Finite Group Databasebeta

← #14659608

Subgroups — #14659608

Order 2816.

1338 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
1C2×#10622825C212yesmaximal
2C2×#10622164C214yesmaximal
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
4C24×C4×C11C2211yescharacteristic
5C22×C11×C22⋊C4C2212yes—
6C22×C42×C11C412yescomplemented
7C22×C22⋊Dic11C2214yes—
8C22×C4⋊Dic11—22no—
9C4×C11×C22⋊C4—22no—
10C4×C11×C22⋊C4—22no—
11C2×C11×#95C412yescomplemented
12#10622825—24no—
13#10622825C418yescomplemented
14C2×C11⋊#95—22no—
15#10622164—28no—
16C25×C11C2311yescharacteristic
17C23×C4×C11—44no—
18C23×C4×C11C2×C414yes—
19C23×C4×C11C2×C411yescharacteristic
20C23×C4×C11C2×C414yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D412yes—
23C23×C4×C11D412yes—
24C23×C4×C11D412yes—
25C23×C4×C11Q812yes—
26C23×Dic11—24no—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—24no—
29C2×C11×C22⋊C4D414yes—
30C2×C11×C22⋊C4Q814yes—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11—44no—
34C2×C22⋊Dic11—28no—
35C2×C22⋊Dic11—28no—
36C2×C22⋊Dic11—24no—
37C2×C22⋊Dic11C2×C418yes—
38C2×C4⋊Dic11—28no—
39C2×C4⋊Dic11—48no—
40C11×#95—24no—
41C11⋊#95—28no—
42#10846—111nomaximal, Sylow
43C24×C11—42no—
44C24×C11—42no—
45C24×C11C22×C411yescharacteristic
46C24×C11C22×C412yes—
47C24×C11C2×D412yes—
48C24×C11C2×D411yescharacteristic
49C24×C11C2×D412yes—
50C24×C11C2×Q811yescharacteristic
51C24×C11C2×Q812yes—
52C24×C11#4114yes—
53C22×C4×C11—28no—
54C22×C4×C11—24no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—48no—
58C22×C4×C11—44no—
59C22×C4×C11—44no—
60C22×C4×C11—42no—
61C22×C4×C11—44no—
62C22×C4×C11—44no—
63C22×C4×C11—44no—
64C22×C4×C11C4212yes—
65C22×C4×C11C4212yes—
66C22×C4×C11C22⋊C414yes—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C414yes—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C4⋊C414yes—
72C22×C4×C11C4⋊C412yes—
73C22×C4×C11C4⋊C414yes—
74C22×C4×C11C4⋊C412yes—
75C22×C4×C11C4⋊C418yescomplemented
76C22×Dic11—28no—
77C22×Dic11—48no—
78C22×Dic11—48no—
79C22×Dic11—48no—
80C11×C22⋊C4—28no—
81C11×C22⋊C4—28no—
82C42×C11—44no—
83C42×C11—44no—
84C22⋊Dic11—216no—
85C22⋊Dic11—44no—
86C22⋊Dic11—44no—
87C4⋊Dic11—416no—
88C2×#380—112no—
89C2×C4×C22⋊C4D1111yescharacteristic
90C2×#342—114no—
91C23×C11—24no—
92C23×C11—22no—
93C23×C11—24no—
94C23×C11—22no—
95C23×C11—42no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—42no—
99C23×C11—44no—
100C23×C11—41no—
101C23×C11—44no—
102C23×C11—41no—
103C23×C11—48no—
104C23×C11C2×C4211yescharacteristic
105C23×C11C2×C22⋊C412yes—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C2×C4⋊C412yes—
108C23×C11C2×C4⋊C411yescharacteristic
109C23×C11C2×C4⋊C412yes—
110C23×C11#11712yes—
111C23×C11C4×D414yes—
112C23×C11C4×Q814yes—
113C23×C11#12114yes—
114C23×C11C22⋊Q814yes—
115C23×C11#12412yes—
116C23×C11#12512yes—
117C23×C11#12711yescharacteristic
118C23×C11C4⋊Q812yes—
119C23×C11C4⋊Q811yescharacteristic
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—28no—
123C2×C4×C11—24no—
124C2×C4×C11—28no—
125C2×C4×C11—24no—
126C2×C4×C11—28no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—48no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—48no—
135C2×C4×C11#9512yes—
136C2×C4×C11#9514yes—
137C2×C4×C11#9512yes—
138C2×C4×C11#9914yes—
139C2×Dic11—48no—
140C2×Dic11—48no—
141C2×Dic11—48no—
142C2×Dic11—816no—
143C24×C4C2×D1111yescharacteristic
144C22×C4⋊C4—222no—
145C22×C22⋊C4—114no—
146C22×C22⋊C4C2×D1112yes—
147C22×C42Dic1112yescomplemented
148#380—118no—
149#380—224no—
150C4×C22⋊C4—22no—
151C4×C22⋊C4—22no—
152C2×#95—222no—
153C2×#95Dic1112yescomplemented
154#342—228no—
155C22×C11—24no—
156C22×C11—24no—
157C22×C11—28no—
158C22×C11—28no—
159C22×C11—21no—
160C22×C11—22no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—21no—
167C22×C11—44no—
168C22×C11—44no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—41no—
172C22×C11—42no—
173C22×C11—41no—
174C22×C11C2×#9511yescharacteristic
175C22×C11C4×C4⋊C412yes—
176C22×C11#38012yes—
177C22×C11#38211yescharacteristic
178C22×C11#38411yescharacteristic
179C22×C11#38914yes—
180C22×C11#39012yes—
181C22×C11#39112yes—
182C22×C11C2×#9912yes—
183C22×C11#41012yes—
184C4×C11—22no—
185C4×C11—24no—
186C4×C11—48no—
187C4×C11#34214yescomplemented
188Dic11—88no—
189C25C22×D1111yescharacteristic
190C23×C4—44no—
191C23×C4—224no—
192C23×C4Dic2212yes—
193C23×C4C4×D1114yes—
194C23×C4D4412yes—
195C23×C4C2×Dic1111yescharacteristic
196C23×C4C2×Dic1114yes—
197C23×C4C2×Dic1111yescharacteristic
198C23×C4C22⋊D1112yes—
199C23×C4C22⋊D1112yes—
200C2×C4⋊C4—228no—
201C2×C4⋊C4—448no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—118no—
205C2×C22⋊C4—228no—
206C2×C22⋊C4—228no—
207C2×C22⋊C4—224no—
208C2×C22⋊C4Dic2214yes—
209C2×C22⋊C4D4414yes—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—44no—
213#95—24no—
214#95—228no—
215C2×C11—22no—
216C2×C11—22no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—24no—
220C2×C11—22no—
221C2×C11C4⋊#9511yescharacteristic
222C2×C11C2×#34211yescharacteristic
223C2×C11#174011yescharacteristic
224C2×C11#179914yes—
225C24—42no—
226C24—42no—
227C24C2×Dic2212yes—
228C24C2×Dic2211yescharacteristic
229C24C2×C4×D1112yes—
230C24C2×D4412yes—
231C24C2×D4411yescharacteristic
232C24#433914yes—
233C24C22×Dic1111yescharacteristic
234C24C2×C22⋊D1112yes—
235C22×C4—24no—
236C22×C4—28no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—44no—
240C22×C4—48no—
241C22×C4—44no—
242C22×C4—42no—
243C22×C4—44no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—228no—
247C22×C4—448no—
248C22×C4—448no—
249C22×C4—448no—
250C22×C4C4×Dic1112yes—
251C22×C4C4×Dic1112yes—
252C22×C4Dic11⋊C414yes—
253C22×C4Dic11⋊C414yes—
254C22×C4C4⋊Dic1112yes—
255C22×C4C4⋊Dic1112yes—
256C22×C4C4⋊Dic1118yescomplemented
257C22×C4(C2×D11)⋊C414yes—
258C22×C4(C2×D11)⋊C414yes—
259C22×C4C22⋊Dic1112yes—
260C22×C4C22⋊Dic1111yescharacteristic
261C22×C4C22⋊Dic1111yescharacteristic
262C4⋊C4—4416no—
263C22⋊C4—28no—
264C22⋊C4—28no—
265C22⋊C4—2216no—
266C22⋊C4—444no—
267C22⋊C4—444no—
268C42—44no—
269C42—44no—
270C11#1084611yescharacteristic, complemented, Sylow
271C23—22no—
272C23—24no—
273C23—22no—
274C23—24no—
275C23—41no—
276C23—42no—
277C23—41no—
278C23—44no—
279C23—41no—
280C23—42no—
281C23—44no—
282C23—41no—
283C23—48no—
284C23C4×Dic2214yes—
285C23#6692212yes—
286C23#6692211yescharacteristic
287C23#6692312yes—
288C23C4×D4414yes—
289C23#6692711yescharacteristic
290C23#6692812yes—
291C23C2×C4×Dic1111yescharacteristic
292C23C2×Dic11⋊C412yes—
293C23#6697714yes—
294C23C2×C4⋊Dic1112yes—
295C23C2×C4⋊Dic1111yescharacteristic
296C23#6697912yes—
297C23C2×(C2×D11)⋊C412yes—
298C23#6698314yes—
299C23C2×C22⋊Dic1111yescharacteristic
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—48no—
315C2×C4—448no—
316C2×C4—448no—
317C2×C4—448no—
318C2×C4—8816no—
319C2×C4C11⋊#9512yes—
320C2×C4C11⋊#9514yes—
321C2×C4C11⋊#9512yes—
322C2×C4#6689814yes—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—21no—
327C22—24no—
328C22—24no—
329C22—28no—
330C22—28no—
331C22—22no—
332C22—21no—
333C22—22no—
334C22—21no—
335C22—44no—
336C22—42no—
337C22—41no—
338C22—42no—
339C22—44no—
340C22—41no—
341C22—42no—
342C22#1062254114yes—
343C22#1062254212yes—
344C22C4×C4⋊Dic1112yes—
345C22#1062254811yescharacteristic
346C22#1062254911yescharacteristic
347C22#1062255212yes—
348C22C2×C11⋊#9511yescharacteristic
349C22#1062282512yes—
350C22C2×#6689812yes—
351C22#1062285312yes—
352C4—22no—
353C4—24no—
354C4—48no—
355C4—888no—
356C4#1062216414yescomplemented
357C2—22no—
358C2—24no—
359C2—22no—
360C2—22no—
361C2—21no—
362C2—21no—
363C2#1306684611yescharacteristic
364C2C2×#1062216411yescharacteristic
365C2#1306834911yescharacteristic
366C2#1306860414yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C2×C42
FrattiniC25C22×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radical, cosocleC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#10846
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×C42×C11C4semidirect
11. C2×C11×#95C4semidirect
13. #10622825C4semidirect
75. C22×C4×C11C4⋊C4semidirect
147. C22×C42Dic11semidirect
153. C2×#95Dic11semidirect
187. C4×C11#342semidirect
256. C22×C4C4⋊Dic11semidirect
270. C11#10846semidirect
356. C4#10622164semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
C2×#106221642
C2×C4×C11×C22⋊C42
#1084611