Finite Group Databasebeta

← #34060121

Subgroups — #34060121

Order 19072.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750644C211yesmaximal, characteristic, complemented
2#23750569C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#23750172C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C4⋊#11924753—21no—
8#18011968C2212yes—
9C4×#11924753—21no—
10(C2×#10597010)⋊C4—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—42no—
26#14558736—42no—
27#14558736—42no—
28C2×Dic298—21no—
29C2×D596—21no—
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C2×C4×D149—21no—
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149C2311yescharacteristic
38C4⋊Dic149C2×C411yescharacteristic
39#14558715—21no—
40C22⋊Dic149—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C2×D4×C149C2×C411yescharacteristic
47C22×C4×C149—21no—
48C4⋊C4×C149C2×C411yescharacteristic
49C22⋊C4×C149—21no—
50C42×C149C2×C411yescharacteristic
51C2×#10597010—42no—
52C2×#10597010—42no—
53C2×#10597010—42no—
54#11924753—42no—
55C22×D149—21no—
56C22×D149C2×D411yescharacteristic
57Dic298—42no—
58D596—41no—
59D596—41no—
60D596—41no—
61C22⋊D149—42no—
62C22⋊D149—41no—
63C22⋊D149—41no—
64C22⋊D149—42no—
65C2×Dic149—21no—
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C2×D411yescharacteristic
69C4×D149—41no—
70C4×D149—41no—
71C4×D149—42no—
72C4×D149D812yes—
73C4×D149SD1612yes—
74C23×C149—21no—
75D4×C149—41no—
76C2×C4×C149—21no—
77C2×C4×C149—42no—
78C2×C4×C149C22⋊C411yescharacteristic
79C2×C4×C149C22⋊C411yescharacteristic
80C2×C4×C149C22×C411yescharacteristic
81C22×C149—41no—
82C22×C149—41no—
83C22×C149—41no—
84C22×C149C2×C22⋊C411yescharacteristic
85C2×D149—21no—
86C2×D149—21no—
87C2×D149—41no—
88C2×D149—41no—
89C2×D149—41no—
90C2×D149C2×D811yescharacteristic
91C2×D149C2×SD1611yescharacteristic
92#10597010—82no—
93C4×C149—21no—
94C4×C149—21no—
95C4×C149—41no—
96C4×C149#10212yes—
97Dic149—21no—
98Dic149—21no—
99Dic149—41no—
100Dic149#10212yes—
101C2×C149—81no—
102C2×C149#41011yescharacteristic
103C2×C149C2×#10211yescharacteristic
104C2×C149#42111yescharacteristic
105D149—21no—
106D149—21no—
107D149—81no—
108C149#151711yescharacteristic, complemented, Sylow
109#1517—1491nomaximal, Sylow
110#532—1491no—
111#431—1491no—
112#382—1491no—
113#327—1492no—
114#327—1492no—
115C2×#41—2981no—
116C4⋊Q8—1491no—
117#127—1491no—
118#124—2981no—
119#121—2981no—
120#121—1491no—
121#121—1491no—
122C4×D4—2981no—
123C4×D4—1491no—
124C4×D4#1059701011yescharacteristic, complemented
125C2×C4⋊C4—2981no—
126C2×C42—1491no—
127C4⋊C8—2981no—
128C22⋊C8—1492no—
129C4×C8—2981no—
130#95—2981no—
131#95—1492no—
132#41—5962no—
133#41—5962no—
134C2×Q8—2981no—
135C2×D4—2981no—
136C2×D4—2981no—
137C2×D4—2981no—
138C2×D4—2981no—
139C2×D4—1491no—
140C2×D4C2×#1059701011yescharacteristic
141C22×C4—21no—
142C22×C4—2981no—
143C22×C4—2982no—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4—1491no—
147C2×C8—2982no—
148C4⋊C4—2981no—
149C4⋊C4—5962no—
150C4⋊C4—1491no—
151C4⋊C4C2×#1059701011yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2981no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C42—1491no—
157C42—1491no—
158C42—1491no—
159C42C2×#1059701011yescharacteristic
160C23—21no—
161C23—2981no—
162C23—1491no—
163Q8—5962no—
164D4—41no—
165D4—5961no—
166D4—5961no—
167D4—5961no—
168D4—5962no—
169D4—5961no—
170D4—5961no—
171D4—5962no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—2981no—
175C2×C4—5961no—
176C2×C4—5961no—
177C2×C4—5962no—
178C2×C4—5962no—
179C2×C4—5962no—
180C2×C4—5962no—
181C2×C4—1491no—
182C2×C4—1491no—
183C2×C4—1491no—
184C2×C4—1492no—
185C2×C4—1492no—
186C2×C4C22⋊#1059701011yescharacteristic
187C2×C4C22⋊#1059701011yescharacteristic
188C2×C4C22×#1059701011yescharacteristic
189C8—5962no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—2981no—
194C22—2981no—
195C22—5961no—
196C22—5961no—
197C22—5961no—
198C22—1491no—
199C22—1491no—
200C22C2×C22⋊#1059701011yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2981no—
205C4—2981no—
206C4—5961no—
207C4—1492no—
208C4—11922no—
209C4#1801197312yes—
210C2—81no—
211C2—2981no—
212C2—2981no—
213C2—11921no—
214C2#2375060411yescharacteristic
215C2C2×#1801197311yescharacteristic
216C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#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#1517
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750644C2semidirect
2. #23750569C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
13. #18011910C4semidirect
14. #18011907C4semidirect
19. C4×D596C4semidirect
22. C4×D4×C149C4semidirect
108. C149#1517semidirect
124. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237505692
#237504772
#237504762
#237501722
#1517149