Finite Group Databasebeta

← #14727960

Subgroups — #14727960

Order 2816.

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

normal subgroups only

This group has 976 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, complemented
2#13079422C212yesmaximal
3#13067657C214yesmaximal, complemented
4#13067555C214yesmaximal, complemented
5#13067135C212yesmaximal, complemented
6#13066946C211yesmaximal, characteristic, complemented
7C11×#2591C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
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×#394C2212yes—
20C11×#388—22no—
21C11×#386—21no—
22C11×#386—21no—
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622831C2214yes—
25#10622820C2212yes—
26#10622655—24no—
27#10622653—22no—
28#10622646—22no—
29#10622583C2214yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C22×D4×C11—21no—
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×Dic22—21no—
38C22×Dic22D412yes—
39C11×#121—22no—
40C11×#121—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C42×C11—21no—
51C2×C22⋊Dic11—22no—
52C2×#4324—24no—
53#66979—24no—
54#66979—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59#66977—24no—
60#66977—22no—
61#66977—22no—
62#66977—24no—
63#66977D414yes—
64#66977C2314yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×#4318—22no—
69#66943—28no—
70#66943—28no—
71#66941—28no—
72#66941—28no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95C2312yes—
76#66896—24no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66874—24no—
80#66871—24no—
81#18326—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—81no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—24no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—81no—
97C22×C4×C11—81no—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C2×Dic22—24no—
107C2×Dic22—22no—
108C2×Dic22—82no—
109C2×Dic22—82no—
110C2×Dic22C2×D414yes—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—44no—
117C11×C22⋊C4—82no—
118C42×C11—81no—
119C22⋊Dic11—24no—
120C22⋊Dic11—24no—
121#4324—84no—
122C4⋊Dic11—24no—
123C4⋊Dic11—24no—
124C4⋊Dic11—24no—
125C4⋊Dic11—22no—
126C4⋊Dic11C2×D414yes—
127Dic11⋊C4—28no—
128Dic11⋊C4—24no—
129Dic11⋊C4—24no—
130C4×Dic11—28no—
131#4318—82no—
132C2×C11⋊C8—24no—
133C2×#544—111no—
134#3193—112no—
135#2591D1111yescharacteristic
136#1617—114no—
137#1599—114no—
138#1508—112no—
139#1463—111no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11#12011yescharacteristic
148C23×C11#12011yescharacteristic
149C23×C11C22×D411yescharacteristic
150D4×C11—44no—
151D4×C11—82no—
152D4×C11—82no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—81no—
170C2×C4×C11#12012yes—
171C2×C4×C11#13714yes—
172C2×C4×C11C22×D412yes—
173C2×Dic11—24no—
174C2×Dic11—24no—
175C2×Dic11—44no—
176C2×Dic11—44no—
177Dic22—44no—
178Dic22—82no—
179Dic22—84no—
180C11⋊C8—44no—
181#544—114no—
182#544—224no—
183#544—222no—
184C2×C4⋊Q8—222no—
185C2×#125—222no—
186C2×C22⋊Q8—112no—
187C2×C22⋊Q8—221no—
188C2×#121C2×D1111yescharacteristic
189C2×#117—221no—
190C22×C4⋊C4C2×D1111yescharacteristic
191#484—114no—
192#480—222no—
193#468—224no—
194#450—114no—
195#448—222no—
196#407—112no—
197#400C2×D1112yes—
198#394C2×D1112yes—
199#388—22no—
200#386—21no—
201#386—21no—
202C4×C22⋊C4C2×D1111yescharacteristic
203#328—118no—
204#324—114no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—44no—
213C22×C11—84no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#45412yes—
218C22×C11C2×#12011yescharacteristic
219C22×C11C2×#13712yes—
220C4×C11—24no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11—81no—
226Dic11—44no—
227Dic11—44no—
228C22×Q8—112no—
229C22×Q8—221no—
230C22×D4—21no—
231C22×D4C22×D1111yescharacteristic
232C23×C4C22⋊D1111yescharacteristic
233C23×C4C22⋊D1111yescharacteristic
234C23×C4C22×D1111yescharacteristic
235C2×SD16—224no—
236C2×M16—222no—
237C4⋊Q8—228no—
238C4⋊Q8—228no—
239#125—228no—
240#125—228no—
241C22⋊Q8—114no—
242C22⋊Q8—114no—
243C22⋊Q8—224no—
244C22⋊Q8—222no—
245C22⋊Q8—222no—
246C22⋊Q8—224no—
247#121—22no—
248#121—22no—
249#117—224no—
250#117—224no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4C22⋊D1112yes—
260C2×C4⋊C4C22×D1111yescharacteristic
261C2×C4⋊C4C22×D1112yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—222no—
267C2×C42—21no—
268C2×C42—222no—
269#107—224no—
270#103—224no—
271#102—224no—
272C22⋊C8—114no—
273C22⋊C8—222no—
274#95—22no—
275#95—22no—
276#95C22×D1112yes—
277C2×C11—22no—
278C2×C11—22no—
279C2×C11—41no—
280C2×C11—161no—
281C2×C11#300411yescharacteristic
282C2×C11C2×#45411yescharacteristic
283C2×C11#302611yescharacteristic
284C24—21no—
285C24C2×C22⋊D1111yescharacteristic
286C2×Q8—114no—
287C2×Q8—224no—
288C2×Q8—222no—
289C2×Q8—882no—
290C2×Q8—882no—
291C2×D4—22no—
292C2×D4—44no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—24no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—81no—
304C22×C4—81no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4D4×D1112yes—
308C22×C4D4×D1112yes—
309C22×C4C2×C22⋊D1112yes—
310C22×C4C2×C22⋊D1112yes—
311C22×C4C2×C22⋊D1111yescharacteristic
312C22×C4C23×D1111yescharacteristic
313SD16—884no—
314M16—882no—
315C2×C8—224no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—114no—
320C4⋊C4—224no—
321C4⋊C4—224no—
322C4⋊C4—224no—
323C4⋊C4—228no—
324C4⋊C4—222no—
325C4⋊C4—224no—
326C4⋊C4—224no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—44no—
330C22⋊C4—82no—
331C22⋊C4—224no—
332C22⋊C4—224no—
333C42—81no—
334C42—228no—
335C11#1832611yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23—41no—
339C23—42no—
340C23—42no—
341C23—41no—
342C23—42no—
343C23#6699011yescharacteristic
344C23#6699011yescharacteristic
345C23C22×C22⋊D1111yescharacteristic
346Q8—444no—
347Q8—882no—
348Q8—884no—
349D4—44no—
350D4—82no—
351D4—82no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4—444no—
372C2×C4—444no—
373C2×C4#6699012yes—
374C2×C4#6700414yes—
375C2×C4C2×D4×D1112yes—
376C8—444no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—84no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#1062267512yes—
390C22C2×#6699011yescharacteristic
391C22C2×#6700412yes—
392C4—24no—
393C4—22no—
394C4—22no—
395C4—42no—
396C4—82no—
397C4—81no—
398C4—444no—
399C4—444no—
400C2—22no—
401C2—22no—
402C2—41no—
403C2—161no—
404C2#1307784911yescharacteristic
405C2C2×#1062267511yescharacteristic
406C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2591C2
socleC22×C11C2×#120
prime radicalC2×C11×#121C22
hypercenter#2591D11
hypocenterC11#18326
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. C2×#10623031C2semidirect
3. #13067657C2semidirect
4. #13067555C2semidirect
5. #13067135C2semidirect
6. #13066946C2semidirect
335. C11#18326semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130794222
#130676572
#130675552
#130671352
#130669462
C11×#25912
#1832611