Finite Group Databasebeta

← #14781146

Subgroups — #14781146

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2#13077135C212yesmaximal
3#13069777C214yesmaximal, complemented
4#13069772C214yesmaximal, complemented
5#13068355C211yesmaximal, characteristic, complemented
6C2×#10622161C212yesmaximal, complemented
7C11×#2297C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2212yes—
12C22×#4318C2212yes—
13#10623050—24no—
14#10623048—24no—
15#10623031C2214yes—
16#10623014—22no—
17#10623001—22no—
18C11×#391C2212yes—
19C11×#390C2212yes—
20C11×#386—22no—
21C4×C11×C22⋊C4—22no—
22#10622846—24no—
23#10622845—24no—
24#10622838C2214yes—
25#10622828C2214yes—
26#10622168C2214yes—
27#10622161C2218yes—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—24no—
32C2×C11×#41Q814yescomplemented
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C11×#117—22no—
40C11×#117—22no—
41C2×C11×C4⋊C4C2312yes—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4D412yes—
44C2×C42×C11—24no—
45C2×C42×C11—21no—
46C2×C42×C11D412yes—
47C2×C42×C11C2312yes—
48C2×C22⋊Dic11—22no—
49#66979—22no—
50#66979—22no—
51#66979D414yes—
52#66979C2314yes—
53C2×C4⋊Dic11D414yes—
54#66977—28no—
55C2×C4×Dic11—22no—
56C2×#4318—22no—
57C2×#4318—24no—
58C2×#4318—24no—
59C2×#4318C2314yes—
60C22×C11⋊C8—22no—
61#66943—28no—
62#66941—28no—
63#66931—216no—
64#66923—24no—
65#66922—24no—
66C4×Dic22—28no—
67C11×#95—24no—
68#66899—28no—
69#66896—28no—
70#23461—111nomaximal, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C11×#41—28no—
74C11×#41—28no—
75C11×#41—44no—
76C11×#41—44no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11C2×Q812yes—
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11C2×Q812yes—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—44no—
92C22×C4×C11—42no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D414yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×Q812yes—
101C22×C4×C11#4114yes—
102C22×C4×C11#4112yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—24no—
105C2×Dic22—28no—
106C11×C4⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—48no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11—24no—
112C42×C11—42no—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C4⋊Dic11—28no—
116C4⋊Dic11—24no—
117C4⋊Dic11C2×D418yes—
118Dic11⋊C4—216no—
119C4×Dic11—24no—
120C4×Dic11—24no—
121#4318—24no—
122#4318—24no—
123#4318—44no—
124C2×C11⋊C8—24no—
125C2×C11⋊C8—44no—
126#3458—111no—
127#2896—112no—
128#2297D1111yescharacteristic
129#2028—114no—
130#2027—114no—
131#1742—111no—
132C2×#339—112no—
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—44no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12012yes—
139C23×C11C22⋊Q812yes—
140C23×C11#12412yes—
141C23×C11C22×D411yescharacteristic
142Q8×C11—24no—
143Q8×C11—42no—
144D4×C11—24no—
145D4×C11—48no—
146D4×C11—42no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—22no—
150C2×C4×C11—42no—
151C2×C4×C11—48no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11C22⋊Q814yes—
161C2×C4×C11C22⋊Q814yes—
162C2×C4×C11C22⋊Q812yes—
163C2×C4×C11#12414yes—
164C2×C4×C11#12414yes—
165C2×C4×C11#12412yes—
166C2×C4×C11C22×D412yes—
167C2×C4×C11C22×Q811yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C11C2×#4112yes—
170C2×Dic11—28no—
171C2×Dic11—84no—
172Dic22—88no—
173C11⋊C8—44no—
174C22×#41C2×D1111yescharacteristic
175C22×M16—112no—
176#544—114no—
177#544—224no—
178#543—222no—
179#533—224no—
180#533—222no—
181C2×#117—112no—
182C2×#117C2×D1111yescharacteristic
183C22×C42C2×D1111yescharacteristic
184#419—114no—
185#418—114no—
186#417—224no—
187#416—224no—
188#391C2×D1112yes—
189#390C2×D1112yes—
190#386—22no—
191C4×C22⋊C4—22no—
192#343—114no—
193#339—118no—
194C22×C11—22no—
195C22×C11—24no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11#39314yes—
203C22×C11C2×#12011yescharacteristic
204C22×C11C2×C22⋊Q811yescharacteristic
205C22×C11C2×#12411yescharacteristic
206C4×C11—44no—
207C4×C11—42no—
208C4×C11—44no—
209C4×C11#39312yes—
210C4×C11#39312yes—
211C4×C11C2×C22⋊Q812yes—
212C4×C11C2×#12412yes—
213Dic11—48no—
214C2×#41—22no—
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—24no—
218C2×#41Dic2214yescomplemented
219C22×Q8C22×D1111yescharacteristic
220C22×D4—21no—
221C22×D4C22×D1111yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4C22×D1111yescharacteristic
225C2×M16—114no—
226C2×M16—222no—
227C2×M16—224no—
228C2×M16—224no—
229C22×C8—222no—
230C4⋊Q8—224no—
231C4⋊Q8—228no—
232#125—224no—
233#125—228no—
234C22⋊Q8—2216no—
235C22⋊Q8—228no—
236C4×Q8—228no—
237#117—22no—
238#117—22no—
239#117—114no—
240#117—114no—
241#117—222no—
242#117—222no—
243C2×C4⋊C4—114no—
244C2×C4⋊C4C22×D1112yes—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—222no—
247C2×C22⋊C4C22⋊D1112yes—
248C2×C42—24no—
249C2×C42—21no—
250C2×C42—222no—
251C2×C42C22⋊D1112yes—
252C2×C42C22×D1112yes—
253#103—228no—
254#102—228no—
255#95—24no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—24no—
259C2×C11—82no—
260C2×C11C2×#39311yescharacteristic
261C2×C11#301812yes—
262C24—21no—
263C24C2×C22⋊D1111yescharacteristic
264#41—28no—
265#41—28no—
266#41—44no—
267#41—44no—
268C2×Q8—21no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—228no—
272C2×Q8C2×Dic2212yes—
273C2×D4—24no—
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4C2×Dic2212yes—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—44no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—224no—
289C22×C4C2×Dic2212yes—
290C22×C4#433912yes—
291C22×C4D4×D1112yes—
292C22×C4D4×D1112yes—
293C22×C4#434114yes—
294C22×C4C2×C22⋊D1114yes—
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C23×D1111yescharacteristic
297M16—224no—
298M16—224no—
299M16—444no—
300C2×C8—224no—
301C2×C8—444no—
302C4⋊C4—24no—
303C4⋊C4—118no—
304C4⋊C4—2216no—
305C4⋊C4—228no—
306C4⋊C4—224no—
307C22⋊C4—24no—
308C22⋊C4—48no—
309C22⋊C4—224no—
310C22⋊C4—224no—
311C42—22no—
312C42—22no—
313C42—24no—
314C42—42no—
315C42—224no—
316C42—224no—
317C11#2346111yescharacteristic, complemented, Sylow
318C23—22no—
319C23—42no—
320C23—44no—
321C23—41no—
322C23—41no—
323C23#6697712yes—
324C23#6698912yes—
325C23#6699012yes—
326C23C22×C22⋊D1111yescharacteristic
327Q8—24no—
328Q8—42no—
329Q8—888no—
330D4—24no—
331D4—48no—
332D4—42no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—42no—
337C2×C4—48no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—228no—
345C2×C4—884no—
346C2×C4#6693114yes—
347C2×C4#6693114yes—
348C2×C4#6693814yes—
349C2×C4#6693814yes—
350C2×C4#6697712yes—
351C2×C4#6698912yes—
352C2×C4#6699011yescharacteristic
353C2×C4#6699011yescharacteristic
354C2×C4C22×Dic2211yescharacteristic
355C2×C4C2×#433911yescharacteristic
356C2×C4C2×D4×D1112yes—
357C2×C4C2×#434112yes—
358C8—444no—
359C22—22no—
360C22—24no—
361C22—42no—
362C22—42no—
363C22—44no—
364C22—42no—
365C22—82no—
366C22—82no—
367C22#1062256014yes—
368C22C2×#6697711yescharacteristic
369C22C2×#6698911yescharacteristic
370C22C2×#6699011yescharacteristic
371C4—44no—
372C4—42no—
373C4—44no—
374C4—448no—
375C4#1062256012yes—
376C4#1062256012yes—
377C4C2×#6693112yes—
378C4C2×#6693812yes—
379C2—21no—
380C2—21no—
381C2—24no—
382C2—82no—
383C2C2×#1062256011yescharacteristic
384C2#1307796412yes—
subgroupG/H
centerC2×C4#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#23461
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
3. #13069777C2semidirect
4. #13069772C2semidirect
5. #13068355C2semidirect
6. C2×#10622161C2semidirect
32. C2×C11×#41Q8semidirect
218. C2×#41Dic22semidirect
317. C11#23461semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130771352
#130697772
#130697722
#130683552
C2×#106221612
C11×#22972
#2346111