Finite Group Databasebeta

← #34060070

Subgroups — #34060070

Order 19072.

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

normal subgroups only

This group has 284 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#23750643C211yesmaximal, characteristic, complemented
2C4×C4⋊#10597010C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#23750172C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C2×C4×#10597010—21no—
8#18011978—21no—
9#18011968C2212yes—
10C4×#11924753—21no—
11(C2×#10597010)⋊C4C2212yes—
12C2×#14558736—21no—
13#18011910C411yescharacteristic, complemented
14#18011907C411yescharacteristic, complemented
15#18011897—21no—
16#18011886C2211yescharacteristic
17#18011884—21no—
18#18011882C2211yescharacteristic
19C4×D596C411yescharacteristic, complemented
20C4×C22⋊D149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4⋊#10597010—24no—
26C4×#10597010—42no—
27#14558736—42no—
28#14558736—42no—
29C2×Dic298—21no—
30C2×D596—21no—
31C2×D596C2×C411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35C2×C4×D149—21no—
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149C2311yescharacteristic
39C4⋊Dic149C2×C411yescharacteristic
40#14558715—21no—
41C22⋊Dic149—21no—
42#14558713—21no—
43#14558713—21no—
44C4×Dic149C2×C411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149D411yescharacteristic
47C2×D4×C149C2×C411yescharacteristic
48C22×C4×C149—21no—
49C4⋊C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—21no—
51C42×C149C2×C411yescharacteristic
52C2×#10597010—24no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149—21no—
57C22×D149C2×D411yescharacteristic
58Dic298—42no—
59D596—41no—
60D596—41no—
61D596—41no—
62C22⋊D149—41no—
63C22⋊D149—41no—
64C22⋊D149—42no—
65C22⋊D149—42no—
66C2×Dic149—21no—
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C22⋊C411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—22no—
71C4×D149—41no—
72C4×D149—42no—
73C4×D149D812yes—
74C4×D149SD1612yes—
75C23×C149—21no—
76D4×C149—41no—
77C2×C4×C149—21no—
78C2×C4×C149—42no—
79C2×C4×C149C22⋊C411yescharacteristic
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22×C411yescharacteristic
82C22×C149—41no—
83C22×C149—41no—
84C22×C149—41no—
85C22×C149C2×C22⋊C411yescharacteristic
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—41no—
89C2×D149—41no—
90C2×D149—41no—
91C2×D149C2×D811yescharacteristic
92C2×D149C2×SD1611yescharacteristic
93#10597010—44no—
94C4×C149—21no—
95C4×C149—21no—
96C4×C149—41no—
97C4×C149#10212yes—
98Dic149—21no—
99Dic149—41no—
100Dic149#10212yes—
101Dic149#10412yes—
102C2×C149—81no—
103C2×C149#41011yescharacteristic
104C2×C149C2×#10211yescharacteristic
105C2×C149C2×#10411yescharacteristic
106D149—21no—
107D149—21no—
108D149—81no—
109C149#150211yescharacteristic, complemented, Sylow
110#1502—1491nomaximal, Sylow
111#532—1491no—
112#431—1491no—
113C4×C4⋊C4—1491no—
114#327—1492no—
115#327—1492no—
116C2×#41—2981no—
117C4⋊Q8—1491no—
118#127—1491no—
119#124—2981no—
120#121—2981no—
121#121—1491no—
122#121—1491no—
123C4×D4—2981no—
124C4×D4—1491no—
125C4×D4#1059701011yescharacteristic, complemented
126C2×C4⋊C4—2981no—
127C2×C42—2981no—
128C2×C42—1491no—
129C4⋊C8—2981no—
130C22⋊C8—1492no—
131C4×C8—2981no—
132#95—1492no—
133#41—5962no—
134#41—5962no—
135C2×Q8—2981no—
136C2×D4—2981no—
137C2×D4—2981no—
138C2×D4—2981no—
139C2×D4—2981no—
140C2×D4—1491no—
141C2×D4C2×#1059701011yescharacteristic
142C22×C4—21no—
143C22×C4—2982no—
144C22×C4—2981no—
145C22×C4—1491no—
146C22×C4—1491no—
147C22×C4—1491no—
148C2×C8—2982no—
149C4⋊C4—2981no—
150C4⋊C4—2984no—
151C4⋊C4—1491no—
152C4⋊C4C2×#1059701011yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C22⋊C4—2981no—
157C42—5962no—
158C42—1491no—
159C42—1491no—
160C42—1491no—
161C42C2×#1059701011yescharacteristic
162C23—21no—
163C23—2981no—
164C23—1491no—
165Q8—5962no—
166D4—41no—
167D4—5961no—
168D4—5961no—
169D4—5961no—
170D4—5961no—
171D4—5961no—
172D4—5962no—
173D4—5962no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—2982no—
177C2×C4—2984no—
178C2×C4—2981no—
179C2×C4—5961no—
180C2×C4—5962no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4—1492no—
187C2×C4—1492no—
188C2×C4C22⋊#1059701011yescharacteristic
189C2×C4C22⋊#1059701011yescharacteristic
190C2×C4C22×#1059701011yescharacteristic
191C8—5962no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—2981no—
196C22—2981no—
197C22—5961no—
198C22—5961no—
199C22—5961no—
200C22—1491no—
201C22—1491no—
202C22C2×C22⋊#1059701011yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—2981no—
207C4—5964no—
208C4—5961no—
209C4—1492no—
210C4—1492no—
211C4#1801197312yes—
212C2—81no—
213C2—2981no—
214C2—2981no—
215C2—11921no—
216C2#2375060411yescharacteristic
217C2C2×#1801197311yescharacteristic
218C2D149⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750172C2
cosocleC2×C4×D149C23
hypercenterC4×D4#10597010
hypocenterC149#1502
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750643C2semidirect
2. C4×C4⋊#10597010C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
13. #18011910C4semidirect
14. #18011907C4semidirect
19. C4×D596C4semidirect
22. C4×D4×C149C4semidirect
109. C149#1502semidirect
125. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506432
C4×C4⋊#105970102
#237504772
#237504762
#237501722
#1502149