Finite Group Databasebeta

← #14756000

Subgroups — #14756000

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071234C211yesmaximal, characteristic
2#13070973C211yesmaximal, characteristic
3#13069203C214yesmaximal, complemented
4#13069196C214yesmaximal, complemented
5#13068335C211yesmaximal, characteristic
6#13068335C211yesmaximal, characteristic
7#13068333C211yesmaximal, characteristic
8#13068312C211yesmaximal, characteristic
9C22×C11×#106C211yesmaximal, characteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×C11×#106C418yescomplemented
18C2×C11×#106C2212yes—
19C2×C11×#106C2212yes—
20#10622825—22no—
21C4×C22⋊Dic11—22no—
22#10622598—22no—
23#10622598C2214yes—
24C4⋊C4×Dic11—22no—
25C4⋊C4×Dic11C2214yes—
26#10622189C2212yes—
27#10622189C2212yes—
28#10622188C2212yes—
29#10622188C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32C23×C4×C11—21no—
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C8×C11—22no—
36C22×C8×C11—22no—
37C22×C8×C11C2×C414yes—
38C22×C8×C11C2311yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2×C414yes—
45C2×C11×C4⋊C4C2×C414yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11D412yes—
51#66979—22no—
52#66979—22no—
53#66979—22no—
54#66979—22no—
55#66979—22no—
56#66979Q814yes—
57C2×C4⋊Dic11—24no—
58C2×C4⋊Dic11D412yes—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—24no—
64C2×C4×Dic11C2312yes—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C22×C11⋊C8C2312yes—
69C11×#106C2×C418yes—
70C11×#106C2×C418yes—
71C11⋊#95—24no—
72C11⋊#95—24no—
73#21038—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—82no—
80C22×C4×C11—82no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11#4112yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11C2×D414yes—
92C2×C8×C11—28no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11C22×C412yes—
98C2×C8×C11C22×C412yes—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4C22×C414yes—
104C11×C4⋊C4C22×C414yes—
105C22⋊Dic11—24no—
106C22⋊Dic11—24no—
107C22⋊Dic11—42no—
108C4⋊Dic11—24no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—84no—
113C4⋊Dic11C2×Q814yes—
114C4×Dic11—24no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—42no—
118C4×Dic11—84no—
119#4318—44no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C22×#106D1111yescharacteristic
124#2316—111no—
125#2274—111no—
126#1920—114no—
127#1919—114no—
128#1736—111no—
129#1736—111no—
130#1735—111no—
131#1729—111no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11C4×D412yes—
135C23×C11C22⋊Q812yes—
136C23×C11#12312yes—
137C23×C11C22×D411yescharacteristic
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—44no—
141C2×C4×C11—44no—
142C2×C4×C11—84no—
143C2×C4×C11—84no—
144C2×C4×C11#11714yes—
145C2×C4×C11C4×D412yes—
146C2×C4×C11C4×Q814yes—
147C2×C4×C11C22⋊Q812yes—
148C2×C4×C11#12312yes—
149C2×C4×C11#12514yes—
150C2×C4×C11#12614yes—
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C22×Q811yescharacteristic
153C2×C4×C11C2×#4111yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×C4×C11C2×#4111yescharacteristic
157C2×Dic11—24no—
158C2×Dic11—24no—
159C2×Dic11—24no—
160C2×Dic11—24no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C8×C11—22no—
167C8×C11—22no—
168C11⋊C8—42no—
169C22×M16—111no—
170C23×C8C2×D1111yescharacteristic
171C2×#117—111no—
172C2×#117—111no—
173C2×#117—111no—
174C22×C4⋊C4C2×D1111yescharacteristic
175C22×C4⋊C4C2×D1111yescharacteristic
176C2×#106Dic1118yescomplemented
177C2×#106C2×D1112yes—
178C2×#106C2×D1112yes—
179#389—114no—
180#389—222no—
181#380—222no—
182C4×C4⋊C4—114no—
183C4×C4⋊C4—222no—
184C4×C22⋊C4—222no—
185#340—112no—
186#340—112no—
187#340—114no—
188#340—114no—
189#336—112no—
190#336—112no—
191C22×C11—24no—
192C22×C11—24no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11#38714yes—
196C22×C11C2×C4×D411yescharacteristic
197C22×C11C2×C22⋊Q811yescharacteristic
198C22×C11C2×#12311yescharacteristic
199C22×C11#57712yes—
200C22×C11#57712yes—
201C4×C11—44no—
202C4×C11—44no—
203C4×C11#38714yes—
204C4×C11C2×#11711yescharacteristic
205C4×C11C2×C4×Q811yescharacteristic
206C4×C11C2×#12511yescharacteristic
207C4×C11C2×#12611yescharacteristic
208Dic11—44no—
209Dic11—44no—
210Dic11—82no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4C22×D1111yescharacteristic
214C2×M16—222no—
215C2×M16—222no—
216C2×M16—222no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—112no—
220C22×C8C2×Dic1114yes—
221C22×C8C22×D1111yescharacteristic
222C22×C8C22×D1111yescharacteristic
223#117—114no—
224#117—222no—
225#117—222no—
226#117—222no—
227#117—222no—
228#117—222no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4C2×Dic1114yes—
238C2×C4⋊C4C2×Dic1114yes—
239C2×C4⋊C4C22×D1112yes—
240C2×C4⋊C4C22×D1112yes—
241C2×C22⋊C4—112no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42—112no—
245C2×C42—221no—
246C2×C42—221no—
247C2×C42—224no—
248#106C2×Dic1118yes—
249#106C2×Dic1118yes—
250#95—224no—
251#95—224no—
252C2×C11—24no—
253C2×C11C2×#38711yescharacteristic
254C2×C11#294911yescharacteristic
255C2×C11#294911yescharacteristic
256C2×C11#308412yes—
257C2×C11#309912yes—
258C24D4×D1111yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—82no—
264C22×C4—82no—
265C22×C4—114no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4#433912yes—
269C22×C4#433912yes—
270C22×C4D4×D1111yescharacteristic
271C22×C4#434112yes—
272C22×C4Q8×D1112yes—
273C22×C4#434312yes—
274C22×C4C22×Dic1112yes—
275C22×C4C23×D1111yescharacteristic
276M16—444no—
277C2×C8—28no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8C22×Dic1112yes—
286C2×C8C22×Dic1112yes—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—114no—
292C4⋊C4—224no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—884no—
297C4⋊C4C22×Dic1114yes—
298C4⋊C4C22×Dic1114yes—
299C22⋊C4—224no—
300C22⋊C4—224no—
301C22⋊C4—442no—
302C42—224no—
303C42—222no—
304C42—222no—
305C42—442no—
306C42—884no—
307C11#2103811yescharacteristic, complemented, Sylow
308C23—22no—
309C23—22no—
310C23#6694712yes—
311C23#6694912yes—
312C23D4×Dic1112yes—
313C23C2×D4×D1111yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—84no—
319C2×C4—84no—
320C2×C4—224no—
321C2×C4—224no—
322C2×C4—224no—
323C2×C4—224no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4#6694214yes—
330C2×C4#6694712yes—
331C2×C4#6694912yes—
332C2×C4#6695114yes—
333C2×C4#6697914yes—
334C2×C4D4×Dic1112yes—
335C2×C4Q8×Dic1114yes—
336C2×C4C2×#433911yescharacteristic
337C2×C4C2×#433911yescharacteristic
338C2×C4C2×#434111yescharacteristic
339C2×C4C2×Q8×D1111yescharacteristic
340C2×C4C2×#434311yescharacteristic
341C2×C4C23×Dic1111yescharacteristic
342C8—22no—
343C8—22no—
344C8—442no—
345C22—24no—
346C22—24no—
347C22—22no—
348C22—22no—
349C22#1062259414yes—
350C22C2×#6694711yescharacteristic
351C22C2×#6694911yescharacteristic
352C22#1062329312yes—
353C22#1062329312yes—
354C22C2×D4×Dic1111yescharacteristic
355C4—44no—
356C4—44no—
357C4—444no—
358C4—444no—
359C4—882no—
360C4#1062259414yes—
361C4C2×#6694211yescharacteristic
362C4C2×#6695111yescharacteristic
363C4C2×#6697911yescharacteristic
364C4C2×Q8×Dic1111yescharacteristic
365C2—24no—
366C2C2×#1062259411yescharacteristic
367C2#1307747611yescharacteristic
368C2#1307747611yescharacteristic
369C2#1307848312yes—
370C2#1307861012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#106C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#106D11
hypocenterC11#21038
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #13069203C2semidirect
4. #13069196C2semidirect
17. C2×C11×#106C4semidirect
176. C2×#106Dic11semidirect
307. C11#21038semidirect

Maximal subgroups

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

subgroupindex
#130712342
#130709732
#130692032
#130691962
#130683352
#130683332
#130683122
C22×C11×#1062
#2103811