Finite Group Databasebeta

← #25078516

Subgroups — #25078516

Order 11008.

920 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145606C212yesmaximal, complemented
2#19145117C211yesmaximal, characteristic, complemented
3#19133912C218yesmaximal, complemented
4#19133233C211yesmaximal, characteristic, complemented
5#19133206C212yesmaximal, complemented
6C43×#3548C211yesmaximal, characteristic
7#14583456C2211yescharacteristic
8#14583309C2214yes—
9#14583305—22no—
10#14583294C2214yes—
11#14583258C2214yes—
12#14583106—22no—
13#14583096—22no—
14#14583061—24no—
15#14582956C2212yes—
16#14582935—22no—
17C2×#13063236C2211yescharacteristic
18#14582641C2214yes—
19#14582639C2218yes—
20C43×#562C2214yes—
21C43×#554—22no—
22C43×#550—22no—
23C43×#547—22no—
24C43×#540—22no—
25C43×#537—24no—
26C43×#533C2211yescharacteristic
27C43×#532C2212yes—
28C2×#10621885—24no—
29C2×#10621883—24no—
30C22×C43⋊C8—21no—
31#13063325C2312yes—
32#13063317—21no—
33#13063304—22no—
34C4×Dic86—22no—
35#13063284—21no—
36#13063258—24no—
37#13063256—24no—
38C4⋊(C43⋊C8)—22no—
39#13063249—24no—
40#13063246—24no—
41C22⋊(C43⋊C8)—22no—
42#13063236—21no—
43#13063236C2312yes—
44#13063236C2314yes—
45C2×#41×C43—24no—
46C2×#41×C43D414yes—
47C4⋊Q8×C43D412yes—
48C4⋊Q8×C43D412yes—
49#127×C43—22no—
50#127×C43D412yes—
51#125×C43—22no—
52#125×C43C2312yes—
53#124×C43C2314yes—
54#123×C43—28no—
55C22⋊Q8×C43—24no—
56C22⋊Q8×C43—28no—
57C22⋊Q8×C43—22no—
58#121×C43—28no—
59#121×C43—24no—
60#121×C43—28no—
61#121×C43—22no—
62#121×C43—22no—
63C4×Q8×C43—22no—
64C4×D4×C43—24no—
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67#117×C43D412yes—
68C2×C4⋊C4×C43—24no—
69C2×C42×C43C2311yescharacteristic
70#41×C43—84no—
71#41×C43—88no—
72C2×Q8×C43—22no—
73C2×Q8×C43C2×D414yes—
74C2×D4×C43—28no—
75C2×D4×C43—22no—
76C2×D4×C43—22no—
77C2×D4×C43—24no—
78C2×D4×C43C2×D414yes—
79C22×C4×C43—28no—
80C22×C4×C43—24no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C2×Dic86—22no—
84C4⋊C4×C43—28no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—24no—
89C4⋊C4×C43C2×D414yes—
90C22⋊C4×C43—28no—
91C22⋊C4×C43—24no—
92C22⋊C4×C43—24no—
93C22⋊C4×C43—22no—
94C42×C43—22no—
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D412yes—
97C42×C43C2411yescharacteristic
98C22⋊Dic43—41no—
99#10621885—84no—
100#10621883—84no—
101C4⋊Dic43—22no—
102C4⋊Dic43—22no—
103Dic43⋊C4—42no—
104C4×Dic43—41no—
105C2×C43⋊C8—24no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—24no—
108C23×C43—24no—
109C23×C43#12011yescharacteristic
110Q8×C43—44no—
111Q8×C43—44no—
112D4×C43—44no—
113D4×C43—44no—
114D4×C43—44no—
115D4×C43—84no—
116D4×C43—88no—
117C2×C4×C43—22no—
118C2×C4×C43—24no—
119C2×C4×C43—24no—
120C2×C4×C43—42no—
121C2×C4×C43—48no—
122C2×C4×C43—88no—
123C2×C4×C43#12012yes—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43C22×D411yescharacteristic
126C2×C4×C43C22×D412yes—
127C2×Dic43—42no—
128Dic86—42no—
129Dic86—42no—
130C43⋊C8—24no—
131C43⋊C8—44no—
132#19065—431nomaximal, Sylow
133C22×C43—21no—
134C22×C43—22no—
135C22×C43—44no—
136C22×C43—44no—
137C22×C43—44no—
138C22×C43C2×#12011yescharacteristic
139C4×C43—21no—
140C4×C43—22no—
141C4×C43—22no—
142C4×C43—44no—
143C4×C43—44no—
144C4×C43#45612yes—
145Dic43—82no—
146#3548D4311yescharacteristic
147#3216—432no—
148#3162—431no—
149#1661—438no—
150#1537—431no—
151#1530—432no—
152C2×C43—41no—
153C2×C43—84no—
154C2×C43C2×#45611yescharacteristic
155C2×C43#301912yes—
156#562C2×D4314yes—
157#554—22no—
158#550—22no—
159#547—22no—
160#540—22no—
161#537—24no—
162#533—431no—
163#533C2×D4311yescharacteristic
164#532C2×D4312yes—
165#501—434no—
166#501—862no—
167#497—434no—
168#489—434no—
169#462—862no—
170#460—862no—
171#452—864no—
172#432—432no—
173#427—862no—
174C2×#97—431no—
175#330—434no—
176#329—438no—
177C43#1906511yescharacteristic, complemented, Sylow
178C2×#41—24no—
179C2×#41C22⋊D4314yes—
180C2×Q16—864no—
181C2×SD16—864no—
182C22×C8—861no—
183C4⋊Q8—432no—
184C4⋊Q8C22⋊D4312yes—
185C4⋊Q8C22⋊D4312yes—
186#127—22no—
187#127C22⋊D4312yes—
188#125—22no—
189#125—861no—
190#125C22×D4312yes—
191#124C22×D4314yes—
192#123—28no—
193C22⋊Q8—24no—
194C22⋊Q8—28no—
195C22⋊Q8—22no—
196C22⋊Q8—862no—
197#121—28no—
198#121—24no—
199#121—28no—
200#121—22no—
201#121—22no—
202C4×Q8—22no—
203C4×Q8—862no—
204C4×D4—24no—
205C4×D4—22no—
206C4×D4—22no—
207#117—861no—
208#117C22⋊D4312yes—
209C2×C4⋊C4—24no—
210C2×C42C22×D4311yescharacteristic
211#107—864no—
212#106—864no—
213C4⋊C8—862no—
214#103—864no—
215#102—864no—
216C22⋊C8—862no—
217#97—432no—
218#97—434no—
219#97—861no—
220#41—84no—
221#41—88no—
222C2×Q8—22no—
223C2×Q8—862no—
224C2×Q8C2×C22⋊D4314yes—
225C2×D4—28no—
226C2×D4—24no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4C2×C22⋊D4314yes—
230C22×C4—28no—
231C22×C4—24no—
232C22×C4C2×C22⋊D4311yescharacteristic
233C22×C4C2×C22⋊D4312yes—
234Q16—3444no—
235SD16—3444no—
236C2×C8—864no—
237C2×C8—862no—
238C2×C8—864no—
239C4⋊C4—28no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—24no—
244C4⋊C4—862no—
245C4⋊C4—862no—
246C4⋊C4—1722no—
247C4⋊C4C2×C22⋊D4314yes—
248C22⋊C4—28no—
249C22⋊C4—22no—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—1721no—
253C42—22no—
254C42—1721no—
255C42C2×C22⋊D4311yescharacteristic
256C42C2×C22⋊D4312yes—
257C42C23×D4311yescharacteristic
258C23—24no—
259C23#1306329411yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—1722no—
263Q8—1722no—
264D4—44no—
265D4—44no—
266D4—44no—
267D4—84no—
268D4—88no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—48no—
274C2×C4—88no—
275C2×C4—1722no—
276C2×C4#1306329412yes—
277C2×C4#1306329411yescharacteristic
278C2×C4C22×C22⋊D4311yescharacteristic
279C2×C4C22×C22⋊D4312yes—
280C8—864no—
281C8—1724no—
282C22—21no—
283C22—22no—
284C22—44no—
285C22—44no—
286C22—44no—
287C22C2×#1306329411yescharacteristic
288C4—21no—
289C4—22no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—3442no—
294C4#1458308212yes—
295C2—41no—
296C2—84no—
297C2C2×#1458308211yescharacteristic
298C2#1914395212yes—
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3548C2
socleC22×C43C2×#120
hypercenter#3548D43
hypocenterC43#19065
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #19145606C2semidirect
2. #19145117C2semidirect
3. #19133912C2semidirect
4. #19133233C2semidirect
5. #19133206C2semidirect
177. C43#19065semidirect

Maximal subgroups

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

subgroupindex
#191456062
#191451172
#191339122
#191332332
#191332062
C43×#35482
#1906543