Finite Group Databasebeta

← #14649404

Subgroups — #14649404

Order 2816.

530 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×#10622539C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3C2×#10622181C212yesmaximal, complemented
4#13066497C212yesmaximal, complemented
5C11×#2851C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C11×#389C411yescharacteristic
9C11×#389C411yescharacteristic
10C11×#387—21no—
11C11×#387—21no—
12C11×#385—21no—
13C11×#385—21no—
14C11×#382C2211yescharacteristic
15C11×#380C411yescharacteristic
16C11×#380C411yescharacteristic
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622539—24no—
20C2×C4⋊(C11⋊C8)—21no—
21C2×#66867C2212yes—
22C2×#66867C2212yes—
23#10622181—24no—
24#10622162—21no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#125—22no—
29C11×#125—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—22no—
41C2×C42×C11—22no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C22×C11⋊C8—22no—
47C22×C11⋊C8—22no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C22⋊(C11⋊C8)—24no—
55C22⋊(C11⋊C8)—24no—
56C4⋊(C11⋊C8)—24no—
57#66867—22no—
58#66867—22no—
59#66867—22no—
60#66867D414yes—
61#9126—111nomaximal, Sylow
62C24×C11C22⋊C411yescharacteristic
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C42×C11—22no—
95C42×C11—21no—
96C42×C11—22no—
97C42×C11—21no—
98C42×C11C2×D412yes—
99C42×C11#4112yes—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—24no—
102C2×C11⋊C8—42no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—42no—
106C2×#432—111no—
107#2851D1111yescharacteristic
108#1749—111no—
109C2×#330—112no—
110#1295—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11#10112yes—
118C23×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11#10412yes—
150C2×C4×C11C4×D412yes—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12112yes—
153C2×C4×C11#12311yescharacteristic
154C11⋊C8—44no—
155C11⋊C8—44no—
156C2×#125C2×D1111yescharacteristic
157C22×C42C2×D1111yescharacteristic
158#432—224no—
159C2×C4⋊C8—221no—
160C2×C22⋊C8—221no—
161C2×C22⋊C8—221no—
162C2×#97—112no—
163C2×#97—112no—
164#389Dic1111yescharacteristic
165#389Dic1111yescharacteristic
166#387—21no—
167#387—21no—
168#385—21no—
169#385—21no—
170#382C2×D1111yescharacteristic
171#380Dic1111yescharacteristic
172#380Dic1111yescharacteristic
173#336—221no—
174#330—224no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11#38611yescharacteristic
183C22×C11C2×#10111yescharacteristic
184C22×C11#41311yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11#42111yescharacteristic
187C22×C11#42111yescharacteristic
188C22×C11#42111yescharacteristic
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C23×C4C2×Dic1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C22×C8—222no—
204C22×C8—222no—
205#125—22no—
206#125—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×Dic1111yescharacteristic
212C2×C4⋊C4C2×Dic1111yescharacteristic
213C2×C4⋊C4C2×Dic1111yescharacteristic
214C2×C4⋊C4C2×Dic1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C2×Dic1111yescharacteristic
220C2×C42C22⋊D1111yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—224no—
224C22⋊C8—224no—
225C22⋊C8—224no—
226#97—114no—
227#97—222no—
228#97—222no—
229#97—222no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236C2×C11—42no—
237C2×C11#152911yescharacteristic
238C2×C11#153111yescharacteristic
239C2×C11#153411yescharacteristic
240C2×C11#153511yescharacteristic
241C2×C11#187111yescharacteristic
242C2×C11#189711yescharacteristic
243C2×C11#190111yescharacteristic
244C24C22⋊Dic1111yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C22⋊Dic1111yescharacteristic
260C22×C4C22⋊Dic1111yescharacteristic
261C22×C4C22⋊Dic1111yescharacteristic
262C22×C4C22×Dic1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C2×C8—224no—
266C2×C8—224no—
267C2×C8—442no—
268C2×C8—442no—
269C2×C8—442no—
270C2×C8—442no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—22no—
283C42—21no—
284C42—21no—
285C42—22no—
286C42D4×D1112yes—
287C42#434112yes—
288C11#912611yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#6690012yes—
296C23C2×C22⋊Dic1111yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4#6690112yes—
328C2×C4D4×Dic1112yes—
329C2×C4#6698811yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699212yes—
332C8—444no—
333C8—444no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1062283311yescharacteristic
342C22C2×#6690011yescharacteristic
343C22C2×#6690111yescharacteristic
344C22#1062284911yescharacteristic
345C22#1062284911yescharacteristic
346C22#1062284911yescharacteristic
347C22#1062285011yescharacteristic
348C4—21no—
349C4—21no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C2—42no—
360C2#1306722311yescharacteristic
361C2#1306723111yescharacteristic
362C2#1306724311yescharacteristic
363C2#1306724711yescharacteristic
364C2#1306891911yescharacteristic
365C2#1306906511yescharacteristic
366C2#1306908511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2851C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2851D11
hypocenterC11#9126
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#10622181C2semidirect
4. #13066497C2semidirect
288. C11#9126semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130683782
C2×#106221812
#130664972
C11×#28512
#912611