Finite Group Databasebeta

← #14671980

Subgroups — #14671980

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077317C211yesmaximal, characteristic
2#13070381C211yesmaximal, characteristic, complemented
3#13070244C211yesmaximal, characteristic, complemented
4C2×#10622152C211yesmaximal, characteristic, complemented
5C2×#10622152C211yesmaximal, characteristic, complemented
6#13070220C211yesmaximal, characteristic, complemented
7C11×#2117C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623359C411yescharacteristic
10C22×#4313C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13#10622847C411yescharacteristic
14#10622741—22no—
15#10622739C411yescharacteristic
16#10622732C411yescharacteristic
17#10622724—22no—
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21C11×#350—22no—
22#10622199—22no—
23#10622152—22no—
24#10622152—22no—
25#10622150—22no—
26#10622149—22no—
27C2×C11×#41C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131—21no—
32C11×#131—21no—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#66999—21no—
38#66991—21no—
39#66990—21no—
40#66988—21no—
41C4×C22⋊D11—22no—
42#66979C2×C411yescharacteristic
43C2×#4318C2×C411yescharacteristic
44C22×C11⋊C8C2×C411yescharacteristic
45C2×#4313—21no—
46C2×#4313—21no—
47C2×#4313—21no—
48C2×#4313—21no—
49C2×#4313—21no—
50C2×#4313—21no—
51C11×M32—21no—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32D412yescomplemented
55C2×C11×C16—21no—
56C2×C11×C16—21no—
57C22⋊(C11⋊C8)—22no—
58(C2×D11)⋊C8—22no—
59#66879D412yes—
60Dic11⋊C8—22no—
61C8×Dic11D412yes—
62#66876—21no—
63#66876—21no—
64#66876—21no—
65#66876D412yescomplemented
66C2×C11⋊C16—21no—
67C2×C11⋊C16—21no—
68#13201—111nomaximal, Sylow
69C23×D11M1611yescharacteristic
70C11×#41—21no—
71C11×#41—21no—
72C11×#41—21no—
73C11×#41—21no—
74C2×Q8×C11M1611yescharacteristic
75C2×D4×C11—21no—
76C2×D4×C11M1611yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11C22×C411yescharacteristic
79C2×C22⋊D11—22no—
80C22×Dic11M1611yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C11×M16—21no—
88C11×M16—21no—
89C11×M16—41no—
90C11×M16—41no—
91C2×C8×C11—21no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C22⋊Dic11—22no—
101C22⋊Dic11—21no—
102(C2×D11)⋊C4—22no—
103C4⋊Dic11—21no—
104Dic11⋊C4—22no—
105C4×Dic11C22⋊C412yes—
106#4318—21no—
107#4318—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8C22⋊C412yes—
112#4313—41no—
113#4313—41no—
114#4313—41no—
115#4313—41no—
116C11×C16—22no—
117C11×C16—41no—
118C11⋊C16—22no—
119C11⋊C16—41no—
120#2930—111no—
121#2153—111no—
122#2117—111no—
123#2117D1111yescharacteristic, complemented
124C2×#349—111no—
125C2×#349—111no—
126#2110—111no—
127C23×C11—21no—
128C23×C11C2×M1611yescharacteristic
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—81no—
133Q8×C11—21no—
134Q8×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C22⋊D11—82no—
149C2×Dic11—22no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C4×D11—41no—
154C4×D11—41no—
155C4×D11—41no—
156C4×D11—41no—
157C8×C11—41no—
158C8×C11#12111yescharacteristic
159C8×C11#12111yescharacteristic
160C8×C11#12411yescharacteristic
161C8×C11#12711yescharacteristic
162C11⋊C8—22no—
163C11⋊C8—41no—
164C2×#131C2×D1111yescharacteristic
165C22×M16—111no—
166#525—111no—
167C2×M32—111no—
168C2×M32—111no—
169C2×M32C2×D1111yescharacteristic
170C2×M32C2×D1111yescharacteristic
171#436—222no—
172#435—222no—
173#424—111no—
174#408—111no—
175#407—111no—
176#405—111no—
177#364—222no—
178#350—22no—
179#350—222no—
180#349—222no—
181#349—222no—
182#347—222no—
183C22×C11—41no—
184C22×C11—42no—
185C22×C11—41no—
186C22×C11#40711yescharacteristic
187C22×C11#43511yescharacteristic
188C22×C11#43511yescharacteristic
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—41no—
195C4×C11#39011yescharacteristic
196C4×C11#40811yescharacteristic
197C4×C11#43511yescharacteristic
198C4×C11#43511yescharacteristic
199Dic11—42no—
200Dic11—41no—
201C2×#41C4×D1111yescharacteristic
202C23×C4—111no—
203#131—21no—
204#131—21no—
205#131—21no—
206#131—21no—
207C2×M16—21no—
208C2×M16—111no—
209C2×M16—221no—
210C2×M16—221no—
211C2×M16—221no—
212C2×M16—221no—
213C2×M16—221no—
214C2×M16—221no—
215C2×M16C4×D1111yescharacteristic
216C22×C8—21no—
217C22×C8—111no—
218C22×C8C22×D1111yescharacteristic
219#123—221no—
220C22⋊Q8—221no—
221#121—221no—
222#120—221no—
223C4×D4—222no—
224#117—111no—
225M32—21no—
226M32—21no—
227M32—21no—
228M32—112no—
229M32—221no—
230M32—221no—
231M32—221no—
232M32C22⋊D1112yescomplemented
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—221no—
236C2×C16—221no—
237C4⋊C8—222no—
238C22⋊C8—222no—
239C22⋊C8—222no—
240#97—112no—
241C4×C8—112no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—81no—
246C2×C11#195511yescharacteristic
247D11—81no—
248C24—111no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253C2×Q8#431311yescharacteristic
254C2×D4—21no—
255C2×D4—222no—
256C2×D4#431311yescharacteristic
257C22×C4—21no—
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4C2×C4×D1111yescharacteristic
266M16—21no—
267M16—21no—
268M16—41no—
269M16—41no—
270M16—221no—
271M16—221no—
272M16—441no—
273M16—441no—
274M16—441no—
275M16—441no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—112no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8—221no—
283C2×C8#433911yescharacteristic
284C2×C8D4×D1111yescharacteristic
285C2×C8D4×D1111yescharacteristic
286C2×C8D4×D1111yescharacteristic
287C2×C8#434111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C4⋊C4—222no—
290C4⋊C4—221no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—221no—
294C42—112no—
295C16—22no—
296C16—41no—
297C16—222no—
298C16—441no—
299C11#1320111yescharacteristic, complemented, Sylow
300C23—21no—
301C23—221no—
302C23—221no—
303C23—221no—
304C23—881no—
305C23M16×D1111yescharacteristic
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—882no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—221no—
317C2×C4—222no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4C22⋊C4×D1111yescharacteristic
325C2×C4(C22⋊D11)⋊C411yescharacteristic
326C2×C4C2×#431311yescharacteristic
327C2×C4#6695411yescharacteristic
328C2×C4#6696011yescharacteristic
329C2×C4C4×C22⋊D1111yescharacteristic
330C8—41no—
331C8—222no—
332C8—441no—
333C8#6693711yescharacteristic
334C8#6693811yescharacteristic
335C8#6699211yescharacteristic
336C8#6699311yescharacteristic
337C22—41no—
338C22—42no—
339C22—41no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—881no—
344C22—881no—
345C22#1062233911yescharacteristic
346C22#1062234111yescharacteristic
347C22#1062274011yescharacteristic
348C4—41no—
349C4—442no—
350C4—441no—
351C4#1062234011yescharacteristic
352C4#1062234311yescharacteristic
353C4#1062257011yescharacteristic
354C4#1062272411yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—881no—
360C2#1306941211yescharacteristic
subgroupG/H
centerC4#10622570
commutatorC22×C4×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2117C2
socleC2×C11#1955
prime radical#10623359C4
cosocleC22×C8×C11C23
hypercenter#2117D11
hypocenterC11#13201
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #13070381C2semidirect
3. #13070244C2semidirect
4. C2×#10622152C2semidirect
5. C2×#10622152C2semidirect
6. #13070220C2semidirect
7. C11×#2117C2semidirect
54. C11×M32D4semidirect
65. #66876D4semidirect
123. #2117D11semidirect
232. M32C22⋊D11semidirect
299. C11#13201semidirect

Maximal subgroups

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

subgroupindex
#130773172
#130703812
#130702442
C2×#106221522
#130702202
C11×#21172
#1320111