Finite Group Databasebeta

← #14650525

Subgroups — #14650525

Order 2816.

488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 113 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#13078409C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic
3#13068623C211yesmaximal, characteristic
4#13067019C211yesmaximal, characteristic, complemented
5#13066512C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622700C412yescomplemented
13#10622697C412yescomplemented
14#10622679—22no—
15#10622614—21no—
16#10622608—21no—
17C2×#66873—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24C11×#328—22no—
25Q8⋊(C11⋊C8)—22no—
26#10622167—21no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×#4318—21no—
42C22×C11⋊C8—21no—
43C2×C8×D11—24no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44C2×C412yes—
47C4×D44D412yes—
48C11×C4⋊C8—21no—
49C11×C22⋊C8D412yes—
50C4×C8×C11—21no—
51C11×#95—21no—
52C11×#95—21no—
53C22⋊(C11⋊C8)—21no—
54(C2×D11)⋊C8—24no—
55#66873—22no—
56#66873—22no—
57#66873—42no—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)C2×C412yes—
65C4×C11⋊C8D412yes—
66#9303—111nomaximal, Sylow
67C23×D11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×Dic11—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44C22⋊C412yes—
79C2×D44SD1612yes—
80C2×D44Q1612yes—
81C2×C4×D11—22no—
82C2×C4×D11—22no—
83C2×C4×D11—82no—
84C2×C8×C11—22no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101C4⋊Dic11—21no—
102C4⋊Dic11C22⋊C412yes—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C8×D11—84no—
111#3077—111no—
112#2972—111no—
113#1804—111no—
114#1518D1111yescharacteristic, complemented
115#1481—111no—
116#1301—111no—
117#1286—111no—
118C23×C11#12111yescharacteristic
119C22×D11—22no—
120C22×D11—22no—
121C22×D11—22no—
122C22×D11—81no—
123C22×D11—81no—
124Q8×C11—42no—
125Q8×C11—81no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11C2×Q1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—81no—
145D44—22no—
146D44—22no—
147D44—22no—
148D44#10314yes—
149C4×D11—44no—
150C4×D11—82no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155#533C2×D1111yescharacteristic
156C2×C4×D4—111no—
157#478—222no—
158#476—112no—
159#474—112no—
160C8×D4—222no—
161C8×D4—222no—
162#431—111no—
163#431C2×D1111yescharacteristic
164#428—221no—
165#423—111no—
166C2×C4⋊C8—111no—
167#418—221no—
168C2×#102—221no—
169C2×C22⋊C8—222no—
170#382C2×D1111yescharacteristic
171#340—221no—
172#328—22no—
173Q8⋊C8—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38611yescharacteristic
177C22×C11#46511yescharacteristic
178C22×C11#46711yescharacteristic
179C2×D11—24no—
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—82no—
183C2×D11—82no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—161no—
191C4×C11C2×#10311yescharacteristic
192C4×C11#41611yescharacteristic
193C4×C11#46511yescharacteristic
194C4×C11#46711yescharacteristic
195Dic11—42no—
196C22×D4—111no—
197C23×C4—221no—
198C2×M16—221no—
199C22×C8—224no—
200C22×C8—221no—
201C4⋊Q8C4×D1111yescharacteristic
202C4⋊Q8C4×D1111yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×D4—112no—
209C4×D4—112no—
210C4×D4—221no—
211C4×D4—221no—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—111no—
215C2×C22⋊C4—221no—
216C2×C42C22×D1111yescharacteristic
217#107—222no—
218#106—222no—
219C4⋊C8—21no—
220C4⋊C8—112no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225#102—222no—
226#102—222no—
227#102—442no—
228C22⋊C8—224no—
229C22⋊C8—221no—
230C22⋊C8C22⋊D1112yes—
231C4×C8—21no—
232C4×C8—112no—
233#95—21no—
234#95—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#188111yescharacteristic
238C2×C11#189211yescharacteristic
239C2×C11#190411yescharacteristic
240D11—44no—
241C24—221no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×D4—112no—
245C2×D4—112no—
246C2×D4—112no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C22×C4—41no—
251C22×C4—221no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4—882no—
255C22×C4D4×D1111yescharacteristic
256C22×C4#434111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—441no—
259M16—441no—
260C2×C8—22no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—884no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—112no—
276C4⋊C4—221no—
277C22⋊C4—41no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C42—41no—
281C42C2×C4×D1111yescharacteristic
282C42#433911yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C11#930311yescharacteristic, complemented, Sylow
286C23—222no—
287C23—222no—
288C23—222no—
289C23—881no—
290C23—881no—
291C23#6699111yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—114no—
295D4—222no—
296D4—222no—
297D4—222no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—222no—
306C2×C4—444no—
307C2×C4—882no—
308C2×C4—881no—
309C2×C4C22⋊C4×D1111yescharacteristic
310C2×C4(C22⋊D11)⋊C411yescharacteristic
311C2×C4#6693611yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4SD16×D1111yescharacteristic
314C2×C4#6696911yescharacteristic
315C2×C4Q16×D1111yescharacteristic
316C2×C4#6697211yescharacteristic
317C2×C4C4×C22⋊D1111yescharacteristic
318C2×C4#6699011yescharacteristic
319C8—42no—
320C8—442no—
321C8—442no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—224no—
326C22—442no—
327C22—442no—
328C22—882no—
329C22—882no—
330C22#1062256911yescharacteristic
331C22#1062278411yescharacteristic
332C22#1062280111yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—81no—
338C4—81no—
339C4—161no—
340C4—442no—
341C4D11×#10311yescharacteristic
342C4#1062241711yescharacteristic
343C4#1062242011yescharacteristic
344C4#1062242611yescharacteristic
345C2—21no—
346C2—21no—
347C2—444no—
348C2#1306897511yescharacteristic
349C2#1306903611yescharacteristic
350C2#1306910611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9303
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
4. #13067019C2semidirect
5. #13066512C2semidirect
6. #13066474C2semidirect
7. C11×#1518C2semidirect
12. #10622700C4semidirect
13. #10622697C4semidirect
114. #1518D11semidirect
285. C11#9303semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130776392
#130686232
#130670192
#130665122
#130664742
C11×#15182
#930311