Finite Group Databasebeta

← #49159944

Subgroups — #49159944

Order 37504.

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

normal subgroups only

This group has 246 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#34036757C211yesmaximal, characteristic
2#34036138C211yesmaximal, characteristic
3#34036036C211yesmaximal, characteristic
4#34035897C211yesmaximal, characteristic
5#34035890C211yesmaximal, characteristic
6#34035888C211yesmaximal, characteristic
7#419×C293C211yesmaximal, characteristic
8C2×#17989786C2211yescharacteristic
9#22627624—21no—
10#22627623—21no—
11#22627616—21no—
12#22627615—21no—
13#22627601—22no—
14#22627583C2211yescharacteristic
15C2×C4⋊Dic293C2211yescharacteristic
16C2×C4×Dic293C2211yescharacteristic
17#22627548—21no—
18#22627548—21no—
19#22627531—22no—
20C22×Q8×C293C2211yescharacteristic
21C2×M16×C293C2211yescharacteristic
22#117×C293C2211yescharacteristic
23#103×C293—21no—
24#103×C293—21no—
25C2×Dic586—22no—
26C22×Dic293—21no—
27C22×Dic293D412yes—
28#17989786—21no—
29#17989786—21no—
30C2×#14556873—21no—
31C4⋊Dic293—22no—
32C4⋊Dic293—21no—
33C4⋊Dic293—21no—
34C4⋊Dic293D411yescharacteristic
35C4⋊Dic293D411yescharacteristic
36#17989781—22no—
37#17989781—22no—
38C22⋊Dic293—21no—
39C4×Dic293—21no—
40C4×Dic293—21no—
41C4×Dic293—21no—
42C2×Q8×C293—21no—
43C2×Q8×C293—21no—
44C2×Q8×C293—21no—
45C2×Q8×C293—21no—
46C2×Q8×C293—21no—
47C2×Q8×C293Q812yescomplemented
48C22×C4×C293—21no—
49C22×C4×C293C2311yescharacteristic
50M16×C293—21no—
51M16×C293—21no—
52C2×C8×C293—21no—
53C4⋊C4×C293D411yescharacteristic
54C4⋊C4×C293D411yescharacteristic
55C22⋊C4×C293—21no—
56C42×C293—21no—
57Dic586—82no—
58C2×Dic293—22no—
59C2×Dic293—21no—
60C2×Dic293—21no—
61C2×Dic293—22no—
62C2×Dic293—41no—
63C2×Dic293—41no—
64C2×Dic293—42no—
65#14556873—41no—
66C23×C293C2×D411yescharacteristic
67Q8×C293—22no—
68Q8×C293—22no—
69Q8×C293—41no—
70Q8×C293—41no—
71C2×C4×C293—21no—
72C2×C4×C293—21no—
73C2×C4×C293—22no—
74C2×C4×C293—41no—
75C2×C4×C293—41no—
76C2×C4×C293C2×D411yescharacteristic
77C2×C4×C293C2×D411yescharacteristic
78C2×C4×C293C2×Q811yescharacteristic
79C2×C4×C293#4111yescharacteristic
80C2×C4×C293#4111yescharacteristic
81C2×C4×C293#4111yescharacteristic
82C8×C293—41no—
83C22×C293—21no—
84C22×C293—21no—
85C22×C293#12011yescharacteristic
86C22×C293C22⋊Q811yescharacteristic
87C22×C293#12411yescharacteristic
88C4×C293—42no—
89C4×C293—41no—
90C4×C293—41no—
91C4×C293C22⋊Q811yescharacteristic
92C4×C293C22⋊Q811yescharacteristic
93C4×C293#12411yescharacteristic
94C4×C293#12411yescharacteristic
95Dic293—42no—
96Dic293—42no—
97Dic293—41no—
98Dic293—41no—
99C2×C293—21no—
100C2×C293—21no—
101C2×C293#39311yescharacteristic
102C2×C293#45511yescharacteristic
103C2×C293#45611yescharacteristic
104C293#202811yescharacteristic, complemented, Sylow
105#2028—2931nomaximal, Sylow
106#544—2931no—
107#419—2931no—
108#419D29311yescharacteristic
109#391—2931no—
110#343—2931no—
111#339—2931no—
112#339—2931no—
113C22×Q8C2×D29311yescharacteristic
114C2×M16—2931no—
115C2×M16C2×D29311yescharacteristic
116C4⋊Q8—5861no—
117C4⋊Q8—5861no—
118#125—5861no—
119#125—5861no—
120C22⋊Q8—5862no—
121#117—2931no—
122#117C2×D29311yescharacteristic
123C2×C4⋊C4—2931no—
124C2×C42—2931no—
125#103—21no—
126#103—21no—
127#103—5861no—
128#103—5861no—
129#95—5862no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—5862no—
136C2×Q8Dic58612yescomplemented
137C22×C4—21no—
138C22×C4—2932no—
139C22×C4—5861no—
140C22×C4C22×D29311yescharacteristic
141M16—21no—
142M16—21no—
143M16—5861no—
144M16—5861no—
145C2×C8—21no—
146C2×C8—5861no—
147C4⋊C4—2931no—
148C4⋊C4—2931no—
149C4⋊C4—5862no—
150C4⋊C4—5862no—
151C4⋊C4—5862no—
152C4⋊C4—5861no—
153C4⋊C4—5861no—
154C4⋊C4C22⋊D29311yescharacteristic
155C4⋊C4C22⋊D29311yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5861no—
158C42—21no—
159C42—5861no—
160C42—5861no—
161C42—5861no—
162C23D4×D29311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—23442no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5862no—
174C2×C4—5861no—
175C2×C4—5861no—
176C2×C4—5862no—
177C2×C4—11721no—
178C2×C4—11721no—
179C2×C4—11722no—
180C2×C4D4×D29311yescharacteristic
181C2×C4C2×C22⋊D29311yescharacteristic
182C2×C4C2×Dic58611yescharacteristic
183C2×C4#1798980111yescharacteristic
184C2×C4#1798980111yescharacteristic
185C2×C4#1798980211yescharacteristic
186C8—41no—
187C8—11721no—
188C22—21no—
189C22—21no—
190C22#2262759211yescharacteristic
191C22#2262760111yescharacteristic
192C22#2262761011yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—11722no—
197C4—11722no—
198C4—11721no—
199C4—11721no—
200C4#2262760111yescharacteristic
201C4#2262760311yescharacteristic
202C4#2262761011yescharacteristic
203C4#2262761111yescharacteristic
204C2—21no—
205C2—21no—
206C2#3403604111yescharacteristic
207C2#3403630511yescharacteristic
208C2#3403631011yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#419×C293C2
socleC22×C293#120
prime radicalC23×C293C2×D4
hypercenter#419D293
hypocenterC293#2028
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C293Q8semidirect
104. C293#2028semidirect
136. C2×Q8Dic586semidirect

Maximal subgroups

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

subgroupindex
#340367572
#340361382
#340360362
#340358972
#340358902
#340358882
#419×C2932
#2028293