Finite Group Databasebeta

← #14781178

Subgroups — #14781178

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2#13070999C212yesmaximal
3#13069783C214yesmaximal, complemented
4#13069780C214yesmaximal
5#13068349C211yesmaximal, characteristic, complemented
6#13068348C212yesmaximal, complemented
7C11×#2280C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2212yes—
12C2×#66979C2212yes—
13#10623050—24no—
14#10623048—24no—
15#10623031—22no—
16#10623014C2214yes—
17#10623001—22no—
18C11×#381C2212yes—
19C11×#380—22no—
20C11×#379C2212yes—
21C4×C11×C22⋊C4—22no—
22#10622860C2214yes—
23#10622825—24no—
24#10622824C2214yes—
25C4×C22⋊Dic11—24no—
26#10622165C2218yes—
27#10622164C2214yes—
28C25×C11C2311yescharacteristic
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—21no—
32C23×C4×C11—21no—
33C23×C4×C11—22no—
34C23×C4×C11—24no—
35C23×C4×C11Q814yescomplemented
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C11×#117—22no—
39C11×#117—22no—
40C11×#117—24no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D412yes—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4C2312yes—
45C2×C11×C22⋊C4C2312yes—
46C2×C42×C11—21no—
47C2×C42×C11D412yes—
48C2×C22⋊Dic11—28no—
49C2×C22⋊Dic11C2314yes—
50C2×C22⋊Dic11C2314yes—
51#66979—22no—
52#66979—22no—
53#66979—22no—
54#66979—22no—
55#66979—24no—
56#66979—24no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11D414yes—
59#66977—28no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11D414yes—
62#66943—28no—
63#66941—28no—
64#66931—216no—
65#66923—24no—
66#66922—24no—
67C4×Dic22—28no—
68C11×#95—24no—
69C11⋊#95—28no—
70#23467—111nomaximal, Sylow
71C24×C11—22no—
72C24×C11—21no—
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—44no—
76C24×C11C2×Q812yes—
77C24×C11C2411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—28no—
83C22×C4×C11—28no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D414yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×Q812yes—
100C22×C4×C11C2×Q812yes—
101C22×C4×C11#4112yes—
102C22×C4×C11#4114yes—
103C22×Dic11—24no—
104C22×Dic11C2×D418yes—
105C2×Dic22—28no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—42no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—48no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—42no—
114C22⋊Dic11—24no—
115C22⋊Dic11—24no—
116C22⋊Dic11—24no—
117C22⋊Dic11—24no—
118C22⋊Dic11—416no—
119C4⋊Dic11—28no—
120C4⋊Dic11—24no—
121C4⋊Dic11—24no—
122C4⋊Dic11—44no—
123Dic11⋊C4—216no—
124C4×Dic11—24no—
125C4×Dic11—24no—
126C4×Dic11—44no—
127#3458—111no—
128#2280—112no—
129#2280D1111yescharacteristic
130#2030—114no—
131#2029—114no—
132#1740—112no—
133#1740—111no—
134C23×C11—28no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11—22no—
138C23×C11—44no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—48no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11C22×D412yes—
148C23×C11C22×D411yescharacteristic
149C23×C11C22×Q811yescharacteristic
150C23×C11C2×#4111yescharacteristic
151C23×C11C2×#4112yes—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—48no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11#12012yes—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11C22⋊Q814yes—
168C2×C4×C11C22⋊Q814yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11C22⋊Q812yes—
171C2×C4×C11#12414yes—
172C2×C4×C11#12414yes—
173C2×C4×C11#12412yes—
174C2×C4×C11#12412yes—
175C2×Dic11—28no—
176C2×Dic11—48no—
177C2×Dic11—48no—
178C2×Dic11—44no—
179Dic22—88no—
180C24×C4C2×D1111yescharacteristic
181#544—224no—
182#544—222no—
183#543—114no—
184#533—224no—
185#533—222no—
186C2×#117—112no—
187C2×#117—112no—
188C2×#117C2×D1111yescharacteristic
189C2×#117C2×D1111yescharacteristic
190#381—114no—
191#381C2×D1112yes—
192#380—22no—
193#380—224no—
194#379—114no—
195#379C2×D1112yes—
196C4×C22⋊C4—22no—
197C4×C22⋊C4—224no—
198#342—114no—
199#342—118no—
200C22×C11—22no—
201C22×C11—24no—
202C22×C11—28no—
203C22×C11—24no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—42no—
207C22×C11—48no—
208C22×C11—44no—
209C22×C11—44no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—44no—
213C22×C11C2×#12011yescharacteristic
214C22×C11C2×C22⋊Q812yes—
215C22×C11C2×C22⋊Q811yescharacteristic
216C22×C11C2×#12412yes—
217C22×C11C2×#12411yescharacteristic
218C4×C11—42no—
219C4×C11—44no—
220C4×C11—82no—
221C4×C11#39314yes—
222C4×C11#39312yes—
223C4×C11#39312yes—
224Dic11—48no—
225Dic11—84no—
226C25C22×D1111yescharacteristic
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4Dic2214yescomplemented
234C23×C4C22×D1111yescharacteristic
235C23×C4C22×D1111yescharacteristic
236C4⋊Q8—224no—
237C4⋊Q8—228no—
238#125—224no—
239#125—228no—
240C22⋊Q8—2216no—
241C22⋊Q8—228no—
242C4×Q8—228no—
243#117—22no—
244#117—22no—
245#117—24no—
246#117—222no—
247#117—222no—
248#117—222no—
249#117—222no—
250#117—224no—
251#117—224no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—222no—
255C2×C4⋊C4C22⋊D1112yes—
256C2×C22⋊C4—24no—
257C2×C22⋊C4—114no—
258C2×C22⋊C4—114no—
259C2×C22⋊C4—228no—
260C2×C22⋊C4C22×D1112yes—
261C2×C22⋊C4C22×D1112yes—
262C2×C42—21no—
263C2×C42—114no—
264C2×C42—222no—
265C2×C42C22⋊D1112yes—
266#95—24no—
267#95—228no—
268C2×C11—22no—
269C2×C11—21no—
270C2×C11—22no—
271C2×C11—21no—
272C2×C11—44no—
273C2×C11C2×#39311yescharacteristic
274C2×C11#302512yes—
275C24—22no—
276C24—21no—
277C24—21no—
278C24—22no—
279C24—44no—
280C24C2×Dic2212yes—
281C24C23×D1111yescharacteristic
282C2×Q8—228no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—28no—
288C22×C4—28no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—118no—
300C22×C4—224no—
301C22×C4C2×Dic2212yes—
302C22×C4C2×Dic2212yes—
303C22×C4#433912yes—
304C22×C4D4×D1112yes—
305C22×C4D4×D1112yes—
306C22×C4#434114yes—
307C22×C4C2×C22⋊D1114yes—
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C4⋊C4—24no—
311C4⋊C4—42no—
312C4⋊C4—2216no—
313C4⋊C4—228no—
314C4⋊C4—224no—
315C4⋊C4—224no—
316C4⋊C4—444no—
317C22⋊C4—24no—
318C22⋊C4—24no—
319C22⋊C4—48no—
320C22⋊C4—224no—
321C22⋊C4—224no—
322C22⋊C4—224no—
323C22⋊C4—224no—
324C22⋊C4—4416no—
325C42—22no—
326C42—22no—
327C42—42no—
328C42—224no—
329C42—224no—
330C42—444no—
331C11#2346711yescharacteristic, complemented, Sylow
332C23—24no—
333C23—28no—
334C23—24no—
335C23—22no—
336C23—44no—
337C23—42no—
338C23—42no—
339C23—44no—
340C23—44no—
341C23—48no—
342C23—42no—
343C23—41no—
344C23—41no—
345C23C22×Dic2211yescharacteristic
346C23C2×#433911yescharacteristic
347C23C2×D4×D1112yes—
348C23C2×#434112yes—
349C23C22×C22⋊D1111yescharacteristic
350Q8—888no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—48no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—228no—
364C2×C4—448no—
365C2×C4—448no—
366C2×C4—444no—
367C2×C4#6693114yes—
368C2×C4#6693114yes—
369C2×C4#6693814yes—
370C2×C4#6693814yes—
371C2×C4#6697712yes—
372C2×C4#6697712yes—
373C2×C4#6698912yes—
374C2×C4#6698912yes—
375C2×C4#6699011yescharacteristic
376C2×C4#6699012yes—
377C2×C4#6699011yescharacteristic
378C22—22no—
379C22—24no—
380C22—28no—
381C22—24no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—44no—
386C22—48no—
387C22—44no—
388C22—42no—
389C22—42no—
390C22—44no—
391C22C2×#6693112yes—
392C22C2×#6693812yes—
393C22C2×#6697711yescharacteristic
394C22C2×#6698911yescharacteristic
395C22C2×#6699011yescharacteristic
396C4—42no—
397C4—44no—
398C4—82no—
399C4—448no—
400C4—884no—
401C4#1062256014yes—
402C4#1062256012yes—
403C4#1062256012yes—
404C2—21no—
405C2—22no—
406C2—22no—
407C2—21no—
408C2—44no—
409C2C2×#1062256011yescharacteristic
410C2#1307800712yes—
subgroupG/H
centerC2×C4#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2280C2
socleC22×C11C2×#120
prime radicalC25×C11C23
hypercenter#2280D11
hypocenterC11#23467
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
3. #13069783C2semidirect
5. #13068349C2semidirect
6. #13068348C2semidirect
35. C23×C4×C11Q8semidirect
233. C23×C4Dic22semidirect
331. C11#23467semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130709992
#130697832
#130697802
#130683492
#130683482
C11×#22802
#2346711