Finite Group Databasebeta

← #14664124

Subgroups — #14664124

Order 2816.

436 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074538C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic
3#13066935C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic, complemented
5#13066636C211yesmaximal, characteristic, complemented
6#13066616C211yesmaximal, characteristic, complemented
7C11×#1344C211yesmaximal, characteristic, complemented
8C2×#66950C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#397C2211yescharacteristic
11#10622593C411yescharacteristic, complemented
12#10622572—21no—
13C2×#66870—21no—
14#10622563—21no—
15#10622560C2211yescharacteristic
16C22⋊C4×Dic11—21no—
17#10622331—21no—
18#10622287—21no—
19#10622277C411yescharacteristic, complemented
20#10622269C411yescharacteristic, complemented
21#10622268—21no—
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×C22⋊D11D411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4C2×C411yescharacteristic
44C2×C4×Dic11—41no—
45C2×C4×Dic11D411yescharacteristic
46#66950—41no—
47#66950—41no—
48(C22⋊D11)⋊C4—41no—
49(C22⋊D11)⋊C4—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#66870—24no—
63#11731—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11C22⋊C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—22no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—41no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—41no—
80C22×Dic11—81no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—81no—
87C2×Dic22—41no—
88C2×Dic22—81no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C22⋊Dic11—22no—
97C22⋊Dic11—41no—
98C22⋊Dic11—81no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—81no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—81no—
105Dic11⋊C4—41no—
106Dic11⋊C4—42no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—82no—
110C2×C11⋊C8—41no—
111#2638—111no—
112C4×#99—111no—
113#1460—111no—
114#1351—111no—
115#1351—111no—
116#1344—111no—
117#1344D1111yescharacteristic, complemented
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11#13511yescharacteristic
124C23×C11#13511yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—41no—
129C22×D11—41no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C22⋊D11—42no—
144C22⋊D11—42no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11#9911yescharacteristic
162C2×Dic11#9911yescharacteristic
163C2×Dic11#10412yes—
164C4×D11—81no—
165C4×D11—81no—
166Dic22—82no—
167C8×C11—81no—
168C11⋊C8—81no—
169C2×C22⋊Q8—111no—
170C2×C4×D4—111no—
171#431—221no—
172C2×#99—221no—
173#398—111no—
174#397—221no—
175#397C2×D1111yescharacteristic
176#395—111no—
177#394—221no—
178#393—111no—
179#387—221no—
180#385—221no—
181#381—111no—
182C4×C22⋊C4—221no—
183#342—111no—
184#342C2×D1111yescharacteristic
185#323—111no—
186#323—221no—
187#323C2×D1111yescharacteristic
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—81no—
197C22×C11C2×#9911yescharacteristic
198C22×C11#41611yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—82no—
209C4×C11—81no—
210Dic11—21no—
211Dic11—21no—
212Dic11—22no—
213Dic11—41no—
214Dic11—81no—
215Dic11—82no—
216Dic11—81no—
217C22×Q8—111no—
218C22×D4—111no—
219C23×C4—111no—
220C23×C4—111no—
221C22⋊Q8—441no—
222C22⋊Q8—441no—
223C4×D4—441no—
224C4×D4—441no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4C22×D1111yescharacteristic
238C2×C42—111no—
239C2×C42—441no—
240C4⋊C8—441no—
241#99—224no—
242C22⋊C8—21no—
243C22⋊C8—221no—
244C4×C8—441no—
245#95—21no—
246#95—111no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—441no—
252#95C4×D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#150111yescharacteristic
258C2×C11#212111yescharacteristic
259C2×C11#212911yescharacteristic
260D11—81no—
261C24—111no—
262C24D4×D1111yescharacteristic
263C2×Q8—441no—
264C2×Q8—881no—
265C2×D4—222no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—441no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—441no—
282C22×C4—881no—
283C22×C4—881no—
284C22×C4C2×C4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C2×C8—41no—
287C2×C8—441no—
288C4⋊C4—41no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C4⋊C4—881no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—222no—
300C22⋊C4—441no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C42—221no—
306C42—221no—
307C42—882no—
308C11#1173111yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—221no—
314C23—221no—
315C23—221no—
316C23—441no—
317C23—441no—
318C23C22⋊C4×D1111yescharacteristic
319C23#6696511yescharacteristic
320C23#6696911yescharacteristic
321Q8—882no—
322D4—442no—
323D4—442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—111no—
338C2×C4—111no—
339C2×C4—112no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C8—81no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—881no—
373C22—881no—
374C22D11×#9911yescharacteristic
375C22#1062238511yescharacteristic
376C22D11×#10411yescharacteristic
377C4—41no—
378C4—41no—
379C4—81no—
380C4—82no—
381C4—81no—
382C4—222no—
383C4—221no—
384C4—221no—
385C4—441no—
386C4—881no—
387C4—882no—
388C4—881no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—881no—
394C2#1306710411yescharacteristic
395C2#1307026111yescharacteristic
396C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11731
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #13066638C2semidirect
5. #13066636C2semidirect
6. #13066616C2semidirect
7. C11×#1344C2semidirect
8. C2×#66950C4semidirect
11. #10622593C4semidirect
19. #10622277C4semidirect
20. #10622269C4semidirect
117. #1344D11semidirect
308. C11#11731semidirect

Maximal subgroups

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

subgroupindex
#130745382
#130684032
#130669352
#130666382
#130666362
#130666162
C11×#13442
#1173111