Finite Group Databasebeta

← #49159306

Subgroups — #49159306

Order 37504.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#34036895C211yesmaximal, characteristic
2#34036705C211yesmaximal, characteristic
3#34036139C211yesmaximal, characteristic, complemented
4#34036137C211yesmaximal, characteristic, complemented
5#34036102C211yesmaximal, characteristic
6#34035885C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C293C211yesmaximal, characteristic, complemented
8C2×#17989802C2211yescharacteristic
9C22×Dic586C2211yescharacteristic
10#22627632—22no—
11#22627630—22no—
12C2×#17989786C2211yescharacteristic
13M16×D293—22no—
14#22627624C412yescomplemented
15#22627612C412yescomplemented
16#22627608—22no—
17#22627604—22no—
18#22627583C2211yescharacteristic
19#22627549—22no—
20#22627547—22no—
21#22627538—22no—
22C2×M16×C293C2211yescharacteristic
23#117×C293C2211yescharacteristic
24#117×C293C2211yescharacteristic
25#17989802—21no—
26#17989802—21no—
27#17989802—21no—
28#17989802—21no—
29C2×Dic586—21no—
30C2×Dic586—21no—
31C2×Dic586—21no—
32C2×Dic586—21no—
33C2×Dic586—21no—
34C2×Dic586C2×C412yes—
35C2×Dic586C2×C411yescharacteristic
36C2×D1172C2×C411yescharacteristic
37C2×C22⋊D293D412yes—
38C22×Dic293—21no—
39C2×C4×D293D412yes—
40#17989786—21no—
41#17989786—21no—
42#17989785—24no—
43C2×#14556873D412yes—
44C8×D293—24no—
45C4⋊Dic293—24no—
46C4⋊Dic293—21no—
47C22⋊Dic293—21no—
48#17989779—24no—
49C4×Dic293—21no—
50C22×C4×C293C2311yescharacteristic
51M16×C293—21no—
52M16×C293—21no—
53C2×C8×C293D412yes—
54C4⋊C4×C293—21no—
55C4⋊C4×C293—21no—
56C22⋊C4×C293—21no—
57C22⋊C4×C293—21no—
58C42×C293—21no—
59C42×C293C2×C412yes—
60C22×D293C22⋊C412yes—
61Dic586—21no—
62Dic586—21no—
63Dic586—22no—
64Dic586—22no—
65Dic586—41no—
66Dic586—41no—
67D1172—21no—
68D1172—21no—
69C22⋊D293—22no—
70C22⋊D293—22no—
71C2×Dic293—22no—
72C2×Dic293—41no—
73C2×Dic293—41no—
74C2×Dic293—41no—
75C2×Dic293C22⋊C412yes—
76C4×D293—22no—
77C4×D293—22no—
78#14556873—22no—
79C23×C293C2×D411yescharacteristic
80C2×C4×C293—22no—
81C2×C4×C293—41no—
82C2×C4×C293C22×C411yescharacteristic
83C2×C4×C293C2×D411yescharacteristic
84C2×C4×C293C2×D411yescharacteristic
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293#4111yescharacteristic
87C2×C4×C293#4111yescharacteristic
88C8×C293—22no—
89C22×C293—41no—
90C22×C293C2×C22⋊C411yescharacteristic
91C22×C293#12111yescharacteristic
92C22×C293#12111yescharacteristic
93C2×D293—22no—
94C2×D293—42no—
95C4×C293—42no—
96C4×C293—81no—
97C4×C293C4×D411yescharacteristic
98C4×C293C4×D411yescharacteristic
99C4×C293#12011yescharacteristic
100C4×C293#12311yescharacteristic
101Dic293—22no—
102Dic293—42no—
103Dic293—81no—
104C2×C293—21no—
105C2×C293—21no—
106C2×C293—21no—
107C2×C293#38611yescharacteristic
108D293—42no—
109C293#190911yescharacteristic, complemented, Sylow
110#1909—2931nomaximal, Sylow
111#568—2931no—
112#536—2931no—
113#419—2931no—
114#419—2931no—
115#410—2931no—
116H(3,ℤ/4)—2931no—
117H(3,ℤ/4)D29311yescharacteristic, complemented
118C2×#41—2931no—
119C22×Q8—2931no—
120#131—5862no—
121#131—5862no—
122C2×M16—2931no—
123C2×M16—5862no—
124C2×M16C2×D29311yescharacteristic
125C4⋊Q8—2932no—
126#124—2932no—
127#123—5862no—
128C22⋊Q8—5862no—
129#117—2931no—
130#117C2×D29311yescharacteristic
131#117C2×D29311yescharacteristic
132#103—5862no—
133#103—5862no—
134#99—5862no—
135#41—5861no—
136#41—5861no—
137#41—5861no—
138#41—5861no—
139C2×Q8—2931no—
140C2×Q8—2932no—
141C2×Q8—5861no—
142C2×Q8—5861no—
143C2×Q8—5861no—
144C2×Q8—5861no—
145C2×Q8—5861no—
146C2×D4—2932no—
147C2×D4—2931no—
148C22×C4—2932no—
149C22×C4—5861no—
150C22×C4C22×D29311yescharacteristic
151M16—21no—
152M16—21no—
153M16—5864no—
154M16—5861no—
155M16—5861no—
156C2×C8—2932no—
157C2×C8—5864no—
158C2×C8D117212yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—5864no—
162C4⋊C4—5861no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—5864no—
166C22⋊C4—5861no—
167C42—21no—
168C42—5861no—
169C42C4×D29312yes—
170C23—2932no—
171C23D4×D29311yescharacteristic
172Q8—5861no—
173Q8—5861no—
174Q8—5862no—
175Q8—5862no—
176Q8—11721no—
177Q8—11721no—
178D4—5862no—
179D4—5862no—
180D4—5861no—
181D4—5861no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—2932no—
185C2×C4—5862no—
186C2×C4—5862no—
187C2×C4—5862no—
188C2×C4—11721no—
189C2×C4—11721no—
190C2×C4—11721no—
191C2×C4C2×C4×D29311yescharacteristic
192C2×C4D4×D29311yescharacteristic
193C2×C4D4×D29311yescharacteristic
194C2×C4C2×D117211yescharacteristic
195C2×C4#1798980211yescharacteristic
196C2×C4#1798980311yescharacteristic
197C8—22no—
198C8—5862no—
199C22—41no—
200C22—5862no—
201C22—11722no—
202C22C22⋊C4×D29311yescharacteristic
203C22#2262759711yescharacteristic
204C22#2262759911yescharacteristic
205C4—42no—
206C4—81no—
207C4—23441no—
208C4—5862no—
209C4—11722no—
210C4#2262758611yescharacteristic
211C4C4×D117211yescharacteristic
212C4#2262759411yescharacteristic
213C4#2262760911yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—11722no—
218C2#3403600711yescharacteristic
subgroupG/H
centerC2#34036007
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
FittingH(3,ℤ/4)×C293C2
socleC2×C293#386
prime radicalC2×#17989802C22
cosocleC22×C4×C293C23
hypercenterH(3,ℤ/4)D293
hypocenterC293#1909
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. #34036139C2semidirect
4. #34036137C2semidirect
6. #34035885C2semidirect
7. H(3,ℤ/4)×C293C2semidirect
14. #22627624C4semidirect
15. #22627612C4semidirect
109. C293#1909semidirect
117. H(3,ℤ/4)D293semidirect

Maximal subgroups

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

subgroupindex
#340368952
#340367052
#340361392
#340361372
#340361022
#340358852
H(3,ℤ/4)×C2932
#1909293