Finite Group Databasebeta

← #14651220

Subgroups — #14651220

Order 2816.

644 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 97 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#13074097C211yesmaximal, characteristic
2#13070971C211yesmaximal, characteristic, complemented
3#13067132C211yesmaximal, characteristic
4#13066945C211yesmaximal, characteristic, complemented
5#13066502C211yesmaximal, characteristic, complemented
6#13066501C211yesmaximal, characteristic, complemented
7C11×#1507C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C11×#407C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622835C412yescomplemented
14#10622833—21no—
15#10622833—21no—
16C4×C22⋊Dic11C2211yescharacteristic
17C4×C22⋊Dic11C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622595C412yescomplemented
20#10622558—22no—
21C22⋊C4×Dic11—21no—
22C4×Dic11⋊C4—22no—
23#10622262—22no—
24C11×#327—22no—
25#10622175—22no—
26#10622107—22no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C2×C11×M16—21no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#121—21no—
36C11×#121—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—22no—
45C2×Dic11⋊C4—22no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4C2×C412yes—
51C2×Dic11⋊C4D412yes—
52C2×C4×Dic11—22no—
53C2×C4×Dic11—22no—
54C2×C4×Dic11—21no—
55C2×C4×Dic11—21no—
56C2×#4318—21no—
57#66930—28no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95D412yes—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95C2×C412yes—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9410—111nomaximal, Sylow
69C24×C11—21no—
70C24×C11C2×D411yescharacteristic
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—81no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—81no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—24no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—81no—
94C22×Dic11C22⋊C412yes—
95C22×Dic11C22⋊C412yes—
96C11×M16—81no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—81no—
104C22⋊Dic11—24no—
105C22⋊Dic11—42no—
106C22⋊Dic11—44no—
107C22⋊Dic11—82no—
108Dic11⋊C4—28no—
109Dic11⋊C4—22no—
110Dic11⋊C4—22no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113C4×Dic11—28no—
114C4×Dic11—81no—
115C4×Dic11—81no—
116C4×Dic11—82no—
117#4318—81no—
118C2×C11⋊C8—41no—
119#2591—111no—
120#2274—111no—
121#1507—111no—
122#1507D1111yescharacteristic
123#1463—111no—
124#1297—111no—
125#1297—111no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—41no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12011yescharacteristic
135C23×C11#12311yescharacteristic
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—82no—
139D4×C11—82no—
140C2×C4×C11—24no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—24no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—24no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—81no—
170C2×Dic11#10414yes—
171C8×C11—81no—
172C11⋊C8—81no—
173C2×#121C2×D1111yescharacteristic
174C2×#117—221no—
175C22×C4⋊C4—111no—
176#407—111no—
177#407C2×D1111yescharacteristic
178#400—112no—
179#394—112no—
180#388—222no—
181#386—221no—
182#386—221no—
183C4×C4⋊C4—222no—
184C4×C4⋊C4—222no—
185C4×C22⋊C4—111no—
186C4×C22⋊C4—111no—
187C4×C22⋊C4—221no—
188C4×C22⋊C4C2×D1111yescharacteristic
189#327—22no—
190#327—222no—
191#324—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—44no—
200C22×C11—84no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11#38611yescharacteristic
205C22×C11C2×#10412yes—
206C22×C11#45412yes—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—44no—
212C4×C11—81no—
213Dic11—24no—
214Dic11—44no—
215Dic11—42no—
216Dic11—82no—
217C22×D4—21no—
218C22×D4C4×D1111yescharacteristic
219C23×C4—111no—
220C23×C4—111no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—21no—
223C2×M16—221no—
224#121—21no—
225#121—21no—
226#121—21no—
227#121—21no—
228#117—228no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—222no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4C4×D1111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—222no—
243C2×C42—21no—
244C2×C42—222no—
245C2×C42—222no—
246C2×C42—221no—
247C2×C42—221no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252#95—112no—
253#95—112no—
254#95—222no—
255#95—222no—
256#95—222no—
257#95C22⋊D1112yes—
258C2×C11—22no—
259C2×C11—22no—
260C2×C11—41no—
261C2×C11—161no—
262C2×C11#188811yescharacteristic
263C2×C11#189611yescharacteristic
264C2×C11#191311yescharacteristic
265C24—21no—
266C24D4×D1111yescharacteristic
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—44no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—81no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—81no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—224no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—222no—
285C22×C4—881no—
286C22×C4C2×C4×D1111yescharacteristic
287C22×C4#433911yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4#434111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292M16—81no—
293M16—881no—
294C2×C8—41no—
295C2×C8—441no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—228no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C22⋊C4—24no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—224no—
307C22⋊C4—444no—
308C22⋊C4—442no—
309C22⋊C4—882no—
310C42—81no—
311C42—228no—
312C42—881no—
313C42—881no—
314C42—882no—
315C11#941011yescharacteristic, complemented, Sylow
316C23—22no—
317C23—22no—
318C23—41no—
319C23—42no—
320C23—42no—
321C23—41no—
322C23—42no—
323C23C22⋊C4×D1111yescharacteristic
324C23#6693611yescharacteristic
325C23#6699011yescharacteristic
326D4—81no—
327D4—81no—
328D4—82no—
329D4—82no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—114no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—224no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—224no—
348C2×C4—222no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—881no—
357C2×C4(C22⋊D11)⋊C411yescharacteristic
358C2×C4#6693711yescharacteristic
359C2×C4C4×C22⋊D1111yescharacteristic
360C2×C4#6699111yescharacteristic
361C8—81no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—84no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22D11×#10412yes—
376C22#1062256911yescharacteristic
377C22#1062281412yes—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—81no—
384C4—224no—
385C4—444no—
386C4—442no—
387C4—882no—
388C2—22no—
389C2—22no—
390C2—41no—
391C2—161no—
392C2#1306901611yescharacteristic
393C2#1306905611yescharacteristic
394C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1507C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1507D11
hypocenterC11#9410
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13070971C2semidirect
4. #13066945C2semidirect
5. #13066502C2semidirect
6. #13066501C2semidirect
13. #10622835C4semidirect
19. #10622595C4semidirect
315. C11#9410semidirect

Maximal subgroups

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

subgroupindex
#130740972
#130709712
#130671322
#130669452
#130665022
#130665012
C11×#15072
#941011