Finite Group Databasebeta

← #14908629

Subgroups — #14908629

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#13078271C211yesmaximal, characteristic
2#13077216C211yesmaximal, characteristic
3#13070825C212yesmaximal, complemented
4#13070825C212yesmaximal, complemented
5#13070819C212yesmaximal, complemented
6#13070814C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8#13070400C211yesmaximal, characteristic, complemented
9#13070337C211yesmaximal, characteristic, complemented
10C2×#10622141C211yesmaximal, characteristic, complemented
11C11×#2113C211yesmaximal, characteristic
12C2×C11×#131C2211yescharacteristic
13#10623358—21no—
14#10623356—21no—
15C22×Dic44C2211yescharacteristic
16C2×C11×M32C2211yescharacteristic
17C22×C11×C16C2211yescharacteristic
18#10622750—22no—
19#10622734—21no—
20#10622734—22no—
21#10622733—21no—
22#10622729C2212yes—
23#10622729C2212yes—
24#10622719C2211yescharacteristic
25#10622719C2211yescharacteristic
26#10622719C2212yes—
27C2×#66882C2211yescharacteristic
28C2×#66882C2212yes—
29C11×C22⋊C16C2212yes—
30C11×C22⋊C16C2212yes—
31#10622143C2211yescharacteristic
32#10622143C2211yescharacteristic
33#10622143C2212yes—
34#10622142C2211yescharacteristic
35#10622142C2211yescharacteristic
36#10622142C2212yes—
37#10622141C2212yes—
38#10622141C2212yes—
39#10622141C2212yes—
40#10622141C2212yes—
41C2×C11×#41D411yescharacteristic
42C22×Dic22—21no—
43C11×#131—22no—
44C11×#131—22no—
45C2×C11×M16D411yescharacteristic
46C2×C11×M16D412yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49Q8×Dic11—41no—
50#66997—41no—
51#66989—41no—
52#66988—42no—
53D4×Dic11—42no—
54D4×Dic11—41no—
55#66979—21no—
56#66979—22no—
57#66979—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60#66977—22no—
61#66977—22no—
62C2×Dic44—22no—
63C2×Dic44—22no—
64C2×Dic44—21no—
65C2×Dic44C2312yes—
66C11×M32—22no—
67C2×C11×C16—22no—
68C2×C11×C16C2311yescharacteristic
69C2×C11×C16C2311yescharacteristic
70C2×C11×C16C2312yes—
71#66882—22no—
72#66882—21no—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66882C2312yes—
77#66882C2311yescharacteristic
78#66881—22no—
79#66881—21no—
80#66881—21no—
81#66880—22no—
82#66880—22no—
83#33651—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C2×Q8×C11D811yescharacteristic
87C2×D4×C11D812yes—
88C2×D4×C11D811yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—41no—
92C22×Dic11—42no—
93C22×Dic11—41no—
94C2×Dic22—22no—
95C2×Dic22—42no—
96C2×Dic22—41no—
97C2×Dic22—42no—
98C11×M16—24no—
99C11×M16—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4112yes—
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C22⋊Dic11—42no—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C4×Dic11—42no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124Dic44—22no—
125Dic44—22no—
126Dic44—42no—
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#2158—111no—
138#2141—111no—
139C2×#358—111no—
140#2113D1111yescharacteristic
141C23×C11C2×D812yes—
142C23×C11C2×D811yescharacteristic
143Q8×C11—22no—
144D4×C11—24no—
145D4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11#12312yes—
149C2×C4×C11C2×D812yes—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11#13712yes—
152C2×C4×C11C22×D411yescharacteristic
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—82no—
160C2×Dic11—161no—
161C2×Dic11—162no—
162Dic22—42no—
163Dic22—42no—
164Dic22—82no—
165C8×C11—22no—
166C8×C11#12312yes—
167C8×C11C2×#4111yescharacteristic
168C8×C11C2×#4111yescharacteristic
169C22×Q16—111no—
170C2×#131C2×D1111yescharacteristic
171#536—221no—
172#520—221no—
173C2×M32C2×D1111yescharacteristic
174C22×C16C2×D1111yescharacteristic
175#470—222no—
176#467—112no—
177#467—112no—
178#428—221no—
179#428—222no—
180#427—111no—
181#427—112no—
182#427—111no—
183C2×#107—111no—
184C2×#107—112no—
185#419—221no—
186#367—111no—
187#367—111no—
188#367—112no—
189#366—111no—
190#366—111no—
191#366—112no—
192#358—112no—
193#358—112no—
194#358—112no—
195#358—112no—
196C22⋊C16C2×D1112yes—
197C22⋊C16C2×D1112yes—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11#48012yes—
204C22×C11C22×D811yescharacteristic
205C4×C11—22no—
206C4×C11#48012yes—
207C4×C11C2×#12311yescharacteristic
208C4×C11C2×#13711yescharacteristic
209Dic11—82no—
210Dic11—81no—
211Dic11—82no—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C2×#41D4411yescharacteristic
216C22×Q8—221no—
217C2×Q16—112no—
218C2×Q16—221no—
219C2×Q16—222no—
220C2×Q16—222no—
221#131—22no—
222#131—22no—
223C2×M16D4411yescharacteristic
224C2×M16D4412yes—
225C22×C8C22×D1112yes—
226C22×C8C22×D1111yescharacteristic
227C4⋊Q8—441no—
228#124—441no—
229#123—442no—
230C22⋊Q8—222no—
231C22⋊Q8—222no—
232C4×Q8—441no—
233C4×D4—442no—
234C4×D4—441no—
235#117—222no—
236#117—221no—
237#117—221no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—221no—
240M32—22no—
241C2×C16—22no—
242C2×C16C22×D1111yescharacteristic
243C2×C16C22×D1112yes—
244C2×C16C22×D1111yescharacteristic
245#107—112no—
246#107—111no—
247#107—111no—
248#107—111no—
249#107—111no—
250#107—222no—
251#107—221no—
252#106—222no—
253#106—221no—
254#106—221no—
255#103—222no—
256#103—222no—
257C2×C11—22no—
258C2×C11—42no—
259C2×C11C2×#48011yescharacteristic
260C2×C11#341611yescharacteristic
261C2×C11#341711yescharacteristic
262#41—22no—
263#41—22no—
264C2×Q8—222no—
265C2×Q8—441no—
266C2×Q8—442no—
267C2×Q8—442no—
268C2×Q8D8811yescharacteristic
269C2×D4D8812yes—
270C2×D4D8811yescharacteristic
271C22×C4—441no—
272C22×C4—442no—
273C22×C4—441no—
274C22×C4C2×D4412yes—
275C22×C4C2×D4411yescharacteristic
276Q16—222no—
277Q16—222no—
278Q16—442no—
279M16—22no—
280M16—24no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8C2×D4412yes—
284C2×C8C2×D4411yescharacteristic
285C2×C8#434112yes—
286C2×C8#434112yes—
287C2×C8C23×D1111yescharacteristic
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—222no—
292C4⋊C4—221no—
293C4⋊C4—442no—
294C4⋊C4—441no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C42—442no—
303C42—441no—
304C42—441no—
305C16—21no—
306C16—21no—
307C16—22no—
308C11#3365111yescharacteristic, complemented, Sylow
309C23C2×D8812yes—
310C23C2×D8811yescharacteristic
311Q8—22no—
312Q8—442no—
313Q8—442no—
314Q8—882no—
315D4—24no—
316D4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—882no—
326C2×C4—1761no—
327C2×C4—1762no—
328C2×C4#6693912yes—
329C2×C4C2×D8812yes—
330C2×C4C2×D8811yescharacteristic
331C2×C4#6696212yes—
332C2×C4C22×D4411yescharacteristic
333C8—22no—
334C8#6693912yes—
335C8C2×#434111yescharacteristic
336C8C2×#434111yescharacteristic
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22#1062234912yes—
343C22C22×D8811yescharacteristic
344C4—22no—
345C4—882no—
346C4—881no—
347C4—881no—
348C4—881no—
349C4—881no—
350C4—882no—
351C4#1062234912yes—
352C4C2×#6693911yescharacteristic
353C4C2×#6696211yescharacteristic
354C2—22no—
355C2—42no—
356C2C2×#1062234911yescharacteristic
357C2#1308176411yescharacteristic
358C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
prime radicalC2×C11×#41D4
hypercenter#2113D11
hypocenterC11#33651
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
3. #13070825C2semidirect
4. #13070825C2semidirect
5. #13070819C2semidirect
6. #13070814C2semidirect
7. #13070404C2semidirect
8. #13070400C2semidirect
9. #13070337C2semidirect
10. C2×#10622141C2semidirect
308. C11#33651semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130772162
#130708252
#130708192
#130708142
#130704042
#130704002
#130703372
C2×#106221412
C11×#21132
#3365111