Finite Group Databasebeta

← #34060069

Subgroups — #34060069

Order 19072.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#18011968C211yesmaximal, characteristic, complemented
2C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
3#23750479C212yesmaximal, complemented
4#23750477C212yesmaximal, complemented
5#23750138C211yesmaximal, characteristic
6C22×#11924753—21no—
7C2×C22⋊#10597010—21no—
8C2×C4×#10597010—21no—
9#18011968—21no—
10#18011968C2212yes—
11(C2×#10597010)⋊C4C2212yes—
12C2×#14558737C411yescharacteristic, complemented
13C22×C4×D149C2211yescharacteristic
14#18011896—21no—
15#18011887C2211yescharacteristic
16#18011886C2211yescharacteristic
17#18011885C411yescharacteristic, complemented
18#18011881—21no—
19#18011873—21no—
20#18011871—21no—
21#18011869C411yescharacteristic, complemented
22C22⋊Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26C22⋊#10597010—24no—
27C4×#10597010—42no—
28C23×D149D411yescharacteristic
29#14558737—42no—
30C2×D596—21no—
31C2×D596—21no—
32C2×D596C2×C411yescharacteristic
33C2×C22⋊D149—21no—
34C22×Dic149D411yescharacteristic
35C2×C4×D149—21no—
36C2×C4×D149—42no—
37C2×C4×D149C2×C411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149D411yescharacteristic
40C2×C4×D149C2311yescharacteristic
41C4⋊Dic149C2×C411yescharacteristic
42#14558715—21no—
43#14558713—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47C4×Dic149—21no—
48C2×Q8×C149C2×C411yescharacteristic
49C22×C4×C149C2×C411yescharacteristic
50C4⋊C4×C149—21no—
51C4⋊C4×C149C2×C411yescharacteristic
52C22⋊C4×C149—21no—
53C2×#10597010—24no—
54C2×#10597010—42no—
55C2×#10597010—42no—
56#11924753—42no—
57C22×D149—22no—
58C22×D149—22no—
59C22×D149—21no—
60C22×D149—41no—
61C22×D149C22⋊C411yescharacteristic
62C22×D149C2×D411yescharacteristic
63D596—41no—
64D596—42no—
65D596—42no—
66C22⋊D149—42no—
67C2×Dic149—22no—
68C2×Dic149—21no—
69C2×Dic149C22⋊C411yescharacteristic
70C2×Dic149C2×D411yescharacteristic
71C4×D149—22no—
72C4×D149—22no—
73C4×D149—41no—
74C4×D149—41no—
75C4×D149—42no—
76C23×C149C22⋊C411yescharacteristic
77Q8×C149—41no—
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—41no—
81C2×C4×C149C22⋊C411yescharacteristic
82C2×C4×C149C22×C411yescharacteristic
83C22×C149—21no—
84C22×C149—21no—
85C22×C149#10412yes—
86C22×C149C2×C22⋊C411yescharacteristic
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—21no—
91C2×D149—21no—
92C2×D149—44no—
93C2×D149—41no—
94C2×D149—41no—
95C2×D149—41no—
96C2×D149#13512yes—
97#10597010—44no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—41no—
101C4×C149—41no—
102Dic149—21no—
103Dic149—41no—
104Dic149#9912yes—
105C2×C149—22no—
106C2×C149C2×#9911yescharacteristic
107C2×C149#41611yescharacteristic
108C2×C149C2×#10411yescharacteristic
109D149—22no—
110D149—41no—
111D149—81no—
112C149#150111yescharacteristic, complemented, Sylow
113#1501—1491nomaximal, Sylow
114#525—1491no—
115C2×C22⋊C8—1491no—
116C4×C22⋊C4—1491no—
117#328—1492no—
118#327—1492no—
119C2×#41—1491no—
120C23×C4—1491no—
121C22×C8—2981no—
122#123—2981no—
123C22⋊Q8—1491no—
124C22⋊Q8#1059701011yescharacteristic, complemented
125#121—1491no—
126#121—1491no—
127#120—2981no—
128C4×D4—2981no—
129C4×D4—2981no—
130#117—1491no—
131C2×C22⋊C4—2981no—
132C2×C42—2981no—
133C22⋊C8—2981no—
134C22⋊C8—1492no—
135#95—1492no—
136C24—1491no—
137#41—5962no—
138C2×Q8C2×#1059701011yescharacteristic
139C2×D4—2981no—
140C2×D4—2981no—
141C2×D4—2981no—
142C2×D4—1491no—
143C22×C4—2981no—
144C22×C4—2982no—
145C22×C4—5962no—
146C22×C4—1491no—
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4C2×#1059701011yescharacteristic
152C2×C8—2982no—
153C2×C8—5962no—
154C4⋊C4—21no—
155C4⋊C4—2981no—
156C4⋊C4—1491no—
157C4⋊C4C2×#1059701011yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—2981no—
160C22⋊C4—2981no—
161C22⋊C4—2981no—
162C22⋊C4—2984no—
163C22⋊C4—2981no—
164C42—2981no—
165C42—5962no—
166C23—2982no—
167C23—2982no—
168C23—2981no—
169C23—5961no—
170C23—1491no—
171C23—1491no—
172C23C22⋊#1059701011yescharacteristic
173Q8—41no—
174D4—5961no—
175D4—5962no—
176D4—5962no—
177D4—5962no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—2984no—
185C2×C4—2981no—
186C2×C4—5961no—
187C2×C4—5961no—
188C2×C4—5962no—
189C2×C4—5962no—
190C2×C4—5962no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4C22⋊#1059701011yescharacteristic
194C2×C4C22×#1059701011yescharacteristic
195C8—5962no—
196C22—21no—
197C22—21no—
198C22—2981no—
199C22—2981no—
200C22—2981no—
201C22—2981no—
202C22—2981no—
203C22—5964no—
204C22—5961no—
205C22—5961no—
206C22—5961no—
207C22—1492no—
208C22#1801197612yes—
209C22C2×C22⋊#1059701011yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—2981no—
215C4—5964no—
216C4—5961no—
217C4—1492no—
218C2—22no—
219C2—2982no—
220C2—5961no—
221C2—11921no—
222C2D149⋊#9911yescharacteristic
223C2#2375061511yescharacteristic
224C2C2×#1801197611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750138C2
cosocleC2×C4×D149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1501
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#18011968C2semidirect
2. C4×C22⋊#10597010C2semidirect
3. #23750479C2semidirect
4. #23750477C2semidirect
12. C2×#14558737C4semidirect
17. #18011885C4semidirect
21. #18011869C4semidirect
22. C22⋊Q8×C149C4semidirect
112. C149#1501semidirect
124. C22⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119682
C4×C22⋊#105970102
#237504792
#237504772
#237501382
#1501149