Finite Group Databasebeta

← #34060821

Subgroups — #34060821

Order 19072.

344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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×#18011974C212yesmaximal, complemented
2C2×#18011973C212yesmaximal
3#23750584C211yesmaximal, characteristic, complemented
4#23750571C211yesmaximal, characteristic, complemented
5#124×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010—22no—
8C2×C4⋊#10597010C2212yes—
9#18011974—24no—
10#18011973—24no—
11#18011966—22no—
12C2×Q8×D149C2211yescharacteristic
13C2×D4×D149C2211yescharacteristic
14#18011900C411yescharacteristic, complemented
15#18011899C411yescharacteristic, complemented
16#18011898C411yescharacteristic, complemented
17#18011897—22no—
18C22⋊C4×D149—22no—
19C42×D149C2211yescharacteristic
20#124×C149C411yescharacteristic, complemented
21C22×#10597010—22no—
22D149⋊C8—22no—
23D149⋊C8D414yes—
24C2×#11924753—22no—
25C4⋊#10597010—22no—
26C4⋊#10597010—22no—
27C4⋊#10597010—44no—
28C23×D149—21no—
29C2×Dic298—21no—
30C2×Dic298C2×C411yescharacteristic
31Q8×D149—22no—
32Q8×D149—22no—
33C2×D596C2×C411yescharacteristic
34C2×C22⋊D149—21no—
35D4×D149—22no—
36D4×D149—22no—
37C2×C4×D149—21no—
38C2×C4×D149D412yes—
39C2×C4×D149C2311yescharacteristic
40C22⋊Dic149—22no—
41#14558713—22no—
42#14558713—22no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149D412yes—
45C2×Q8×C149C2×C411yescharacteristic
46C2×D4×C149C2×C411yescharacteristic
47C22⋊C4×C149—22no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—42no—
50C2×#10597010—44no—
51#11924753—24no—
52C22×D149—21no—
53C22×D149—41no—
54C22×D149—41no—
55C22×D149—42no—
56C22×D149—42no—
57C22×D149C2×D411yescharacteristic
58Dic298—22no—
59Dic298—42no—
60D596—22no—
61C22⋊D149—42no—
62C2×Dic149—21no—
63C2×Dic149C22⋊C412yes—
64C2×Dic149C2×D411yescharacteristic
65C4×D149—22no—
66C4×D149—22no—
67C4×D149—41no—
68C4×D149—41no—
69C4×D149C2×D412yes—
70C4×D149#4112yes—
71C23×C149—21no—
72Q8×C149—22no—
73D4×C149—22no—
74C2×C4×C149—21no—
75C2×C4×C149C22⋊C412yes—
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—41no—
78C22×C149—42no—
79C22×C149C2×C22⋊C411yescharacteristic
80C2×D149—41no—
81C2×D149—42no—
82C2×D149—82no—
83C2×D149—81no—
84C2×D149—81no—
85C2×D149#12411yescharacteristic
86C2×D149#12711yescharacteristic
87C2×D149AGL(1,ℤ/8)12yes—
88C2×D149#13712yes—
89#10597010—82no—
90C4×C149—22no—
91C4×C149—41no—
92C4×C149C4×D412yes—
93Dic149—22no—
94Dic149—41no—
95Dic149#12112yes—
96C2×C149—81no—
97C2×C149#39011yescharacteristic
98C2×C149#41712yes—
99D149—81no—
100D149#48912yes—
101D149#49611yescharacteristic
102D149#49711yescharacteristic
103C149#195911yescharacteristic, complemented, Sylow
104#1959—1491nomaximal, Sylow
105C2×#124—1491no—
106C2×#103—1492no—
107C2×#102—1492no—
108C2×#97—1491no—
109#384—1491no—
110C22×Q8—1491no—
111C22×D4—1491no—
112C22×C8—1492no—
113#124—2982no—
114#124—1491no—
115#124—1491no—
116#124—1491no—
117#124#1059701011yescharacteristic, complemented
118C2×C4⋊C4—2982no—
119C2×C4⋊C4—1492no—
120C2×C22⋊C4—2982no—
121C2×C42—1491no—
122#103—2984no—
123#102—2984no—
124#97—2982no—
125C24—2981no—
126C2×Q8—2981no—
127C2×Q8—2982no—
128C2×Q8—2982no—
129C2×Q8—1491no—
130C2×Q8C2×#1059701011yescharacteristic
131C2×D4—2982no—
132C2×D4—2982no—
133C2×D4—2981no—
134C2×D4—1491no—
135C2×D4C2×#1059701011yescharacteristic
136C22×C4—2981no—
137C22×C4—2982no—
138C22×C4—1492no—
139C22×C4—1491no—
140C2×C8—2982no—
141C2×C8—2982no—
142C2×C8—1494no—
143C4⋊C4—2982no—
144C4⋊C4—2982no—
145C4⋊C4—5964no—
146C22⋊C4—22no—
147C22⋊C4—2982no—
148C22⋊C4—2982no—
149C22⋊C4—2982no—
150C42—1492no—
151C42—1491no—
152C42C2×#1059701011yescharacteristic
153C23—21no—
154C23—2981no—
155C23—5961no—
156C23—5961no—
157C23—5962no—
158C23—5962no—
159C23—1491no—
160Q8—22no—
161Q8—2982no—
162Q8—5962no—
163D4—22no—
164D4—2982no—
165D4—5962no—
166C2×C4—21no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2981no—
170C2×C4—5961no—
171C2×C4—5961no—
172C2×C4—5962no—
173C2×C4—5964no—
174C2×C4—1492no—
175C2×C4—1491no—
176C2×C4—1492no—
177C2×C4—1492no—
178C2×C4C22⋊#1059701012yes—
179C2×C4C22×#1059701011yescharacteristic
180C8—2984no—
181C22—41no—
182C22—42no—
183C22—5961no—
184C22—5962no—
185C22—1491no—
186C22—1491no—
187C22—1492no—
188C22—1492no—
189C22—11921no—
190C22—11922no—
191C22—11921no—
192C22C2×C22⋊#1059701011yescharacteristic
193C4—22no—
194C4—41no—
195C4—2982no—
196C4—5961no—
197C4—1492no—
198C4—11922no—
199C4D4×#1059701012yes—
200C2—81no—
201C2—1491no—
202C2—1492no—
203C2—1491no—
204C2—11921no—
205C2#2375057711yescharacteristic
206C2#2375061612yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C22
cosocleC2×C4×D149C23
hypercenter#124#10597010
hypocenterC149#1959
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#18011974C2semidirect
3. #23750584C2semidirect
4. #23750571C2semidirect
14. #18011900C4semidirect
15. #18011899C4semidirect
16. #18011898C4semidirect
20. #124×C149C4semidirect
103. C149#1959semidirect
117. #124#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119742
C2×#180119732
#237505842
#237505712
#124×D1492
#1959149