Finite Group Databasebeta

← #14649230

Subgroups — #14649230

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×#10622631C211yesmaximal, characteristic
3#13067012C211yesmaximal, characteristic, complemented
4#13066937C211yesmaximal, characteristic
5#13066460C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4324C411yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×#66896C411yescharacteristic
14#10622631—22no—
15#10622631—22no—
16C2×#66874C411yescharacteristic
17C2×#66871C411yescharacteristic
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622444—22no—
22#10622332—22no—
23#10622292—22no—
24C11×D4⋊C8—22no—
25#10622163—22no—
26#10622094—22no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C22×Dic22C2×C411yescharacteristic
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4324—22no—
38C2×#4324—22no—
39C2×#4324—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
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—
53C4×C8×C11—21no—
54C4×C8×C11D412yes—
55#66896—22no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66879—24no—
59Dic11⋊C8—24no—
60#66874—22no—
61#66871—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#9094—111nomaximal, Sylow
69C24×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11M1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—82no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22C22⋊C412yes—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101#4324—28no—
102C4⋊Dic11—21no—
103C4⋊Dic11C22⋊C412yes—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8M1612yes—
116#2983—111no—
117C2×#440—111no—
118#1479—111no—
119#1478D1111yescharacteristic
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
129D4×C11—22no—
130D4×C11—22no—
131D4×C11—41no—
132D4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11—81no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11C2×M1611yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—81no—
154Dic22—22no—
155Dic22—22no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—42no—
159C8×C11—81no—
160C11⋊C8—22no—
161C11⋊C8—42no—
162C11⋊C8—41no—
163C11⋊C8—81no—
164C22×SD16—111no—
165C2×C4×Q8—111no—
166C2×C4×D4C2×D1111yescharacteristic
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×#97—111no—
180Q8⋊C8—222no—
181D4⋊C8—22no—
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—81no—
198C4×C11#40711yescharacteristic
199C4×C11#40811yescharacteristic
200C4×C11#43511yescharacteristic
201C4×C11#43611yescharacteristic
202Dic11—42no—
203Dic11—42no—
204C22×Q8—111no—
205C22×D4C4×D1111yescharacteristic
206C23×C4—21no—
207C2×SD16—222no—
208C2×SD16—222no—
209C2×SD16—222no—
210C22×C8—111no—
211C22×C8—111no—
212C4×Q8—112no—
213C4×Q8—112no—
214C4×Q8—221no—
215C4×Q8—221no—
216C4×D4—21no—
217C4×D4—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C22⋊C4—21no—
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—224no—
239#97—221no—
240#97—221no—
241C4×C8—21no—
242C4×C8—221no—
243C4×C8—221no—
244C4×C8C22⋊D1112yes—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—82no—
248C2×C11#187011yescharacteristic
249C2×C11#190311yescharacteristic
250C2×C11#190511yescharacteristic
251C24—21no—
252C2×Q8—112no—
253C2×Q8—221no—
254C2×Q8—221no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—221no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4#431312yes—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—82no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273SD16—228no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—112no—
277C2×C8—221no—
278C2×C8—221no—
279C2×C8—221no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—112no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—222no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—222no—
293C42—222no—
294C42#433911yescharacteristic
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C11#909411yescharacteristic, complemented, Sylow
299C23—22no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23(C22⋊D11)⋊C411yescharacteristic
305Q8—222no—
306Q8—222no—
307Q8—441no—
308Q8—441no—
309D4—22no—
310D4—22no—
311D4—41no—
312D4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—81no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4C22⋊C4×D1111yescharacteristic
325C2×C4#6693611yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4C2×#431311yescharacteristic
328C2×C4#6695411yescharacteristic
329C2×C4M16×D1111yescharacteristic
330C2×C4#6696011yescharacteristic
331C2×C4C4×C22⋊D1111yescharacteristic
332C2×C4#6699011yescharacteristic
333C2×C4#6699111yescharacteristic
334C8—42no—
335C8—81no—
336C8—222no—
337C8—442no—
338C8—441no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—82no—
344C22—82no—
345C22—81no—
346C22—81no—
347C22#1062234211yescharacteristic
348C22#1062234311yescharacteristic
349C22#1062256911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—81no—
355C4—442no—
356C4—442no—
357C4#1062233911yescharacteristic
358C4#1062234011yescharacteristic
359C4#1062272411yescharacteristic
360C4#1062274111yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1306891011yescharacteristic
365C2#1306909311yescharacteristic
366C2#1306910711yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1478D11
hypocenterC11#9094
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #13077699C2semidirect
3. #13067012C2semidirect
5. #13066460C2semidirect
6. #13066446C2semidirect
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×#106226312
#130670122
#130669372
#130664602
#130664462
C11×#14782
#909411