Finite Group Databasebeta

← #14664167

Subgroups — #14664167

Order 2816.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66897C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic
3#13066646C212yesmaximal, complemented
4#13066622C212yesmaximal, complemented
5C11×#2638C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#398C2211yescharacteristic
9C11×#397—21no—
10C11×#397C411yescharacteristic
11C11×#395C2211yescharacteristic
12C11×#394—21no—
13C11×#393C411yescharacteristic
14C11×#387—21no—
15C11×#385—21no—
16C11×#381C411yescharacteristic
17C2×#66897—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C4×#4318—21no—
20#10622168C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×Q8×C11C2×C411yescharacteristic
24C22×D4×C11D411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C11×C22⋊Q8—41no—
28C11×C22⋊Q8—41no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×#4318—22no—
44C22×C11⋊C8—41no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95C2×C411yescharacteristic
51C11×#95C2×C411yescharacteristic
52#66897—24no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—41no—
55#66867—41no—
56C4×C11⋊C8—41no—
57#11739—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C2×Q8×C11—41no—
61C2×Q8×C11—81no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—81no—
74C22×C4×C11—81no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—81no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—81no—
91C11×C22⋊C4—81no—
92C42×C11—21no—
93C42×C11—21no—
94#4318—24no—
95#4318—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—82no—
99#2638D1111yescharacteristic
100C4×#100—111no—
101#1459—111no—
102#1354—112no—
103#1346—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11#10412yes—
114C23×C11C2×C22⋊C411yescharacteristic
115Q8×C11—82no—
116D4×C11—44no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#9911yescharacteristic
144C2×C4×C11#13512yes—
145C11⋊C8—44no—
146C11⋊C8—82no—
147C2×C22⋊Q8Dic1111yescharacteristic
148C2×C4×D4C2×D1111yescharacteristic
149C2×#100—221no—
150C2×C22⋊C8—221no—
151C4×M16—221no—
152#398C2×D1111yescharacteristic
153#397—21no—
154#397Dic1111yescharacteristic
155#395C2×D1111yescharacteristic
156#394—21no—
157#393Dic1111yescharacteristic
158#387—21no—
159#385—21no—
160#381Dic1111yescharacteristic
161#343—112no—
162#324—112no—
163#323—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—42no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11C2×#9911yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—81no—
189C22×Q8C2×Dic1111yescharacteristic
190C22×D4C22⋊D1111yescharacteristic
191C23×C4C2×Dic1111yescharacteristic
192C23×C4C22⋊D1111yescharacteristic
193C2×M16—222no—
194C22×C8—441no—
195C22⋊Q8—41no—
196C22⋊Q8—41no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic1111yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4C2×Dic1111yescharacteristic
209C2×C22⋊C4C22⋊D1111yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211#100—224no—
212C22⋊C8—222no—
213C22⋊C8—441no—
214#97—441no—
215C4×C8—441no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×Dic1111yescharacteristic
222#95C2×Dic1111yescharacteristic
223C2×C11—21no—
224C2×C11—21no—
225C2×C11—42no—
226C2×C11—81no—
227C2×C11#150111yescharacteristic
228C2×C11#212111yescharacteristic
229C2×C11#213511yescharacteristic
230C24C22⋊Dic1111yescharacteristic
231C24C22⋊Dic1111yescharacteristic
232C2×Q8—41no—
233C2×Q8—81no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4C22⋊Dic1111yescharacteristic
248C22×C4C22⋊Dic1111yescharacteristic
249C22×C4C22×Dic1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252M16—224no—
253M16—442no—
254C2×C8—442no—
255C2×C8—442no—
256C2×C8—882no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C42—21no—
270C42—21no—
271C11#1173911yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#6690112yes—
282C23C2×C22⋊Dic1111yescharacteristic
283Q8—82no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#6689811yescharacteristic
311C2×C4#6689811yescharacteristic
312C2×C4#6700312yes—
313C8—444no—
314C8—882no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#6689811yescharacteristic
328C22#1062284611yescharacteristic
329C22C2×#6690111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1306710711yescharacteristic
345C2#1307026211yescharacteristic
346C2#1307031111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2638C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#2638D11
hypocenterC11#11739
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #13066646C2semidirect
4. #13066622C2semidirect
271. C11#11739semidirect

Maximal subgroups

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

subgroupindex
C4×#668972
#130669342
#130666462
#130666222
C11×#26382
#1173911