Finite Group Databasebeta

← #14664933

Subgroups — #14664933

Order 2816.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#13073792C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066644C212yesmaximal, complemented
5C11×#1459C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9#10622833—21no—
10C2×#66897—21no—
11#10622823—21no—
12C2×C11⋊#95C411yescharacteristic
13#10622599C2211yescharacteristic
14#10622592C2211yescharacteristic
15#10622562C411yescharacteristic
16#10622560C411yescharacteristic
17#10622555—21no—
18#10622546—21no—
19#10622537—21no—
20C11×#324C2212yes—
21C11×#323—21no—
22#10622168C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C22×Dic22C2×C411yescharacteristic
28C22×C8×C11—41no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—41no—
40#66977—41no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×#4318—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—41no—
47#66897—42no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C4⋊(C11⋊C8)—41no—
56C4⋊(C11⋊C8)—41no—
57#11906—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11SD1612yes—
63C2×D4×C11Q1612yes—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—42no—
80C22×Dic11—42no—
81C22×Dic11—81no—
82C2×Dic22—41no—
83C2×Dic22—81no—
84C2×C8×C11—42no—
85C2×C8×C11—82no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C22⋊Dic11—81no—
94C4⋊Dic11—41no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99#4318—42no—
100#4318—42no—
101C2×C11⋊C8—42no—
102#2564—111no—
103#1800—111no—
104#1459D1111yescharacteristic
105#1354—112no—
106#1353—112no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10312yes—
116C23×C11#10312yes—
117C23×C11C2×C22⋊C411yescharacteristic
118D4×C11—42no—
119D4×C11—42no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11C2×Q1611yescharacteristic
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—84no—
150Dic22—82no—
151C8×C11—82no—
152C11⋊C8—82no—
153C2×C22⋊Q8—111no—
154C2×C4×D4C2×D1111yescharacteristic
155#423—221no—
156C2×#100—221no—
157C2×C22⋊C8—21no—
158#400—111no—
159#399—111no—
160#395—111no—
161#393—111no—
162#387—221no—
163#386—221no—
164#385—221no—
165#380—221no—
166C2×#95—111no—
167#343—112no—
168#324C2×D1112yes—
169#323—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—81no—
182C22×C11C2×#9911yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#42111yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195Dic11—81no—
196C22×Q8—111no—
197C22×D4D4411yescharacteristic
198C23×C4—221no—
199C23×C4C4×D1111yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C2×M16—222no—
202C22×C8—41no—
203C22⋊Q8—441no—
204C22⋊Q8—441no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4C4×D1111yescharacteristic
216C2×C22⋊C4C22⋊D1111yescharacteristic
217C2×C42D4411yescharacteristic
218C4⋊C8—441no—
219C4⋊C8—441no—
220#100—442no—
221C22⋊C8—22no—
222C22⋊C8—41no—
223#95—111no—
224#95—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—42no—
233C2×C11—42no—
234C2×C11#152011yescharacteristic
235C2×C11#212111yescharacteristic
236C2×C11#213211yescharacteristic
237C24(C2×D11)⋊C411yescharacteristic
238C24(C2×D11)⋊C411yescharacteristic
239C2×Q8—441no—
240C2×Q8—881no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4#431412yes—
244C2×D4Dic4412yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4—881no—
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263M16—442no—
264M16—442no—
265C2×C8—42no—
266C2×C8—82no—
267C2×C8—442no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—442no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—881no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—881no—
279C42—21no—
280C42—21no—
281C11#1190611yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#6688012yes—
291C23#6688012yes—
292C23C2×(C2×D11)⋊C411yescharacteristic
293Q8—882no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—222no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—884no—
322C2×C4#6687011yescharacteristic
323C2×C4#6687011yescharacteristic
324C2×C4C2×#431411yescharacteristic
325C2×C4C2×Dic4411yescharacteristic
326C8—82no—
327C8—882no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#6687011yescharacteristic
341C22C2×#6688011yescharacteristic
342C22#1062275211yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—442no—
351C4—881no—
352C4—881no—
353C4—881no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#1306718911yescharacteristic
359C2#1307026011yescharacteristic
360C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#1459D11
hypocenterC11#11906
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066644C2semidirect
281. C11#11906semidirect

Maximal subgroups

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

subgroupindex
#130737922
#130686082
#130666472
#130666442
C11×#14592
#1190611