Finite Group Databasebeta

← #18006397

Subgroups — #18006397

Order 4736.

444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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#14558349C212yesmaximal, complemented
2#14558348C212yesmaximal, complemented
3#14557912C211yesmaximal, characteristic, complemented
4#14557807C212yesmaximal, complemented
5#14557806C212yesmaximal, complemented
6#14557717C212yesmaximal, complemented
7#14557715C211yesmaximal, characteristic, complemented
8#14557647C212yesmaximal, complemented
9C37×#456C211yesmaximal, characteristic, complemented
10#11924584C2211yescharacteristic
11#11924583C2212yes—
12#11924569C2212yes—
13#11924568—22no—
14#11924567—22no—
15#11924567C2212yes—
16#11924566—22no—
17#11924566C2212yes—
18#11924565—22no—
19#11924557—22no—
20#11924556—22no—
21#11924556C2212yes—
22C2×#10596942—22no—
23C2×#10596942C2212yes—
24C2×#10596942C2212yes—
25Q16×D37—22no—
26#11924544C2212yes—
27#11924543C2212yes—
28#11924536C2211yescharacteristic
29#11924471C2212yes—
30#11924464C2212yes—
31#11924455C2211yescharacteristic
32#11924454C2212yes—
33C4×#64436C2211yescharacteristic
342−1+4×C37C2211yescharacteristic
35#137×C37C2212yes—
36C4⋊Q8×C37C2211yescharacteristic
37#104×C37C2212yes—
38#101×C37C2211yescharacteristic
39#41×C37—22no—
40#41×C37—41no—
41#41×C37C2312yes—
42C2×Q8×C37—22no—
43C2×Q8×C37C2311yescharacteristic
44C2×Q8×C37C2311yescharacteristic
45#10596966—22no—
46Q8×D37—22no—
47Q8×D37—22no—
48#10596964—22no—
49#10596964—42no—
50#10596962—22no—
51#10596962—41no—
52#10596962C2312yes—
53C2×Dic74—22no—
54C2×Dic74C2312yes—
55Q16×C37—22no—
56SD16×C37—22no—
57M16×C37C2312yes—
58C4⋊C4×C37—41no—
59C42×C37C2311yescharacteristic
60#10596942—22no—
61#10596942—22no—
62#10596942—22no—
63#10596942—22no—
64#10596942—22no—
65#10596942—22no—
66#10596942D412yes—
67#10596941—22no—
68#10596941D412yes—
69#10596940—22no—
70#10596940D412yes—
71#10596939D412yes—
72C4⋊Dic37—41no—
73#10596934—22no—
74#10596934C2312yes—
75C2×#64436—22no—
76C2×#64436C2312yes—
77Dic148—22no—
78#10596930—22no—
79#10596929—22no—
80C8×D37—22no—
81Q8×C37—22no—
82Q8×C37—22no—
83Q8×C37—41no—
84Q8×C37C2×D412yes—
85D4×C37—22no—
86D4×C37—41no—
87D4×C37C2×D412yes—
88C2×C4×C37—21no—
89C2×C4×C37—22no—
90C2×C4×C37—21no—
91C2×C4×C37—21no—
92C2×C4×C37—42no—
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—22no—
95C22⋊D37—42no—
96C2×Dic37—22no—
97C2×Dic37—42no—
98D148—41no—
99D148C2×D412yes—
100C4×D37—22no—
101C4×D37—42no—
102C4×D37—42no—
103Dic74—22no—
104Dic74—22no—
105Dic74—41no—
106Dic74—42no—
107Dic74C2×D412yes—
108C8×C37—22no—
109#64436—22no—
110#64436C2×D412yes—
111#64436C2×D412yes—
112C22×C37—22no—
113C22×C37H(5,𝔽2)11yescharacteristic
114C2×D37—22no—
115C4×C37—22no—
116C4×C37—22no—
117C4×C37—41no—
118C4×C37—41no—
119C4×C37C22×D412yes—
120Dic37—22no—
121Dic37—42no—
122#3293—371nomaximal, Sylow
123C2×C37—21no—
124C2×C37—42no—
125C2×C37D4211yescharacteristic
126D37—42no—
127#578—372no—
128#578—372no—
129#494—371no—
130#473—372no—
131#473—372no—
132#456—371no—
133#456—372no—
134#456D3711yescharacteristic, complemented
135#443—372no—
136C37#329311yescharacteristic, complemented, Sylow
1372−1+4—372no—
1382−1+4—371no—
1392−1+4C2×D3711yescharacteristic
140#137—372no—
141#137—372no—
142#137—372no—
143#137—742no—
144#137—742no—
145#137—742no—
146#137—742no—
147#137C2×D3712yes—
148#135—372no—
149#135—742no—
150#135—742no—
151C2×Q16—372no—
152C2×Q16—372no—
153C2×Q16—742no—
154C2×Q16—742no—
155#131—372no—
156#131—372no—
157C4⋊Q8—371no—
158C4⋊Q8C2×D3711yescharacteristic
159#108—372no—
160#104—372no—
161#104C2×D3712yes—
162#101—371no—
163#101—372no—
164#101C2×D3711yescharacteristic
165C4×C8—371no—
166#41—22no—
167#41—41no—
168#41—372no—
169#41—742no—
170#41—742no—
171#41—742no—
172#41—1481no—
173#41—1482no—
174#41C22×D3712yes—
175C2×Q8—22no—
176C2×Q8—372no—
177C2×Q8—742no—
178C2×Q8—742no—
179C2×Q8—742no—
180C2×Q8C22×D3711yescharacteristic
181C2×Q8C22×D3711yescharacteristic
182Q16—22no—
183Q16—372no—
184Q16—742no—
185Q16—742no—
186Q16—742no—
187Q16—742no—
188Q16—742no—
189Q16—742no—
190Q16—742no—
191SD16—22no—
192SD16—372no—
193SD16—372no—
194SD16—742no—
195SD16—742no—
196SD16—742no—
197D8—372no—
198M16—372no—
199M16—742no—
200M16—742no—
201M16C22×D3712yes—
202C2×C8—372no—
203C2×C8—742no—
204C2×C8—742no—
205C4⋊C4—41no—
206C4⋊C4—1481no—
207C42C22×D3711yescharacteristic
208Q8—22no—
209Q8—22no—
210Q8—41no—
211Q8—372no—
212Q8—742no—
213Q8—742no—
214Q8—1482no—
215Q8—1481no—
216Q8D4×D3712yes—
217D4—22no—
218D4—41no—
219D4—372no—
220D4—742no—
221D4—1481no—
222D4—1482no—
223D4D4×D3712yes—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—742no—
230C2×C4—742no—
231C2×C4—1482no—
232C2×C4—1482no—
233C2×C4—1482no—
234C2×C4C23×D3711yescharacteristic
235C8—22no—
236C8—372no—
237C8—372no—
238C8—742no—
239C22—22no—
240C22—742no—
241C22#1192458111yescharacteristic
242C4—22no—
243C4—22no—
244C4—41no—
245C4—41no—
246C4—742no—
247C4—1482no—
248C4C2×D4×D3712yes—
249C2—21no—
250C2—42no—
251C2—1482no—
252C2#1455816511yescharacteristic
subgroupG/H
centerC2#14558165
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#456C2
socleC2×C37D42
hypercenter#456D37
hypocenterC37#3293
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14558349C2semidirect
2. #14558348C2semidirect
3. #14557912C2semidirect
4. #14557807C2semidirect
5. #14557806C2semidirect
6. #14557717C2semidirect
7. #14557715C2semidirect
8. #14557647C2semidirect
9. C37×#456C2semidirect
134. #456D37semidirect
136. C37#3293semidirect

Maximal subgroups

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

subgroupindex
#145583492
#145583482
#145579122
#145578072
#145578062
#145577172
#145577152
#145576472
C37×#4562
#329337