Finite Group Databasebeta

← #14649453

Subgroups — #14649453

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622119C212yesmaximal, complemented
4#13066500C212yesmaximal, complemented
5C2×C11×#432C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C412yes—
8C2×#66922C2211yescharacteristic
9C11×#432—24no—
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C22⋊C8—21no—
12C2×C11×#97—21no—
13#10622825—21no—
14#10622825—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622548C2211yescharacteristic
17#10622542C412yes—
18#10622541—21no—
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622119—24no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C412yes—
27C22×C8×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C412yes—
40#66977—44no—
41C2×Dic11⋊C4—22no—
42C22×C11⋊C8—22no—
43#66922—22no—
44#66922—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8D414yes—
47C11×C22⋊C8—24no—
48C11×#97—24no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C22⋊(C11⋊C8)—42no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#9136—111nomaximal, Sylow
55C24×C11C22⋊C411yescharacteristic
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—22no—
75C2×Dic22—24no—
76C2×Dic22—42no—
77C2×Dic22—42no—
78C2×C8×C11—24no—
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C42×C11—22no—
82C42×C11—21no—
83C42×C11—22no—
84C42×C11—21no—
85C42×C11C2×D412yes—
86C42×C11#4112yes—
87C22⋊Dic11—44no—
88C4⋊Dic11—42no—
89C4⋊Dic11—41no—
90C4⋊Dic11—42no—
91C4⋊Dic11—41no—
92C4⋊Dic11—42no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—44no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99C2×#432D1111yescharacteristic
100#2857—111no—
101#1797—111no—
102C2×#333—112no—
103#1296—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11#10012yes—
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—44no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C4×D412yes—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12112yes—
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#13512yes—
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11#13712yes—
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13712yes—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143Dic22—84no—
144C8×C11—44no—
145C11⋊C8—82no—
146C2×C4⋊Q8—111no—
147C2×C22⋊Q8—112no—
148C22×C42C2×D1111yescharacteristic
149#432—24no—
150C2×C4⋊C8—112no—
151C2×C4⋊C8C2×D1112yes—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—221no—
154C2×#97—21no—
155#391—112no—
156#389—221no—
157#389—221no—
158#384—111no—
159#380—221no—
160#380—221no—
161#336—221no—
162#333—224no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11#38611yescharacteristic
171C22×C11C2×#10011yescharacteristic
172C22×C11#41311yescharacteristic
173C22×C11#41611yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11#41911yescharacteristic
176C22×C11#41911yescharacteristic
177C4×C11—22no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11#45212yes—
182C4×C11#46812yes—
183C4×C11#47012yes—
184C4×C11#48512yes—
185Dic11—82no—
186Dic11—82no—
187C22×Q8—112no—
188C23×C4C4×D1111yescharacteristic
189C23×C4D4411yescharacteristic
190C23×C4C22⋊D1111yescharacteristic
191C22×C8—22no—
192C22×C8—222no—
193C4⋊Q8—222no—
194C4⋊Q8—222no—
195C22⋊Q8—444no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C22⋊C4—222no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42C4×D1111yescharacteristic
206C2×C42D4411yescharacteristic
207C2×C42C22⋊D1111yescharacteristic
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—22no—
210C4⋊C8—222no—
211C4⋊C8—222no—
212C4⋊C8C22⋊D1114yes—
213C22⋊C8—24no—
214C22⋊C8—442no—
215#97—24no—
216#95—222no—
217#95—222no—
218C2×C11—42no—
219C2×C11#155111yescharacteristic
220C2×C11#155411yescharacteristic
221C2×C11#155811yescharacteristic
222C2×C11#155911yescharacteristic
223C2×C11#187311yescharacteristic
224C2×C11#189411yescharacteristic
225C2×C11#190011yescharacteristic
226C24(C2×D11)⋊C411yescharacteristic
227C2×Q8—224no—
228C2×Q8—442no—
229C2×Q8—442no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4C2×D4411yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249C2×C8—24no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—442no—
253C2×C8—442no—
254C2×C8—442no—
255C4⋊C4—442no—
256C4⋊C4—444no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C22⋊C4—444no—
264C42—22no—
265C42—21no—
266C42—22no—
267C42—21no—
268C42#433912yes—
269C42C2×C22⋊D1112yes—
270C11#913611yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23#6688712yes—
278C23C2×(C2×D11)⋊C411yescharacteristic
279Q8—884no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4#6696111yescharacteristic
303C2×C4#6696212yes—
304C2×C4#6696211yescharacteristic
305C2×C4C4×C22⋊D1112yes—
306C2×C4#6698211yescharacteristic
307C2×C4#6698312yes—
308C2×C4#6700312yes—
309C2×C4#6700412yes—
310C2×C4#6700611yescharacteristic
311C8—44no—
312C8—882no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1062261511yescharacteristic
321C22#1062261711yescharacteristic
322C22#1062273311yescharacteristic
323C22C2×#6688711yescharacteristic
324C22#1062274511yescharacteristic
325C22#1062274611yescharacteristic
326C22#1062282611yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—882no—
332C4—882no—
333C4#1062260912yes—
334C4#1062274712yes—
335C4#1062275012yes—
336C4#1062285212yes—
337C2—42no—
338C2#1306731211yescharacteristic
339C2#1306732711yescharacteristic
340C2#1306734111yescharacteristic
341C2#1306734711yescharacteristic
342C2#1306892811yescharacteristic
343C2#1306904911yescharacteristic
344C2#1306907911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#432C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#432D11
hypocenterC11#9136
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. C2×#10622119C2semidirect
4. #13066500C2semidirect
270. C11#9136semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
C2×#106221192
#130665002
C2×C11×#4322
#913611