Finite Group Databasebeta

← #25084389

Subgroups — #25084389

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145174C211yesmaximal, characteristic, complemented
2#19145170C212yesmaximal, complemented
3#19145021C212yesmaximal, complemented
4#19134268C212yesmaximal, complemented
5#19134265C212yesmaximal, complemented
6#19134263C212yesmaximal, complemented
7#19134260C212yesmaximal, complemented
8C2×#14582621C211yesmaximal, characteristic, complemented
9C43×#3169C211yesmaximal, characteristic, complemented
10C2×#13063345—24no—
11#14583449C2212yes—
12#14583304C2211yescharacteristic
13#14583302C2212yes—
14#14583281—24no—
15#14583278C2212yes—
16#14583276C2211yescharacteristic
17#14583275C2212yes—
18#14583275C2212yes—
19#14583273C2212yes—
20#14583271C2212yes—
21#14583247C2212yes—
22#14583246C2212yes—
23#14583245C2212yes—
24#14583135—22no—
25#14583133—24no—
26C4×D344—22no—
27C4×#10621882—24no—
28C2×C4×C43⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582621C2212yes—
31#14582621C2212yes—
32C43×#532C2212yes—
33C43×#500C2211yescharacteristic
34C43×#493C2211yescharacteristic
35C43×#486C2212yes—
36C43×#466—22no—
37C4×D8×C43—22no—
38C2×C4×C8×C43C2211yescharacteristic
39C2×#10621898—22no—
40#13063345—416no—
41C2×#10621885—24no—
42C2×#10621883—24no—
43C2×#10621884—24no—
44C2×D344—22no—
45C2×#10621882—24no—
46C2×#10621882—24no—
47C22×C43⋊C8D412yes—
48C22×C43⋊C8D412yes—
49#13063325C2312yes—
50#13063322C2312yes—
51#13063313—22no—
52#13063299—22no—
53#13063299—22no—
54C4×D172—22no—
55C4×D172—22no—
56#13063259—22no—
57#13063258—24no—
58#13063247—24no—
59#13063246—24no—
60#13063245—24no—
61C4×C43⋊C8D412yes—
62C4×C43⋊C8D412yes—
63C4×C43⋊C8C2312yes—
64C4×C43⋊C8C2312yes—
65C2×#41×C43—22no—
66C2×D8×C43—22no—
67C22×C8×C43D412yes—
68C4⋊Q8×C43C2312yes—
69#127×C43C2312yes—
70#124×C43—22no—
71#121×C43—22no—
72#121×C43—22no—
73C4×D4×C43—22no—
74C4×D4×C43—22no—
75C2×C42×C43C2311yescharacteristic
76#107×C43—22no—
77#102×C43—24no—
78C4×C8×C43D412yes—
79C4×C8×C43C2311yescharacteristic
80C4×C8×C43C2311yescharacteristic
81#41×C43—48no—
82C2×Q8×C43—22no—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—42no—
92#10621898—48no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—22no—
96C2×C4×D43—42no—
97C2×Dic86—22no—
98D8×C43—44no—
99C2×C8×C43—42no—
100C2×C8×C43C2×D412yes—
101C2×C8×C43C2×D412yes—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C22⋊C4×C43—42no—
105C22⋊C4×C43—42no—
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2411yescharacteristic
110#10621885—48no—
111#10621884—48no—
112#10621883—48no—
113#10621882—48no—
114#10621882—48no—
115(C2×D43)⋊C4—42no—
116(C2×D43)⋊C4—42no—
117C4⋊Dic43—22no—
118C4⋊Dic43—22no—
119C2×C43⋊C8—42no—
120C2×C43⋊C8D818yescomplemented
121C2×C43⋊C8C2×D414yes—
122C2×C43⋊C8C2×D414yes—
123D344—44no—
124C23×C43—42no—
125C23×C43#12711yescharacteristic
126C22×D43—42no—
127Q8×C43—44no—
128D4×C43—44no—
129D4×C43—44no—
130D4×C43—44no—
131D4×C43—84no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—42no—
135C2×C4×C43—84no—
136C2×C4×C43#12711yescharacteristic
137C2×C4×C43#12711yescharacteristic
138C2×C4×C43#12711yescharacteristic
139C2×C4×C43C2×D814yes—
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C22×D411yescharacteristic
142C2×C4×C43C22×D411yescharacteristic
143C22⋊D43—84no—
144C2×Dic43—42no—
145D172—44no—
146D172—44no—
147D172—44no—
148C4×D43—84no—
149Dic86—44no—
150C8×C43—22no—
151C8×C43—22no—
152C43⋊C8—24no—
153C43⋊C8C2×D818yes—
154#19616—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—82no—
158C22×C43—82no—
159C22×C43—82no—
160C22×C43#49312yes—
161C22×C43C2×#12711yescharacteristic
162C2×D43—82no—
163C2×D43—82no—
164C2×D43—82no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—82no—
168C4×C43#49312yes—
169C4×C43C22×D812yes—
170C4×C43#57512yes—
171C4×C43#57512yes—
172Dic43—82no—
173#3169—431no—
174#3169—432no—
175#3169D4311yescharacteristic, complemented
176#3147—432no—
177#1722—432no—
178#1722—432no—
179#1721—432no—
180#1721—432no—
181C2×#322—431no—
182C2×C43—22no—
183C2×C43—162no—
184C2×C43C2×#49311yescharacteristic
185C2×C43#315011yescharacteristic
186C2×C43#315011yescharacteristic
187D43—162no—
188C2×#135—864no—
189#532—432no—
190#532C2×D4312yes—
191#500—432no—
192#500—431no—
193#500C2×D4311yescharacteristic
194#495—864no—
195#494—432no—
196#493—432no—
197#493—432no—
198#493—431no—
199#493C2×D4311yescharacteristic
200#492—432no—
201#492—432no—
202#486—432no—
203#486—432no—
204#486—432no—
205#486C2×D4312yes—
206#466—22no—
207#466—864no—
208#466—862no—
209C4×D8—22no—
210C4×D8—864no—
211C4×D8—862no—
212C2×C4×C8—431no—
213C2×C4×C8—431no—
214C2×C4×C8C2×D4311yescharacteristic
215#322—432no—
216#322—432no—
217C43#1961611yescharacteristic, complemented, Sylow
218C2×#41—22no—
219C2×#41—862no—
220#135—17216no—
221C2×Q16—864no—
222C2×SD16—864no—
223C2×SD16—864no—
224C2×D8—22no—
225C2×D8—864no—
226C2×D8—864no—
227C2×D8—862no—
228C22×C8—432no—
229C22×C8—432no—
230C22×C8C22⋊D4312yes—
231C4⋊Q8—432no—
232C4⋊Q8C22×D4312yes—
233#127—432no—
234#127C22×D4312yes—
235#124—22no—
236#124—862no—
237#121—22no—
238#121—22no—
239#121—862no—
240#121—862no—
241C4×D4—22no—
242C4×D4—22no—
243C4×D4—862no—
244C4×D4—862no—
245C2×C42C22×D4311yescharacteristic
246#107—22no—
247#107—864no—
248#107—862no—
249#102—24no—
250#102—864no—
251#102—864no—
252#102—864no—
253C4×C8—432no—
254C4×C8—432no—
255C4×C8—432no—
256C4×C8—432no—
257C4×C8C22⋊D4312yes—
258C4×C8C22×D4311yescharacteristic
259C4×C8C22×D4311yescharacteristic
260#41—48no—
261#41—1728no—
262C2×Q8—22no—
263C2×Q8—862no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—42no—
268C2×D4—862no—
269C2×D4—862no—
270C2×D4—862no—
271C2×D4—1722no—
272C22×C4—42no—
273C22×C4—1722no—
274C22×C4D4×D4311yescharacteristic
275C22×C4D4×D4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277Q16—1728no—
278SD16—1728no—
279SD16—1728no—
280D8—44no—
281D8—1724no—
282D8—1728no—
283D8—1728no—
284C2×C8—42no—
285C2×C8—438no—
286C2×C8—434no—
287C2×C8—434no—
288C2×C8—1722no—
289C2×C8C2×C22⋊D4312yes—
290C2×C8C2×C22⋊D4312yes—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—1722no—
298C22⋊C4—1722no—
299C42D4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42C2×C22⋊D4311yescharacteristic
302C42C23×D4311yescharacteristic
303C23—42no—
304C23—1722no—
305C23#1306332111yescharacteristic
306Q8—44no—
307Q8—1724no—
308D4—44no—
309D4—44no—
310D4—44no—
311D4—84no—
312D4—3444no—
313D4—1724no—
314D4—1724no—
315D4—1724no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—84no—
320C2×C4—3444no—
321C2×C4—1722no—
322C2×C4#1306332111yescharacteristic
323C2×C4#1306332111yescharacteristic
324C2×C4#1306332111yescharacteristic
325C2×C4D8×D4314yes—
326C2×C4C2×D4×D4311yescharacteristic
327C2×C4C2×D4×D4311yescharacteristic
328C2×C4C22×C22⋊D4311yescharacteristic
329C8—22no—
330C8—22no—
331C8—438no—
332C8—864no—
333C22—21no—
334C22—21no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—3442no—
339C22—3442no—
340C22—3442no—
341C22#1458327412yes—
342C22C2×#1306332111yescharacteristic
343C4—21no—
344C4—21no—
345C4—82no—
346C4—3442no—
347C4#1458327412yes—
348C4C2×D8×D4312yes—
349C4#1458369612yes—
350C4#1458369712yes—
351C2—22no—
352C2—162no—
353C2—6882no—
354C2C2×#1458327411yescharacteristic
355C2#1914503811yescharacteristic
356C2#1914504011yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3169C2
socleC22×C43C2×#127
hypercenter#3169D43
hypocenterC43#19616
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #19145174C2semidirect
2. #19145170C2semidirect
3. #19145021C2semidirect
4. #19134268C2semidirect
5. #19134265C2semidirect
6. #19134263C2semidirect
7. #19134260C2semidirect
8. C2×#14582621C2semidirect
9. C43×#3169C2semidirect
120. C2×C43⋊C8D8semidirect
175. #3169D43semidirect
217. C43#19616semidirect

Maximal subgroups

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

subgroupindex
#191451742
#191451702
#191450212
#191342682
#191342652
#191342632
#191342602
C2×#145826212
C43×#31692
#1961643