Finite Group Databasebeta

← #25105450

Subgroups — #25105450

Order 11008.

654 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#19145107C211yesmaximal, characteristic
2#19143534C212yesmaximal
3#19135574C212yesmaximal
4#19135345C212yesmaximal
5#19135343C211yesmaximal, characteristic
6#19134765C211yesmaximal, characteristic
7#19134478C212yesmaximal
8#19134477C211yesmaximal, characteristic
9#19134476C211yesmaximal, characteristic
10#19134281C211yesmaximal, characteristic
11C43×#1945C211yesmaximal, characteristic
12#14583452C2212yes—
13#14583303C412yescomplemented
14#14583300C412yescomplemented
15#14583299C412yescomplemented
16#14583296C412yescomplemented
17#14583028—24no—
18#14583026—24no—
19C2×#13063261C2211yescharacteristic
20C2×#13063260C2212yes—
21#14582937C2211yescharacteristic
22#14582935C2212yes—
23#14582925C2212yes—
24#14582922C2212yes—
25#14582857C2212yes—
26#14582855C2212yes—
27C2×#13063236C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582745C2211yescharacteristic
33#14582660C2212yes—
34#14582659C2212yes—
35#14582658C2212yes—
36C2×#108×C43C2211yescharacteristic
37C43×#427C2211yescharacteristic
38C43×#424C2212yes—
39C2×C4×C8×C43C2211yescharacteristic
40C43×#339C2212yes—
41C2×#10621877C2312yes—
42C22×C43⋊C8C2311yescharacteristic
43C22×C43⋊C8C2311yescharacteristic
44#13063324C2×C414yes—
45#13063316C2×C414yes—
46#13063302—24no—
47C4×Dic86—24no—
48#13063284C2312yes—
49C2×C4×Dic43C2311yescharacteristic
50C2×C4×Dic43C2311yescharacteristic
51#13063261—22no—
52#13063260—24no—
53#13063259C2×C412yes—
54#13063258C2×C414yes—
55#13063257C2×C412yes—
56#13063256C2×C414yes—
57Dic43⋊C8—24no—
58Dic43⋊C8—24no—
59#13063236—22no—
60#13063236Q814yescomplemented
61#13063235—22no—
62#13063235—22no—
63#13063235D412yes—
64#13063235D412yes—
65C4×C43⋊C8—22no—
66C8×Dic43—22no—
67C8×Dic43C2×C411yescharacteristic
68C8×Dic43C2×C411yescharacteristic
69C8×Dic43C2×C411yescharacteristic
70C8×Dic43C2×C411yescharacteristic
71C8×Dic43Q814yescomplemented
72C43⋊#95—22no—
73C2×M16×C43C2312yes—
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76#117×C43C2312yes—
77C2×C42×C43C2311yescharacteristic
78#108×C43—22no—
79#107×C43C2×C412yes—
80#106×C43C2×C412yes—
81C4⋊C8×C43—24no—
82C4×C8×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43C2411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43#4112yes—
87C2×Dic86—24no—
88M16×C43—22no—
89M16×C43—22no—
90C2×C8×C43—21no—
91C2×C8×C43—21no—
92C2×C8×C43—22no—
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C22×C411yescharacteristic
95C2×C8×C43C2×D412yes—
96C2×C8×C43C2×Q812yes—
97C2×C8×C43#4112yes—
98C4⋊C4×C43C22×C414yes—
99C22⋊C4×C43—22no—
100C42×C43—22no—
101C42×C43—21no—
102C42×C43C2×Q812yes—
103C22⋊Dic43—22no—
104C4⋊Dic43—24no—
105C4⋊Dic43C22×C414yes—
106Dic43⋊C4—24no—
107Dic43⋊C4—24no—
108C4×Dic43—22no—
109C4×Dic43—21no—
110C4×Dic43C22×C411yescharacteristic
111C4×Dic43C22×C411yescharacteristic
112C4×Dic43C2×D412yes—
113C4×Dic43C2×Q812yes—
114#10621877—22no—
115#10621877—22no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8C22×C411yescharacteristic
118C2×C43⋊C8C22×C411yescharacteristic
119C2×C43⋊C8C2×D411yescharacteristic
120C2×C43⋊C8C2×D411yescharacteristic
121C2×C43⋊C8C2×Q812yes—
122C2×C43⋊C8C2×Q812yes—
123C2×C43⋊C8C2×Q812yes—
124C2×C43⋊C8#4112yes—
125C23×C43C2×#4111yescharacteristic
126C2×C4×C43—24no—
127C2×C4×C43—22no—
128C2×C4×C43—42no—
129C2×C4×C43C23×C411yescharacteristic
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C22×Q811yescharacteristic
132C2×C4×C43C22×Q811yescharacteristic
133C2×C4×C43C2×#4111yescharacteristic
134C2×C4×C43C2×#4111yescharacteristic
135C2×Dic43—24no—
136C2×Dic43—22no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43C4×D412yes—
140C2×Dic43C4×D412yes—
141Dic86—84no—
142C8×C43—22no—
143C8×C43—42no—
144C8×C43C4×Q812yes—
145C8×C43C4×Q812yes—
146C43⋊C8—42no—
147C43⋊C8C4×Q812yes—
148C43⋊C8C4×Q812yes—
149C43⋊C8C4⋊Q812yes—
150C43⋊C8C4⋊Q812yes—
151#21733—431nomaximal, Sylow
152C22×C43—22no—
153C22×C43C2×C4×D411yescharacteristic
154C22×C43#53311yescharacteristic
155C22×C43#53311yescharacteristic
156C4×C43—42no—
157C4×C43—44no—
158C4×C43C2×C4×Q811yescharacteristic
159C4×C43C2×C4×Q811yescharacteristic
160C4×C43C2×C4⋊Q811yescharacteristic
161C4×C43#53211yescharacteristic
162Dic43—22no—
163Dic43—22no—
164Dic43—42no—
165Dic43—44no—
166#3160—431no—
167#2961—432no—
168#1995—432no—
169#1946—432no—
170#1945—431no—
171#1945D4311yescharacteristic
172#1848—431no—
173#1773—432no—
174#1772—431no—
175#1772—431no—
176#1726—431no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43C4×C4⋊Q811yescharacteristic
180C2×C43#295712yes—
181#533—432no—
182#500—432no—
183#499—432no—
184#499—432no—
185#498—432no—
186#446—864no—
187#446—864no—
188C2×#108—432no—
189C2×#108—431no—
190C2×#108C2×D4311yescharacteristic
191#427—431no—
192#427—432no—
193#427C2×D4311yescharacteristic
194#424—432no—
195#424C2×D4312yes—
196#423—432no—
197#405—432no—
198#405—432no—
199C2×#97—431no—
200C2×#97—431no—
201C2×#97—431no—
202C2×C4×C8—431no—
203C2×C4×C8—431no—
204C2×C4×C8C2×D4311yescharacteristic
205#376—431no—
206#339—432no—
207#339—432no—
208#339—432no—
209#339C2×D4312yes—
210C43#2173311yescharacteristic, complemented, Sylow
211C2×M16—432no—
212C2×M16C22×D4312yes—
213C22×C8—431no—
214C22×C8—431no—
215C22×C8C22×D4311yescharacteristic
216C22×C8C22×D4311yescharacteristic
217C4⋊Q8—434no—
218#125—434no—
219C22⋊Q8—864no—
220C4×Q8—864no—
221#117—432no—
222#117C22×D4312yes—
223C2×C42—431no—
224C2×C42—431no—
225C2×C42C22×D4311yescharacteristic
226#108—22no—
227#108—864no—
228#108—862no—
229#107—432no—
230#107—434no—
231#107C4×D4312yes—
232#106—432no—
233#106—434no—
234#106C4×D4312yes—
235C4⋊C8—24no—
236C4⋊C8—864no—
237C4⋊C8—864no—
238#97—432no—
239#97—432no—
240#97—434no—
241#97—862no—
242#97—862no—
243#97—862no—
244C4×C8—22no—
245C4×C8—431no—
246C4×C8—431no—
247C4×C8—431no—
248C4×C8—431no—
249C4×C8—434no—
250C4×C8—862no—
251C4×C8—862no—
252#95—862no—
253C2×Q8—864no—
254C22×C4—21no—
255C22×C4—432no—
256C22×C4—861no—
257C22×C4C23×D4311yescharacteristic
258M16—22no—
259M16—22no—
260M16—862no—
261M16—862no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—432no—
270C2×C8—432no—
271C2×C8—432no—
272C2×C8—432no—
273C2×C8—862no—
274C2×C8C2×C4×D4311yescharacteristic
275C2×C8C2×C4×D4311yescharacteristic
276C2×C8D4×D4312yes—
277C2×C8#1062190012yes—
278C2×C8Q8×D4312yes—
279C4⋊C4—434no—
280C4⋊C4—864no—
281C4⋊C4—864no—
282C4⋊C4—864no—
283C4⋊C4C2×C4×D4314yes—
284C22⋊C4—22no—
285C22⋊C4—862no—
286C42—22no—
287C42—21no—
288C42—431no—
289C42—431no—
290C42—432no—
291C42—432no—
292C42—862no—
293C42—861no—
294C42Q8×D4312yes—
295C23#41×D4311yescharacteristic
296Q8—3444no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—432no—
301C2×C4—432no—
302C2×C4—864no—
303C2×C4—862no—
304C2×C4—1722no—
305C2×C4—1722no—
306C2×C4C22×C4×D4311yescharacteristic
307C2×C4C2×D4×D4311yescharacteristic
308C2×C4C2×Q8×D4311yescharacteristic
309C2×C4C2×Q8×D4311yescharacteristic
310C2×C4#41×D4311yescharacteristic
311C2×C4C2×#1062190011yescharacteristic
312C8—22no—
313C8—42no—
314C8—432no—
315C8—432no—
316C8—432no—
317C8—432no—
318C8—1722no—
319C8#1306329012yes—
320C8#1306329012yes—
321C22—22no—
322C22C4×D4×D4311yescharacteristic
323C22#1458345111yescharacteristic
324C22#1458345511yescharacteristic
325C4—42no—
326C4—44no—
327C4—862no—
328C4—862no—
329C4—1722no—
330C4—1724no—
331C4C4×Q8×D4311yescharacteristic
332C4C2×#1306329011yescharacteristic
333C4C4⋊Q8×D4311yescharacteristic
334C4#1458344411yescharacteristic
335C2—21no—
336C2—21no—
337C2#1913716611yescharacteristic
338C2#1914350712yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1945C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C2×#41
cosocleC22×C4×C43C24
hypercenter#1945D43
hypocenterC43#21733
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
13. #14583303C4semidirect
14. #14583300C4semidirect
15. #14583299C4semidirect
16. #14583296C4semidirect
60. #13063236Q8semidirect
71. C8×Dic43Q8semidirect
210. C43#21733semidirect

Maximal subgroups

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

subgroupindex
#191451072
#191435342
#191355742
#191353452
#191353432
#191347652
#191344782
#191344772
#191344762
#191342812
C43×#19452
#2173343