Finite Group Databasebeta

← #34070798

Subgroups — #34070798

Order 19328.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752787C211yesmaximal, characteristic
2#101×D151C212yesmaximal, complemented
3#23752011C211yesmaximal, characteristic, complemented
4#23752008C212yesmaximal, complemented
5#356×C151C211yesmaximal, characteristic, complemented
6C2×#14559005C411yescharacteristic
7C2×Q8×D151C2211yescharacteristic
8M16×D151—22no—
9#18012737C411yescharacteristic
10#18012728C2211yescharacteristic
11#18012727C411yescharacteristic
12#18012724—22no—
13#18012717—22no—
14#18012696C411yescharacteristic
15#18012658C2212yes—
16#18012657—22no—
17C4⋊Q8×C151C2211yescharacteristic
18#101×C151C2212yes—
19#14559005—42no—
20C2×Dic302C2×C411yescharacteristic
21C2×Dic302D412yes—
22Q8×D151—42no—
23C2×D604—21no—
24C2×D604C2×C411yescharacteristic
25C2×C4×D151—21no—
26C2×C4×D151C2×C411yescharacteristic
27C2×C4×D151D412yes—
28#14558988—22no—
29#14558987—42no—
30C8×D151—42no—
31Dic151⋊C4—21no—
32Dic151⋊C4—22no—
33(C2×D151)⋊C4—21no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36C4×Dic151C2×C411yescharacteristic
37C2×Q8×C151C2×C411yescharacteristic
38C2×Q8×C151C2311yescharacteristic
39M16×C151—22no—
40C4⋊C4×C151—22no—
41C42×C151C2×C411yescharacteristic
42C22×D151—21no—
43C22×D151C22⋊C411yescharacteristic
44Dic302—41no—
45Dic302—42no—
46D604—41no—
47D604—42no—
48C2×Dic151—21no—
49C2×Dic151C22⋊C412yes—
50C2×Dic151C22⋊C411yescharacteristic
51C4×D151—22no—
52C4×D151—22no—
53C4×D151—22no—
54C4×D151—42no—
55C151⋊C8—42no—
56Q8×C151—41no—
57Q8×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151C22×C411yescharacteristic
61C2×C4×C151C2×D412yes—
62C8×C151—42no—
63C22×C151C2×C22⋊C411yescharacteristic
64C2×D151—41no—
65C2×D151—42no—
66C2×D151—41no—
67C2×D151#9912yes—
68C4×C151—22no—
69C4×C151—21no—
70C4×C151—41no—
71C4×C151—41no—
72Dic151—21no—
73Dic151—22no—
74Dic151—41no—
75C2×C151—21no—
76C2×C151C2×#9911yescharacteristic
77D151—22no—
78D151—81no—
79C151#213311yescharacteristic, complemented, Sylow
80#2133—1511nomaximal, Sylow
81#536—1511no—
82C2×#101—1512no—
83#356—1511no—
84#356D15111yescharacteristic, complemented
85#355—1512no—
86C2×#41—1511no—
87C22×Q8—1511no—
88C2×M16—3022no—
89C4⋊Q8—1511no—
90C4⋊Q8C2×D15111yescharacteristic
91#124—1511no—
92#124—1511no—
93#123—3022no—
94C22⋊Q8—3022no—
95#117—1511no—
96#101—3022no—
97#101—1512no—
98#101C2×D15112yes—
99#41—6042no—
100C2×Q8—6042no—
101C2×Q8—1511no—
102C2×Q8—1512no—
103C2×Q8C4×D15111yescharacteristic
104C2×Q8C22×D15111yescharacteristic
105C2×D4—3021no—
106C2×D4—1511no—
107C22×C4—3021no—
108C22×C4—1511no—
109C22×C4—1512no—
110M16—22no—
111M16—3022no—
112M16—6042no—
113C2×C8—6042no—
114C4⋊C4—22no—
115C4⋊C4—3021no—
116C4⋊C4—3022no—
117C22⋊C4—3021no—
118C22⋊C4—3022no—
119C22⋊C4—3022no—
120C42—1511no—
121C42C4×D15111yescharacteristic
122C23—3021no—
123C23—1511no—
124Q8—41no—
125Q8—41no—
126Q8—6042no—
127Q8—6041no—
128D4—6041no—
129D4—6042no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3022no—
133C2×C4—3022no—
134C2×C4—3022no—
135C2×C4—3021no—
136C2×C4—6042no—
137C2×C4—1512no—
138C2×C4—1511no—
139C2×C4C2×C4×D15111yescharacteristic
140C2×C4D4×D15112yes—
141C8—42no—
142C8—6042no—
143C22—6041no—
144C22—6042no—
145C22—6041no—
146C22—1512no—
147C22C22⋊C4×D15111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—3021no—
153C4—3022no—
154C4—6041no—
155C2—21no—
156C2—3022no—
157C2—12081no—
158C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC2×C4×C151C22×C4
FrattiniC2×Q8C22×D151
Fitting#356×C151C2
socleC2×C151C2×#99
prime radicalC2×#14559005C4
cosocleC2×Q8×C151C23
hypercenter#356D151
hypocenterC151#2133
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D151C2semidirect
3. #23752011C2semidirect
4. #23752008C2semidirect
5. #356×C151C2semidirect
79. C151#2133semidirect
84. #356D151semidirect

Maximal subgroups

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

subgroupindex
#237527872
#101×D1512
#237520112
#237520082
#356×C1512
#2133151