Finite Group Databasebeta

← #49168582

Subgroups — #49168582

Order 37504.

440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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#34036429C214yesmaximal, complemented
3#34036419C212yesmaximal, complemented
4#34036409C212yesmaximal, complemented
5#34036169C212yesmaximal, complemented
6#34036153C211yesmaximal, characteristic, complemented
7#34036134C212yesmaximal
8C2×C4×D4×C293C211yesmaximal, characteristic
9C2×#17989786C2212yes—
10#22627624C2211yescharacteristic, complemented
11#22627624C2211yescharacteristic, complemented
12#22627616C2212yescomplemented
13#22627603—21no—
14#22627603—21no—
15C4×Dic586—21no—
16C4×Dic586—21no—
17#22627583C2212yes—
18#22627557C2214yescomplemented
19#22627555C2214yescomplemented
20C4⋊#14556873C2212yescomplemented
21C4⋊#14556873C2212yescomplemented
22#22627545C2214yes—
23#22627545C2214yes—
24C22×D4×C293C2211yescharacteristic
25C23×C4×C293—21no—
26C4×D4×C293—21no—
27C4×D4×C293—21no—
28C4×D4×C293C2212yes—
29C4×D4×C293C2212yes—
30C2×C4⋊C4×C293C2211yescharacteristic
31C2×C22⋊C4×C293—21no—
32C2×C42×C293C2211yescharacteristic
33C2×Dic586—21no—
34C2×Dic586—21no—
35#17989786—24no—
36C2×#14556873C2314yes—
37C4⋊Dic293—21no—
38C4⋊Dic293—21no—
39C4⋊Dic293C2312yes—
40C4⋊Dic293C2312yes—
41#17989781—22no—
42#17989781—22no—
43C22⋊Dic293—22no—
44C4×Dic293—22no—
45C24×C293—21no—
46C2×D4×C293—21no—
47C2×D4×C293—22no—
48C2×D4×C293Q814yescomplemented
49C2×D4×C293C2312yes—
50C22×C4×C293—21no—
51C22×C4×C293—22no—
52C22×C4×C293—22no—
53C22×C4×C293—44no—
54C22×C4×C293D411yescharacteristic
55C22×C4×C293D411yescharacteristic
56C22×C4×C293C2311yescharacteristic
57C4⋊C4×C293—21no—
58C4⋊C4×C293C2312yes—
59C22⋊C4×C293—22no—
60C22⋊C4×C293—22no—
61C42×C293D411yescharacteristic
62C42×C293D411yescharacteristic
63C42×C293C2311yescharacteristic
64C42×C293C2311yescharacteristic
65Dic586—42no—
66Dic586—42no—
67C2×Dic293—22no—
68C2×Dic293—22no—
69#14556873—24no—
70C23×C293—24no—
71C23×C293—22no—
72C23×C293—42no—
73C23×C293—42no—
74C23×C293C2×D411yescharacteristic
75D4×C293—24no—
76D4×C293—22no—
77D4×C293C2×Q814yes—
78C2×C4×C293—22no—
79C2×C4×C293—22no—
80C2×C4×C293—41no—
81C2×C4×C293—44no—
82C2×C4×C293—42no—
83C2×C4×C293—44no—
84C2×C4×C293C2×D411yescharacteristic
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2×D411yescharacteristic
87C2×C4×C293C2×D411yescharacteristic
88C2×C4×C293C2×D411yescharacteristic
89C2×C4×C293C2×Q812yes—
90C2×C4×C293#4112yes—
91C2×C4×C293C2411yescharacteristic
92C22×C293—21no—
93C22×C293—21no—
94C22×C293—24no—
95C22×C293—48no—
96C22×C293—42no—
97C22×C293—42no—
98C22×C293C22⋊Q812yes—
99C22×C293C22×D411yescharacteristic
100C4×C293—21no—
101C4×C293—21no—
102C4×C293—21no—
103C4×C293—42no—
104C4×C293C22⋊Q812yes—
105C4×C293AGL(1,ℤ/8)12yes—
106C4×C293C22×Q811yescharacteristic
107C4×C293C2×#4111yescharacteristic
108Dic293—42no—
109Dic293—42no—
110C2×C293—22no—
111C2×C293—44no—
112C2×C293C2×C22⋊Q811yescharacteristic
113C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
114C2×C293#57511yescharacteristic
115C293#307711yescharacteristic, complemented, Sylow
116#3077—2931nomaximal, Sylow
117#533—2931no—
118C2×C4×D4D29311yescharacteristic
119#478—2934no—
120#476—2932no—
121#474—2932no—
122#428—2932no—
123#423—2931no—
124#418—2932no—
125C22×D4C2×D29311yescharacteristic
126C23×C4—21no—
127C2×M16—2932no—
128C4⋊Q8—2931no—
129C4⋊Q8—2931no—
130#125—2932no—
131C22⋊Q8—5861no—
132C22⋊Q8—5861no—
133C4×Q8—5861no—
134C4×Q8—5861no—
135C4×D4—21no—
136C4×D4—21no—
137C4×D4C2×D29312yes—
138C4×D4C2×D29312yes—
139#117—2932no—
140C2×C4⋊C4C2×D29311yescharacteristic
141C2×C22⋊C4—21no—
142C2×C42C2×D29311yescharacteristic
143#107—2934no—
144#106—2934no—
145C4⋊C8—2932no—
146C4⋊C8—2932no—
147#102—2934no—
148#102—2934no—
149C24—21no—
150C2×Q8—5861no—
151C2×Q8—5861no—
152C2×D4—21no—
153C2×D4—22no—
154C2×D4Dic58614yescomplemented
155C2×D4C22×D29312yes—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—44no—
160C22×C4C22⋊D29311yescharacteristic
161C22×C4C22⋊D29311yescharacteristic
162C22×C4C22×D29311yescharacteristic
163M16—5864no—
164C2×C8—2934no—
165C4⋊C4—21no—
166C4⋊C4—2932no—
167C4⋊C4—2932no—
168C4⋊C4—5862no—
169C4⋊C4—5862no—
170C4⋊C4—5861no—
171C4⋊C4—5861no—
172C4⋊C4C22×D29312yes—
173C22⋊C4—22no—
174C22⋊C4—22no—
175C22⋊C4—5862no—
176C42—5862no—
177C42C22⋊D29311yescharacteristic
178C42C22⋊D29311yescharacteristic
179C42C22×D29311yescharacteristic
180C42C22×D29311yescharacteristic
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23C2×C22⋊D29311yescharacteristic
186Q8—11722no—
187Q8—11722no—
188D4—24no—
189D4—22no—
190D4C2×Dic58614yes—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—44no—
197C2×C4—5862no—
198C2×C4—5862no—
199C2×C4C2×C22⋊D29311yescharacteristic
200C2×C4C2×C22⋊D29311yescharacteristic
201C2×C4C2×C22⋊D29311yescharacteristic
202C2×C4C2×C22⋊D29311yescharacteristic
203C2×C4C2×C22⋊D29311yescharacteristic
204C2×C4C2×Dic58612yes—
205C2×C4#1798980212yes—
206C2×C4C23×D29311yescharacteristic
207C8—5864no—
208C22—21no—
209C22—21no—
210C22—24no—
211C22—48no—
212C22—42no—
213C22—42no—
214C22#2262760312yes—
215C22C22×C22⋊D29311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—11722no—
221C4—11722no—
222C4#2262760312yes—
223C4#2262765012yes—
224C4C22×Dic58611yescharacteristic
225C4C2×#1798980211yescharacteristic
226C2—22no—
227C2—44no—
228C2C2×#2262760311yescharacteristic
229C2C2×#2262765011yescharacteristic
230C2#3403692711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×C4×D4×C293C2
socleC22×C293C22×D4
prime radicalC22×D4×C293C22
hypercenterC2×C4×D4D293
hypocenterC293#3077
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #34036686C2semidirect
2. #34036429C2semidirect
3. #34036419C2semidirect
4. #34036409C2semidirect
5. #34036169C2semidirect
6. #34036153C2semidirect
10. #22627624C22semidirect
11. #22627624C22semidirect
12. #22627616C22semidirect
18. #22627557C22semidirect
19. #22627555C22semidirect
20. C4⋊#14556873C22semidirect
21. C4⋊#14556873C22semidirect
48. C2×D4×C293Q8semidirect
115. C293#3077semidirect
154. C2×D4Dic586semidirect

Maximal subgroups

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

subgroupindex
#340366862
#340364292
#340364192
#340364092
#340361692
#340361532
#340361342
C2×C4×D4×C2932
#3077293