Finite Group Databasebeta

← #34069493

Subgroups — #34069493

Order 19328.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#23752758C211yesmaximal, characteristic
2#23752228C212yesmaximal, complemented
3#23752186C211yesmaximal, characteristic, complemented
4#23751973C212yesmaximal, complemented
5#568×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7#18012737C411yescharacteristic, complemented
8#18012735C411yescharacteristic, complemented
9#18012728C411yescharacteristic, complemented
10#18012726C411yescharacteristic, complemented
11#18012711—22no—
12C4×C22⋊D151—22no—
13#18012698C2212yes—
14C2×C4×Dic151C2211yescharacteristic
15#18012665—24no—
16#18012654—22no—
17C2×#41×C151C2211yescharacteristic
18#131×C151—24no—
19C2×M16×C151—22no—
20C2×M16×C151C2212yes—
21#14559004—22no—
22#14559004—22no—
23C2×Dic302C2×C411yescharacteristic
24C2×D604C2×C411yescharacteristic
25C2×C22⋊D151—22no—
26C2×C22⋊D151—21no—
27C22×Dic151—21no—
28C2×C4×D151—21no—
29C4⋊Dic151—22no—
30Dic151⋊C4—22no—
31C22⋊Dic151—22no—
32C22⋊Dic151—22no—
33(C2×D151)⋊C4—22no—
34C4×Dic151—21no—
35C4×Dic151—22no—
36C4×Dic151C2×C411yescharacteristic
37C4×Dic151C2×C411yescharacteristic
38#41×C151—22no—
39#41×C151—22no—
40C2×Q8×C151C2×C411yescharacteristic
41C2×D4×C151C2×C411yescharacteristic
42C2×D4×C151D412yes—
43C22×C4×C151D412yes—
44C22×C4×C151C2311yescharacteristic
45M16×C151—24no—
46M16×C151—22no—
47M16×C151D414yescomplemented
48C2×C8×C151—24no—
49C2×C8×C151—22no—
50C22×D151—21no—
51Dic302—22no—
52D604—22no—
53C22⋊D151—44no—
54C22⋊D151—42no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—42no—
59C2×Dic151—42no—
60C4×D151—41no—
61C4×D151—41no—
62C23×C151C22⋊C412yes—
63C23×C151C2×D411yescharacteristic
64Q8×C151—22no—
65D4×C151—24no—
66D4×C151—22no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151C22⋊C412yes—
70C2×C4×C151C22×C411yescharacteristic
71C2×C4×C151C2×D412yes—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151#4112yes—
74C8×C151—24no—
75C22×C151—22no—
76C22×C151—41no—
77C22×C151—42no—
78C22×C151C2×C22⋊C411yescharacteristic
79C22×C151#12112yes—
80C2×D151—42no—
81C2×D151—41no—
82C4×C151—22no—
83C4×C151C4×D412yes—
84C4×C151#12011yescharacteristic
85C4×C151#12311yescharacteristic
86Dic151—22no—
87Dic151—41no—
88Dic151—41no—
89Dic151—82no—
90C2×C151—21no—
91C2×C151—22no—
92C2×C151—42no—
93C2×C151#38611yescharacteristic
94D151—81no—
95C151#188411yescharacteristic, complemented, Sylow
96#1884—1511nomaximal, Sylow
97#568D15111yescharacteristic, complemented
98#532—1511no—
99#421—1512no—
100#410—1511no—
101#339—1512no—
102C2×#41—1511no—
103C2×#41C2×D15111yescharacteristic
104#131—24no—
105C2×M16—22no—
106C2×M16C2×D15112yes—
107C4⋊Q8—1511no—
108#127—1511no—
109#124—1511no—
110#124—1511no—
111#121—3022no—
112C4×D4—3022no—
113#117—1512no—
114C2×C42—1511no—
115#104—3024no—
116#99—3022no—
117#41—22no—
118#41—22no—
119#41—3022no—
120#41—3022no—
121C2×Q8—1511no—
122C2×Q8C4×D15111yescharacteristic
123C2×D4—3022no—
124C2×D4—3021no—
125C2×D4—1511no—
126C2×D4C4×D15111yescharacteristic
127C2×D4D60412yes—
128C22×C4—3021no—
129C22×C4—3021no—
130C22×C4C22⋊D15112yes—
131C22×C4C22×D15111yescharacteristic
132M16—24no—
133M16—22no—
134M16C22⋊D15114yescomplemented
135C2×C8—24no—
136C2×C8—22no—
137C4⋊C4—3022no—
138C4⋊C4—3022no—
139C22⋊C4—3022no—
140C22⋊C4—3022no—
141C22⋊C4—3022no—
142C42—3021no—
143C42—3022no—
144C42—1511no—
145C42—1511no—
146C23—3021no—
147C23(C2×D151)⋊C412yes—
148C23C2×D60411yescharacteristic
149Q8—22no—
150Q8—3022no—
151D4—24no—
152D4—22no—
153D4—3022no—
154D4—6044no—
155D4—6042no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—3021no—
159C2×C4—3021no—
160C2×C4—3021no—
161C2×C4—6042no—
162C2×C4—6041no—
163C2×C4—6041no—
164C2×C4—6042no—
165C2×C4(C2×D151)⋊C412yes—
166C2×C4C2×C4×D15111yescharacteristic
167C2×C4C2×C22⋊D15112yes—
168C2×C4C2×C22⋊D15111yescharacteristic
169C2×C4#1455900412yes—
170C8—24no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—6042no—
175C22—6041no—
176C22C2×(C2×D151)⋊C411yescharacteristic
177C22#1801271312yes—
178C4—22no—
179C4—3022no—
180C4—6041no—
181C4—6041no—
182C4—12082no—
183C4C4×C22⋊D15112yes—
184C4#1801270811yescharacteristic
185C4#1801272211yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—12081no—
190C2#2375209111yescharacteristic
subgroupG/H
centerC4#18012708
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#568×C151C2
socleC2×C151#386
prime radical#23752758C2
cosocleC22×C4×C151C23
hypercenter#568D151
hypocenterC151#1884
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #23752228C2semidirect
3. #23752186C2semidirect
4. #23751973C2semidirect
5. #568×C151C2semidirect
7. #18012737C4semidirect
8. #18012735C4semidirect
9. #18012728C4semidirect
10. #18012726C4semidirect
47. M16×C151D4semidirect
95. C151#1884semidirect
97. #568D151semidirect
134. M16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527582
#237522282
#237521862
#237519732
#568×C1512
#1884151