Finite Group Databasebeta

← #25249206

Subgroups — #25249206

Order 11008.

806 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583307C212yesmaximal
2C2×#14583299C211yesmaximal, characteristic
3C2×#14583296C211yesmaximal, characteristic
4#19140719C212yesmaximal
5#19134764C212yesmaximal
6#19134762C212yesmaximal
7#19134756C211yesmaximal, characteristic
8#19134752C211yesmaximal, characteristic
9#19134750C211yesmaximal, characteristic
10#19134281C211yesmaximal, characteristic
11C43×#1846C211yesmaximal, characteristic
12C2×#13063324C2212yes—
13C2×#13063316C2212yes—
14#14583307—28no—
15#14583299—24no—
16#14583296—24no—
17C2×#13063258C2212yes—
18C2×#13063258C2212yes—
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2212yes—
22C2×#13063256C2212yes—
23C2×#13063256C2212yes—
24C2×#13063236C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582833—24no—
30#14582820—24no—
31#14582769C2212yes—
32#14582768C2212yes—
33#14582764C2212yes—
34#14582745C2211yescharacteristic
35C2×#107×C43C2212yes—
36C2×#106×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×C4×C8×C43C2211yescharacteristic
39C43×#382C2212yes—
40C22×Dic86—22no—
41C22×C43⋊C8C2311yescharacteristic
42C22×C43⋊C8C2311yescharacteristic
43#13063324—24no—
44#13063324—24no—
45#13063316—24no—
46#13063316—24no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—24no—
49C2×C4⋊Dic43C2312yes—
50C2×C4⋊Dic43C2312yes—
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—24no—
54C2×C4×Dic43C2311yescharacteristic
55C2×C4×Dic43C2311yescharacteristic
56#13063258—24no—
57#13063258—24no—
58#13063257—22no—
59#13063257—22no—
60#13063257—24no—
61#13063256—24no—
62#13063256—24no—
63#13063236Q814yescomplemented
64#13063235D414yes—
65#13063235Q814yescomplemented
66C8×Dic43D414yes—
67C8×Dic43Q814yescomplemented
68C43⋊#95—24no—
69C43⋊#95D414yes—
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C2×C4⋊C4×C43C2312yes—
73C2×C4⋊C4×C43C2312yes—
74C2×C42×C43C2311yescharacteristic
75#107×C43—24no—
76#106×C43—22no—
77#106×C43—22no—
78C4×C8×C43Q814yescomplemented
79#95×C43—24no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2411yescharacteristic
84C22×Dic43—22no—
85C22×Dic43—22no—
86C22×Dic43C2×D412yes—
87C22×Dic43C2×D412yes—
88C2×Dic86—44no—
89C2×Dic86—84no—
90C2×C8×C43C2×D412yes—
91C2×C8×C43C2×D412yes—
92C2×C8×C43C2×Q812yes—
93C2×C8×C43C2×Q812yes—
94C2×C8×C43C2×Q812yes—
95C2×C8×C43C2×Q812yes—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C42×C43C2×Q812yes—
101C42×C43C2×Q812yes—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43—44no—
107C4⋊Dic43—84no—
108Dic43⋊C4—44no—
109Dic43⋊C4—44no—
110Dic43⋊C4—84no—
111C4×Dic43C2×D412yes—
112C4×Dic43C2×D412yes—
113C4×Dic43C2×Q812yes—
114C4×Dic43C2×Q812yes—
115C2×C43⋊C8C2×D412yes—
116C2×C43⋊C8C2×D412yes—
117C2×C43⋊C8C2×Q812yes—
118C2×C43⋊C8C2×Q812yes—
119C2×C43⋊C8C2×Q812yes—
120C2×C43⋊C8C2×Q812yes—
121C23×C43C22×D411yescharacteristic
122C2×C4×C43—24no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—44no—
126C2×C4×C43—44no—
127C2×C4×C43C4⋊Q814yes—
128C2×C4×C43C22×D411yescharacteristic
129C2×C4×C43C22×D411yescharacteristic
130C2×C4×C43C22×Q811yescharacteristic
131C2×C4×C43C22×Q811yescharacteristic
132C2×C4×C43C22×Q811yescharacteristic
133C2×C4×C43C22×Q811yescharacteristic
134C2×Dic43—24no—
135C2×Dic43—24no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—44no—
139C2×Dic43—44no—
140C2×Dic43#12714yes—
141C2×Dic43C4⋊Q814yes—
142Dic86—88no—
143C8×C43C4⋊Q814yes—
144C8×C43C4⋊Q814yes—
145C43⋊C8C4⋊Q814yes—
146C43⋊C8C4⋊Q814yes—
147#33318—431nomaximal, Sylow
148C22×C43C2×#12711yescharacteristic
149C22×C43C2×C4⋊Q811yescharacteristic
150C22×C43C2×C4⋊Q811yescharacteristic
151C22×C43#57714yes—
152C4×C43—24no—
153C4×C43—82no—
154C4×C43—82no—
155C4×C43C2×C4⋊Q811yescharacteristic
156C4×C43C2×C4⋊Q811yescharacteristic
157C4×C43C2×C4⋊Q811yescharacteristic
158C4×C43C2×C4⋊Q811yescharacteristic
159Dic43—24no—
160Dic43—24no—
161Dic43—82no—
162Dic43—82no—
163C2×#501—432no—
164C2×#499—431no—
165C2×#498—431no—
166#2660—432no—
167#1847—432no—
168#1847—432no—
169#1846—431no—
170#1846D4311yescharacteristic
171#1844—431no—
172#1844—431no—
173#1726—431no—
174C2×C43#286811yescharacteristic
175C2×C43#315412yes—
176C2×C43#316312yes—
177C2×C43#316312yes—
178C2×C4⋊Q8—432no—
179C2×#125—432no—
180#501—868no—
181#499—864no—
182#498—864no—
183C2×#107—432no—
184C2×#107—432no—
185C2×#107C2×D4312yes—
186C2×#106—431no—
187C2×#106—431no—
188C2×#106—432no—
189C2×#106—432no—
190C2×#106—432no—
191C2×#106C2×D4311yescharacteristic
192C2×#106C2×D4311yescharacteristic
193C2×#97—431no—
194C2×#97—431no—
195C2×#97—431no—
196C2×C4×C8—431no—
197C2×C4×C8—431no—
198C2×C4×C8C2×D4311yescharacteristic
199#398—864no—
200#395—864no—
201#384—432no—
202#384—432no—
203#382—432no—
204#382C2×D4312yes—
205#376—431no—
206C43#3331811yescharacteristic, complemented, Sylow
207C22×Q8—862no—
208C22×C8—431no—
209C22×C8—431no—
210C22×C8C22×D4311yescharacteristic
211C22×C8C22×D4311yescharacteristic
212C4⋊Q8—864no—
213C4⋊Q8—864no—
214#125—864no—
215#125—864no—
216C2×C4⋊C4—432no—
217C2×C4⋊C4—432no—
218C2×C4⋊C4—864no—
219C2×C4⋊C4—864no—
220C2×C4⋊C4—862no—
221C2×C4⋊C4—862no—
222C2×C4⋊C4—862no—
223C2×C4⋊C4C22×D4312yes—
224C2×C4⋊C4C22×D4312yes—
225C2×C42—431no—
226C2×C42—431no—
227C2×C42C22×D4311yescharacteristic
228#107—24no—
229#107—864no—
230#107—864no—
231#106—22no—
232#106—22no—
233#106—864no—
234#106—864no—
235#106—862no—
236#106—862no—
237#106—864no—
238#97—434no—
239#97—434no—
240#97—434no—
241C4×C8—434no—
242C4×C8—434no—
243C4×C8Dic8614yescomplemented
244#95—24no—
245#95—434no—
246#95—864no—
247C2×Q8—3444no—
248C2×Q8—1724no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—432no—
252C22×C4—432no—
253C22×C4—862no—
254C22×C4—862no—
255C22×C4D4×D4312yes—
256C22×C4C23×D4311yescharacteristic
257C2×C8—432no—
258C2×C8—432no—
259C2×C8—432no—
260C2×C8—432no—
261C2×C8—432no—
262C2×C8—432no—
263C2×C8C2×Dic8612yes—
264C2×C8C2×Dic8612yes—
265C2×C8D4×D4312yes—
266C2×C8D4×D4312yes—
267C2×C8Q8×D4312yes—
268C2×C8Q8×D4312yes—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—862no—
274C4⋊C4—862no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—3444no—
278C4⋊C4—3444no—
279C4⋊C4—1724no—
280C4⋊C4—1724no—
281C4⋊C4—1724no—
282C42—432no—
283C42—432no—
284C42—432no—
285C42—432no—
286C42C2×Dic8612yes—
287C42Q8×D4312yes—
288C23C2×D4×D4311yescharacteristic
289Q8—3448no—
290C2×C4—24no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—434no—
296C2×C4—434no—
297C2×C4—864no—
298C2×C4—864no—
299C2×C4—1722no—
300C2×C4—1722no—
301C2×C4—1724no—
302C2×C4—1724no—
303C2×C4#1306332414yes—
304C2×C4C2×D4×D4311yescharacteristic
305C2×C4C2×D4×D4311yescharacteristic
306C2×C4C2×Q8×D4311yescharacteristic
307C2×C4C2×Q8×D4311yescharacteristic
308C2×C4C2×Q8×D4311yescharacteristic
309C2×C4C22×Dic8611yescharacteristic
310C8—434no—
311C8—434no—
312C8#1306332414yes—
313C8#1306332414yes—
314C22#127×D4311yescharacteristic
315C22C4⋊Q8×D4311yescharacteristic
316C22C2×#1306332411yescharacteristic
317C22#1458370614yes—
318C4—24no—
319C4—82no—
320C4—82no—
321C4—864no—
322C4—864no—
323C4—3442no—
324C4—3442no—
325C4C4⋊Q8×D4311yescharacteristic
326C4C4⋊Q8×D4311yescharacteristic
327C4C2×#1306332411yescharacteristic
328C4C2×#1306332411yescharacteristic
329C2#1914299211yescharacteristic
330C2#1914506612yes—
331C2#1914512412yes—
332C2#1914512712yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1846C2
socle, prime radicalC23×C43C22×D4
hypercenter#1846D43
hypocenterC43#33318
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
63. #13063236Q8semidirect
65. #13063235Q8semidirect
67. C8×Dic43Q8semidirect
78. C4×C8×C43Q8semidirect
206. C43#33318semidirect
243. C4×C8Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145833072
C2×#145832992
C2×#145832962
#191407192
#191347642
#191347622
#191347562
#191347522
#191347502
#191342812
C43×#18462
#3331843