Finite Group Databasebeta

← #24987646

Subgroups — #24987646

Order 11008.

392 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143571C211yesmaximal, characteristic
2#19134348C211yesmaximal, characteristic, complemented
3#19133081C211yesmaximal, characteristic
4#19132882C211yesmaximal, characteristic, complemented
5#19132494C211yesmaximal, characteristic, complemented
6#19132489C211yesmaximal, characteristic, complemented
7C43×#1524C211yesmaximal, characteristic
8#14583030C411yescharacteristic, complemented
9Q8×C43⋊C8C411yescharacteristic, complemented
10#14582977C411yescharacteristic, complemented
11#14582971—21no—
12D4×C43⋊C8—21no—
13D4×C43⋊C8C411yescharacteristic, complemented
14#14582960—21no—
15#14582956C2211yescharacteristic
16#14582952C2211yescharacteristic
17#14582855—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582745C2211yescharacteristic
20#14582653—21no—
21#14582653—21no—
22#14582636C412yes—
23#14582633C412yes—
24#14582621—21no—
25#14582621—21no—
26C43×#529C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C43×#330C412yescomplemented
30C43×#329C412yescomplemented
31C2×#10621877—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)C2×C411yescharacteristic
40C4⋊(C43⋊C8)C2×C411yescharacteristic
41C22⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)C2×C412yes—
45#13063236—21no—
46#13063236—21no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8C2×C411yescharacteristic
50C4×C43⋊C8C2×C411yescharacteristic
51C4×C43⋊C8D411yescharacteristic
52C4×C43⋊C8D411yescharacteristic
53C43⋊#95—21no—
54C43⋊#95C2×C412yes—
55C2×M16×C43—21no—
56C22×C8×C43—21no—
57#126×C43—21no—
58#125×C43C2×C411yescharacteristic
59#124×C43C2×C411yescharacteristic
60#123×C43—21no—
61C22⋊Q8×C43C2×C411yescharacteristic
62#121×C43C2×C411yescharacteristic
63C4×Q8×C43C2×C411yescharacteristic
64C4×D4×C43—21no—
65C4×D4×C43C2×C411yescharacteristic
66#117×C43—21no—
67C2×C42×C43C2311yescharacteristic
68#97×C43—21no—
69#97×C43C2×C412yes—
70#97×C43C2×C412yes—
71C4×C8×C43—21no—
72C2×Q8×C43C4211yescharacteristic
73C2×D4×C43—21no—
74C2×D4×C43C4211yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—22no—
80M16×C43—42no—
81C2×C8×C43—22no—
82C2×C8×C43—22no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43C4211yescharacteristic
90C4⋊C4×C43C4211yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C42×C43—21no—
97C42×C43C22×C411yescharacteristic
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43#4111yescharacteristic
101C4×Dic43—41no—
102C4×Dic43—41no—
103#10621877—42no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—42no—
110C2×C43⋊C8C22⋊C411yescharacteristic
111C2×C43⋊C8C22⋊C411yescharacteristic
112C2×C43⋊C8C22⋊C411yescharacteristic
113C2×C43⋊C8C22⋊C411yescharacteristic
114C23×C43—21no—
115C23×C43C4×D411yescharacteristic
116Q8×C43—41no—
117D4×C43—41no—
118D4×C43—42no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C4211yescharacteristic
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43#11711yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C8×C43—42no—
138C8×C43—42no—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—42no—
144C43⋊C8—41no—
145C43⋊C8—41no—
146#8248—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C4×C22⋊C411yescharacteristic
153C22×C43#44412yes—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43#42111yescharacteristic
163C4×C43#42111yescharacteristic
164Dic43—82no—
165#2966—431no—
166#1746—431no—
167#1524D4311yescharacteristic
168#1500—431no—
169#1451—431no—
170#1302—431no—
171#1300—431no—
172C2×C43—22no—
173C2×C43—81no—
174C2×C43#175711yescharacteristic
175C2×C43#175911yescharacteristic
176C2×C43#176511yescharacteristic
177#529C2×D4311yescharacteristic
178#446—431no—
179C8×Q8—431no—
180#436—431no—
181#435—861no—
182C8×D4—431no—
183C8×D4—861no—
184#433—861no—
185#432—431no—
186#431—431no—
187#405—861no—
188C4×M16C2×D4311yescharacteristic
189C2×#97C2×D4311yescharacteristic
190C2×C4×C8—431no—
191#376—431no—
192#336—861no—
193#336—861no—
194#330Dic4312yescomplemented
195#329Dic4312yescomplemented
196#328—432no—
197#327—432no—
198#322—861no—
199#322—861no—
200C43#824811yescharacteristic, complemented, Sylow
201C2×M16—21no—
202C2×M16—861no—
203C22×C8—21no—
204C22×C8—431no—
205C22×C8—431no—
206C22×C8—861no—
207#126—21no—
208#125C2×Dic4311yescharacteristic
209#124C2×Dic4311yescharacteristic
210#123—21no—
211C22⋊Q8C4×D4311yescharacteristic
212#121C4×D4311yescharacteristic
213C4×Q8C4×D4311yescharacteristic
214C4×D4—21no—
215C4×D4C4×D4311yescharacteristic
216#117—21no—
217C2×C42—861no—
218C2×C42C22×D4311yescharacteristic
219C4⋊C8—431no—
220C4⋊C8—431no—
221C4⋊C8—861no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C22⋊C8—432no—
225C22⋊C8—861no—
226C22⋊C8—861no—
227C22⋊C8—861no—
228#97—21no—
229#97—861no—
230#97—861no—
231#97C2×Dic4312yes—
232#97C2×Dic4312yes—
233C4×C8—21no—
234C4×C8—431no—
235C4×C8—431no—
236C4×C8—431no—
237C4×C8—431no—
238C4×C8—861no—
239C4×C8—861no—
240#95—432no—
241#95—861no—
242C2×Q8C4×Dic4311yescharacteristic
243C2×D4—21no—
244C2×D4C4×Dic4311yescharacteristic
245C22×C4—21no—
246C22×C4—862no—
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4D4×D4311yescharacteristic
249C22×C4#1062190011yescharacteristic
250M16—42no—
251M16—1722no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—431no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—861no—
261C2×C8—861no—
262C2×C8—862no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1722no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4C4×Dic4311yescharacteristic
271C4⋊C4C4×Dic4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C42—21no—
278C42—1721no—
279C42—1721no—
280C42C2×C4×D4311yescharacteristic
281C42D4×D4311yescharacteristic
282C42#1062190011yescharacteristic
283C42C22×Dic4311yescharacteristic
284C23—21no—
285C23(C22⋊D43)⋊C411yescharacteristic
286Q8—41no—
287D4—41no—
288D4—42no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—1722no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4C2×C4×Dic4311yescharacteristic
302C2×C4C22⋊C4×D4311yescharacteristic
303C2×C4#1306328111yescharacteristic
304C2×C4(C22⋊D43)⋊C411yescharacteristic
305C2×C4D4×Dic4311yescharacteristic
306C2×C4D4×Dic4311yescharacteristic
307C8—42no—
308C8—42no—
309C8—861no—
310C8—861no—
311C8—861no—
312C8—861no—
313C8—1722no—
314C8—1721no—
315C8—1721no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22C22⋊C4×Dic4311yescharacteristic
322C22#1458301812yes—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3442no—
332C4#1458291411yescharacteristic
333C4#1458291411yescharacteristic
334C2—22no—
335C2—81no—
336C2#1913439811yescharacteristic
337C2#1913440711yescharacteristic
338C2#1913444011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1524C2
socleC22×C43C4×C22⋊C4
prime radical#121×C43C2×C4
cosocleC2×C42×C43C23
hypercenter#1524D43
hypocenterC43#8248
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #19134348C2semidirect
4. #19132882C2semidirect
5. #19132494C2semidirect
6. #19132489C2semidirect
8. #14583030C4semidirect
9. Q8×C43⋊C8C4semidirect
10. #14582977C4semidirect
13. D4×C43⋊C8C4semidirect
29. C43×#330C4semidirect
30. C43×#329C4semidirect
194. #330Dic43semidirect
195. #329Dic43semidirect
200. C43#8248semidirect

Maximal subgroups

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

subgroupindex
#191435712
#191343482
#191330812
#191328822
#191324942
#191324892
C43×#15242
#824843