Finite Group Databasebeta

← #17995654

Subgroups — #17995654

Order 4736.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#14558331C211yesmaximal, characteristic
2#14558107C211yesmaximal, characteristic, complemented
3#14557549C211yesmaximal, characteristic, complemented
4#14557542C211yesmaximal, characteristic, complemented
5#14557507C211yesmaximal, characteristic, complemented
6#14557305C211yesmaximal, characteristic, complemented
7C2×#137×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—21no—
10#11924566—21no—
11#11924562—21no—
12#11924561—21no—
13#11924556—22no—
14C2×#10596934C2211yescharacteristic
15#11924534—21no—
16#11924525—21no—
17#11924519—22no—
18#11924512—22no—
19#11924495C2211yescharacteristic
20#11924495C2211yescharacteristic
21#11924462—22no—
22#11924460—22no—
23#11924451—22no—
24C2×#41×C37C2211yescharacteristic
25C22×Q8×C37C2211yescharacteristic
26#137×C37—22no—
27#137×C37—22no—
28C2×Q16×C37—21no—
29C2×SD16×C37—21no—
30C2×M16×C37C2211yescharacteristic
31#41×C37—21no—
32#41×C37—21no—
33#41×C37—21no—
34#41×C37—21no—
35C2×Q8×C37—21no—
36C2×Q8×C37—21no—
37C2×Q8×C37—21no—
38C2×Q8×C37—21no—
39C2×Q8×C37—21no—
40C2×Q8×C37D412yes—
41C2×Q8×C37D411yescharacteristic
42C2×D4×C37—21no—
43C2×D4×C37D411yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37—21no—
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—21no—
48#10596962—21no—
49#10596962—21no—
50#10596962—21no—
51#10596962—21no—
52C2×D148D411yescharacteristic
53C2×C4×D37—21no—
54C2×Dic74D411yescharacteristic
55Q16×C37—24no—
56SD16×C37—24no—
57M16×C37—21no—
58M16×C37D412yes—
59C2×C8×C37—21no—
60C22⋊Dic37—21no—
61C22⋊Dic37D412yes—
62#10596942—22no—
63#10596941—22no—
64#10596940—22no—
65#10596939—22no—
66#10596938—24no—
67C4⋊Dic37—21no—
68C4⋊Dic37—21no—
69#10596936—24no—
70C4×Dic37—21no—
71C4×Dic37—21no—
72#10596934—21no—
73#10596934—21no—
74C2×#64436D412yes—
75C23×C37—21no—
76C23×C37C2×D411yescharacteristic
77C22×D37—21no—
78Q8×C37—21no—
79Q8×C37—22no—
80Q8×C37—21no—
81Q8×C37—22no—
82Q8×C37—41no—
83Q8×C37—41no—
84D4×C37—21no—
85D4×C37—21no—
86D4×C37—41no—
87D4×C37—41no—
88C2×C4×C37—22no—
89C2×C4×C37—21no—
90C2×C4×C37—41no—
91C2×C4×C37—41no—
92C2×C4×C37—41no—
93C2×C4×C37—41no—
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37#4111yescharacteristic
100C22⋊D37—41no—
101C22⋊D37—41no—
102C2×Dic37—22no—
103C2×Dic37—21no—
104C2×Dic37—41no—
105D148—21no—
106D148—21no—
107C4×D37—41no—
108C4×D37—41no—
109Dic74—21no—
110Dic74—21no—
111C8×C37—22no—
112#64436—22no—
113C22×C37—41no—
114C22×C37—41no—
115C22×C37—81no—
116C22×C37#12011yescharacteristic
117C22×C37#12111yescharacteristic
118C22×C37#12711yescharacteristic
119C2×D37—42no—
120C2×D37—41no—
121C4×C37—41no—
122C4×C37—42no—
123C4×C37#12011yescharacteristic
124C4×C37#12011yescharacteristic
125C4×C37#12111yescharacteristic
126C4×C37#12111yescharacteristic
127Dic37—42no—
128Dic37—41no—
129Dic37—81no—
130#2009—371nomaximal, Sylow
131C2×C37—21no—
132C2×C37—21no—
133C2×C37—21no—
134C2×C37—81no—
135C2×C37#39211yescharacteristic
136D37—81no—
137#575—371no—
138C2×#137D3711yescharacteristic, complemented
139#536—371no—
140#421—371no—
141#419—371no—
142#410—371no—
143#344—371no—
144C37#200911yescharacteristic, complemented, Sylow
145C2×#41—371no—
146C2×#41C2×D3711yescharacteristic
147C22×Q8C2×D3711yescharacteristic
148#137—22no—
149#137—22no—
150#137—741no—
151#137—741no—
152AGL(1,ℤ/8)—741no—
153AGL(1,ℤ/8)—741no—
154#135—742no—
155C2×Q16—21no—
156C2×SD16—21no—
157C2×M16—371no—
158C2×M16C2×D3711yescharacteristic
159C4⋊Q8—741no—
160#124—741no—
161#123—742no—
162C22⋊Q8—742no—
163#117—371no—
164#117—371no—
165#104—742no—
166#103—742no—
167#99—742no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—741no—
173#41—741no—
174#41—741no—
175#41—741no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—371no—
182C2×Q8C22⋊D3712yes—
183C2×Q8C22⋊D3711yescharacteristic
184C2×D4—21no—
185C2×D4—371no—
186C2×D4—741no—
187C2×D4C22⋊D3711yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—741no—
191C22×C4C22×D3711yescharacteristic
192Q16—24no—
193Q16—742no—
194SD16—24no—
195SD16—742no—
196SD16—742no—
197D8—742no—
198M16—21no—
199M16—741no—
200M16—741no—
201M16C22⋊D3712yes—
202C2×C8—21no—
203C2×C8—372no—
204C4⋊C4—744no—
205C4⋊C4—741no—
206C4⋊C4—741no—
207C22⋊C4—372no—
208C22⋊C4—744no—
209C22⋊C4—741no—
210C42—741no—
211C42—741no—
212C23—21no—
213C23—741no—
214C23D4×D3711yescharacteristic
215Q8—21no—
216Q8—22no—
217Q8—21no—
218Q8—22no—
219Q8—41no—
220Q8—41no—
221Q8—741no—
222Q8—741no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—741no—
228D4—741no—
229D4—1481no—
230D4—1481no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—742no—
238C2×C4—741no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4—1481no—
242C2×C4D4×D3711yescharacteristic
243C2×C4D4×D3711yescharacteristic
244C2×C4#1059696411yescharacteristic
245C2×C4C2×C22⋊D3711yescharacteristic
246C2×C4C2×C22⋊D3711yescharacteristic
247C2×C4C2×C22⋊D3711yescharacteristic
248C8—22no—
249C8—742no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—1482no—
254C22—1481no—
255C22#1192450411yescharacteristic
256C22#1192450811yescharacteristic
257C22#1192453211yescharacteristic
258C4—41no—
259C4—42no—
260C4—2961no—
261C4—1482no—
262C4—1481no—
263C4#1192450411yescharacteristic
264C4#1192450511yescharacteristic
265C4#1192450711yescharacteristic
266C4#1192450811yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—2961no—
272C2#1455744111yescharacteristic
subgroupG/H
centerC2#14557441
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#137×C37C2
socleC2×C37#392
prime radical#14558331C2
hypercenterC2×#137D37
hypocenterC37#2009
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. #14558107C2semidirect
3. #14557549C2semidirect
4. #14557542C2semidirect
5. #14557507C2semidirect
6. #14557305C2semidirect
7. C2×#137×C37C2semidirect
138. C2×#137D37semidirect
144. C37#2009semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145581072
#145575492
#145575422
#145575072
#145573052
C2×#137×C372
#200937