Finite Group Databasebeta

← #14649454

Subgroups — #14649454

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
1C2×#10622539C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal, complemented
4#13066499C212yesmaximal, complemented
5C11×#2857C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C22⋊Q8C412yes—
8C22×C42×C11C2211yescharacteristic
9C11×#391C412yes—
10C11×#389—21no—
11C11×#389—21no—
12C11×#384C2211yescharacteristic
13C11×#380—21no—
14C11×#380—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C22⋊(C11⋊C8)—21no—
17#10622539—24no—
18C2×C4⋊(C11⋊C8)C2212yes—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×#66867—21no—
21#10622184—24no—
22#10622162—21no—
23C22×Q8×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8—22no—
29C11×C22⋊Q8—44no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11—22no—
38C2×C42×C11—22no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C22×C11⋊C8—22no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—22no—
47C22⋊(C11⋊C8)—24no—
48C22⋊(C11⋊C8)—42no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)—22no—
52C4⋊(C11⋊C8)D414yes—
53#66867—24no—
54#9136—111nomaximal, Sylow
55C24×C11C22⋊C411yescharacteristic
56C2×Q8×C11—24no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C11×C4⋊C4—44no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—44no—
87C42×C11—22no—
88C42×C11—21no—
89C42×C11—22no—
90C42×C11—21no—
91C42×C11C2×D412yes—
92C42×C11#4112yes—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99C2×#432—111no—
100#2857D1111yescharacteristic
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
112Q8×C11—84no—
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—21no—
124C2×C4×C11—44no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C4×D412yes—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12112yes—
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#13512yes—
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13712yes—
142C2×C4×C11#13712yes—
143C2×C4×C11#13711yescharacteristic
144C11⋊C8—44no—
145C11⋊C8—82no—
146C2×C4⋊Q8C2×D1111yescharacteristic
147C2×C22⋊Q8Dic1112yes—
148C22×C42C2×D1111yescharacteristic
149#432—224no—
150C2×C4⋊C8—112no—
151C2×C4⋊C8—112no—
152C2×C22⋊C8—221no—
153C2×C22⋊C8—221no—
154C2×#97—221no—
155#391Dic1112yes—
156#389—21no—
157#389—21no—
158#384C2×D1111yescharacteristic
159#380—21no—
160#380—21no—
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—82no—
182C4×C11—82no—
183C4×C11#45212yes—
184C4×C11#46812yes—
185C4×C11#47012yes—
186C4×C11#48512yes—
187C22×Q8C2×Dic1112yes—
188C23×C4C2×Dic1111yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C23×C4C22⋊D1111yescharacteristic
191C22×C8—222no—
192C22×C8—222no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C22⋊Q8—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic1112yes—
202C2×C22⋊C4—22no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42C2×Dic1111yescharacteristic
206C2×C42C22⋊D1111yescharacteristic
207C2×C42C22⋊D1111yescharacteristic
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—114no—
210C4⋊C8—222no—
211C4⋊C8—222no—
212C4⋊C8—222no—
213C22⋊C8—224no—
214C22⋊C8—442no—
215#97—224no—
216#95—22no—
217#95—22no—
218C2×C11—42no—
219C2×C11#155111yescharacteristic
220C2×C11#155411yescharacteristic
221C2×C11#155811yescharacteristic
222C2×C11#155911yescharacteristic
223C2×C11#187311yescharacteristic
224C2×C11#189411yescharacteristic
225C2×C11#190011yescharacteristic
226C24C22⋊Dic1111yescharacteristic
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4C22⋊Dic1111yescharacteristic
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4C22⋊Dic1111yescharacteristic
246C22×C4C22×Dic1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249C2×C8—224no—
250C2×C8—442no—
251C2×C8—442no—
252C2×C8—442no—
253C2×C8—442no—
254C2×C8—442no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C22⋊C4—44no—
264C42—22no—
265C42—21no—
266C42—21no—
267C42—22no—
268C42D4×D1112yes—
269C42#434112yes—
270C11#913611yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23#6689712yes—
278C23C2×C22⋊Dic1111yescharacteristic
279Q8—84no—
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—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4D4×Dic1112yes—
303C2×C4#6698811yescharacteristic
304C2×C4#6699011yescharacteristic
305C2×C4#6699212yes—
306C2×C4#6699512yes—
307C2×C4#6699512yes—
308C2×C4#6700211yescharacteristic
309C2×C4#6700312yes—
310C2×C4#6700411yescharacteristic
311C8—444no—
312C8—882no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22C2×#6689711yescharacteristic
321C22#1062283311yescharacteristic
322C22#1062283811yescharacteristic
323C22#1062283811yescharacteristic
324C22#1062284511yescharacteristic
325C22#1062284611yescharacteristic
326C22#1062285011yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—82no—
332C4—82no—
333C4#1062265812yes—
334C4#1062266012yes—
335C4#1062266212yes—
336C4#1062266512yes—
337C2—42no—
338C2#1306731111yescharacteristic
339C2#1306732611yescharacteristic
340C2#1306734211yescharacteristic
341C2#1306734611yescharacteristic
342C2#1306892911yescharacteristic
343C2#1306905011yescharacteristic
344C2#1306908011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2857D11
hypocenterC11#9136
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. C2×#10622184C2semidirect
4. #13066499C2semidirect
270. C11#9136semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130685962
C2×#106221842
#130664992
C11×#28572
#913611