Finite Group Databasebeta

← #14649235

Subgroups — #14649235

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077701C211yesmaximal, characteristic, complemented
2#13067011C211yesmaximal, characteristic, complemented
3#13067007C211yesmaximal, characteristic
4#13066937C211yesmaximal, characteristic
5#13066461C211yesmaximal, characteristic, complemented
6#13066447C211yesmaximal, characteristic, complemented
7C2×C11×#440C211yesmaximal, characteristic
8C22×C11×SD16C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#440—22no—
12C11×#440—22no—
13C2×C11×#107C411yescharacteristic
14C2×C11×#103C411yescharacteristic
15C2×C11×#102C411yescharacteristic
16C2×C11×#97C2211yescharacteristic
17#10622637—22no—
18#10622637—22no—
19#10622539—22no—
20#10622538C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24Q8⋊(C11⋊C8)—22no—
25D4⋊(C11⋊C8)—22no—
26#10622163—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C2×C11×SD16—22no—
31C2×C11×SD16—22no—
32C2×C11×SD16—22no—
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11C2×C411yescharacteristic
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11D412yes—
38C4×Q8×C11D412yes—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C11×#107—22no—
50C11×#103—22no—
51C11×#102—22no—
52C11×#97—21no—
53C11×#97—21no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)—24no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—24no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D412yes—
68#9094—111nomaximal, Sylow
69C24×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11C22⋊C412yes—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11M1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—82no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C11×SD16—28no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11M1612yes—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4C22⋊C412yes—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2983—111no—
117C2×#440D1111yescharacteristic
118#1479—111no—
119#1478—111no—
120#1460—111no—
121#1281—111no—
122#1275—111no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11C4×D411yescharacteristic
129Q8×C11—22no—
130Q8×C11—22no—
131Q8×C11—41no—
132Q8×C11—41no—
133D4×C11—22no—
134D4×C11—22no—
135D4×C11—41no—
136D4×C11—41no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11C2×M1611yescharacteristic
155C2×C4×C11C2×M1611yescharacteristic
156C2×C4×C11#13111yescharacteristic
157C2×C4×C11#13111yescharacteristic
158C8×C11—22no—
159C8×C11—41no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C11⋊C8—81no—
164C22×SD16Dic1111yescharacteristic
165C2×C4×Q8C2×D1111yescharacteristic
166C2×C4×D4C2×D1111yescharacteristic
167#446—222no—
168#446—222no—
169#440—22no—
170#440—22no—
171#432—222no—
172#431—111no—
173#431—111no—
174#431—111no—
175#431—111no—
176C2×#107Dic1111yescharacteristic
177C2×#103Dic1111yescharacteristic
178C2×#102Dic1111yescharacteristic
179C2×#97C2×D1111yescharacteristic
180Q8⋊C8—222no—
181D4⋊C8—222no—
182#323—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—42no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11#38611yescharacteristic
191C22×C11#43511yescharacteristic
192C22×C11#43611yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—42no—
199C4×C11—81no—
200C4×C11#40711yescharacteristic
201C4×C11#40811yescharacteristic
202C4×C11#43511yescharacteristic
203C4×C11#43611yescharacteristic
204C22×Q8C2×Dic1111yescharacteristic
205C22×D4C2×Dic1111yescharacteristic
206C23×C4—21no—
207C2×SD16—22no—
208C2×SD16—22no—
209C2×SD16—22no—
210C22×C8C2×Dic1111yescharacteristic
211C22×C8C2×Dic1111yescharacteristic
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8C22⋊D1112yes—
215C4×Q8C22⋊D1112yes—
216C4×D4—21no—
217C4×D4—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×Dic1111yescharacteristic
222C2×C4⋊C4C2×Dic1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226#107—22no—
227C4⋊C8—224no—
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—22no—
233#102—22no—
234C22⋊C8—112no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238#97—21no—
239#97—21no—
240#97—224no—
241C4×C8—112no—
242C4×C8—221no—
243C4×C8—221no—
244C4×C8—221no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—82no—
248C2×C11#187011yescharacteristic
249C2×C11#190311yescharacteristic
250C2×C11#190511yescharacteristic
251C24—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C22⋊Dic1112yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4#431812yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—82no—
270C22×C4D4×D1111yescharacteristic
271C22×C4#434111yescharacteristic
272C22×C4C22×Dic1111yescharacteristic
273SD16—28no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8—441no—
282C2×C8—441no—
283C2×C8#431812yes—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4C22⋊Dic1112yes—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C11#909411yescharacteristic, complemented, Sylow
299C23—22no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23D4×Dic1111yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309D4—22no—
310D4—22no—
311D4—41no—
312D4—41no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×#431811yescharacteristic
325C2×C4C2×#431811yescharacteristic
326C2×C4D4×Dic1111yescharacteristic
327C2×C4#6698811yescharacteristic
328C2×C4#6699011yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4#6700111yescharacteristic
332C2×C4#6700111yescharacteristic
333C2×C4C2×C22⋊Dic1111yescharacteristic
334C8—22no—
335C8—41no—
336C8—442no—
337C8—442no—
338C8—881no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—82no—
344C22—82no—
345C22—81no—
346C22—81no—
347C22#1062262411yescharacteristic
348C22#1062262511yescharacteristic
349C22#1062283311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—81no—
357C4#1062262411yescharacteristic
358C4#1062262511yescharacteristic
359C4#1062282011yescharacteristic
360C4#1062284711yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1306891411yescharacteristic
365C2#1306909811yescharacteristic
366C2#1306911211yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#440C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#440D11
hypocenterC11#9094
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
2. #13067011C2semidirect
5. #13066461C2semidirect
6. #13066447C2semidirect
298. C11#9094semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130670112
#130670072
#130669372
#130664612
#130664472
C2×C11×#4402
#909411