Finite Group Databasebeta

← #34060106

Subgroups — #34060106

Order 19072.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750596C211yesmaximal, characteristic, complemented
2#23750567C211yesmaximal, characteristic, complemented
3#23750479C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#23750132C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×C4⋊#10597010—21no—
8C2×C22⋊#10597010—21no—
9#18011968C2212yes—
10C22⋊#11924753—21no—
11(C2×#10597010)⋊C4C2212yes—
12C22×C4×D149C2211yescharacteristic
13#18011892—21no—
14#18011887C411yescharacteristic, complemented
15#18011887C2211yescharacteristic
16#18011882C411yescharacteristic, complemented
17#18011882C2211yescharacteristic
18#18011879—21no—
19C4×C22⋊D149—21no—
20C4×C22⋊D149—21no—
21#18011870C411yescharacteristic, complemented
22C2×#41×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24#14558746—42no—
25C2×#11924753—22no—
26C4⋊#10597010—42no—
27C22⋊#10597010—42no—
28C23×D149D411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C22×Dic149D411yescharacteristic
32C2×C4×D149—42no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149C2×C411yescharacteristic
38C4⋊Dic149C2×C411yescharacteristic
39#14558715—21no—
40#14558715—21no—
41C22⋊Dic149—21no—
42C22⋊Dic149—21no—
43C22⋊Dic149—21no—
44#14558713—21no—
45#14558713—21no—
46C4×Dic149—21no—
47#41×C149—42no—
48C2×Q8×C149C2×C411yescharacteristic
49C2×D4×C149—21no—
50C2×D4×C149C2×C411yescharacteristic
51C22×C4×C149—21no—
52C22×C4×C149C2×C411yescharacteristic
53C2×#10597010—42no—
54C2×#10597010—42no—
55C2×#10597010—42no—
56#11924753—42no—
57C22×D149—21no—
58C22×D149—21no—
59C22×D149—41no—
60C22×D149—41no—
61C22×D149C22⋊C411yescharacteristic
62C22×D149C2×D411yescharacteristic
63C22⋊D149—42no—
64C22⋊D149—41no—
65C22⋊D149—41no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149—41no—
69C2×Dic149C22⋊C411yescharacteristic
70C2×Dic149C2×D411yescharacteristic
71C4×D149—22no—
72C4×D149—22no—
73C4×D149—41no—
74C4×D149—41no—
75C23×C149—21no—
76C23×C149C22⋊C411yescharacteristic
77Q8×C149—41no—
78D4×C149—41no—
79D4×C149—42no—
80C2×C4×C149—22no—
81C2×C4×C149—21no—
82C2×C4×C149—42no—
83C2×C4×C149C22⋊C411yescharacteristic
84C2×C4×C149C22×C411yescharacteristic
85C22×C149—21no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149C2×C22⋊C411yescharacteristic
92C2×D149—21no—
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149—21no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149AGL(1,ℤ/8)11yescharacteristic
100C2×D149#13711yescharacteristic
101#10597010—82no—
102C4×C149—21no—
103C4×C149—41no—
104C4×C149#9912yes—
105Dic149—21no—
106Dic149—21no—
107Dic149—41no—
108Dic149—41no—
109C2×C149—41no—
110C2×C149—81no—
111C2×C149C2×#9911yescharacteristic
112C2×C149#41711yescharacteristic
113C2×C149#42111yescharacteristic
114D149—21no—
115D149—21no—
116D149—41no—
117C149#151311yescharacteristic, complemented, Sylow
118#1513—1491nomaximal, Sylow
119#525—1491no—
120#407—1491no—
121#380—1491no—
122#328—1492no—
123#327—1492no—
124C2×#41#1059701011yescharacteristic, complemented
125C23×C4—1491no—
126C2×M16—2981no—
127#123—2981no—
128C22⋊Q8—1491no—
129C22⋊Q8—1491no—
130#121—1491no—
131#121—1491no—
132#120—2981no—
133C4×D4—2981no—
134C4×D4—2981no—
135#117—1491no—
136C2×C4⋊C4—2981no—
137C2×C22⋊C4—2981no—
138C22⋊C8—2981no—
139C22⋊C8—1492no—
140#95—1492no—
141C24—1491no—
142#41—42no—
143C2×Q8C2×#1059701011yescharacteristic
144C2×D4—21no—
145C2×D4—2981no—
146C2×D4—2981no—
147C2×D4C2×#1059701011yescharacteristic
148C22×C4—21no—
149C22×C4—2982no—
150C22×C4—5962no—
151C22×C4—1491no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4—1491no—
155C22×C4—1491no—
156C22×C4C2×#1059701011yescharacteristic
157M16—5962no—
158C2×C8—2982no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—5962no—
162C4⋊C4—1491no—
163C4⋊C4—1491no—
164C22⋊C4—2981no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C22⋊C4—5962no—
170C42—2981no—
171C23—21no—
172C23—2981no—
173C23—2981no—
174C23—5961no—
175C23—5961no—
176C23—1491no—
177C23—1491no—
178C23C22⋊#1059701011yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—5962no—
183D4—5961no—
184D4—5961no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—5961no—
193C2×C4—5961no—
194C2×C4—5961no—
195C2×C4—5962no—
196C2×C4—5962no—
197C2×C4—5962no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4C22⋊#1059701011yescharacteristic
201C2×C4C22×#1059701011yescharacteristic
202C8—5962no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—2981no—
210C22—2981no—
211C22—2981no—
212C22—2981no—
213C22—2981no—
214C22—5962no—
215C22—5962no—
216C22—1491no—
217C22—1491no—
218C22C2×C22⋊#1059701011yescharacteristic
219C4—21no—
220C4—41no—
221C4—2981no—
222C4—2981no—
223C4—5961no—
224C4—5961no—
225C4—11922no—
226C4#1801196912yes—
227C2—41no—
228C2—81no—
229C2—2981no—
230C2—2981no—
231C2—5961no—
232C2C2×#1801196911yescharacteristic
233C2#2375061611yescharacteristic
234C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750132C2
cosocleC2×C4×D149C23
hypercenterC2×#41#10597010
hypocenterC149#1513
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750596C2semidirect
2. #23750567C2semidirect
3. #23750479C2semidirect
4. #23750476C2semidirect
14. #18011887C4semidirect
16. #18011882C4semidirect
21. #18011870C4semidirect
22. C2×#41×C149C4semidirect
117. C149#1513semidirect
124. C2×#41#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
#237505672
#237504792
#237504762
#237501322
#1513149