Finite Group Databasebeta

← #14726266

Subgroups — #14726266

Order 2816.

930 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#10623031C211yesmaximal, characteristic
2#13078564C212yesmaximal
3#13067657C214yesmaximal, complemented
4#13067623C214yesmaximal, complemented
5#13067148C212yesmaximal
6#13066946C211yesmaximal, characteristic
7C11×#2484C211yesmaximal, characteristic
8C2×C11×#117C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66979—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623031—22no—
14#10623031—24no—
15#10623031C2214yes—
16C2×#66943—22no—
17C2×#66941—22no—
18C11×#400C2212yes—
19C11×#398C2212yes—
20C11×#387—22no—
21C11×#385—21no—
22C11×#381—21no—
23C11×#381C2211yescharacteristic
24#10622820C2212yes—
25#10622617—22no—
26#10622609—24no—
27#10622608—22no—
28#10622584C2214yes—
29#10622583C2214yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×Dic22—21no—
36C22×Dic22D412yes—
37C11×#117—22no—
38C11×#117—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D412yes—
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11—21no—
49C2×C22⋊Dic11—22no—
50#66979—24no—
51#66979—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D412yes—
56#66977—24no—
57#66977—22no—
58#66977—22no—
59#66977—24no—
60#66977D414yes—
61#66977C2314yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—22no—
65C2×#4318—22no—
66#66943—28no—
67#66943—28no—
68#66941—28no—
69#66941—28no—
70C11×#95—22no—
71C11×#95—22no—
72C11×#95—21no—
73C11×#95—22no—
74C11×#95C2312yes—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66874—24no—
79#66872—24no—
80#66871—24no—
81#18148—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—22no—
101C2×Dic22—24no—
102C2×Dic22—22no—
103C2×Dic22—44no—
104C2×Dic22—82no—
105C2×Dic22C2×D414yes—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—44no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—42no—
115C22⋊Dic11—24no—
116C22⋊Dic11—24no—
117C4⋊Dic11—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—24no—
120C4⋊Dic11—22no—
121C4⋊Dic11C2×D414yes—
122Dic11⋊C4—28no—
123Dic11⋊C4—24no—
124Dic11⋊C4—24no—
125C4×Dic11—28no—
126#4318—44no—
127C2×C11⋊C8—24no—
128C2×#544—111no—
129#3095—112no—
130#2484D1111yescharacteristic
131#1617—114no—
132#1611—114no—
133#1511—112no—
134#1463—111no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139C23×C11#12011yescharacteristic
140C23×C11C22×D411yescharacteristic
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—81no—
160C2×C4×C11#12012yes—
161C2×C4×C11#13714yes—
162C2×C4×C11C22×D412yes—
163C2×Dic11—24no—
164C2×Dic11—24no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167Dic22—44no—
168Dic22—82no—
169Dic22—84no—
170C11⋊C8—44no—
171#544—114no—
172#544—224no—
173#544—222no—
174C2×C4⋊Q8—222no—
175C2×#125—222no—
176C2×C22⋊Q8—112no—
177C2×C22⋊Q8—221no—
178C2×#117—221no—
179C2×#117C2×D1111yescharacteristic
180C22×C4⋊C4C2×D1111yescharacteristic
181#485—224no—
182#484—114no—
183#483—114no—
184#428—222no—
185#419—222no—
186#407—112no—
187#400C2×D1112yes—
188#398C2×D1112yes—
189#387—22no—
190#385—21no—
191#381—21no—
192#381C2×D1111yescharacteristic
193#328—118no—
194#324—114no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—44no—
203C22×C11#45812yes—
204C22×C11C2×#12011yescharacteristic
205C22×C11C2×#13712yes—
206C4×C11—24no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—42no—
210C4×C11—82no—
211C4×C11—81no—
212C4×C11—81no—
213Dic11—44no—
214Dic11—44no—
215C22×Q8—112no—
216C22×Q8—221no—
217C23×C4C22⋊D1111yescharacteristic
218C23×C4C22⋊D1111yescharacteristic
219C23×C4C22×D1111yescharacteristic
220C2×M16—222no—
221C4⋊Q8—228no—
222C4⋊Q8—228no—
223#125—228no—
224#125—228no—
225C22⋊Q8—114no—
226C22⋊Q8—114no—
227C22⋊Q8—224no—
228C22⋊Q8—222no—
229C22⋊Q8—222no—
230C22⋊Q8—224no—
231#117—22no—
232#117—22no—
233#117—224no—
234#117—224no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4C22⋊D1112yes—
245C2×C4⋊C4C22×D1111yescharacteristic
246C2×C4⋊C4C22×D1111yescharacteristic
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—222no—
251C2×C42—21no—
252C2×C42—222no—
253#107—224no—
254#106—224no—
255#103—224no—
256#103—224no—
257C22⋊C8—114no—
258C22⋊C8—222no—
259#95—22no—
260#95—22no—
261#95—21no—
262#95—22no—
263#95C22×D1112yes—
264C2×C11—22no—
265C2×C11—22no—
266C2×C11—41no—
267C2×C11#300411yescharacteristic
268C2×C11#302011yescharacteristic
269C2×C11C2×#45811yescharacteristic
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—114no—
272C2×Q8—224no—
273C2×Q8—222no—
274C2×Q8—444no—
275C2×Q8—882no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—24no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4D4×D1112yes—
289C22×C4D4×D1112yes—
290C22×C4C2×C22⋊D1112yes—
291C22×C4C2×C22⋊D1112yes—
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C23×D1111yescharacteristic
294M16—444no—
295C2×C8—224no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—44no—
301C4⋊C4—114no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—224no—
305C4⋊C4—228no—
306C4⋊C4—222no—
307C4⋊C4—224no—
308C4⋊C4—224no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—224no—
313C22⋊C4—224no—
314C42—42no—
315C42—228no—
316C11#1814811yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23—41no—
320C23#6699011yescharacteristic
321C23#6699011yescharacteristic
322C23C22×C22⋊D1111yescharacteristic
323Q8—444no—
324Q8—882no—
325Q8—884no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—224no—
346C2×C4—224no—
347C2×C4—444no—
348C2×C4—444no—
349C2×C4#6699012yes—
350C2×C4#6700414yes—
351C2×C4C2×D4×D1112yes—
352C8—444no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#1062266612yes—
362C22C2×#6699011yescharacteristic
363C22C2×#6700412yes—
364C4—24no—
365C4—22no—
366C4—22no—
367C4—42no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4—444no—
372C4—444no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1307784911yescharacteristic
377C2#1307797911yescharacteristic
378C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2484C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#2484D11
hypocenterC11#18148
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #13067657C2semidirect
4. #13067623C2semidirect
316. C11#18148semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130785642
#130676572
#130676232
#130671482
#130669462
C11×#24842
#1814811