Finite Group Databasebeta

← #18010761

Subgroups — #18010761

Order 4736.

336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#11924601C212yesmaximal, complemented
2C2×#11924600C212yesmaximal, complemented
3C4×#10596953C211yesmaximal, characteristic, complemented
4C4×C4⋊#3866C211yesmaximal, characteristic, complemented
5#14558082C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C4⋊#3866—21no—
8C2×C4×#3866C2212yes—
9#11924601—24no—
10#11924600—24no—
11#11924591—21no—
12C4×#64438—21no—
13(C2×#3866)⋊C4—21no—
14C2×#10596966C2211yescharacteristic
15C2×#10596964C2211yescharacteristic
16#11924534C411yescharacteristic, complemented
17#11924532C411yescharacteristic, complemented
18#11924524C411yescharacteristic, complemented
19#11924509—21no—
20#11924509—21no—
21#11924496—21no—
22#11924496—21no—
23C42×D37C2211yescharacteristic
24#124×C37C411yescharacteristic, complemented
25C22×#3866—22no—
26C2×Q8×C37C2×C411yescharacteristic
27C2×D4×C37C2×C411yescharacteristic
28C2×C22⋊D37—21no—
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32#10596966—22no—
33#10596966—22no—
34#10596964—22no—
35#10596964—22no—
36C2×D148—21no—
37C2×D148C2×C411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37C2311yescharacteristic
42C2×Dic74C2×C411yescharacteristic
43C2×#64438—22no—
44C4⋊#3866—24no—
45C4×#3866—22no—
46C4×#3866—22no—
47#10596953—22no—
48#10596953D414yescomplemented
49C22⋊C4×C37—21no—
50C22⋊C4×C37—21no—
51C42×C37C2×C411yescharacteristic
52#10596938—21no—
53#10596938—21no—
54#10596936—21no—
55#10596936—21no—
56C4×Dic37C2×C411yescharacteristic
57C4×Dic37D411yescharacteristic
58C4×Dic37D411yescharacteristic
59C23×C37—21no—
60C22×D37—21no—
61C22×D37C2×D411yescharacteristic
62C2×#3866—24no—
63C2×#3866—42no—
64C2×#3866—42no—
65Q8×C37—22no—
66D4×C37—22no—
67C2×C4×C37—21no—
68C2×C4×C37C22⋊C411yescharacteristic
69C2×C4×C37C22⋊C411yescharacteristic
70C2×C4×C37C22×C411yescharacteristic
71C22⋊D37—42no—
72C22⋊D37—41no—
73C22⋊D37—41no—
74C22⋊D37—42no—
75C2×Dic37—21no—
76C2×Dic37—42no—
77C2×Dic37C22⋊C411yescharacteristic
78C2×Dic37C22⋊C411yescharacteristic
79C2×Dic37C2×D411yescharacteristic
80D148—22no—
81D148—41no—
82D148—41no—
83C4×D37—22no—
84C4×D37—41no—
85C4×D37—42no—
86C4×D37C2×D412yes—
87C4×D37#4112yes—
88Dic74—22no—
89#64438—24no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37#12411yescharacteristic
100C2×D37#12711yescharacteristic
101#3866—44no—
102C4×C37—21no—
103C4×C37—21no—
104C4×C37—41no—
105C4×C37C4×D412yes—
106Dic37—21no—
107Dic37—41no—
108Dic37#10412yescomplemented
109Dic37#12112yes—
110#1980—371nomaximal, Sylow
111C2×C37—81no—
112C2×C37#39011yescharacteristic
113C2×C37C2×#10411yescharacteristic
114C2×C37#42111yescharacteristic
115D37—21no—
116D37—21no—
117D37—81no—
118#532—371no—
119C2×#104—372no—
120C2×#104—372no—
121C4×M16—371no—
122C4×C4⋊C4—371no—
123C37#198011yescharacteristic, complemented, Sylow
124C2×#41—371no—
125C2×#41—371no—
126C2×M16—372no—
127C4⋊Q8—371no—
128#127—371no—
129#124—371no—
130#124#386611yescharacteristic, complemented
131#121—741no—
132#121—741no—
133C4×D4—741no—
134C4×D4—741no—
135C2×C4⋊C4—741no—
136C2×C42—371no—
137C2×C42—372no—
138#104—744no—
139#104—744no—
140#97—741no—
141C4×C8—741no—
142#95—741no—
143#41—742no—
144#41—742no—
145#41—742no—
146#41—742no—
147C2×Q8—371no—
148C2×Q8C2×#386611yescharacteristic
149C2×D4—371no—
150C2×D4—741no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4—741no—
154C2×D4C2×#386611yescharacteristic
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—741no—
159C22×C4—741no—
160C22×C4—742no—
161M16—374no—
162M16—742no—
163C2×C8—742no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—744no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C42—371no—
172C42—371no—
173C42—371no—
174C42—742no—
175C42—742no—
176C42C2×#386611yescharacteristic
177C23—21no—
178C23—371no—
179C23—741no—
180Q8—22no—
181Q8—742no—
182D4—22no—
183D4—742no—
184D4—1481no—
185D4—1481no—
186D4—1482no—
187D4—1482no—
188D4—1481no—
189D4—1481no—
190C2×C4—21no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—372no—
194C2×C4—372no—
195C2×C4—371no—
196C2×C4—742no—
197C2×C4—744no—
198C2×C4—741no—
199C2×C4—1481no—
200C2×C4—1482no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1482no—
204C2×C4C22⋊#386611yescharacteristic
205C2×C4C22⋊#386611yescharacteristic
206C2×C4C22×#386611yescharacteristic
207C8—744no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—371no—
212C22—371no—
213C22—741no—
214C22—741no—
215C22—1481no—
216C22—1481no—
217C22—1481no—
218C22C2×C22⋊#386611yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—372no—
223C4—372no—
224C4—741no—
225C4—1484no—
226C4—1481no—
227C4D4×#386612yes—
228C2—81no—
229C2—2961no—
230C2—741no—
231C2—741no—
232C2#1455848511yescharacteristic
233C2D37⋊#10411yescharacteristic
234C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558082C2
cosocleC2×C4×D37C23
hypercenter#124#3866
hypocenterC37#1980
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#11924601C2semidirect
2. C2×#11924600C2semidirect
3. C4×#10596953C2semidirect
4. C4×C4⋊#3866C2semidirect
16. #11924534C4semidirect
17. #11924532C4semidirect
18. #11924524C4semidirect
24. #124×C37C4semidirect
48. #10596953D4semidirect
108. Dic37#104semidirect
123. C37#1980semidirect
130. #124#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246012
C2×#119246002
C4×#105969532
C4×C4⋊#38662
#145580822
#198037