Finite Group Databasebeta

← #14664913

Subgroups — #14664913

Order 2816.

452 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 77 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#13073791C211yesmaximal, characteristic
2#13068603C211yesmaximal, characteristic
3#13066935C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066638C211yesmaximal, characteristic, complemented
6#13066636C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66950C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#399C2211yescharacteristic
11#10622600—21no—
12#10622595C411yescharacteristic, complemented
13#10622594—21no—
14#10622569—21no—
15C2×#66870—21no—
16#10622563—21no—
17#10622560C2211yescharacteristic
18#10622555—21no—
19#10622331—21no—
20D11×#95C411yescharacteristic, complemented
21#10622269C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×C22⋊D11D411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×C4×D11—21no—
30C22×C4×D11C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4D411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—41no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46#66950—41no—
47#66950—41no—
48(C22⋊D11)⋊C4—41no—
49(C22⋊D11)⋊C4—41no—
50C11×C22⋊C8—21no—
51C11×#95C2×C411yescharacteristic
52C11⋊#95—21no—
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—42no—
63#11902—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—41no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11SD1612yes—
74C2×C22⋊D11Q1612yes—
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—42no—
87C2×C4×D11—42no—
88C2×C4×D11—81no—
89C2×C4×D11—81no—
90C2×Dic22—41no—
91C2×Dic22—81no—
92C2×C8×C11—41no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—81no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—81no—
107Dic11⋊C4—41no—
108Dic11⋊C4—82no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C2×C11⋊C8—41no—
112#2564—111no—
113#1799—111no—
114#1460—111no—
115#1352—111no—
116#1352D1111yescharacteristic, complemented
117#1351—111no—
118#1351—111no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11C2×SD1611yescharacteristic
125C23×C11C2×Q1611yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11#10312yes—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
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—
143C2×C4×C11—81no—
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11#9911yescharacteristic
163C2×Dic11#9911yescharacteristic
164C2×Dic11#10312yes—
165C4×D11—81no—
166C4×D11—81no—
167C4×D11—84no—
168Dic22—82no—
169C8×C11—81no—
170C11⋊C8—81no—
171C2×C22⋊Q8—111no—
172C2×C4×D4—111no—
173#431—221no—
174C2×#99—221no—
175#400—111no—
176#399C2×D1111yescharacteristic
177#395—111no—
178#393—111no—
179#387—221no—
180#386—221no—
181#385—221no—
182#380—221no—
183#380—221no—
184C2×#95—111no—
185#342—111no—
186#342C2×D1111yescharacteristic
187#323—111no—
188#323—221no—
189#323C2×D1111yescharacteristic
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—81no—
199C22×C11C2×#9911yescharacteristic
200C22×C11C2×#10311yescharacteristic
201C22×C11#42111yescharacteristic
202C2×D11—22no—
203C2×D11—42no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—42no—
207C4×C11—42no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—161no—
212Dic11—21no—
213Dic11—21no—
214Dic11—22no—
215Dic11—41no—
216Dic11—81no—
217Dic11—81no—
218Dic11—161no—
219C22×Q8—111no—
220C22×D4—111no—
221C23×C4—111no—
222C23×C4—111no—
223C23×C4—221no—
224C22⋊Q8—441no—
225C22⋊Q8—441no—
226C4×D4—441no—
227C4×D4—441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—441no—
233C2×C4⋊C4C4×D1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4C22×D1111yescharacteristic
241C2×C42—111no—
242C4⋊C8—441no—
243#99—442no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C4×C8—441no—
247#95—111no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—441no—
254#95C4×D1111yescharacteristic
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—41no—
258C2×C11—41no—
259C2×C11#152011yescharacteristic
260C2×C11#212111yescharacteristic
261C2×C11#212611yescharacteristic
262D11—42no—
263C24—111no—
264C24D4×D1111yescharacteristic
265C2×Q8—441no—
266C2×Q8—881no—
267C2×D4—112no—
268C2×D4—112no—
269C2×D4—441no—
270C2×D4—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—442no—
284C22×C4—442no—
285C22×C4—441no—
286C22×C4—881no—
287C22×C4—881no—
288C22×C4—881no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C2×C8—41no—
292C2×C8—441no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—881no—
299C4⋊C4—882no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C22⋊C4—442no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—881no—
309C42—221no—
310C42—221no—
311C11#1190211yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—112no—
317C23—221no—
318C23—221no—
319C23—441no—
320C23—441no—
321C23C22⋊C4×D1111yescharacteristic
322C23SD16×D1111yescharacteristic
323C23Q16×D1111yescharacteristic
324Q8—882no—
325D4—442no—
326D4—442no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—112no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—441no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—884no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4—881no—
361C2×C4—881no—
362C8—81no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—222no—
374C22—442no—
375C22—442no—
376C22—441no—
377C22—441no—
378C22D11×#9911yescharacteristic
379C22D11×#10311yescharacteristic
380C22#1062243411yescharacteristic
381C4—42no—
382C4—41no—
383C4—41no—
384C4—81no—
385C4—161no—
386C4—222no—
387C4—221no—
388C4—221no—
389C4—441no—
390C4—881no—
391C4—881no—
392C4—1761no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—442no—
398C2#1306718611yescharacteristic
399C2#1307026111yescharacteristic
400C2#1307027811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11902
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066638C2semidirect
6. #13066636C2semidirect
7. C11×#1352C2semidirect
8. C2×#66950C4semidirect
12. #10622595C4semidirect
20. D11×#95C4semidirect
21. #10622269C4semidirect
116. #1352D11semidirect
311. C11#11902semidirect

Maximal subgroups

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

subgroupindex
#130737912
#130686032
#130669352
#130666402
#130666382
#130666362
C11×#13522
#1190211