Finite Group Databasebeta

← #14723927

Subgroups — #14723927

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077711C211yesmaximal, characteristic
2#13077697C211yesmaximal, characteristic
3#13067488C212yesmaximal, complemented
4#13067467C212yesmaximal, complemented
5#13067435C212yesmaximal, complemented
6Q16×C11⋊C8C212yesmaximal, complemented
7#13067396C211yesmaximal, characteristic
8#13067063C211yesmaximal, characteristic
9#13067037C211yesmaximal, characteristic
10#13066911C211yesmaximal, characteristic
11C11×#3104C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C11×#484C412yes—
15C11×#477C412yes—
16C11×#462C412yes—
17C11×#451C412yes—
18C4×C11×Q16C2212yes—
19C4×C11×Q16C2212yes—
20C11×#431C2211yescharacteristic
21#10622637—22no—
22#10622637C2212yes—
23Q8×C11⋊C8—22no—
24Q8×C11⋊C8C2212yes—
25Q8×C11⋊C8C2212yes—
26Q8×C11⋊C8C2212yes—
27#10622613—22no—
28#10622539C2211yescharacteristic
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C4×#4318C2211yescharacteristic
33Q8⋊(C11⋊C8)C2212yes—
34Q8⋊(C11⋊C8)C2212yes—
35Q8⋊(C11⋊C8)C2212yes—
36Q8⋊(C11⋊C8)C2212yes—
37#10622096C2212yes—
38#10622095C2212yes—
39#10622093C2211yescharacteristic
40#10622092C2211yescharacteristic
41#10622092C2211yescharacteristic
42C8×C11⋊C8C2211yescharacteristic
43C22×Q8×C11C2×C411yescharacteristic
44C2×C11×Q16C2×C412yes—
45C2×C11×Q16C2×C412yes—
46C11×C4⋊Q8C2×C411yescharacteristic
47C11×C4⋊Q8C2×C411yescharacteristic
48C11×#125—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8C2×C412yes—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11C2×C412yes—
55C4×Q8×C11C2312yes—
56C4×Q8×C11C2312yes—
57C11×#117—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4318—21no—
63C11×#107C2×C412yes—
64C11×#107C2×C412yes—
65C11×C4⋊C8C2×C412yes—
66C11×#103C2×C412yes—
67C11×#103C2×C412yes—
68C11×#103C2×C412yes—
69C11×#103C2×C412yes—
70C11×C22⋊C8C2×C412yes—
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)—22no—
79C4⋊(C11⋊C8)—22no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83#66867—21no—
84#66867—21no—
85#66867—22no—
86C4×C11⋊C8—21no—
87C4×C11⋊C8—22no—
88C4×C11⋊C8—22no—
89C4×C11⋊C8—22no—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#17925—111nomaximal, Sylow
95C2×Q8×C11—24no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11C22×C412yes—
99C2×Q8×C11C22×C412yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C11×Q16—24no—
106C11×Q16—24no—
107C2×C8×C11C22×C412yes—
108C2×C8×C11C22×C412yes—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4C22×C412yes—
118C11×C4⋊C4C22×C412yes—
119C11×C22⋊C4—22no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11C22×C411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127#4318—42no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8C2×D412yes—
133C2×C11⋊C8C2×D412yes—
134#3104D1111yescharacteristic
135#2985—111no—
136#2982—111no—
137#1587—112no—
138#1584—112no—
139#1579—112no—
140C8×Q16—112no—
141#1572—111no—
142#1491—111no—
143#1485—111no—
144#1453—111no—
145C23×C11C4×D411yescharacteristic
146Q8×C11—24no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—22no—
150Q8×C11—81no—
151Q8×C11#13114yes—
152C2×C4×C11—24no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C8×C11—22no—
168C8×C11—22no—
169C11⋊C8—22no—
170C11⋊C8—22no—
171C11⋊C8—22no—
172C11⋊C8—41no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175#533C2×D1111yescharacteristic
176C2×C4×Q8C2×D1111yescharacteristic
177#484Dic1112yes—
178#477Dic1112yes—
179#462Dic1112yes—
180#451Dic1112yes—
181#446—112no—
182#446—222no—
183C8×Q8—112no—
184C8×Q8—112no—
185C8×Q8—112no—
186C8×Q8—222no—
187C4×Q16C2×D1112yes—
188C4×Q16C2×D1112yes—
189#433—222no—
190#432—111no—
191#431—111no—
192#431—111no—
193#431—222no—
194#431C2×D1111yescharacteristic
195C4×M16—111no—
196#335—112no—
197#334—112no—
198Q8⋊C8—112no—
199Q8⋊C8—112no—
200Q8⋊C8—112no—
201Q8⋊C8—112no—
202#322—111no—
203#322—111no—
204#322—111no—
205C82—111no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11C2×C4×D411yescharacteristic
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—42no—
218C4×C11C2×#13112yes—
219C4×C11#57812yes—
220C22×Q8C2×Dic1111yescharacteristic
221C2×Q16C2×Dic1112yes—
222C2×Q16C2×Dic1112yes—
223C2×M16—221no—
224C4⋊Q8C2×Dic1111yescharacteristic
225C4⋊Q8C2×Dic1111yescharacteristic
226#125—21no—
227C22⋊Q8—21no—
228C22⋊Q8C2×Dic1112yes—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8C2×Dic1112yes—
233C4×Q8C22×D1112yes—
234C4×Q8C22×D1112yes—
235#117—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×Dic1111yescharacteristic
238C2×C42—21no—
239C2×C42C22×D1111yescharacteristic
240#107C2×Dic1112yes—
241#107C2×Dic1112yes—
242C4⋊C8—112no—
243C4⋊C8—112no—
244C4⋊C8—112no—
245C4⋊C8—222no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248C4⋊C8—222no—
249C4⋊C8C2×Dic1112yes—
250#103C2×Dic1112yes—
251#103C2×Dic1112yes—
252#103C2×Dic1112yes—
253#103C2×Dic1112yes—
254C22⋊C8—112no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257C22⋊C8C2×Dic1112yes—
258#97—222no—
259#97—221no—
260#97—221no—
261C4×C8—111no—
262C4×C8—111no—
263C4×C8—111no—
264C4×C8—111no—
265C4×C8—222no—
266C4×C8—222no—
267C4×C8—222no—
268C4×C8—221no—
269C4×C8C22×D1111yescharacteristic
270C4×C8C22×D1111yescharacteristic
271C2×C11—41no—
272C2×C11#292911yescharacteristic
273C2×C11#295011yescharacteristic
274C2×C11#295611yescharacteristic
275C2×Q8—24no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8C22×Dic1112yes—
279C2×Q8C22×Dic1112yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C22×Dic1111yescharacteristic
285Q16—24no—
286Q16—24no—
287M16—442no—
288C2×C8—112no—
289C2×C8—112no—
290C2×C8—221no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—221no—
294C2×C8C22×Dic1112yes—
295C2×C8C22×Dic1112yes—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4C22×Dic1112yes—
305C4⋊C4C22×Dic1112yes—
306C22⋊C4—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C22×Dic1111yescharacteristic
313C42C23×D1111yescharacteristic
314C11#1792511yescharacteristic, complemented, Sylow
315C23D4×Dic1111yescharacteristic
316Q8—24no—
317Q8—22no—
318Q8—22no—
319Q8—22no—
320Q8—81no—
321Q8#6700114yes—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4D4×Dic1111yescharacteristic
332C2×C4D4×Dic1111yescharacteristic
333C2×C4D4×Dic1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C2×C4C2×#434111yescharacteristic
336C2×C4C23×Dic1111yescharacteristic
337C8—22no—
338C8—22no—
339C8—222no—
340C8—222no—
341C8—222no—
342C8—441no—
343C8—442no—
344C8—442no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22C2×D4×Dic1111yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—42no—
357C4#1062329712yes—
358C4C2×#6700112yes—
359C2—41no—
360C2#1307731111yescharacteristic
361C2#1307748411yescharacteristic
362C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3104C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#3104D11
hypocenterC11#17925
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #13067488C2semidirect
4. #13067467C2semidirect
5. #13067435C2semidirect
6. Q16×C11⋊C8C2semidirect
314. C11#17925semidirect

Maximal subgroups

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

subgroupindex
#130777112
#130776972
#130674882
#130674672
#130674352
Q16×C11⋊C82
#130673962
#130670632
#130670372
#130669112
C11×#31042
#1792511