Finite Group Databasebeta

← #14664565

Subgroups — #14664565

Order 2816.

414 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074533C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066638C212yesmaximal, complemented
4#13066617C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic, complemented
8C11×#432—21no—
9#10622835—21no—
10C2×#66898—21no—
11#10622825—21no—
12#10622824C411yescharacteristic, complemented
13#10622823—21no—
14#10622596C411yescharacteristic, complemented
15#10622592C411yescharacteristic, complemented
16#10622566C2211yescharacteristic
17#10622565—21no—
18#10622560C2211yescharacteristic
19#10622546—21no—
20C11×#323—21no—
21C11×#323C2212yes—
22#10622164C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C4×D4×C11—41no—
28C4×D4×C11—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—41no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—41no—
41#66977—41no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C11×C4⋊C8—41no—
46C11×C22⋊C8—22no—
47C11×#97—41no—
48#66898—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—41no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11826—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
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×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—42no—
80C2×Dic22—41no—
81C2×Dic22—81no—
82C2×C8×C11—42no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C22⋊Dic11—41no—
91C22⋊Dic11—42no—
92C22⋊Dic11—41no—
93C22⋊Dic11—81no—
94C22⋊Dic11—81no—
95C4⋊Dic11—41no—
96C4⋊Dic11—82no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—81no—
101#2638—111no—
102#1799—111no—
103#1466D1111yescharacteristic
104#1351—112no—
105#1344—112no—
106C23×C11—21no—
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×C11C2×C22⋊C411yescharacteristic
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C23×C11#13711yescharacteristic
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—21no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#9911yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—41no—
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—82no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151Dic22—82no—
152C8×C11—82no—
153C2×C22⋊Q8—111no—
154C2×C4×D4C2×D1111yescharacteristic
155#432—21no—
156C2×#99—221no—
157#398—111no—
158#397—111no—
159#397—221no—
160#395—111no—
161#394—221no—
162#393—111no—
163#387—221no—
164#385—221no—
165#381—111no—
166#380—221no—
167#342—112no—
168#323—21no—
169#323C2×D1112yes—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11C2×#9911yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#42111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193Dic11—81no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—162no—
198C22×Q8—111no—
199C22×D4D4411yescharacteristic
200C23×C4C4×D1111yescharacteristic
201C23×C4D4411yescharacteristic
202C22⋊Q8—441no—
203C22⋊Q8—441no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—441no—
211C2×C4⋊C4C4×D1111yescharacteristic
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—222no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4C22⋊D1111yescharacteristic
218C2×C22⋊C4C22×D1111yescharacteristic
219C2×C42C22⋊D1111yescharacteristic
220C4⋊C8—41no—
221#99—442no—
222C22⋊C8—22no—
223#97—41no—
224#95—111no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—441no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—41no—
235C2×C11—41no—
236C2×C11—81no—
237C2×C11#151311yescharacteristic
238C2×C11#212111yescharacteristic
239C2×C11#212911yescharacteristic
240C24(C2×D11)⋊C411yescharacteristic
241C24C2×D4411yescharacteristic
242C2×Q8—441no—
243C2×Q8—881no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—442no—
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4(C2×D11)⋊C411yescharacteristic
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4C2×C4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C2×C8—42no—
265C4⋊C4—41no—
266C4⋊C4—441no—
267C4⋊C4—442no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—881no—
271C4⋊C4—882no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—442no—
275C22⋊C4—441no—
276C22⋊C4—441no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—881no—
280C22⋊C4—881no—
281C42—21no—
282C42—21no—
283C11#1182611yescharacteristic, complemented, Sylow
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23#6696111yescharacteristic
294C23#6696211yescharacteristic
295C23C2×(C2×D11)⋊C411yescharacteristic
296Q8—882no—
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
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—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—882no—
326C2×C4—882no—
327C2×C4—882no—
328C2×C4#6687011yescharacteristic
329C2×C4#6687011yescharacteristic
330C8—82no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×#6687011yescharacteristic
346C22#1062274611yescharacteristic
347C22#1062275211yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—881no—
355C4—881no—
356C4—881no—
357C4—881no—
358C4—1762no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#1306716011yescharacteristic
365C2#1307026311yescharacteristic
366C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11826
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13066638C2semidirect
4. #13066617C2semidirect
7. C2×#66977C4semidirect
12. #10622824C4semidirect
14. #10622596C4semidirect
15. #10622592C4semidirect
283. C11#11826semidirect

Maximal subgroups

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

subgroupindex
#130745332
#130686042
#130666382
#130666172
C11×#14662
#1182611