Finite Group Databasebeta

← #14664125

Subgroups — #14664125

Order 2816.

436 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 83 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#13066937C211yesmaximal, characteristic
3#13066636C212yesmaximal, complemented
4#13066615C212yesmaximal, complemented
5C4×C11×#99C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C4×C11×C22⋊C4—21no—
10#10622835—21no—
11#10622824C411yescharacteristic, complemented
12#10622823—21no—
13#10622596C411yescharacteristic, complemented
14#10622592C411yescharacteristic, complemented
15#10622566C2211yescharacteristic
16#10622565—21no—
17#10622560C2211yescharacteristic
18#10622546—21no—
19#10622538—21no—
20C11×#342C2212yes—
21#10622163—21no—
22#10622163C2212yes—
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⋊C4—22no—
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11—41no—
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—41no—
41#66977—41no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C11×#99—24no—
46C11×#95—41no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11731—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—42no—
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—
79C2×Dic22—41no—
80C2×Dic22—81no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—24no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—42no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—82no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—81no—
92C22⋊Dic11—81no—
93C4⋊Dic11—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—42no—
97Dic11⋊C4—81no—
98C2×C11⋊C8—42no—
99#2638—111no—
100C4×#99D1111yescharacteristic
101#1460—111no—
102#1351—112no—
103#1344—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×C11C2×C22⋊C411yescharacteristic
114C23×C11#13512yes—
115D4×C11—44no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—44no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#10412yes—
135C2×Dic11—41no—
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—
147Dic22—82no—
148C11⋊C8—82no—
149C2×C22⋊Q8—111no—
150C2×C4×D4C2×D1111yescharacteristic
151#431—221no—
152C2×#99—21no—
153#398—111no—
154#397—111no—
155#397—221no—
156#395—111no—
157#394—221no—
158#393—111no—
159#387—221no—
160#385—221no—
161#381—111no—
162C4×C22⋊C4—21no—
163#342C2×D1112yes—
164#323—112no—
165#323—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—22no—
169C22×C11—42no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11C2×#9911yescharacteristic
179C22×C11#41611yescharacteristic
180C22×C11C2×#10411yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—84no—
188Dic11—81no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192C22×Q8—111no—
193C22×D4C22⋊D1111yescharacteristic
194C23×C4C4×D1111yescharacteristic
195C23×C4C22⋊D1111yescharacteristic
196C22⋊Q8—441no—
197C22⋊Q8—441no—
198C4×D4—41no—
199C4×D4—41no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4C4×D1111yescharacteristic
205C2×C22⋊C4—22no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4D4411yescharacteristic
211C2×C22⋊C4C22×D1111yescharacteristic
212C2×C42—41no—
213C2×C42D4411yescharacteristic
214C4⋊C8—441no—
215#99—24no—
216C22⋊C8—222no—
217C4×C8—441no—
218#95—41no—
219#95—111no—
220#95—111no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—42no—
229C2×C11—81no—
230C2×C11#150111yescharacteristic
231C2×C11#212111yescharacteristic
232C2×C11#212911yescharacteristic
233C24(C2×D11)⋊C411yescharacteristic
234C24C2×C22⋊D1111yescharacteristic
235C2×Q8—441no—
236C2×Q8—881no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4C2×D4411yescharacteristic
256C2×C8—442no—
257C4⋊C4—41no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—881no—
263C22⋊C4—24no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—881no—
270C22⋊C4—881no—
271C42—21no—
272C42—21no—
273C42—82no—
274C11#1173111yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23C2×(C2×D11)⋊C411yescharacteristic
285C23#6700312yes—
286Q8—882no—
287D4—44no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—44no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4#6686912yes—
317C2×C4#6687011yescharacteristic
318C2×C4#6687011yescharacteristic
319C8—882no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22C2×#6686911yescharacteristic
333C22C2×#6687011yescharacteristic
334C22#1062261511yescharacteristic
335C4—22no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—84no—
342C4—881no—
343C4—881no—
344C4—881no—
345C4—881no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1306710511yescharacteristic
351C2#1307026011yescharacteristic
352C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#99D11
hypocenterC11#11731
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13066636C2semidirect
4. #13066615C2semidirect
7. C2×#66977C4semidirect
11. #10622824C4semidirect
13. #10622596C4semidirect
14. #10622592C4semidirect
274. C11#11731semidirect

Maximal subgroups

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

subgroupindex
#130745332
#130669372
#130666362
#130666152
C4×C11×#992
#1173111