Finite Group Databasebeta

← #18010448

Subgroups — #18010448

Order 4736.

536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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#14558532C212yesmaximal, complemented
2#14558526C212yesmaximal, complemented
3#14558519C211yesmaximal, characteristic, complemented
4#14558512C211yesmaximal, characteristic, complemented
5C2×#11924584C211yesmaximal, characteristic
6D37⋊M16C2212yes—
7#11924615C2212yes—
8#11924601—24no—
9#11924599—24no—
10#11924597—21no—
11#11924596—21no—
12#11924595—21no—
13#11924594—21no—
14#11924584—24no—
15#11924584—24no—
16C2×#10596966—21no—
17C2×#10596966C411yescharacteristic, complemented
18C2×#10596966C2211yescharacteristic
19C2×#10596962—21no—
20C2×#10596962—21no—
21C2×#10596962C411yescharacteristic, complemented
22C2×#10596962C2211yescharacteristic
23C2×Q8×D37—21no—
24C2×Q8×D37C411yescharacteristic, complemented
25C2×Q8×D37C2211yescharacteristic
26C22×Q8×C37C411yescharacteristic, complemented
27C2×Q8×C37—22no—
28C2×Q8×C37—22no—
29C2×Q8×C37—21no—
30C2×Q8×C37C2×C411yescharacteristic
31C2×Q8×C37C2×C411yescharacteristic
32C22×C4×C37—21no—
33C22×C4×C37C2×C411yescharacteristic
34C2×C22⋊D37—21no—
35C2×C22⋊D37D411yescharacteristic
36C2×C22⋊D37D411yescharacteristic
37#10596966—28no—
38#10596966—22no—
39#10596966—22no—
40#10596966—22no—
41#10596966D414yes—
42Q8×D37—28no—
43Q8×D37—22no—
44Q8×D37—22no—
45Q8×D37—22no—
46Q8×D37D414yes—
47#10596962—28no—
48#10596962—28no—
49#10596962—22no—
50#10596962—22no—
51#10596962—22no—
52#10596962—22no—
53C2×D148—21no—
54C2×D148—21no—
55C2×D148C2×C411yescharacteristic
56C2×D148D411yescharacteristic
57C2×C4×D37—21no—
58C2×C4×D37—21no—
59C2×C4×D37—21no—
60C2×C4×D37—21no—
61C2×C4×D37—21no—
62C2×C4×D37C2×C411yescharacteristic
63C2×C4×D37C2311yescharacteristic
64C2×Dic74—21no—
65C2×Dic74—21no—
66C2×Dic74C2×C411yescharacteristic
67C2×Dic74D411yescharacteristic
68C22⋊#3866—22no—
69#10596957—22no—
70C4⋊#3866—22no—
71C4×#3866—22no—
72#10596953—22no—
73D37⋊C8—22no—
74C23×C37C22⋊C411yescharacteristic
75C22×D37—21no—
76C22×D37C22⋊C411yescharacteristic
77C22×D37C2×D411yescharacteristic
78C2×#3866—42no—
79Q8×C37—24no—
80Q8×C37—21no—
81Q8×C37—21no—
82Q8×C37C22⋊C412yes—
83Q8×C37C22⋊C412yes—
84C2×C4×C37—24no—
85C2×C4×C37—21no—
86C2×C4×C37—21no—
87C2×C4×C37—21no—
88C2×C4×C37—21no—
89C2×C4×C37C22⋊C411yescharacteristic
90C2×C4×C37C22×C411yescharacteristic
91C22⋊D37—24no—
92C22⋊D37—22no—
93C22⋊D37—22no—
94C2×Dic37—21no—
95C2×Dic37C22⋊C411yescharacteristic
96C2×Dic37C2×D411yescharacteristic
97D148—24no—
98D148—24no—
99D148—22no—
100D148—21no—
101D148C22⋊C412yes—
102C4×D37—24no—
103C4×D37—24no—
104C4×D37—24no—
105C4×D37—24no—
106C4×D37—21no—
107C4×D37—21no—
108C4×D37—24no—
109C4×D37C2×D412yes—
110C4×D37C2×D412yes—
111Dic74—24no—
112Dic74—21no—
113Dic74—24no—
114Dic74—22no—
115Dic74C22⋊C412yes—
116#64438—42no—
117C22×C37—21no—
118C22×C37—41no—
119C22×C37C2×C22⋊C411yescharacteristic
120C2×D37—21no—
121C2×D37—22no—
122C2×D37—41no—
123C2×D37—42no—
124C2×D37—41no—
125C2×D37#12012yes—
126#3866—82no—
127C4×C37—22no—
128C4×C37—22no—
129C4×C37—21no—
130C4×C37C2×C22⋊C411yescharacteristic
131C4×C37C2×C22⋊C411yescharacteristic
132Dic37—21no—
133Dic37—22no—
134Dic37#12012yes—
135#1796—371nomaximal, Sylow
136C2×C37—21no—
137C2×C37—41no—
138C2×C37#37911yescharacteristic
139D37—22no—
140D37—41no—
141D37—42no—
142C2×2−1+4—371no—
143#421—372no—
144#419—372no—
145#413—371no—
146#410—371no—
147C37#179611yescharacteristic, complemented, Sylow
1482−1+4—744no—
1492−1+4—744no—
150C2×#41—371no—
151C2×#41—371no—
152C2×#41—371no—
153C2×#41—371no—
154C2×#41—741no—
155C2×#41—741no—
156C2×#41—741no—
157C22×Q8—371no—
158C22×Q8—371no—
159C22×Q8—741no—
160C22×Q8#386611yescharacteristic, complemented
161C2×M16—372no—
162#117—372no—
163#104—744no—
164#103—744no—
165#101—741no—
166#100—741no—
167#99—741no—
168#99—741no—
169#41—374no—
170#41—742no—
171#41—742no—
172#41—742no—
173#41—742no—
174#41—748no—
175#41—748no—
176#41—742no—
177#41—742no—
178#41—748no—
179#41—742no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—371no—
184C2×Q8—374no—
185C2×Q8—371no—
186C2×Q8—741no—
187C2×Q8—741no—
188C2×Q8—742no—
189C2×Q8—742no—
190C2×Q8—748no—
191C2×Q8—742no—
192C2×Q8C2×#386611yescharacteristic
193C2×Q8C2×#386611yescharacteristic
194C2×D4—371no—
195C2×D4—371no—
196C2×D4—371no—
197C2×D4—371no—
198C2×D4—741no—
199C2×D4—741no—
200C2×D4—741no—
201C22×C4—21no—
202C22×C4—371no—
203C22×C4—371no—
204C22×C4—741no—
205C22×C4—741no—
206C22×C4—741no—
207C22×C4—741no—
208C22×C4—741no—
209C22×C4C2×#386611yescharacteristic
210M16—742no—
211M16—742no—
212C2×C8—742no—
213C4⋊C4—742no—
214C22⋊C4—742no—
215C42—742no—
216C23—371no—
217C23—371no—
218C23—741no—
219C23C22⋊#386611yescharacteristic
220Q8—24no—
221Q8—21no—
222Q8—21no—
223Q8—372no—
224Q8—744no—
225Q8—742no—
226Q8—744no—
227Q8—741no—
228Q8C22⋊#386612yes—
229Q8C22⋊#386612yes—
230D4—372no—
231D4—742no—
232D4—744no—
233D4—744no—
234D4—742no—
235D4—742no—
236D4—744no—
237D4—741no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—371no—
244C2×C4—372no—
245C2×C4—372no—
246C2×C4—371no—
247C2×C4—744no—
248C2×C4—744no—
249C2×C4—744no—
250C2×C4—744no—
251C2×C4—744no—
252C2×C4—741no—
253C2×C4—741no—
254C2×C4—741no—
255C2×C4—1482no—
256C2×C4C22⋊#386611yescharacteristic
257C2×C4C22×#386611yescharacteristic
258C8—1482no—
259C22—21no—
260C22—41no—
261C22—372no—
262C22—742no—
263C22—741no—
264C22—1481no—
265C22—1481no—
266C22—1482no—
267C22C2×C22⋊#386611yescharacteristic
268C4—22no—
269C4—22no—
270C4—21no—
271C4—372no—
272C4—2962no—
273C4—741no—
274C4—742no—
275C4C2×C22⋊#386611yescharacteristic
276C4C2×C22⋊#386611yescharacteristic
277C2—21no—
278C2—41no—
279C2—742no—
280C2—1482no—
281C2—1481no—
282C2#1455847411yescharacteristic
subgroupG/H
centerC2#14558474
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC2×C37#379
prime radicalC2×#11924584C2
cosocleC2×C4×D37C23
hypercenterC22×Q8#3866
hypocenterC37#1796
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #14558532C2semidirect
2. #14558526C2semidirect
3. #14558519C2semidirect
4. #14558512C2semidirect
17. C2×#10596966C4semidirect
21. C2×#10596962C4semidirect
24. C2×Q8×D37C4semidirect
26. C22×Q8×C37C4semidirect
147. C37#1796semidirect
160. C22×Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585322
#145585262
#145585192
#145585122
C2×#119245842
#179637