Finite Group Databasebeta

← #25114732

Subgroups — #25114732

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D172C211yesmaximal, characteristic
2C2×#14582934C212yesmaximal, complemented
3#19137546C212yesmaximal
4#19135351C212yesmaximal, complemented
5#19134793C214yesmaximal, complemented
6#19134617C212yesmaximal, complemented
7C4×#13063257C211yesmaximal, characteristic, complemented
8C43×#1844C211yesmaximal, characteristic, complemented
9C22×C8×D43C2212yes—
10C2×C4×D172C2211yescharacteristic
11C2×#13063283C2214yes—
12C8×D172C418yescomplemented
13#14582934—28no—
14C2×#13063258C2214yes—
15C2×#13063257C2211yescharacteristic
16C2×#13063257C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2211yescharacteristic
18C2×(C2×D43)⋊C8C2212yes—
19#14582800—22no—
20#14582789—24no—
21#14582756C2214yes—
22C4⋊C4×Dic43—22no—
23C4×C4⋊Dic43C2212yes—
24#14582662C2212yes—
25#14582661C2214yes—
26C2×#106×C43C2212yes—
27C2×#106×C43C2212yes—
28C2×C4×C8×C43C2211yescharacteristic
29C43×#384C2212yes—
30C22×D172D411yescharacteristic
31C22×C4×D43C2312yes—
32C22×C43⋊C8C2312yes—
33C2×C8×D43—24no—
34C2×C8×D43—24no—
35C2×C8×D43C2×C418yes—
36C4×D172C2×C414yes—
37C4×D172Q814yes—
38#13063283—28no—
39#13063283—44no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43C2312yes—
42C2×C4⋊Dic43C2312yes—
43C2×(C2×D43)⋊C4—24no—
44C2×(C2×D43)⋊C4—24no—
45C2×(C2×D43)⋊C4D412yes—
46C2×C4×Dic43—22no—
47C2×C4×Dic43—24no—
48#13063258—28no—
49#13063257—22no—
50#13063257D414yescomplemented
51C4⋊(C43⋊C8)C2×C414yes—
52(C2×D43)⋊C8C2×C418yes—
53C43⋊#95—22no—
54C43⋊#95—24no—
55C22×C8×C43C2311yescharacteristic
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43C2314yes—
60C2×C42×C43C2311yescharacteristic
61#106×C43—24no—
62#106×C43—42no—
63C4×C8×C43C2×C414yes—
64C23×D43C2×D412yes—
65C22×C4×C43—24no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2411yescharacteristic
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43C2×D412yes—
72C2×D172—24no—
73C2×D172C4⋊C414yes—
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—22no—
78C2×C4×D43C22×C414yes—
79C2×C4×D43C2×Q814yes—
80C2×C8×C43—21no—
81C2×C8×C43—21no—
82C2×C8×C43C22×C412yes—
83C2×C8×C43C22×C412yes—
84C2×C8×C43C2×D412yes—
85C2×C8×C43#4112yes—
86C4⋊C4×C43—24no—
87C4⋊C4×C43—24no—
88C4⋊C4×C43—44no—
89C4⋊C4×C43—82no—
90C42×C43C22×C412yes—
91C42×C43C2×Q812yes—
92(C2×D43)⋊C4—48no—
93(C2×D43)⋊C4—84no—
94(C2×D43)⋊C4C4⋊C418yes—
95C4⋊Dic43—22no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98C4⋊Dic43C4⋊C414yes—
99C4⋊Dic43C2×D414yes—
100C4×Dic43—48no—
101C4×Dic43—44no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8C22×C414yes—
105C8×D43—216no—
106C23×C43C22×D411yescharacteristic
107C22×D43—22no—
108C22×D43—22no—
109C22×D43—24no—
110C22×D43—24no—
111C22×D43C2×C4⋊C414yes—
112C2×C4×C43—22no—
113C2×C4×C43—44no—
114C2×C4×C43—44no—
115C2×C4×C43—44no—
116C2×C4×C43C2×C4⋊C412yes—
117C2×C4×C43C2×C4⋊C412yes—
118C2×C4×C43#13514yes—
119C2×C4×C43C23×C411yescharacteristic
120C2×C4×C43C22×D411yescharacteristic
121C2×C4×C43C22×Q811yescharacteristic
122C2×C4×C43C2×#4111yescharacteristic
123C2×C4×C43H(5,𝔽2)11yescharacteristic
124C2×C4×C432−1+411yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—24no—
128C2×Dic43—42no—
129C2×Dic43—42no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43C2×C4⋊C414yes—
134D172—28no—
135C4×D43—24no—
136C4×D43—24no—
137C4×D43—24no—
138C4×D43—24no—
139C8×C43—22no—
140C8×C43C4×D414yes—
141C43⋊C8—24no—
142#22657—431nomaximal, Sylow
143C22×C43C22×C4⋊C411yescharacteristic
144C22×C43D4211yescharacteristic
145C22×C43#54711yescharacteristic
146C22×C43C2×#13512yes—
147C22×C43#57712yes—
148C2×D43—24no—
149C2×D43—24no—
150C2×D43—24no—
151C2×D43—44no—
152C2×D43—44no—
153C4×C43—22no—
154C4×C43—84no—
155C4×C43#42714yescomplemented
156C4×C43C2×C4×D411yescharacteristic
157C4×C43#52011yescharacteristic
158C4×C43D4×Q811yescharacteristic
159C4×C43#55411yescharacteristic
160Dic43—24no—
161Dic43—44no—
162Dic43—82no—
163C2×C8×D4—431no—
164C2×#427—432no—
165#2354—432no—
166#1947—432no—
167#1854—434no—
168#1844D4311yescharacteristic, complemented
169#1807—432no—
170C4×#106—431no—
171C2×C43D4×C4⋊C411yescharacteristic
172C2×C43C2×#42711yescharacteristic
173C2×C43#291211yescharacteristic
174C2×C43#328412yes—
175C2×C43#334012yes—
176D43—44no—
177C23×C8—432no—
178C2×C4×D4—431no—
179C2×#117—434no—
180C8×D4—438no—
181#427—868no—
182C2×#107—434no—
183C2×#106—431no—
184C2×#106—431no—
185C2×#106C2×D4312yes—
186C2×#106C2×D4312yes—
187C2×C4⋊C8—431no—
188C2×C22⋊C8—432no—
189C2×C4×C8C2×D4311yescharacteristic
190#390—862no—
191#388—864no—
192#384C2×D4312yes—
193#380—434no—
194C4×C4⋊C4—432no—
195C4×C4⋊C4—862no—
196#340—432no—
197#340—434no—
198C43#2265711yescharacteristic, complemented, Sylow
199C22×D4—431no—
200C23×C4—432no—
201C22×C8—432no—
202C22×C8—438no—
203C22×C8—864no—
204C22×C8—864no—
205C22×C8C22×D4311yescharacteristic
206C22×C8C22×D4311yescharacteristic
207C4×D4—434no—
208C4×D4—434no—
209#117—868no—
210#117—1724no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—432no—
215C2×C4⋊C4—432no—
216C2×C4⋊C4C22×D4314yes—
217C2×C22⋊C4—432no—
218C2×C22⋊C4—864no—
219C2×C22⋊C4—864no—
220C2×C42—864no—
221C2×C42—862no—
222C2×C42C22×D4311yescharacteristic
223#107—868no—
224#106—24no—
225#106—42no—
226#106—434no—
227#106—862no—
228C4⋊C8—434no—
229C22⋊C8—438no—
230C4×C8C4×D4314yes—
231#95—864no—
232#95—862no—
233C24—432no—
234C2×D4—434no—
235C2×D4—864no—
236C22×C4—24no—
237C22×C4—432no—
238C22×C4—434no—
239C22×C4—434no—
240C22×C4—862no—
241C22×C4—862no—
242C22×C4—862no—
243C22×C4—862no—
244C22×C4—862no—
245C22×C4—862no—
246C22×C4D4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248C22×C4C23×D4311yescharacteristic
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—434no—
252C2×C8—862no—
253C2×C8—862no—
254C2×C8—8616no—
255C2×C8C2×C4×D4312yes—
256C2×C8C2×C4×D4312yes—
257C2×C8D4×D4312yes—
258C2×C8#1062190212yes—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—44no—
262C4⋊C4—82no—
263C4⋊C4—434no—
264C4⋊C4—434no—
265C4⋊C4—862no—
266C4⋊C4—862no—
267C4⋊C4—862no—
268C22⋊C4—438no—
269C22⋊C4—3444no—
270C22⋊C4—1728no—
271C42—1728no—
272C42—1724no—
273C42C2×C4×D4312yes—
274C42Q8×D4312yes—
275C23—434no—
276C23—862no—
277C23—864no—
278C23—864no—
279C23—862no—
280C23C2×D4×D4311yescharacteristic
281D4—868no—
282C2×C4—22no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—434no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—864no—
290C2×C4—864no—
291C2×C4—864no—
292C2×C4—864no—
293C2×C4—864no—
294C2×C4—1722no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4C4⋊C4×D4312yes—
300C2×C4C4⋊C4×D4312yes—
301C2×C4#1306334614yes—
302C2×C4C22×C4×D4311yescharacteristic
303C2×C4C2×D4×D4311yescharacteristic
304C2×C4C2×Q8×D4311yescharacteristic
305C2×C4C2×#1062190211yescharacteristic
306C2×C4#1306337011yescharacteristic
307C2×C4#1306337311yescharacteristic
308C8—22no—
309C8—864no—
310C8#1306328714yes—
311C22—864no—
312C22—864no—
313C22—864no—
314C22—1724no—
315C22—1724no—
316C22C2×C4⋊C4×D4311yescharacteristic
317C22#1458353411yescharacteristic
318C22#1458355211yescharacteristic
319C22C2×#1306334612yes—
320C22#1458370512yes—
321C4—22no—
322C4—84no—
323C4—864no—
324C4—3442no—
325C4—1724no—
326C4#1458293414yescomplemented
327C4C2×#1306328711yescharacteristic
328C4#1458338011yescharacteristic
329C4#1458356411yescharacteristic
330C4#1458361011yescharacteristic
331C2—1724no—
332C2#1913749511yescharacteristic
333C2C2×#1458293411yescharacteristic
334C2#1914318611yescharacteristic
335C2#1914632412yes—
336C2#1914700712yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1844C2
socleC23×C43C22×D4
prime radicalC22×D172D4
cosocleC22×C4×C43C24
hypercenter#1844D43
hypocenterC43#22657
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
2. C2×#14582934C2semidirect
4. #19135351C2semidirect
5. #19134793C2semidirect
6. #19134617C2semidirect
7. C4×#13063257C2semidirect
8. C43×#1844C2semidirect
12. C8×D172C4semidirect
50. #13063257D4semidirect
155. C4×C43#427semidirect
168. #1844D43semidirect
198. C43#22657semidirect
326. C4#14582934semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D1722
C2×#145829342
#191375462
#191353512
#191347932
#191346172
C4×#130632572
C43×#18442
#2265743