Finite Group Databasebeta

← #17995658

Subgroups — #17995658

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#14558333C211yesmaximal, characteristic
2C2×#11924567C211yesmaximal, characteristic, complemented
3#14558107C211yesmaximal, characteristic, complemented
4#14557551C211yesmaximal, characteristic, complemented
5#14557506C211yesmaximal, characteristic, complemented
6#14557304C211yesmaximal, characteristic, complemented
7C37×#419C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596962C2211yescharacteristic
10#11924569—21no—
11#11924569—21no—
12#11924567—22no—
13#11924567—22no—
14#11924564—21no—
15#11924564—21no—
16#11924558—22no—
17C2×#10596942—21no—
18C2×#10596941—21no—
19C2×#10596934C2211yescharacteristic
20#11924534—21no—
21#11924525—21no—
22#11924519—22no—
23#11924512—22no—
24#11924495C2211yescharacteristic
25#11924464—22no—
26#11924450—22no—
27C22×Q8×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#103×C37—22no—
31C2×Q8×C37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37—21no—
34C2×Q8×C37—21no—
35C2×Q8×C37—21no—
36C2×Q8×C37D412yes—
37C22×C4×C37—21no—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—21no—
40C2×C22⋊D37—21no—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45#10596962—21no—
46#10596962—21no—
47#10596962—21no—
48#10596962—21no—
49C2×D148D411yescharacteristic
50C2×D148D411yescharacteristic
51C2×C4×D37—21no—
52C2×C4×D37—21no—
53C2×Dic74D411yescharacteristic
54C2×Dic74D411yescharacteristic
55M16×C37—21no—
56M16×C37—21no—
57C2×C8×C37D412yes—
58C4⋊C4×C37—21no—
59C22⋊C4×C37—21no—
60C42×C37—21no—
61C22⋊Dic37D412yes—
62#10596942—24no—
63#10596941—24no—
64#10596938—24no—
65C4⋊Dic37—21no—
66#10596936—24no—
67C4×Dic37—21no—
68#10596934—21no—
69#10596934D412yes—
70C2×#64436—21no—
71Dic148—22no—
72D296—22no—
73#10596930—22no—
74#10596930—22no—
75C23×C37C2×D411yescharacteristic
76C22×D37—21no—
77C22×D37—21no—
78Q8×C37—22no—
79Q8×C37—22no—
80Q8×C37—41no—
81Q8×C37—41no—
82C2×C4×C37—22no—
83C2×C4×C37—41no—
84C2×C4×C37—41no—
85C2×C4×C37—41no—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37#4111yescharacteristic
92C22⋊D37—41no—
93C22⋊D37—41no—
94C22⋊D37—41no—
95C22⋊D37—41no—
96C2×Dic37—22no—
97C2×Dic37—21no—
98C2×Dic37—21no—
99D148—21no—
100D148—21no—
101D148—21no—
102D148—21no—
103C4×D37—41no—
104C4×D37—41no—
105C4×D37—41no—
106C4×D37—41no—
107Dic74—21no—
108Dic74—21no—
109Dic74—21no—
110Dic74—21no—
111C8×C37—22no—
112#64436—22no—
113C22×C37—41no—
114C22×C37#12011yescharacteristic
115C22×C37#12111yescharacteristic
116C22×C37#12711yescharacteristic
117C2×D37—42no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—81no—
121C4×C37—42no—
122C4×C37—81no—
123C4×C37#12011yescharacteristic
124C4×C37#12011yescharacteristic
125C4×C37#12111yescharacteristic
126C4×C37#12111yescharacteristic
127Dic37—42no—
128Dic37—41no—
129Dic37—41no—
130#2009—371nomaximal, Sylow
131C2×C37—21no—
132C2×C37—21no—
133C2×C37—21no—
134C2×C37#39211yescharacteristic
135D37—81no—
136D37—81no—
137#575—371no—
138C2×#137—371no—
139#536—371no—
140#421—371no—
141#419D3711yescharacteristic, complemented
142#410—371no—
143#344—371no—
144C37#200911yescharacteristic, complemented, Sylow
145C2×#41—371no—
146C2×#41—371no—
147C22×Q8C2×D3711yescharacteristic
148#137—741no—
149#137—741no—
150#137—742no—
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—742no—
166#103—22no—
167#99—742no—
168#41—741no—
169#41—741no—
170#41—741no—
171#41—741no—
172#41—741no—
173#41—741no—
174#41—741no—
175#41—741no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—371no—
182C2×Q8—371no—
183C2×Q8D14812yes—
184C2×D4—371no—
185C2×D4—371no—
186C2×D4—741no—
187C2×D4—741no—
188C22×C4—21no—
189C22×C4—741no—
190C22×C4—741no—
191C22×C4C22×D3711yescharacteristic
192Q16—742no—
193Q16—744no—
194SD16—742no—
195SD16—742no—
196SD16—744no—
197D8—742no—
198M16—21no—
199M16—21no—
200M16—372no—
201M16—741no—
202C2×C8—741no—
203C2×C8C22⋊D3712yes—
204C4⋊C4—21no—
205C4⋊C4—744no—
206C4⋊C4—741no—
207C22⋊C4—21no—
208C22⋊C4—372no—
209C22⋊C4—744no—
210C42—21no—
211C42—741no—
212C23—741no—
213C23—741no—
214C23D4×D3711yescharacteristic
215Q8—22no—
216Q8—22no—
217Q8—41no—
218Q8—41no—
219Q8—741no—
220Q8—741no—
221Q8—741no—
222Q8—741no—
223D4—741no—
224D4—741no—
225D4—741no—
226D4—741no—
227D4—1481no—
228D4—1481no—
229D4—1481no—
230D4—1481no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—742no—
236C2×C4—741no—
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—2961no—
252C22—1482no—
253C22—1481no—
254C22—1481no—
255C22#1192450611yescharacteristic
256C22#1192450911yescharacteristic
257C22#1192453211yescharacteristic
258C4—42no—
259C4—81no—
260C4—1482no—
261C4—1481no—
262C4—1481no—
263C4#1192450411yescharacteristic
264C4#1192450611yescharacteristic
265C4#1192450911yescharacteristic
266C4#1192451011yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—2961no—
271C2—2961no—
272C2#1455744211yescharacteristic
subgroupG/H
centerC2#14557442
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#419C2
socleC2×C37#392
prime radical#14558333C2
hypercenter#419D37
hypocenterC37#2009
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#11924567C2semidirect
3. #14558107C2semidirect
4. #14557551C2semidirect
5. #14557506C2semidirect
6. #14557304C2semidirect
7. C37×#419C2semidirect
141. #419D37semidirect
144. C37#2009semidirect

Maximal subgroups

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

subgroupindex
#145583332
C2×#119245672
#145581072
#145575512
#145575062
#145573042
C37×#4192
#200937