Finite Group Databasebeta

← #14644166

Subgroups — #14644166

Order 2816.

568 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#13077246C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13066527C211yesmaximal, characteristic, complemented
5#13066526C211yesmaximal, characteristic, complemented
6#13066526C211yesmaximal, characteristic, complemented
7C11×#1307C211yesmaximal, characteristic, complemented
8C2×M16×D11C412yes—
9C2×C42×D11C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622731C412yes—
14#10622539C2211yescharacteristic
15#10622539C2211yescharacteristic
16#10622537C2211yescharacteristic
17#10622450—21no—
18#10622450—21no—
19#10622450—21no—
20#10622448—21no—
21#10622446—21no—
22D11×C4⋊C8—21no—
23D11×C4⋊C8—21no—
24D11×C4⋊C8—21no—
25#10622339C412yes—
26D11×C22⋊C8C412yes—
27#10622332C412yes—
28#10622331C412yes—
29#10622320—21no—
30#10622318—21no—
31#10622318—21no—
32D11×#97—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11C2×C411yescharacteristic
36C2×C11×M16C2×C412yes—
37C2×C42×C11C2311yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×#4318C2×C412yes—
42M16×D11—44no—
43C2×#4313—22no—
44C2×#4313—22no—
45C2×C8×D11—22no—
46C2×C8×D11—22no—
47C42×D11D411yescharacteristic
48C42×D11D411yescharacteristic
49C42×D11D411yescharacteristic
50C42×D11D411yescharacteristic
51C42×D11D411yescharacteristic
52C42×D11D411yescharacteristic
53C42×D11Q811yescharacteristic
54C42×D11Q811yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C22⋊C8C2×C412yes—
60C11×C22⋊C8C2×C412yes—
61C11×#97—21no—
62C11×#97—21no—
63C22⋊(C11⋊C8)C2×C412yes—
64C22⋊(C11⋊C8)C2×C412yes—
65(C2×D11)⋊C8—22no—
66(C2×D11)⋊C8—22no—
67#66879—22no—
68Dic11⋊C8—22no—
69Dic11⋊C8—22no—
70Dic11⋊C8—22no—
71Dic11⋊C8—22no—
72C8×Dic11—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77#66867—21no—
78#66867—21no—
79#8121—111nomaximal, Sylow
80C23×D11C4211yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×Dic11C4211yescharacteristic
85C22×Dic11C4211yescharacteristic
86C22×Dic11C4211yescharacteristic
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—42no—
90C2×C4×D11—42no—
91C2×C4×D11C22⋊C411yescharacteristic
92C2×C4×D11C22⋊C411yescharacteristic
93C2×C4×D11C22⋊C411yescharacteristic
94C2×C4×D11C22⋊C411yescharacteristic
95C2×C4×D11C22⋊C411yescharacteristic
96C2×C4×D11C22⋊C411yescharacteristic
97C2×C4×D11C4⋊C411yescharacteristic
98C2×C4×D11C4⋊C411yescharacteristic
99C2×C4×D11C4⋊C411yescharacteristic
100C2×C4×D11C4⋊C411yescharacteristic
101C2×C4×D11C4⋊C411yescharacteristic
102C2×C4×D11C4⋊C411yescharacteristic
103C11×M16—42no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×Q811yescharacteristic
111C4×Dic11C22⋊C411yescharacteristic
112C4×Dic11C22⋊C411yescharacteristic
113C4×Dic11C22⋊C411yescharacteristic
114C4×Dic11C22⋊C411yescharacteristic
115C4×Dic11C22⋊C411yescharacteristic
116C4×Dic11C22⋊C411yescharacteristic
117C4×Dic11C4⋊C411yescharacteristic
118C4×Dic11C4⋊C411yescharacteristic
119C4×Dic11C4⋊C411yescharacteristic
120C4×Dic11C4⋊C411yescharacteristic
121C4×Dic11C4⋊C411yescharacteristic
122C4×Dic11C4⋊C411yescharacteristic
123#4318—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127#4313—44no—
128#4313—44no—
129C8×D11—44no—
130C8×D11—44no—
131#2920—111no—
132C2×#432—111no—
133C2×#423—111no—
134#1307—111no—
135#1307—111no—
136#1307—111no—
137#1307D1111yescharacteristic, complemented
138C23×C11C2×C4211yescharacteristic
139C22×D11—22no—
140C22×D11—22no—
141C22×D11—41no—
142C22×D11#9511yescharacteristic
143C22×D11#9511yescharacteristic
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11C2×C4⋊C411yescharacteristic
152C2×C4×C11C2×C4⋊C411yescharacteristic
153C2×C4×C11C2×C4⋊C411yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—41no—
157C2×Dic11#9511yescharacteristic
158C2×Dic11#9511yescharacteristic
159C2×Dic11#9511yescharacteristic
160C2×Dic11#9511yescharacteristic
161C2×Dic11#9511yescharacteristic
162C2×Dic11#9511yescharacteristic
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—21no—
167C4×D11—21no—
168C4×D11—22no—
169C4×D11—22no—
170C4×D11—22no—
171C4×D11—41no—
172C4×D11—41no—
173C4×D11—41no—
174C4×D11—41no—
175C4×D11#10012yes—
176C4×D11#10112yes—
177C8×C11—42no—
178C8×C11—42no—
179C8×C11—42no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C22×M16—112no—
184C22×C42—111no—
185#432—111no—
186#432—111no—
187#432—112no—
188#432—221no—
189#432—221no—
190#432—221no—
191#432C2×D1111yescharacteristic
192#432C2×D1111yescharacteristic
193#431—112no—
194#431—221no—
195#423—112no—
196#423—111no—
197#423—221no—
198#423—221no—
199#423—221no—
200#423C2×D1111yescharacteristic
201C2×C4⋊C8—221no—
202C2×C4⋊C8—221no—
203C2×C4⋊C8—221no—
204#407—112no—
205C2×C22⋊C8—112no—
206C4×M16—221no—
207C2×#97—221no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11C2×#9511yescharacteristic
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—21no—
216C2×D11—44no—
217C2×D11#34312yes—
218C2×D11#34412yes—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11C2×#10011yescharacteristic
225C4×C11C2×#10111yescharacteristic
226Dic11—21no—
227Dic11—21no—
228Dic11—21no—
229Dic11—21no—
230Dic11#34312yes—
231Dic11#34412yes—
232C23×C4—111no—
233C23×C4—111no—
234C23×C4—111no—
235C2×M16—112no—
236C2×M16—222no—
237C2×M16—222no—
238C2×M16—444no—
239C2×M16C4×D1112yes—
240C22×C8—222no—
241C22×C8—222no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—111no—
246C2×C42—111no—
247C2×C42—111no—
248C2×C42—111no—
249C2×C42—111no—
250C2×C42—111no—
251C2×C42—111no—
252C2×C42—111no—
253C2×C42C22×D1111yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—222no—
259C4⋊C8—222no—
260C4⋊C8—222no—
261C4⋊C8—222no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C22⋊C8—112no—
267C22⋊C8—112no—
268C22⋊C8—222no—
269C22⋊C8—222no—
270C22⋊C8C4×D1112yes—
271C22⋊C8C4×D1112yes—
272#97—21no—
273#97—21no—
274#97—222no—
275#97—221no—
276#97—221no—
277C4×C8—222no—
278C2×C11—41no—
279C2×C11C2×#34311yescharacteristic
280C2×C11C2×#34411yescharacteristic
281C2×C11C2×#34411yescharacteristic
282D11—22no—
283D11—22no—
284C24—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4C2×C4×D1111yescharacteristic
305C22×C4C2×C4×D1111yescharacteristic
306C22×C4C2×C4×D1111yescharacteristic
307M16—42no—
308M16—444no—
309M16—444no—
310M16—442no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—444no—
318C2×C8—444no—
319C42—111no—
320C42—111no—
321C42—111no—
322C42—111no—
323C42—111no—
324C42—111no—
325C42—111no—
326C42—111no—
327C42—111no—
328C42—111no—
329C42—111no—
330C42—111no—
331C42D4×D1111yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42Q8×D1111yescharacteristic
335C11#812111yescharacteristic, complemented, Sylow
336C23—111no—
337C23—111no—
338C23—222no—
339C23—222no—
340C23—441no—
341C23C42×D1111yescharacteristic
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—111no—
347C2×C4—111no—
348C2×C4—112no—
349C2×C4—112no—
350C2×C4—111no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4C22⋊C4×D1111yescharacteristic
370C2×C4C22⋊C4×D1111yescharacteristic
371C2×C4C22⋊C4×D1111yescharacteristic
372C2×C4C4⋊C4×D1111yescharacteristic
373C2×C4C4⋊C4×D1111yescharacteristic
374C2×C4C4⋊C4×D1111yescharacteristic
375C8—42no—
376C8—42no—
377C8—42no—
378C8—442no—
379C8—442no—
380C8—442no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—112no—
385C22—112no—
386C22—221no—
387C22—221no—
388C22—221no—
389C22—221no—
390C22—444no—
391C22D11×#9511yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—112no—
398C4—112no—
399C4—221no—
400C4—221no—
401C4—221no—
402C4—221no—
403C4D11×#10011yescharacteristic
404C4D11×#10111yescharacteristic
405C2—41no—
406C2—222no—
407C2—222no—
408C2D11×#34311yescharacteristic
409C2D11×#34411yescharacteristic
410C2D11×#34411yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11C2×#95
prime radicalC23×D11C42
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8121
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
4. #13066527C2semidirect
5. #13066526C2semidirect
6. #13066526C2semidirect
7. C11×#1307C2semidirect
137. #1307D11semidirect
335. C11#8121semidirect

Maximal subgroups

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

subgroupindex
#130772462
D11×#4322
D11×#4232
#130665272
#130665262
C11×#13072
#812111