Finite Group Databasebeta

← #14647643

Subgroups — #14647643

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077656C211yesmaximal, characteristic
2#13069409C211yesmaximal, characteristic
3C4×#66887C211yesmaximal, characteristic
4#13067366C211yesmaximal, characteristic, complemented
5#13066454C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1565C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66887C411yescharacteristic
13C2×#66887C411yescharacteristic
14C2×(C2×D11)⋊C8—22no—
15#10622538C2211yescharacteristic
16C4×#4318C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622451—21no—
19#10622451—21no—
20#10622339—22no—
21#10622301—21no—
22#10622301—21no—
23C11×#335—21no—
24C11×#334—21no—
25#10622192C411yescharacteristic
26#10622192C411yescharacteristic
27#10622118—21no—
28#10622117—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11D412yes—
31C2×C11×M16C2×C411yescharacteristic
32C2×C11×M16C2×C411yescharacteristic
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4Q812yes—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×#4318C2×C411yescharacteristic
38C2×#4318C2×C411yescharacteristic
39C22×C11⋊C8—21no—
40C2×#4313—22no—
41C2×#4313—22no—
42C4×D44—21no—
43C4×D44—21no—
44C4×D44—21no—
45C4×D44—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66887—22no—
56#66887—22no—
57(C2×D11)⋊C8—22no—
58(C2×D11)⋊C8—22no—
59(C2×D11)⋊C8—44no—
60C4⋊(C11⋊C8)D411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62#66867—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67#8837—111nomaximal, Sylow
68C23×D11C4⋊C412yes—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×Q811yescharacteristic
72C22×Dic11C4⋊C412yes—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—42no—
82C2×C4×D11—42no—
83C11×M16—21no—
84C11×M16—21no—
85C11×M16—21no—
86C11×M16M1612yescomplemented
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—42no—
92C2×C8×C11—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101#4318—21no—
102#4318—21no—
103#4318—21no—
104#4318M1612yescomplemented
105C2×C11⋊C8—22no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#4313—82no—
113#4313—82no—
114#2975—111no—
115#1954—111no—
116C4×#100—111no—
117#1565—111no—
118#1565D1111yescharacteristic, complemented
119#1278—111no—
120#1278—111no—
121C23×C11C2×C4⋊C411yescharacteristic
122C22×D11—22no—
123C22×D11—22no—
124C22×D11—22no—
125C22×D11—42no—
126C22×D11—42no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11C2×M1611yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C2×C4×C11#13111yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—42no—
142D44—41no—
143D44—41no—
144D44—41no—
145D44—41no—
146C4×D11—42no—
147C4×D11—42no—
148C4×D11—82no—
149C8×C11—22no—
150C8×C11—41no—
151C8×C11—41no—
152C8×C11—41no—
153C8×C11—81no—
154C11⋊C8—22no—
155C11⋊C8—42no—
156C11⋊C8—41no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C2×C4×D4—111no—
160#436—221no—
161#436—221no—
162#436—221no—
163#436—221no—
164#431—111no—
165#431C2×D1111yescharacteristic
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×#100—111no—
168C2×#100—111no—
169#407—222no—
170C2×C22⋊C8—222no—
171C4×M16—111no—
172C4×M16C2×D1111yescharacteristic
173C2×C4×C8—111no—
174#343—111no—
175#343—111no—
176#335—21no—
177#335—221no—
178#334—21no—
179#334—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#38511yescharacteristic
183C22×C11#42311yescharacteristic
184C22×C11#42411yescharacteristic
185C2×D11—44no—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—82no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11#43511yescharacteristic
194C4×C11#43511yescharacteristic
195C4×C11#43611yescharacteristic
196C4×C11#43611yescharacteristic
197C4×C11#45311yescharacteristic
198C4×C11#45511yescharacteristic
199Dic11—42no—
200C22×D4—111no—
201C23×C4—112no—
202C2×M16—111no—
203C2×M16—111no—
204C2×M16—222no—
205C2×M16—222no—
206C2×M16C4×D1111yescharacteristic
207C2×M16C4×D1111yescharacteristic
208C22×C8—21no—
209C22×C8—221no—
210C4×D4—221no—
211C4×D4—221no—
212C4×D4—221no—
213C4×D4—221no—
214C2×C4⋊C4—111no—
215C2×C22⋊C4—112no—
216C2×C42C22×D1111yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221C4⋊C8C22⋊D1111yescharacteristic
222C4⋊C8C22⋊D1111yescharacteristic
223#100—222no—
224#100—222no—
225C22⋊C8—21no—
226C22⋊C8—222no—
227C22⋊C8—222no—
228C22⋊C8—221no—
229C22⋊C8—444no—
230#97—21no—
231#97—221no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—221no—
235C4×C8—221no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11#185111yescharacteristic
241C2×C11#185611yescharacteristic
242C2×C11#185811yescharacteristic
243D11—82no—
244C24—112no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4—221no—
251C22×C4—112no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4Q8×D1111yescharacteristic
259M16—21no—
260M16—21no—
261M16—21no—
262M16—112no—
263M16—221no—
264M16—221no—
265M16—221no—
266M16—882no—
267M16—882no—
268M16#431312yescomplemented
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—221no—
276C2×C8—222no—
277C2×C8—221no—
278C2×C8—221no—
279C2×C8—221no—
280C2×C8—441no—
281C2×C8—441no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C22⋊C4—222no—
285C22⋊C4—222no—
286C42#433911yescharacteristic
287C42D4×D1111yescharacteristic
288C42#434311yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#883711yescharacteristic, complemented, Sylow
291C23—222no—
292C23—222no—
293C23—222no—
294C23—442no—
295C23—442no—
296C23C4⋊C4×D1111yescharacteristic
297D4—441no—
298D4—441no—
299D4—441no—
300D4—441no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—222no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—882no—
309C2×C4#6694611yescharacteristic
310C2×C4#6694711yescharacteristic
311C2×C4#6694911yescharacteristic
312C2×C4C2×#431311yescharacteristic
313C2×C4#6695411yescharacteristic
314C2×C4M16×D1111yescharacteristic
315C2×C4#6696011yescharacteristic
316C2×C4C4×C22⋊D1111yescharacteristic
317C2×C4#6699011yescharacteristic
318C2×C4#6699911yescharacteristic
319C8—22no—
320C8—41no—
321C8—41no—
322C8—41no—
323C8—81no—
324C8—222no—
325C8—442no—
326C8—441no—
327C8—441no—
328C8—441no—
329C22—21no—
330C22—21no—
331C22—444no—
332C22—442no—
333C22—442no—
334C22—442no—
335C22—882no—
336C22#1062245011yescharacteristic
337C22#1062245211yescharacteristic
338C22#1062260211yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—442no—
343C4#1062244911yescharacteristic
344C4#1062245111yescharacteristic
345C4#1062272411yescharacteristic
346C4#1062274111yescharacteristic
347C4#1062281111yescharacteristic
348C4#1062281511yescharacteristic
349C2—21no—
350C2—21no—
351C2—882no—
352C2#1306879711yescharacteristic
353C2#1306882411yescharacteristic
354C2#1306883411yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1565C2
socleC22×C11#385
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1565D11
hypocenterC11#8837
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #13067366C2semidirect
5. #13066454C2semidirect
6. #13066452C2semidirect
7. C11×#1565C2semidirect
86. C11×M16M16semidirect
104. #4318M16semidirect
118. #1565D11semidirect
268. M16#4313semidirect
290. C11#8837semidirect

Maximal subgroups

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

subgroupindex
#130776562
#130694092
C4×#668872
#130673662
#130664542
#130664522
C11×#15652
#883711