Finite Group Databasebeta

← #17994570

Subgroups — #17994570

Order 4736.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11924583C211yesmaximal, characteristic
2#14557550C211yesmaximal, characteristic, complemented
3#14557543C211yesmaximal, characteristic, complemented
4#14557541C211yesmaximal, characteristic, complemented
5#14557515C211yesmaximal, characteristic, complemented
6#14557506C211yesmaximal, characteristic, complemented
7C37×#421C211yesmaximal, characteristic, complemented
8#11924583—22no—
9#11924583—22no—
10#11924583—22no—
11#11924583—22no—
12C2×#10596962—21no—
13C2×#10596962C2211yescharacteristic
14C2×#10596964—22no—
15C2×#10596964C412yescomplemented
16C22×Dic74—21no—
17C22×Dic74C2211yescharacteristic
18C2×Q8×D37C412yescomplemented
19C2×#10596934C2211yescharacteristic
20#11924495C2211yescharacteristic
21#11924463—22no—
22#11924461—22no—
23#11924459—22no—
24#11924454—21no—
25#11924452—21no—
26#11924450—22no—
27C2×#41×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#104×C37—22no—
31#41×C37—21no—
32#41×C37—21no—
33#41×C37D412yes—
34#41×C37D412yes—
35C2×Q8×C37C2×C411yescharacteristic
36C2×D4×C37—21no—
37C2×D4×C37C2×C411yescharacteristic
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—22no—
41C2×C22⋊D37D412yes—
42C22×Dic37—21no—
43C22×Dic37—22no—
44Q8×D37—24no—
45Q8×D37—24no—
46#10596964—28no—
47#10596964—28no—
48#10596964—24no—
49#10596964—24no—
50#10596962—24no—
51#10596962—24no—
52#10596962—21no—
53#10596962—21no—
54#10596962—21no—
55#10596962—21no—
56C2×D148D411yescharacteristic
57C2×C4×D37—22no—
58C2×C4×D37C2×C412yes—
59C2×Dic74—24no—
60C2×Dic74—24no—
61C2×Dic74—21no—
62C2×Dic74—21no—
63C2×Dic74—21no—
64C2×Dic74—22no—
65C2×Dic74C2×C412yes—
66C2×Dic74D411yescharacteristic
67C2×Dic74D412yes—
68C2×Dic74D412yes—
69M16×C37—21no—
70M16×C37—21no—
71C2×C8×C37—21no—
72C4⋊C4×C37—21no—
73C22⋊C4×C37—21no—
74C42×C37—21no—
75C22⋊Dic37—21no—
76C4⋊Dic37—21no—
77C4×Dic37—21no—
78#10596934—21no—
79#10596934—21no—
80C2×#64436—21no—
81C23×C37—21no—
82C23×C37C2×D411yescharacteristic
83C22×D37C22⋊C412yes—
84Q8×C37—21no—
85Q8×C37C22⋊C412yes—
86D4×C37—22no—
87D4×C37—22no—
88D4×C37—21no—
89D4×C37C22⋊C412yes—
90C2×C4×C37—21no—
91C2×C4×C37—22no—
92C2×C4×C37—22no—
93C2×C4×C37—41no—
94C2×C4×C37C22×C411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C22⋊D37—28no—
101C22⋊D37—22no—
102C22⋊D37—22no—
103C2×Dic37—28no—
104C2×Dic37—22no—
105C2×Dic37—22no—
106C2×Dic37—22no—
107C2×Dic37—41no—
108C2×Dic37C22⋊C412yes—
109D148—21no—
110D148—21no—
111C4×D37—28no—
112C4×D37—22no—
113C4×D37—22no—
114Dic74—28no—
115Dic74—22no—
116Dic74—21no—
117Dic74—22no—
118Dic74—21no—
119Dic74—22no—
120Dic74C22⋊C414yes—
121C8×C37—41no—
122#64436—41no—
123C22×C37—22no—
124C22×C37—41no—
125C22×C37—42no—
126C22×C37C2×C22⋊C411yescharacteristic
127C22×C37#12011yescharacteristic
128C22×C37#12011yescharacteristic
129C2×D37—22no—
130C2×D37—42no—
131C4×C37—22no—
132C4×C37—81no—
133C4×C37C2×C22⋊C411yescharacteristic
134C4×C37C2×C22⋊C411yescharacteristic
135C4×C37#12011yescharacteristic
136C4×C37#12011yescharacteristic
137Dic37—22no—
138Dic37—24no—
139Dic37—81no—
140#1796—371nomaximal, Sylow
141C2×C37—21no—
142C2×C37—21no—
143C2×C37—21no—
144C2×C37—42no—
145C2×C37#37911yescharacteristic
146D37—42no—
147C2×2−1+4—371no—
148#421—371no—
149#421D3711yescharacteristic, complemented
150#419—371no—
151#419—371no—
152#413—371no—
153#410—371no—
154C37#179611yescharacteristic, complemented, Sylow
1552−1+4—742no—
1562−1+4—742no—
1572−1+4—742no—
1582−1+4—742no—
159C2×#41—371no—
160C2×#41—372no—
161C2×#41—741no—
162C2×#41—742no—
163C2×#41C2×D3711yescharacteristic
164C22×Q8—372no—
165C22×Q8—371no—
166C22×Q8—741no—
167C2×M16—371no—
168C2×M16C2×D3711yescharacteristic
169#117—371no—
170#117C2×D3711yescharacteristic
171#104—22no—
172#104—742no—
173#103—742no—
174#103—742no—
175#101—741no—
176#100—741no—
177#99—742no—
178#41—21no—
179#41—21no—
180#41—744no—
181#41—744no—
182#41—744no—
183#41—748no—
184#41—748no—
185#41—744no—
186#41—741no—
187#41—741no—
188#41—741no—
189#41—741no—
190#41D14812yes—
191#41C22⋊D3712yes—
192C2×Q8—371no—
193C2×Q8—372no—
194C2×Q8—372no—
195C2×Q8—372no—
196C2×Q8—742no—
197C2×Q8—744no—
198C2×Q8—744no—
199C2×Q8—744no—
200C2×Q8—744no—
201C2×Q8—741no—
202C2×Q8—741no—
203C2×Q8—741no—
204C2×Q8C4×D3711yescharacteristic
205C2×D4—21no—
206C2×D4—372no—
207C2×D4—371no—
208C2×D4—742no—
209C2×D4C4×D3711yescharacteristic
210C22×C4—21no—
211C22×C4—372no—
212C22×C4—742no—
213C22×C4—742no—
214C22×C4—741no—
215C22×C4C22×D3711yescharacteristic
216M16—21no—
217M16—21no—
218M16—741no—
219M16—741no—
220C2×C8—21no—
221C2×C8—741no—
222C4⋊C4—21no—
223C4⋊C4—741no—
224C22⋊C4—21no—
225C22⋊C4—741no—
226C42—21no—
227C42—741no—
228C23—21no—
229C23—372no—
230C23D4×D3711yescharacteristic
231Q8—21no—
232Q8—374no—
233Q8—748no—
234Q8—742no—
235Q8—741no—
236Q8—742no—
237Q8—741no—
238Q8—742no—
239Q8#1059693812yes—
240D4—22no—
241D4—22no—
242D4—21no—
243D4—748no—
244D4—742no—
245D4—742no—
246D4—741no—
247D4—741no—
248D4#1059693812yes—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—372no—
254C2×C4—748no—
255C2×C4—748no—
256C2×C4—742no—
257C2×C4—742no—
258C2×C4—742no—
259C2×C4—742no—
260C2×C4—742no—
261C2×C4—1481no—
262C2×C4C2×C4×D3711yescharacteristic
263C2×C4C2×D14811yescharacteristic
264C2×C4D4×D3711yescharacteristic
265C2×C4D4×D3711yescharacteristic
266C2×C4D4×D3711yescharacteristic
267C2×C4C2×C22⋊D3711yescharacteristic
268C8—41no—
269C8—1481no—
270C22—22no—
271C22—41no—
272C22—42no—
273C22—742no—
274C22—1482no—
275C22C22⋊C4×D3711yescharacteristic
276C22#1192450411yescharacteristic
277C22#1192450611yescharacteristic
278C4—22no—
279C4—81no—
280C4—2961no—
281C4—742no—
282C4—744no—
283C4C22⋊C4×D3711yescharacteristic
284C4C2×#1059693811yescharacteristic
285C4#1192450411yescharacteristic
286C4#1192450611yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—42no—
291C2—1482no—
292C2#1455738811yescharacteristic
subgroupG/H
centerC2#14557388
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#421C2
socleC2×C37#379
prime radicalC2×#11924583C2
cosocleC22×C4×C37C23
hypercenter#421D37
hypocenterC37#1796
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14557550C2semidirect
3. #14557543C2semidirect
4. #14557541C2semidirect
5. #14557515C2semidirect
6. #14557506C2semidirect
7. C37×#421C2semidirect
15. C2×#10596964C4semidirect
18. C2×Q8×D37C4semidirect
149. #421D37semidirect
154. C37#1796semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
#145575502
#145575432
#145575412
#145575152
#145575062
C37×#4212
#179637