Finite Group Databasebeta

← #14908631

Subgroups — #14908631

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078272C211yesmaximal, characteristic
2#13077213C211yesmaximal, characteristic
3#13070827C212yesmaximal, complemented
4#13070826C212yesmaximal, complemented
5#13070820C212yesmaximal, complemented
6#13070815C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070335C211yesmaximal, characteristic, complemented
9C2×#10622141C211yesmaximal, characteristic, complemented
10#13070229C211yesmaximal, characteristic
11C11×#2158C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14#10623057—21no—
15#10623054—21no—
16C22×C11×C16C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622617—21no—
22#10622608—21no—
23#10622500C2212yes—
24#10622500C2212yes—
25#10622493C2212yes—
26D11×#107C2212yes—
27#10622481—22no—
28#10622474—22no—
29C11×#367C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#366C2211yescharacteristic
32C11×#366C2211yescharacteristic
33(C2×D11)⋊C16C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622141C2212yes—
36#10622141C2212yes—
37#10622130C2212yes—
38#10622130C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×#4339D411yescharacteristic
42C22×Dic22—21no—
43C22×C8×C11C2311yescharacteristic
44C11×#117—21no—
45C11×#117—21no—
46C2×C4⋊Dic11—21no—
47C2×#4318D411yescharacteristic
48C2×Dic44—22no—
49C2×Dic44—22no—
50C2×Dic44—21no—
51C2×Dic44C2312yes—
52#66954—22no—
53#66954—22no—
54C2×#4313D412yes—
55C2×C8×D11C2312yes—
56#66950—22no—
57#66950—22no—
58#66945—22no—
59C4⋊C4×D11—22no—
60#66939—42no—
61(C22⋊D11)⋊C4—42no—
62#66928—41no—
63C4×D44—41no—
64#66922—41no—
65C4×Dic22—41no—
66C2×C11×C16—22no—
67C2×C11×C16C2311yescharacteristic
68C2×C11×C16C2311yescharacteristic
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#107C2311yescharacteristic
72C11×#107C2311yescharacteristic
73C11×#106—21no—
74C11×#106—21no—
75#66882—21no—
76#66882C2312yes—
77#66876—22no—
78C2×C11⋊C16C2312yes—
79#66874—22no—
80#66874—22no—
81#66872—22no—
82#66871—22no—
83#33651—111nomaximal, Sylow
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11D812yes—
86C22×Dic11—41no—
87C22×Dic11—41no—
88#4339—22no—
89#4339—22no—
90C2×D44D811yescharacteristic
91C2×C4×D11—42no—
92C2×C4×D11C2×D412yes—
93C2×Dic22—22no—
94C2×Dic22—42no—
95C2×Dic22—41no—
96C2×Dic22—42no—
97C2×Dic22D811yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11#4112yes—
100C2×C8×C11#4112yes—
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11—41no—
109C42×C11—41no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—22no—
114C4⋊Dic11—42no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119#4318—22no—
120C2×C11⋊C8C2×D412yes—
121Dic44—22no—
122Dic44—22no—
123Dic44—42no—
124#4313—24no—
125C8×D11—22no—
126C8×D11—22no—
127C11×C16—21no—
128C11×C16—21no—
129C11⋊C16—22no—
130#3059—111no—
131#2913—111no—
132#2237—112no—
133#2237—112no—
134#2236—112no—
135#2235—112no—
136#2159—111no—
137#2158D1111yescharacteristic, complemented
138#2141—111no—
139C2×#358—111no—
140#2113—111no—
141C23×C11C2×D811yescharacteristic
142C22×D11C2×D812yes—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11#12312yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11#13712yes—
150C2×C4×C11C22×D411yescharacteristic
151C22⋊D11—24no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—82no—
155C2×Dic11—161no—
156C2×Dic11C2×D812yes—
157D44—22no—
158C4×D11—22no—
159C4×D11—22no—
160C4×D11—162no—
161Dic22—22no—
162Dic22—42no—
163Dic22—42no—
164Dic22—82no—
165C8×C11#12312yes—
166C8×C11C2×#4111yescharacteristic
167C8×C11C2×#4111yescharacteristic
168C11⋊C8—22no—
169C22×Q16—111no—
170C2×#131—111no—
171#536—221no—
172#520—221no—
173C2×M32—111no—
174C22×C16C2×D1111yescharacteristic
175#470—222no—
176#467—112no—
177#467—112no—
178#428—222no—
179#428—221no—
180#427—112no—
181#427C2×D1111yescharacteristic
182#427C2×D1111yescharacteristic
183C2×#107—111no—
184C2×#107—112no—
185#419—221no—
186#367—112no—
187#367C2×D1111yescharacteristic
188#367C2×D1111yescharacteristic
189#366—112no—
190#366C2×D1111yescharacteristic
191#366C2×D1111yescharacteristic
192#358—112no—
193#358—112no—
194#358—112no—
195#358—112no—
196C22⋊C16—112no—
197C22⋊C16—112no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#48012yes—
201C22×C11C22×D811yescharacteristic
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#48012yes—
210C4×C11C2×#12311yescharacteristic
211C4×C11C2×#13711yescharacteristic
212Dic11—22no—
213Dic11—82no—
214Dic11—82no—
215C2×#41—111no—
216C22×Q8—221no—
217C2×Q16—112no—
218C2×Q16—222no—
219C2×Q16—221no—
220C2×Q16—222no—
221#131—222no—
222#131—222no—
223C2×M16—111no—
224C2×M16—112no—
225C22×C8—112no—
226C22×C8C22×D1111yescharacteristic
227C4⋊Q8—441no—
228#124—441no—
229#123—442no—
230C22⋊Q8—222no—
231C22⋊Q8—222no—
232C4×Q8—441no—
233C4×D4—441no—
234C4×D4—442no—
235#117—21no—
236#117—21no—
237#117—222no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—221no—
240M32—222no—
241C2×C16—22no—
242C2×C16—112no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245#107—112no—
246#107—222no—
247#107—221no—
248#107C22×D1111yescharacteristic
249#107C22×D1111yescharacteristic
250#107C22×D1111yescharacteristic
251#107C22×D1111yescharacteristic
252#106—21no—
253#106—21no—
254#106—222no—
255#103—222no—
256#103—222no—
257C2×C11—22no—
258C2×C11C2×#48011yescharacteristic
259C2×C11#341611yescharacteristic
260C2×C11#341711yescharacteristic
261D11—42no—
262#41—222no—
263#41—222no—
264C2×Q8—111no—
265C2×Q8—222no—
266C2×Q8—441no—
267C2×Q8—442no—
268C2×Q8—442no—
269C2×D4—112no—
270C2×D4—111no—
271C22×C4—112no—
272C22×C4—442no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4D4×D1111yescharacteristic
276Q16—222no—
277Q16—222no—
278Q16—442no—
279M16—222no—
280M16—224no—
281C2×C8—112no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8#433912yes—
285C2×C8D4×D1111yescharacteristic
286C2×C8#434312yes—
287C2×C8C23×D1111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—222no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C42—41no—
303C42—41no—
304C42—442no—
305C16—21no—
306C16—21no—
307C16—222no—
308C11#3365111yescharacteristic, complemented, Sylow
309C23—112no—
310C23D8×D1111yescharacteristic
311Q8—222no—
312Q8—442no—
313Q8—442no—
314Q8—882no—
315D4—224no—
316D4—222no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—112no—
322C2×C4—222no—
323C2×C4—222no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—882no—
327C2×C4—1762no—
328C2×C4—1761no—
329C2×C4#6694712yes—
330C2×C4D8×D1111yescharacteristic
331C2×C4#6697112yes—
332C2×C4C2×D4×D1111yescharacteristic
333C8—222no—
334C8#6694712yes—
335C8C2×#433911yescharacteristic
336C8C2×#434311yescharacteristic
337C22—21no—
338C22—21no—
339C22—222no—
340C22—222no—
341C22—222no—
342C22#1062249512yes—
343C22C2×D8×D1111yescharacteristic
344C4—81no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—222no—
349C4—882no—
350C4—882no—
351C4#1062249512yes—
352C4C2×#6694711yescharacteristic
353C4C2×#6697111yescharacteristic
354C2—22no—
355C2—442no—
356C2C2×#1062249511yescharacteristic
357C2#1308175911yescharacteristic
358C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2158C2
socleC22×C11C22×D8
prime radicalC2×#4339D4
hypercenter#2158D11
hypocenterC11#33651
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
3. #13070827C2semidirect
4. #13070826C2semidirect
5. #13070820C2semidirect
6. #13070815C2semidirect
7. #13070405C2semidirect
8. #13070335C2semidirect
9. C2×#10622141C2semidirect
11. C11×#2158C2semidirect
137. #2158D11semidirect
308. C11#33651semidirect

Maximal subgroups

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

subgroupindex
#130782722
#130772132
#130708272
#130708262
#130708202
#130708152
#130704052
#130703352
C2×#106221412
#130702292
C11×#21582
#3365111