Finite Group Databasebeta

← #49169392

Subgroups — #49169392

Order 37504.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036686C211yesmaximal, characteristic, complemented
2#34036539C211yesmaximal, characteristic, complemented
3#34036524C211yesmaximal, characteristic, complemented
4#34036499C211yesmaximal, characteristic, complemented
5#34036488C211yesmaximal, characteristic, complemented
6#34036385C212yesmaximal, complemented
7#34036373C212yesmaximal
8C4×#17989792C212yesmaximal, complemented
9C4×#17989790C212yesmaximal, complemented
10C4×#17989786C211yesmaximal, characteristic, complemented
11#529×C293C211yesmaximal, characteristic
12C2×#17989792C2212yes—
13C2×#17989790C2212yes—
14C2×#17989786C2212yes—
15#22627624C2211yescharacteristic
16#22627624C2211yescharacteristic
17#22627616—21no—
18#22627603—21no—
19#22627603C2212yes—
20C4×Dic586—21no—
21C4×Dic586C2212yes—
22#22627583—21no—
23#22627557C2212yes—
24#22627555C2212yes—
25#22627548C2212yes—
26#22627547C2212yes—
27#22627547C2212yes—
28#22627545C2212yes—
29#22627535C2211yescharacteristic
30#22627535C2211yescharacteristic
31C4×#14556873C2212yes—
32#126×C293—21no—
33#125×C293C2211yescharacteristic
34#124×C293C2211yescharacteristic
35#123×C293—21no—
36C22⋊Q8×C293C2211yescharacteristic
37#121×C293C2211yescharacteristic
38C4×Q8×C293C2211yescharacteristic
39C4×D4×C293—21no—
40C4×D4×C293C2211yescharacteristic
41#117×C293—21no—
42C2×C42×C293C2211yescharacteristic
43C2×Dic586—21no—
44C2×Dic586C2312yes—
45#17989792—24no—
46#17989790—24no—
47#17989786—24no—
48C2×#14556873C2312yes—
49C2×#14556873C2312yes—
50C4⋊Dic293—21no—
51C4⋊Dic293—21no—
52C4⋊Dic293—21no—
53C4⋊Dic293C2312yes—
54#17989781—22no—
55#17989781—22no—
56C22⋊Dic293—22no—
57C4×Dic293—22no—
58C2×Q8×C293C2311yescharacteristic
59C2×D4×C293—21no—
60C2×D4×C293C2311yescharacteristic
61C22×C4×C293—21no—
62C22×C4×C293D411yescharacteristic
63C22×C4×C293D411yescharacteristic
64C22×C4×C293C2311yescharacteristic
65C4⋊C4×C293—21no—
66C4⋊C4×C293—21no—
67C4⋊C4×C293—21no—
68C4⋊C4×C293—21no—
69C4⋊C4×C293C2311yescharacteristic
70C4⋊C4×C293C2311yescharacteristic
71C22⋊C4×C293—21no—
72C22⋊C4×C293—21no—
73C22⋊C4×C293—21no—
74C22⋊C4×C293—21no—
75C22⋊C4×C293—21no—
76C42×C293—21no—
77C42×C293D411yescharacteristic
78C42×C293D411yescharacteristic
79C42×C293C2311yescharacteristic
80C42×C293C2311yescharacteristic
81Dic586—22no—
82Dic586—22no—
83Dic586—42no—
84C2×Dic293—22no—
85C2×Dic293—22no—
86#14556873—22no—
87#14556873#4114yes—
88C23×C293—21no—
89C23×C293C2×D411yescharacteristic
90Q8×C293—22no—
91D4×C293—22no—
92D4×C293—42no—
93C2×C4×C293—22no—
94C2×C4×C293—22no—
95C2×C4×C293—21no—
96C2×C4×C293—21no—
97C2×C4×C293—21no—
98C2×C4×C293—41no—
99C2×C4×C293—42no—
100C2×C4×C293C2×D411yescharacteristic
101C2×C4×C293C2×D411yescharacteristic
102C2×C4×C293C2×D411yescharacteristic
103C2×C4×C293C2×D411yescharacteristic
104C2×C4×C293C2×D411yescharacteristic
105C2×C4×C293C2411yescharacteristic
106C22×C293—21no—
107C22×C293—21no—
108C22×C293—21no—
109C22×C293—41no—
110C22×C293—41no—
111C22×C293—41no—
112C22×C293C22×D411yescharacteristic
113C4×C293—21no—
114C4×C293—21no—
115C4×C293—21no—
116C4×C293—21no—
117C4×C293—41no—
118C4×C293—41no—
119C4×C293—41no—
120C4×C293#13712yes—
121C4×C293C2×#4112yes—
122Dic293—42no—
123Dic293—42no—
124C2×C293—41no—
125C2×C293—81no—
126C2×C293#53211yescharacteristic
127C2×C293C2×#13711yescharacteristic
128C2×C293#57511yescharacteristic
129C293#317211yescharacteristic, complemented, Sylow
130#3172—2931nomaximal, Sylow
131#533—2931no—
132#529D29311yescharacteristic
133#501—2931no—
134#497—2931no—
135#491—2931no—
136#489—2931no—
137#470—2932no—
138#468—2932no—
139C4×Q16—2932no—
140C4×SD16—2932no—
141C4×M16—2931no—
142C2×Q16—2932no—
143C2×SD16—2932no—
144C2×M16—2932no—
145C4⋊Q8—2931no—
146C4⋊Q8—2931no—
147#126—21no—
148#125—5861no—
149#125C2×D29311yescharacteristic
150#124C2×D29311yescharacteristic
151#123—21no—
152C22⋊Q8—2932no—
153C22⋊Q8—5861no—
154C22⋊Q8C2×D29311yescharacteristic
155#121C2×D29311yescharacteristic
156C4×Q8—2932no—
157C4×Q8—5861no—
158C4×Q8C2×D29311yescharacteristic
159C4×D4—21no—
160C4×D4C2×D29311yescharacteristic
161#117—21no—
162#117—5861no—
163C2×C42C2×D29311yescharacteristic
164#107—2932no—
165#106—2932no—
166#103—2932no—
167#103—2932no—
168#103—2932no—
169#102—2932no—
170#97—2931no—
171#97—2931no—
172C4×C8—2932no—
173C2×Q8—2932no—
174C2×Q8—5861no—
175C2×Q8C22×D29311yescharacteristic
176C2×D4—21no—
177C2×D4C22×D29311yescharacteristic
178C22×C4—21no—
179C22×C4C22⋊D29311yescharacteristic
180C22×C4C22⋊D29311yescharacteristic
181C22×C4C22×D29311yescharacteristic
182Q16—5864no—
183SD16—5864no—
184M16—5864no—
185C2×C8—2932no—
186C2×C8—2932no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—2932no—
192C4⋊C4—5861no—
193C4⋊C4—5861no—
194C4⋊C4—5862no—
195C4⋊C4—5862no—
196C4⋊C4—5861no—
197C4⋊C4C22×D29311yescharacteristic
198C4⋊C4C22×D29311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—21no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—5862no—
205C42—21no—
206C42—5862no—
207C42C22⋊D29311yescharacteristic
208C42C22⋊D29311yescharacteristic
209C42C22×D29311yescharacteristic
210C42C22×D29311yescharacteristic
211C23—21no—
212C23C2×C22⋊D29311yescharacteristic
213Q8—22no—
214Q8—5862no—
215Q8—5862no—
216Q8—11722no—
217D4—22no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—5862no—
227C2×C4—5862no—
228C2×C4C2×C22⋊D29311yescharacteristic
229C2×C4C2×C22⋊D29311yescharacteristic
230C2×C4C2×C22⋊D29311yescharacteristic
231C2×C4C2×C22⋊D29311yescharacteristic
232C2×C4C2×C22⋊D29311yescharacteristic
233C2×C4C23×D29311yescharacteristic
234C8—2934no—
235C8—5862no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22C22×C22⋊D29311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—11722no—
251C4—11722no—
252C4#2262765412yes—
253C4#41×D29312yes—
254C2—41no—
255C2—81no—
256C2#3403667511yescharacteristic
257C2C2×#2262765411yescharacteristic
258C2#3403692711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#529×C293C2
socleC22×C293C22×D4
prime radical#121×C293C22
hypercenter#529D293
hypocenterC293#3172
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #34036686C2semidirect
2. #34036539C2semidirect
3. #34036524C2semidirect
4. #34036499C2semidirect
5. #34036488C2semidirect
6. #34036385C2semidirect
8. C4×#17989792C2semidirect
9. C4×#17989790C2semidirect
10. C4×#17989786C2semidirect
129. C293#3172semidirect

Maximal subgroups

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

subgroupindex
#340366862
#340365392
#340365242
#340364992
#340364882
#340363852
#340363732
C4×#179897922
C4×#179897902
C4×#179897862
#529×C2932
#3172293