Finite Group Databasebeta

← #34060203

Subgroups — #34060203

Order 19072.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750628C211yesmaximal, characteristic, complemented
2C2×#18011978C211yesmaximal, characteristic, complemented
3#23750484C212yesmaximal, complemented
4#23750483C212yesmaximal, complemented
5#23750170C211yesmaximal, characteristic
6C2×#14558745—21no—
7C22×#11924753—21no—
8#18011978—21no—
9#18011978C2212yes—
10#18011978C2212yes—
11C4⋊#11924753—21no—
12C2×#14558735—21no—
13#18011910C2211yescharacteristic
14#18011907C2211yescharacteristic
15#18011897—21no—
16#18011885C411yescharacteristic
17#18011883—21no—
18D4×Dic149C411yescharacteristic
19#18011873C411yescharacteristic
20#18011871—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23#14558745—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×#11924753—42no—
27#14558735—42no—
28#14558735—42no—
29C2×Dic298—21no—
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C22×Dic149D411yescharacteristic
36C22×Dic149D411yescharacteristic
37C2×C4×D149—21no—
38C4⋊Dic149C2×C411yescharacteristic
39#14558715—21no—
40C22⋊Dic149—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149C2311yescharacteristic
47C2×D4×C149—21no—
48C2×D4×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C4⋊C4×C149C2×C411yescharacteristic
51C22⋊C4×C149—21no—
52#11924753—42no—
53#11924753—42no—
54C22×D149—21no—
55Dic298—41no—
56Dic298—41no—
57D596—41no—
58C22⋊D149—42no—
59C22⋊D149—41no—
60C22⋊D149—41no—
61C22⋊D149—41no—
62C22⋊D149—41no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—42no—
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C22⋊C411yescharacteristic
69C2×Dic149D812yes—
70C2×Dic149SD1612yes—
71C2×Dic149C2×D411yescharacteristic
72C2×Dic149C2×D411yescharacteristic
73C4×D149—42no—
74C23×C149—21no—
75C23×C149C22⋊C411yescharacteristic
76D4×C149—41no—
77D4×C149—42no—
78C2×C4×C149—21no—
79C2×C4×C149—41no—
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22×C411yescharacteristic
82C22×C149—21no—
83C22×C149—21no—
84C22×C149—41no—
85C22×C149—41no—
86C22×C149—41no—
87C22×C149#10212yes—
88C22×C149C2×C22⋊C411yescharacteristic
89C2×D149—41no—
90C2×D149—41no—
91C2×D149—41no—
92C4×C149—21no—
93C4×C149—21no—
94C4×C149—41no—
95Dic149—21no—
96Dic149—41no—
97Dic149#10212yes—
98Dic149C2×D811yescharacteristic
99Dic149C2×SD1611yescharacteristic
100Dic149AGL(1,ℤ/8)11yescharacteristic
101Dic149#13711yescharacteristic
102C2×C149—22no—
103C2×C149—81no—
104C2×C149#41311yescharacteristic
105C2×C149C2×#10211yescharacteristic
106C2×C149#41711yescharacteristic
107D149—81no—
108C149#154711yescharacteristic, complemented, Sylow
109#1547—1491nomaximal, Sylow
110#532—1491no—
111#423—1491no—
112C2×C4⋊C8—1491no—
113#332—1492no—
114#331—1492no—
115C2×#41—2981no—
116C2×M16—2981no—
117C22×C8—2981no—
118C4⋊Q8—1491no—
119#127—1491no—
120#124—2981no—
121#121—2981no—
122#121—1491no—
123#121#1059701011yescharacteristic
124C4×D4—2981no—
125C4×D4—1491no—
126C4×D4—1491no—
127C2×C42—1491no—
128C4⋊C8—2981no—
129C4⋊C8—2981no—
130C4⋊C8—1492no—
131C4⋊C8—1492no—
132#41—5962no—
133#41—5962no—
134C2×Q8—2981no—
135C2×D4—21no—
136C2×D4—2981no—
137C2×D4—2981no—
138C2×D4—2981no—
139C2×D4—1491no—
140C2×D4C2×#1059701011yescharacteristic
141C22×C4—2981no—
142C22×C4—2981no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4C2×#1059701011yescharacteristic
146M16—5962no—
147C2×C8—2982no—
148C2×C8—2982no—
149C2×C8—5962no—
150C4⋊C4—2981no—
151C4⋊C4—1491no—
152C4⋊C4C2×#1059701011yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C22⋊C4—2981no—
157C42—1491no—
158C42—1491no—
159C42—1491no—
160C42—1491no—
161C23—21no—
162C23—2981no—
163C23C22⋊#1059701011yescharacteristic
164Q8—5961no—
165Q8—5961no—
166D4—41no—
167D4—42no—
168D4—5961no—
169D4—5962no—
170D4—5961no—
171D4—5961no—
172D4—5961no—
173D4—5961no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—2981no—
177C2×C4—2981no—
178C2×C4—2981no—
179C2×C4—5962no—
180C2×C4—5962no—
181C2×C4—1491no—
182C2×C4—1492no—
183C2×C4—1492no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4—1491no—
187C2×C4C22⋊#1059701011yescharacteristic
188C2×C4C22×#1059701011yescharacteristic
189C8—5962no—
190C8—5962no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—5961no—
197C22—5961no—
198C22—5961no—
199C22#1801197312yes—
200C22C2×C22⋊#1059701011yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2981no—
205C4—5961no—
206C4—1491no—
207C4—1492no—
208C4—1491no—
209C4—1491no—
210C4—1491no—
211C2—22no—
212C2—81no—
213C2—11921no—
214C2#2375061211yescharacteristic
215C2C2×#1801197311yescharacteristic
216C2#2375061611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#121×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750170C2
cosocleC4×Dic149C23
hypercenter#121#10597010
hypocenterC149#1547
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
2. C2×#18011978C2semidirect
3. #23750484C2semidirect
4. #23750483C2semidirect
108. C149#1547semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×#180119782
#237504842
#237504832
#237501702
#1547149