescharacteristic
354C4#1062239811yescharacteristic
355C4#1062276911yescharacteristic
356C4#1062278511yescharacteristic
357C2—21no—
358C2—21no—
359C2—882no—
360C2#1306896111yescharacteristic
361C2#1306909211yescharacteristic
362C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9291
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. #13069437C2semidirect
5. #13066476C2semidirect
6. #13066446C2semidirect
7. C11×#1546C2semidirect
16. #10622701C4semidirect
18. #10622691C4semidirect
120. #1546D11semidirect
297. C11#9291semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130773332
#130694372
#130671772
#130664762
#130664462
C11×#15462
#929111