Finite Group Databasebeta

← #14651122

Subgroups — #14651122

Order 2816.

446 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077252C211yesmaximal, characteristic
2#13074308C211yesmaximal, characteristic
3#13067219C211yesmaximal, characteristic, complemented
4#13067217C211yesmaximal, characteristic, complemented
5#13066948C211yesmaximal, characteristic
6#13066509C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C2×#66925C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622739—21no—
14#10622731—21no—
15#10622553—21no—
16#10622541—21no—
17#10622539C2211yescharacteristic
18C4×#4318C2211yescharacteristic
19#10622322—22no—
20#10622303—22no—
21#10622290C411yescharacteristic
22#10622287C411yescharacteristic
23#10622281—21no—
24#10622274C411yescharacteristic
25#10622272C411yescharacteristic
26#10622266—21no—
27#10622107—21no—
28#10622106—21no—
29#10622103—22no—
30#10622103—22no—
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4C2×C411yescharacteristic
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49#66925—21no—
50#66925—21no—
51#66925—21no—
52#66925—21no—
53#66923—21no—
54#66923—21no—
55#66923—21no—
56#66923—21no—
57C11×C4⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97D412yes—
61C4×C8×C11—21no—
62C11×#95—21no—
63C11×#95C2×C411yescharacteristic
64C11×#95C2×C411yescharacteristic
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—24no—
71Dic11⋊C8—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74#66867D412yes—
75C4×C11⋊C8—21no—
76#9390—111nomaximal, Sylow
77C23×D11C22⋊C411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—41no—
91C2×C4×D11—41no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C42×C11—42no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4⋊Dic11—42no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#2921—111no—
128#2611—111no—
129#1528—111no—
130#1528—111no—
131#1464—111no—
132#1300—111no—
133#1300D1111yescharacteristic, complemented
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C4×D11—42no—
170C4×D11—42no—
171C8×C11—42no—
172C8×C11—81no—
173C11⋊C8—42no—
174C11⋊C8—81no—
175C2×#125—111no—
176C2×#117—111no—
177#433—222no—
178#433—222no—
179#432—111no—
180#432C2×D1111yescharacteristic
181#423—221no—
182#407—221no—
183C4×M16—111no—
184C4×M16C2×D1111yescharacteristic
185#400—111no—
186#399—111no—
187#398—111no—
188#397—111no—
189#389—221no—
190#388—221no—
191#387—221no—
192#385—221no—
193#376C2×D1111yescharacteristic
194#330—222no—
195#330—222no—
196#324—221no—
197#323—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#38611yescharacteristic
201C22×C11#42111yescharacteristic
202C22×C11#42111yescharacteristic
203C2×D11—42no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219Dic11—81no—
220Dic11—81no—
221C23×C4—111no—
222C2×M16—21no—
223C2×M16—221no—
224#125—221no—
225#125—221no—
226#125—221no—
227#125—221no—
228#117—221no—
229#117—221no—
230#117—221no—
231#117—221no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42—21no—
245C2×C42—111no—
246C2×C42C22×D1111yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—224no—
249C4⋊C8—221no—
250C22⋊C8—21no—
251C22⋊C8—224no—
252C22⋊C8—221no—
253#97—21no—
254#97—112no—
255#97—221no—
256#97D4412yes—
257C4×C8—21no—
258C4×C8—221no—
259#95—21no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95C4×D1111yescharacteristic
265#95C4×D1111yescharacteristic
266C2×C11—21no—
267C2×C11—21no—
268C2×C11#188411yescharacteristic
269C2×C11#189711yescharacteristic
270C2×C11#191511yescharacteristic
271D11—81no—
272C24—111no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4C2×C4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287M16—41no—
288M16—41no—
289M16—441no—
290M16—441no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—442no—
304C4⋊C4—442no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—442no—
314C22⋊C4—442no—
315C42—42no—
316C42—221no—
317C42—221no—
318C42C2×D4411yescharacteristic
319C42#433911yescharacteristic
320C42D4×D1111yescharacteristic
321C42#434311yescharacteristic
322C11#939011yescharacteristic, complemented, Sylow
323C23—221no—
324C23—221no—
325C23—221no—
326C23—441no—
327C23—441no—
328C23C22⋊C4×D1111yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4C4×D4411yescharacteristic
355C2×C4#6693511yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4#6694611yescharacteristic
358C2×C4#6694711yescharacteristic
359C2×C4#6694811yescharacteristic
360C8—42no—
361C8—81no—
362C8—442no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—442no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—881no—
371C22#1062227811yescharacteristic
372C22#1062243411yescharacteristic
373C22#1062243411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—81no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4—881no—
386C4—881no—
387C2—21no—
388C2—21no—
389C2—881no—
390C2#1306899811yescharacteristic
391C2#1306906311yescharacteristic
392C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1300C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1300D11
hypocenterC11#9390
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
3. #13067219C2semidirect
4. #13067217C2semidirect
6. #13066509C2semidirect
7. C11×#1300C2semidirect
133. #1300D11semidirect
322. C11#9390semidirect

Maximal subgroups

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

subgroupindex
#130772522
#130743082
#130672192
#130672172
#130669482
#130665092
C11×#13002
#939011