Finite Group Databasebeta

← #14757306

Subgroups — #14757306

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66886C211yesmaximal, characteristic
2#13077179C211yesmaximal, characteristic
3C2×#10622732C211yesmaximal, characteristic
4#13077034C211yesmaximal, characteristic
5#13069388C218yesmaximal, complemented
6#13068343C211yesmaximal, characteristic
7C2×#10622196C211yesmaximal, characteristic
8C2×C11×#430C211yesmaximal, characteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#430—24no—
17C2×C11×#108C2214yes—
18C2×#66886—24no—
19C2×#66886C2214yes—
20#10622735—22no—
21#10622732—22no—
22#10622732C414yes—
23#10622732C414yes—
24#10622731C2214yes—
25M16×Dic11C2214yes—
26#10622715—22no—
27#10622714—22no—
28C2×Dic11⋊C8C2214yes—
29#10622196C2214yes—
30#10622190C2214yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—21no—
33C2×C11×M16—22no—
34C2×C11×M16—22no—
35C2×C11×M16—22no—
36C2×C11×M16—21no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16C2×C412yes—
40C2×C11×M16C2×C412yes—
41C2×C11×M16D414yes—
42C2×C11×M16C2312yes—
43C2×C11×M16C2312yes—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C22×C8×C11C2312yes—
47C2×C22⋊Dic11Q812yes—
48#66979C2×C412yes—
49#66979C2×C412yes—
50#66979D412yes—
51#66979D412yes—
52C2×C4⋊Dic11Q812yes—
53C2×C4×Dic11C2312yes—
54C2×#4318—21no—
55C2×#4318—22no—
56C2×#4318—21no—
57C2×#4318—22no—
58C2×#4318—22no—
59C2×#4318Q814yes—
60C2×#4318C2312yes—
61C2×#4318C2312yes—
62C22×C11⋊C8—21no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8—22no—
65C22×C11⋊C8—21no—
66C22×C11⋊C8C2×C412yes—
67C22×C11⋊C8C2×C412yes—
68C22×C11⋊C8C2312yes—
69C11×#108—28no—
70#66886—28no—
71#66879—24no—
72Dic11⋊C8—28no—
73Dic11⋊C8C2×C4116yes—
74C8×Dic11—24no—
75#21178—111nomaximal, Sylow
76C24×C11C2×Q811yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11C2×Q814yes—
88C11×M16—24no—
89C11×M16—24no—
90C11×M16—24no—
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—42no—
95C11×M16C2×D414yes—
96C2×C8×C11—24no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—42no—
102C2×C8×C11C22×C414yes—
103C22⋊Dic11C4⋊C414yes—
104C22⋊Dic11C4⋊C414yes—
105C4⋊Dic11C4⋊C414yes—
106C4⋊Dic11C4⋊C414yes—
107C4×Dic11C22×C414yes—
108C4×Dic11C2×D414yes—
109#4318—24no—
110#4318—22no—
111#4318—22no—
112#4318—22no—
113#4318—42no—
114#4318C2×Q814yes—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8C22×C414yes—
124C2×#430D1111yescharacteristic
125C22×#108—111no—
126#2905—111no—
127C2×#424—111no—
128#2873—111no—
129#1950—118no—
130#1738—111no—
131C2×#341—111no—
132C23×C11—42no—
133C23×C11C2×C4⋊C411yescharacteristic
134C23×C11C2×C4⋊C411yescharacteristic
135C23×C11#12512yes—
136C23×C11C4⋊Q812yes—
137C23×C11C22×Q811yescharacteristic
138C2×C4×C11C2×C4⋊C411yescharacteristic
139C2×C4×C11C2×C4⋊C411yescharacteristic
140C2×C4×C11C4×D412yes—
141C2×C4×C11C4×D412yes—
142C2×C4×C11C4×Q812yes—
143C2×C4×C11C4×Q812yes—
144C2×C4×C11#12112yes—
145C2×C4×C11#12112yes—
146C2×C4×C11C22⋊Q812yes—
147C2×C4×C11C22⋊Q812yes—
148C2×C4×C11#12512yes—
149C2×C4×C11C4⋊Q812yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×Q811yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×Dic11—44no—
157C2×Dic11C2×C4⋊C418yes—
158C8×C11—24no—
159C8×C11—24no—
160C8×C11—42no—
161C11⋊C8—24no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164C22×M16—111no—
165C22×M16—111no—
166C22×M16C2×D1111yescharacteristic
167C22×M16C2×D1111yescharacteristic
168C22×M16C2×D1111yescharacteristic
169C23×C8—111no—
170C2×#117—111no—
171#430—24no—
172C2×#108—114no—
173C2×#108—224no—
174C2×#108C2×D1114yes—
175#424—114no—
176#424—114no—
177#424—222no—
178#424—222no—
179#423—114no—
180C2×C4⋊C8—114no—
181#405—222no—
182#405—222no—
183C4×M16—114no—
184#341—114no—
185#341—114no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11#38912yes—
192C22×C11#38912yes—
193C22×C11C22×C4⋊C411yescharacteristic
194C22×C11C2×#12511yescharacteristic
195C22×C11C2×C4⋊Q811yescharacteristic
196C4×C11#38912yes—
197C4×C11#38912yes—
198C4×C11C2×C4×D411yescharacteristic
199C4×C11C2×C4×Q811yescharacteristic
200C4×C11C2×#12111yescharacteristic
201C4×C11C2×C22⋊Q811yescharacteristic
202Dic11—28no—
203C23×C4C22×D1111yescharacteristic
204C2×M16—22no—
205C2×M16—21no—
206C2×M16—22no—
207C2×M16—22no—
208C2×M16—21no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—114no—
212C2×M16—112no—
213C2×M16—112no—
214C2×M16—222no—
215C2×M16—221no—
216C2×M16—221no—
217C2×M16—222no—
218C2×M16—222no—
219C2×M16C4×D1112yes—
220C2×M16C4×D1112yes—
221C2×M16C22⋊D1114yes—
222C2×M16C22×D1112yes—
223C2×M16C22×D1112yes—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—112no—
227C22×C8—112no—
228C22×C8—112no—
229C22×C8—222no—
230C22×C8—221no—
231C22×C8—222no—
232C22×C8—221no—
233C22×C8C22×D1112yes—
234#117—112no—
235#117—112no—
236#117—112no—
237#117—112no—
238C2×C4⋊C4—112no—
239C2×C22⋊C4—112no—
240C2×C42—112no—
241#108—28no—
242#108—228no—
243C4⋊C8—1116no—
244C4⋊C8—228no—
245#97—224no—
246C4×C8—224no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—22no—
250C2×C11—22no—
251C2×C11C2×#38911yescharacteristic
252C2×C11#291612yes—
253C24Q8×D1111yescharacteristic
254C22×C4—114no—
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4#433912yes—
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4#434112yes—
261C22×C4Q8×D1112yes—
262C22×C4Q8×D1111yescharacteristic
263C22×C4C2×C22⋊D1112yes—
264C22×C4C23×D1111yescharacteristic
265M16—24no—
266M16—24no—
267M16—24no—
268M16—22no—
269M16—22no—
270M16—22no—
271M16—42no—
272M16—114no—
273M16—224no—
274M16—222no—
275M16—222no—
276M16—222no—
277M16—442no—
278M16C2×C22⋊D1114yes—
279C2×C8—24no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—42no—
285C2×C8—114no—
286C2×C8—224no—
287C2×C8—224no—
288C2×C8—224no—
289C2×C8—222no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—442no—
294C2×C8C2×C4×D1114yes—
295C4⋊C4—114no—
296C4⋊C4—114no—
297C22⋊C4—114no—
298C22⋊C4—114no—
299C42—114no—
300C42—114no—
301C11#2117811yescharacteristic, complemented, Sylow
302C23—42no—
303C23#6694212yes—
304C23C4⋊C4×D1111yescharacteristic
305C23C4⋊C4×D1111yescharacteristic
306C23#6699712yes—
307C23C2×Q8×D1111yescharacteristic
308C2×C4—118no—
309C2×C4—444no—
310C2×C4#6694012yes—
311C2×C4#6694012yes—
312C2×C4#6694212yes—
313C2×C4C4⋊C4×D1111yescharacteristic
314C2×C4C4⋊C4×D1111yescharacteristic
315C2×C4#6694912yes—
316C2×C4#6694912yes—
317C2×C4C4×C22⋊D1112yes—
318C2×C4C4×C22⋊D1112yes—
319C2×C4#6699212yes—
320C2×C4#6699212yes—
321C2×C4#6699712yes—
322C2×C4C22×C4×D1111yescharacteristic
323C2×C4C2×#433911yescharacteristic
324C2×C4C2×D4×D1111yescharacteristic
325C2×C4C2×#434111yescharacteristic
326C2×C4C2×Q8×D1111yescharacteristic
327C2×C4C22×C22⋊D1111yescharacteristic
328C8—24no—
329C8—24no—
330C8—42no—
331C8—224no—
332C8—224no—
333C8—442no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—42no—
338C22—42no—
339C22#1062258512yes—
340C22#1062258512yes—
341C22C2×#6694211yescharacteristic
342C22C2×C4⋊C4×D1111yescharacteristic
343C22C2×#6699711yescharacteristic
344C4—228no—
345C4#1062258512yes—
346C4#1062258512yes—
347C4C2×#6694011yescharacteristic
348C4C2×#6694911yescharacteristic
349C4C2×C4×C22⋊D1111yescharacteristic
350C4C2×#6699211yescharacteristic
351C2—21no—
352C2—21no—
353C2—22no—
354C2—22no—
355C2C2×#1062258511yescharacteristic
356C2#1307722612yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC22×C11C22×C4⋊C4
prime radicalC24×C11C2×Q8
cosocleC22×C4×C11C24
hypercenterC2×#430D11
hypocenterC11#21178
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
5. #13069388C2semidirect
301. C11#21178semidirect

Maximal subgroups

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

subgroupindex
C22×#668862
#130771792
C2×#106227322
#130770342
#130693882
#130683432
C2×#106221962
C2×C11×#4302
#2117811