Finite Group Databasebeta

← #49171507

Subgroups — #49171507

Order 37504.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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#34036853C211yesmaximal, characteristic, complemented
2D4×Dic586C211yesmaximal, characteristic, complemented
3#34036490C212yesmaximal, complemented
4#34036479C211yesmaximal, characteristic, complemented
5#34036422C212yesmaximal, complemented
6#34036410C211yesmaximal, characteristic, complemented
7#34036346C212yesmaximal
8#34036256C211yesmaximal, characteristic, complemented
9#34036230C212yesmaximal, complemented
10C4×#17989787C211yesmaximal, characteristic
11#461×C293C211yesmaximal, characteristic, complemented
12C22×Dic586—21no—
13C2×#17989787C2211yescharacteristic
14#22627624C2211yescharacteristic
15#22627623C2212yes—
16#22627619—22no—
17#22627613C2212yes—
18#22627604—21no—
19#22627603—21no—
20#22627601—22no—
21Q8×Dic293C2212yes—
22C4×Dic586C2211yescharacteristic
23C4×D1172C2211yescharacteristic
24D4×Dic293C2212yes—
25#22627582—21no—
26#22627558C2212yes—
27#22627557C2211yescharacteristic
28#22627553C2212yes—
29#22627548C2212yes—
30#22627548C2212yes—
31#22627546C2212yes—
32#22627545C2211yescharacteristic
33#22627544C2211yescharacteristic
34#22627534C2212yes—
35C4×#14556873C2211yescharacteristic
36C2×SD16×C293C2212yes—
37C4⋊Q8×C293C2211yescharacteristic
38C4×D4×C293C2211yescharacteristic
39C4⋊C8×C293C2211yescharacteristic
40#103×C293C2212yes—
41C2×Dic586—22no—
42C2×Dic586—21no—
43C2×Dic586—44no—
44C2×Dic586D411yescharacteristic
45C2×D1172C2311yescharacteristic
46C22×Dic293—22no—
47C2×C4×D293—21no—
48#17989787—22no—
49C2×#14556873C2311yescharacteristic
50C2×#14556873C2311yescharacteristic
51C4⋊Dic293—22no—
52C4⋊Dic293—21no—
53C4⋊Dic293D411yescharacteristic
54C4⋊Dic293C2312yes—
55C4⋊Dic293C2311yescharacteristic
56#17989781—22no—
57#17989781D412yes—
58C22⋊Dic293—22no—
59#17989779—22no—
60#17989779—22no—
61#17989779—21no—
62C4×Dic293—22no—
63C4×Dic293C2312yes—
64C2×Q8×C293C2312yes—
65C2×D4×C293C2311yescharacteristic
66C22×C4×C293—21no—
67SD16×C293—24no—
68C2×C8×C293C2312yes—
69C4⋊C4×C293—21no—
70C4⋊C4×C293—21no—
71C4⋊C4×C293C2311yescharacteristic
72C22⋊C4×C293—21no—
73C42×C293C2311yescharacteristic
74C22×D293—21no—
75Dic586—22no—
76Dic586—44no—
77Dic586—42no—
78D1172—21no—
79D1172—21no—
80C2×Dic293—21no—
81C2×Dic293—22no—
82C2×Dic293—44no—
83C2×Dic293C2×D412yes—
84C2×Dic293C2×D412yes—
85C4×D293—42no—
86#14556873—21no—
87#14556873—21no—
88C23×C293—21no—
89Q8×C293—22no—
90Q8×C293—22no—
91D4×C293—21no—
92D4×C293#4112yes—
93C2×C4×C293—21no—
94C2×C4×C293—22no—
95C2×C4×C293—42no—
96C2×C4×C293C2×D411yescharacteristic
97C2×C4×C293C2×D411yescharacteristic
98C2×C4×C293C2411yescharacteristic
99C8×C293—22no—
100C22×C293—22no—
101C22×C293—41no—
102C22×C293—41no—
103C22×C293C22×D411yescharacteristic
104C2×D293—41no—
105C2×D293—41no—
106C2×D293—41no—
107C4×C293—21no—
108C4×C293—42no—
109C4×C293—41no—
110C4×C293AGL(1,ℤ/8)12yes—
111C4×C293C2×#4111yescharacteristic
112C4×C2932−1+411yescharacteristic
113Dic293—22no—
114Dic293—22no—
115Dic293—41no—
116Dic293—42no—
117C2×C293—42no—
118C2×C293#54811yescharacteristic
119C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C293#57811yescharacteristic
121D293—81no—
122C293#336711yescharacteristic, complemented, Sylow
123#3367—2931nomaximal, Sylow
124#556—2931no—
125D4×Q8—2931no—
126#489—2932no—
127#487—2931no—
128#477—2932no—
129#474—2931no—
130#463—2932no—
131#461D29311yescharacteristic, complemented
132#446—2931no—
133#440—2932no—
134C4×D8—2931no—
135C22×Q8—5861no—
136C2×SD16C2×D29312yes—
137C2×D8—2931no—
138C4⋊Q8—2932no—
139C4⋊Q8—2931no—
140C4⋊Q8C2×D29311yescharacteristic
141#126—5862no—
142#124—2932no—
143C22⋊Q8—5862no—
144C22⋊Q8—5861no—
145C22⋊Q8—5861no—
146C4×Q8—2931no—
147C4×Q8—2932no—
148C4×D4—2932no—
149C4×D4—2931no—
150C4×D4C2×D29311yescharacteristic
151#117—5861no—
152#107—2932no—
153#107—2931no—
154C4⋊C8—2932no—
155C4⋊C8C2×D29311yescharacteristic
156#103—2932no—
157#103—2932no—
158#103C2×D29312yes—
159#102—2931no—
160#102—2932no—
161#102—2931no—
162#97—2932no—
163C4×C8—2931no—
164C2×Q8—2931no—
165C2×Q8—5862no—
166C2×Q8—5861no—
167C2×Q8—11724no—
168C2×Q8C22×D29312yes—
169C2×D4—2931no—
170C2×D4C22×D29311yescharacteristic
171C22×C4—21no—
172C22×C4—5862no—
173C22×C4—5861no—
174SD16—24no—
175D8—5862no—
176C2×C8—2931no—
177C2×C8—2931no—
178C2×C8C22×D29312yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—2931no—
182C4⋊C4—2932no—
183C4⋊C4—2932no—
184C4⋊C4—2931no—
185C4⋊C4—5862no—
186C4⋊C4—5862no—
187C4⋊C4—5861no—
188C4⋊C4C22×D29311yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—5862no—
191C22⋊C4—5862no—
192C22⋊C4—5862no—
193C22⋊C4—5861no—
194C42—2932no—
195C42—5862no—
196C42C22×D29311yescharacteristic
197C23—21no—
198C23—5861no—
199Q8—22no—
200Q8—22no—
201Q8—5862no—
202Q8—11724no—
203Q8—11722no—
204D4—21no—
205D4—5861no—
206D4—5861no—
207D4#1798980112yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—2932no—
212C2×C4—2932no—
213C2×C4—5861no—
214C2×C4—5862no—
215C2×C4—11724no—
216C2×C4—11722no—
217C2×C4D4×D29311yescharacteristic
218C2×C4D4×D29311yescharacteristic
219C2×C4C23×D29311yescharacteristic
220C8—22no—
221C8—5861no—
222C8—5861no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—11721no—
227C22—11721no—
228C22—11721no—
229C22C2×D4×D29311yescharacteristic
230C4—21no—
231C4—42no—
232C4—41no—
233C4—5862no—
234C4—5862no—
235C4—11722no—
236C4—11721no—
237C4#2262765112yes—
238C4C2×#1798980111yescharacteristic
239C4#2262767111yescharacteristic
240C2—42no—
241C2—23441no—
242C2#3403678511yescharacteristic
243C2C2×#2262765111yescharacteristic
244C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#461×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989787C22
hypercenter#461D293
hypocenterC293#3367
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #34036853C2semidirect
2. D4×Dic586C2semidirect
3. #34036490C2semidirect
4. #34036479C2semidirect
5. #34036422C2semidirect
6. #34036410C2semidirect
8. #34036256C2semidirect
9. #34036230C2semidirect
11. #461×C293C2semidirect
122. C293#3367semidirect
131. #461D293semidirect

Maximal subgroups

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

subgroupindex
#340368532
D4×Dic5862
#340364902
#340364792
#340364222
#340364102
#340363462
#340362562
#340362302
C4×#179897872
#461×C2932
#3367293