Finite Group Databasebeta

← #14649234

Subgroups — #14649234

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#13077699C211yesmaximal, characteristic, complemented
2C2×#10622323C211yesmaximal, characteristic
3#13067010C211yesmaximal, characteristic, complemented
4#13067008C211yesmaximal, characteristic
5#13066936C211yesmaximal, characteristic
6#13066461C211yesmaximal, characteristic, complemented
7C11×#1275C211yesmaximal, characteristic, complemented
8C22×#4314C411yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14C2×#66885C411yescharacteristic
15C2×#66882C411yescharacteristic
16C2×#66880C411yescharacteristic
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622444—22no—
20#10622332—22no—
21#10622323—22no—
22#10622323—22no—
23#10622292—22no—
24#10622122—22no—
25#10622106—22no—
26#10622097—22no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22C2×C411yescharacteristic
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11C2×C411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×C4×Dic11—21no—
38C2×#4314—22no—
39C2×#4314—22no—
40C2×#4314—22no—
41C4×D44—21no—
42C4×D44—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C4×Dic22D412yes—
48C4×Dic22D412yes—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97—21no—
55C4×C8×C11—21no—
56C4×C8×C11D412yes—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)D412yes—
59#66885—22no—
60#66882—22no—
61#66880—22no—
62#66879—24no—
63Dic11⋊C8—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#9094—111nomaximal, Sylow
69C23×D11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44M1612yes—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—82no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22C22⋊C412yes—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—22no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11—41no—
98C2×C8×C11M1612yes—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11C22⋊C412yes—
109Dic11⋊C4—22no—
110Dic11⋊C4—22no—
111C4×Dic11—22no—
112C4×Dic11—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115#4314—28no—
116#2983—111no—
117C2×#440—111no—
118#1479—111no—
119#1478—111no—
120#1460—111no—
121#1281—111no—
122#1275D1111yescharacteristic, complemented
123C23×C11C4×D411yescharacteristic
124C22×D11—22no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—81no—
128C22×D11—81no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×M1611yescharacteristic
138C2×C4×C11C2×M1611yescharacteristic
139C2×C4×C11#13111yescharacteristic
140C2×C4×C11#13111yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148D44—22no—
149D44—22no—
150D44—41no—
151D44—41no—
152C4×D11—82no—
153C4×D11—82no—
154Dic22—22no—
155Dic22—22no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—22no—
159C8×C11—42no—
160C8×C11—41no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164C22×SD16—111no—
165C2×C4×Q8—111no—
166C2×C4×D4—111no—
167#446—222no—
168#446—222no—
169#440—222no—
170#440—222no—
171#432—222no—
172#431—111no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#431C2×D1111yescharacteristic
176C2×#107—111no—
177C2×#103—111no—
178C2×#102—111no—
179C2×#97C2×D1111yescharacteristic
180Q8⋊C8—222no—
181D4⋊C8—222no—
182#323—222no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#38611yescharacteristic
186C22×C11#43511yescharacteristic
187C22×C11#43611yescharacteristic
188C2×D11—42no—
189C2×D11—82no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11#40711yescharacteristic
198C4×C11#40811yescharacteristic
199C4×C11#43511yescharacteristic
200C4×C11#43611yescharacteristic
201Dic11—42no—
202Dic11—42no—
203Dic11—81no—
204C22×Q8—111no—
205C22×D4—111no—
206C23×C4—221no—
207C2×SD16—222no—
208C2×SD16—222no—
209C2×SD16—222no—
210C22×C8C4×D1111yescharacteristic
211C22×C8C4×D1111yescharacteristic
212C4×Q8—112no—
213C4×Q8—112no—
214C4×Q8—221no—
215C4×Q8—221no—
216C4×D4—221no—
217C4×D4—221no—
218C4×D4—221no—
219C4×D4—221no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—224no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—222no—
233#102—222no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—112no—
237C22⋊C8—221no—
238#97—21no—
239#97—21no—
240#97—224no—
241C4×C8—21no—
242C4×C8—221no—
243C4×C8—221no—
244C4×C8D4412yes—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11#187011yescharacteristic
248C2×C11#190311yescharacteristic
249C2×C11#190511yescharacteristic
250D11—82no—
251C24—221no—
252C2×Q8—112no—
253C2×Q8—221no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—112no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—882no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C22×C4#434311yescharacteristic
273SD16—228no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8#431312yes—
284C4⋊C4—112no—
285C4⋊C4—221no—
286C4⋊C4—222no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C42—222no—
293C42—222no—
294C42C2×D4411yescharacteristic
295C42#433911yescharacteristic
296C42D4×D1111yescharacteristic
297C42D4×D1111yescharacteristic
298C11#909411yescharacteristic, complemented, Sylow
299C23—222no—
300C23—441no—
301C23—441no—
302C23—881no—
303C23—881no—
304C23#6694611yescharacteristic
305Q8—222no—
306Q8—222no—
307Q8—441no—
308Q8—441no—
309D4—222no—
310D4—222no—
311D4—441no—
312D4—441no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—882no—
321C2×C4—882no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4C4×D4411yescharacteristic
325C2×C4C22⋊C4×D1111yescharacteristic
326C2×C4#6693511yescharacteristic
327C2×C4#6693711yescharacteristic
328C2×C4#6694711yescharacteristic
329C2×C4#6694811yescharacteristic
330C2×C4C2×#431311yescharacteristic
331C2×C4#6695411yescharacteristic
332C2×C4M16×D1111yescharacteristic
333C2×C4#6696011yescharacteristic
334C8—22no—
335C8—42no—
336C8—41no—
337C8—81no—
338C8—442no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—442no—
343C22—882no—
344C22—882no—
345C22—881no—
346C22—881no—
347C22#1062227811yescharacteristic
348C22#1062244911yescharacteristic
349C22#1062245111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—442no—
355C4—442no—
356C4—881no—
357C4#1062230111yescharacteristic
358C4#1062231911yescharacteristic
359C4#1062233911yescharacteristic
360C4#1062234011yescharacteristic
361C2—21no—
362C2—21no—
363C2—882no—
364C2#1306891211yescharacteristic
365C2#1306909711yescharacteristic
366C2#1306911111yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1275D11
hypocenterC11#9094
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
1. #13077699C2semidirect
3. #13067010C2semidirect
6. #13066461C2semidirect
7. C11×#1275C2semidirect
122. #1275D11semidirect
298. C11#9094semidirect

Maximal subgroups

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

subgroupindex
#130776992
C2×#106223232
#130670102
#130670082
#130669362
#130664612
C11×#12752
#909411