Finite Group Databasebeta

← #14719826

Subgroups — #14719826

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623113C211yesmaximal, characteristic
2#13077701C211yesmaximal, characteristic, complemented
3#13066983C214yesmaximal, complemented
4#13066967C214yesmaximal, complemented
5#13066936C212yesmaximal, complemented
6#13066928C212yesmaximal, complemented
7C11×#2982C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000C411yescharacteristic
10C2×#66999C411yescharacteristic
11#10623113—24no—
12#10623113—24no—
13C2×#66949C412yes—
14C2×#66948C411yescharacteristic
15C2×#66947C412yes—
16C2×#66941C411yescharacteristic
17C2×#66929C2212yes—
18C2×#66928C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C8×Q8×C11—24no—
22C11×#431C2212yes—
23C11×#431C2214yes—
24#10622637—24no—
25#10622539C2214yes—
26#10622538C2212yes—
27#10622107C2214yes—
28#10622106C2214yes—
29#10622106C2218yes—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D44C2×C411yescharacteristic
32C22×D44C2×C412yes—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11C2×C412yes—
35C22×Dic22C2×C412yes—
36C4×Q8×C11D414yes—
37C4×Q8×C11D414yes—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C412yes—
40C2×C42×C11C2311yescharacteristic
41C2×C42×C11C2312yes—
42#67000—24no—
43#66999—24no—
44C2×(C2×D11)⋊C4C2×C411yescharacteristic
45C2×(C2×D11)⋊C4C2×C412yes—
46C2×(C2×D11)⋊C4C2×C412yes—
47C2×(C2×D11)⋊C4C2×C412yes—
48C2×(C2×D11)⋊C4C2×C412yes—
49C2×(C2×D11)⋊C4C2311yescharacteristic
50C2×(C2×D11)⋊C4C2312yes—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×Dic11⋊C4C2×C411yescharacteristic
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2311yescharacteristic
56C2×C4×Dic11C2×C411yescharacteristic
57#66949—28no—
58#66948—24no—
59#66947—28no—
60#66941—24no—
61#66929—24no—
62#66929—24no—
63#66928—24no—
64#66928—24no—
65C4×D44—22no—
66C4×D44—22no—
67#66925—22no—
68#66925—22no—
69C11×C4⋊C8—22no—
70C11×C4⋊C8—24no—
71C11×C22⋊C8C2314yes—
72C4×C8×C11—22no—
73C4×C8×C11—24no—
74C22⋊(C11⋊C8)C2314yes—
75C4⋊(C11⋊C8)—22no—
76C4⋊(C11⋊C8)—24no—
77#66867—24no—
78C4×C11⋊C8—22no—
79#17390—111nomaximal, Sylow
80C23×D11C22×C411yescharacteristic
81C23×D11C22×C412yes—
82C2×Q8×C11—24no—
83C2×Q8×C11C22⋊C414yes—
84C22×C4×C11C22×C412yes—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2411yescharacteristic
89C22×Dic11C22×C411yescharacteristic
90C22×Dic11C22×C411yescharacteristic
91C22×Dic11C22×C411yescharacteristic
92C22×Dic11C22×C412yes—
93C2×D44—22no—
94C2×D44—24no—
95C2×D44—24no—
96C2×D44—82no—
97C2×C4×D11—22no—
98C2×C4×D11—24no—
99C2×C4×D11—24no—
100C2×C4×D11—82no—
101C2×Dic22—24no—
102C2×Dic22—82no—
103C2×C8×C11—24no—
104C11×C4⋊C4C22⋊C414yes—
105C11×C4⋊C4C22⋊C418yes—
106C42×C11C2×D412yes—
107C42×C11C2×D414yes—
108C42×C11C2×D412yes—
109C42×C11C2×D414yes—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—24no—
112(C2×D11)⋊C4—24no—
113(C2×D11)⋊C4—24no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119C4⋊Dic11—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—24no—
122Dic11⋊C4—24no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125C4×Dic11—22no—
126C2×C11⋊C8—24no—
127C2×#542—111no—
128#2983—111no—
129#2982D1111yescharacteristic, complemented
130#1473—114no—
131#1469—114no—
132#1460—112no—
133#1458—112no—
134C23×C11C23×C411yescharacteristic
135C22×D11—21no—
136C22×D11—22no—
137C22×D11—22no—
138C22×D11—24no—
139C22×D11—42no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—42no—
143Q8×C11—28no—
144C2×C4×C11—24no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11C2×C22⋊C414yes—
149C2×C4×C11C2×C22⋊C414yes—
150C2×C4×C11C2×C22⋊C412yes—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11#13114yes—
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163D44—44no—
164D44—84no—
165C4×D11—44no—
166C4×D11—84no—
167Dic22—84no—
168C8×C11—44no—
169C11⋊C8—44no—
170#542—224no—
171#542—224no—
172C2×C4⋊Q8—111no—
173C2×#126—112no—
174C2×#124—111no—
175C2×#124—112no—
176C2×#123—112no—
177C2×C22⋊Q8—111no—
178C2×C22⋊Q8—112no—
179C2×#121—111no—
180C2×C4×Q8C2×D1111yescharacteristic
181C2×C4×D4—111no—
182C2×#117—111no—
183#446—224no—
184C8×Q8—24no—
185#432—114no—
186#431—112no—
187#431C2×D1112yes—
188#431C2×D1114yes—
189#324—114no—
190#323—114no—
191#323—118no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11C22×C22⋊C411yescharacteristic
195C22×C11C2×#13112yes—
196C2×D11—41no—
197C2×D11—42no—
198C2×D11—41no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—41no—
202C2×D11—82no—
203C2×D11—84no—
204C4×C11—24no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—24no—
208C4×C11—22no—
209C4×C11#40814yes—
210Dic11—41no—
211Dic11—41no—
212Dic11—41no—
213Dic11—42no—
214C22×Q8—112no—
215C22×Q8C4×D1111yescharacteristic
216C22×D4—111no—
217C22×D4—112no—
218C23×C4—111no—
219C23×C4—112no—
220C4⋊Q8—224no—
221#126—224no—
222#126—224no—
223#124—224no—
224#124—224no—
225#124—224no—
226#123—228no—
227C22⋊Q8—224no—
228C22⋊Q8—228no—
229#121—224no—
230C4×Q8D4414yes—
231C4×Q8C22⋊D1114yes—
232C4×D4—222no—
233C4×D4—222no—
234#117—222no—
235#117—222no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4C4×D1111yescharacteristic
242C2×C4⋊C4C4×D1112yes—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—112no—
245C2×C22⋊C4—112no—
246C2×C22⋊C4—112no—
247C2×C22⋊C4—112no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—112no—
250C2×C42—111no—
251C2×C42C22×D1111yescharacteristic
252C2×C42C22×D1112yes—
253C4⋊C8—22no—
254C4⋊C8—24no—
255C4⋊C8—222no—
256C4⋊C8—224no—
257C22⋊C8—114no—
258C22⋊C8C22×D1114yes—
259#97—224no—
260C4×C8—22no—
261C4×C8—24no—
262C4×C8—222no—
263C2×C11—22no—
264C2×C11C2×#40811yescharacteristic
265C2×C11#288411yescharacteristic
266C2×C11#288811yescharacteristic
267D11—81no—
268D11—82no—
269C24—111no—
270C24—112no—
271C2×Q8—24no—
272C2×Q8—224no—
273C2×Q8—882no—
274C2×Q8(C2×D11)⋊C414yes—
275C2×D4—224no—
276C2×D4—222no—
277C2×D4—224no—
278C2×D4—882no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—112no—
283C22×C4—224no—
284C22×C4—222no—
285C22×C4—224no—
286C22×C4—882no—
287C22×C4C2×C4×D1112yes—
288C22×C4C2×C4×D1111yescharacteristic
289C22×C4C2×C4×D1112yes—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C23×D1111yescharacteristic
292C2×C8—24no—
293C2×C8—224no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—224no—
297C4⋊C4—224no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4(C2×D11)⋊C414yes—
301C4⋊C4(C2×D11)⋊C418yes—
302C22⋊C4—222no—
303C22⋊C4—224no—
304C22⋊C4—224no—
305C22⋊C4—224no—
306C22⋊C4—224no—
307C22⋊C4—221no—
308C22⋊C4—222no—
309C22⋊C4—221no—
310C22⋊C4—222no—
311C42—222no—
312C42C2×D4412yes—
313C42C2×D4414yes—
314C42C2×C22⋊D1112yes—
315C42C2×C22⋊D1114yes—
316C11#1739011yescharacteristic, complemented, Sylow
317C23—221no—
318C23—222no—
319C23—222no—
320C23—224no—
321C23—442no—
322C23—441no—
323C23—441no—
324C23—442no—
325C23C22×C4×D1111yescharacteristic
326Q8—28no—
327Q8—884no—
328D4—444no—
329D4—884no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—222no—
339C2×C4—444no—
340C2×C4—442no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—884no—
344C2×C4#6695414yes—
345C2×C4C2×(C2×D11)⋊C414yes—
346C2×C4C2×(C2×D11)⋊C412yes—
347C2×C4C2×(C2×D11)⋊C414yes—
348C2×C4C2×(C2×D11)⋊C412yes—
349C2×C4C22×D4411yescharacteristic
350C2×C4C22×C22⋊D1111yescharacteristic
351C8—44no—
352C8—444no—
353C22—21no—
354C22—21no—
355C22—441no—
356C22—442no—
357C22—441no—
358C22—442no—
359C22—442no—
360C22—441no—
361C22—882no—
362C22—884no—
363C22C2×#6695412yes—
364C22C22×(C2×D11)⋊C411yescharacteristic
365C4—24no—
366C4—21no—
367C4—21no—
368C4—22no—
369C4—24no—
370C4—441no—
371C4—441no—
372C4—442no—
373C4—441no—
374C4#1062272314yes—
375C2—22no—
376C2—881no—
377C2—882no—
378C2C2×#1062272311yescharacteristic
379C2#1307707911yescharacteristic
380C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2982C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#2982D11
hypocenterC11#17390
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13077701C2semidirect
3. #13066983C2semidirect
4. #13066967C2semidirect
5. #13066936C2semidirect
6. #13066928C2semidirect
7. C11×#2982C2semidirect
129. #2982D11semidirect
316. C11#17390semidirect

Maximal subgroups

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

subgroupindex
C2×#106231132
#130777012
#130669832
#130669672
#130669362
#130669282
C11×#29822
#1739011