Finite Group Databasebeta

← #17995657

Subgroups — #17995657

Order 4736.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#11924569C211yesmaximal, characteristic, complemented
3#14558104C211yesmaximal, characteristic, complemented
4#14557541C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic, complemented
6#14557305C211yesmaximal, characteristic, complemented
7C37×#421C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569—22no—
12#11924567—21no—
13#11924566—21no—
14#11924562—21no—
15#11924561—21no—
16#11924556—22no—
17C2×Dic148—21no—
18C2×#10596930—21no—
19C2×#10596934C2211yescharacteristic
20#11924534—21no—
21#11924523—21no—
22#11924517—22no—
23#11924515—22no—
24#11924495C2211yescharacteristic
25#11924459—22no—
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×C37—21no—
34#41×C37—21no—
35C2×Q8×C37D411yescharacteristic
36C2×D4×C37—21no—
37C2×D4×C37D411yescharacteristic
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—21no—
41C22×Dic37—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45#10596962—21no—
46C2×D148D411yescharacteristic
47C2×C4×D37—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74—21no—
52C2×Dic74—21no—
53C2×Dic74D412yes—
54C2×Dic74D411yescharacteristic
55M16×C37—21no—
56M16×C37D412yes—
57C2×C8×C37—21no—
58C4⋊C4×C37—21no—
59C22⋊C4×C37—21no—
60C42×C37—21no—
61C22⋊Dic37—24no—
62C22⋊Dic37D412yes—
63#10596942—22no—
64#10596941—22no—
65#10596940—22no—
66#10596939—22no—
67C4⋊Dic37—21no—
68#10596936—24no—
69C4×Dic37—21no—
70#10596934—21no—
71#10596934—21no—
72C2×#64436D412yes—
73Dic148—24no—
74#10596930—24no—
75C23×C37—21no—
76C23×C37C2×D411yescharacteristic
77C22×D37—21no—
78Q8×C37—21no—
79Q8×C37—21no—
80D4×C37—21no—
81D4×C37—21no—
82D4×C37—41no—
83D4×C37—41no—
84C2×C4×C37—21no—
85C2×C4×C37—41no—
86C2×C4×C37—41no—
87C2×C4×C37—41no—
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37#4111yescharacteristic
94C22⋊D37—41no—
95C22⋊D37—41no—
96C2×Dic37—22no—
97C2×Dic37—22no—
98C2×Dic37—21no—
99C2×Dic37—41no—
100C2×Dic37—41no—
101D148—21no—
102D148—21no—
103C4×D37—41no—
104C4×D37—41no—
105Dic74—22no—
106Dic74—21no—
107Dic74—21no—
108Dic74—22no—
109Dic74—41no—
110Dic74—41no—
111C8×C37—22no—
112#64436—22no—
113C22×C37—41no—
114C22×C37—42no—
115C22×C37—41no—
116C22×C37#12011yescharacteristic
117C22×C37#12111yescharacteristic
118C22×C37#12711yescharacteristic
119C2×D37—41no—
120C2×D37—81no—
121C4×C37—41no—
122C4×C37—81no—
123C4×C37#12011yescharacteristic
124C4×C37#12011yescharacteristic
125C4×C37#12111yescharacteristic
126C4×C37#12111yescharacteristic
127Dic37—42no—
128Dic37—42no—
129Dic37—41no—
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×#137—371no—
139#536—371no—
140#421D3711yescharacteristic, complemented
141#419—371no—
142#410—371no—
143#344—371no—
144C37#200911yescharacteristic, complemented, Sylow
145C2×#41—371no—
146C2×#41C2×D3711yescharacteristic
147C22×Q8—371no—
148#137—742no—
149#137—741no—
150#137—741no—
151#137—742no—
152AGL(1,ℤ/8)—741no—
153AGL(1,ℤ/8)—741no—
154#135—742no—
155C2×Q16—741no—
156C2×SD16—741no—
157C2×M16—371no—
158C2×M16C2×D3711yescharacteristic
159C4⋊Q8—741no—
160#124—741no—
161#123—742no—
162C22⋊Q8—742no—
163#117—371no—
164#117C2×D3711yescharacteristic
165#104—22no—
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—372no—
177C2×Q8—371no—
178C2×Q8—741no—
179C2×Q8—741no—
180C2×Q8—741no—
181C2×Q8—741no—
182C2×Q8—741no—
183C2×Q8D14811yescharacteristic
184C2×D4—21no—
185C2×D4—371no—
186C2×D4—741no—
187C2×D4D14811yescharacteristic
188C22×C4—21no—
189C22×C4—741no—
190C22×C4—741no—
191C22×C4C22×D3711yescharacteristic
192Q16—744no—
193Q16—742no—
194SD16—744no—
195SD16—742no—
196SD16—742no—
197D8—742no—
198M16—21no—
199M16—741no—
200M16—741no—
201M16C22⋊D3712yes—
202C2×C8—21no—
203C2×C8—372no—
204C4⋊C4—21no—
205C4⋊C4—744no—
206C4⋊C4—741no—
207C22⋊C4—21no—
208C22⋊C4—372no—
209C22⋊C4—744no—
210C42—21no—
211C42—741no—
212C23—21no—
213C23—741no—
214C23D4×D3711yescharacteristic
215Q8—21no—
216Q8—21no—
217Q8—742no—
218Q8—741no—
219Q8—741no—
220Q8—742no—
221Q8—1481no—
222Q8—1481no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—741no—
228D4—741no—
229D4—1481no—
230D4—1481no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—741no—
238C2×C4—1481no—
239C2×C4—1481no—
240C2×C4—1481no—
241C2×C4—1481no—
242C2×C4C2×D14811yescharacteristic
243C2×C4#1059696211yescharacteristic
244C2×C4D4×D3711yescharacteristic
245C2×C4D4×D3711yescharacteristic
246C2×C4D4×D3711yescharacteristic
247C2×C4C2×C22⋊D3711yescharacteristic
248C8—22no—
249C8—742no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—2961no—
254C22—1481no—
255C22#1192450611yescharacteristic
256C22#1192450911yescharacteristic
257C22#1192453211yescharacteristic
258C4—41no—
259C4—81no—
260C4—1482no—
261C4—1481no—
262C4—1482no—
263C4#1192450411yescharacteristic
264C4#1192450611yescharacteristic
265C4#1192450911yescharacteristic
266C4#1192451011yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—2961no—
272C2#1455744211yescharacteristic
subgroupG/H
centerC2#14557442
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#421C2
socleC2×C37#392
prime radical#14558331C2
hypercenter#421D37
hypocenterC37#2009
LCSG ▷ C22×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. C2×#11924569C2semidirect
3. #14558104C2semidirect
4. #14557541C2semidirect
5. #14557506C2semidirect
6. #14557305C2semidirect
7. C37×#421C2semidirect
140. #421D37semidirect
144. C37#2009semidirect

Maximal subgroups

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

subgroupindex
#145583312
C2×#119245692
#145581042
#145575412
#145575062
#145573052
C37×#4212
#200937