Finite Group Databasebeta

← #34060736

Subgroups — #34060736

Order 19072.

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

normal subgroups only

This group has 362 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#23750692C211yesmaximal, characteristic, complemented
2#23750624C212yesmaximal, complemented
3D149⋊#100C211yesmaximal, characteristic, complemented
4#23750492C212yesmaximal, complemented
5#23750193C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7D4×#10597010—24no—
8#18011990C2212yes—
9C2×C22⋊#10597010—22no—
10#18011976—24no—
11#18011971—22no—
12C2×#14558737C2211yescharacteristic
13C2×D4×D149C2211yescharacteristic
14#18011908C411yescharacteristic, complemented
15#18011907C411yescharacteristic, complemented
16#18011900C411yescharacteristic, complemented
17#18011884—22no—
18#18011881—22no—
19#18011868C2211yescharacteristic
20#124×C149C411yescharacteristic, complemented
21C22×#10597010—24no—
22#14558746—22no—
23#14558745—22no—
24D149⋊C8—22no—
25C4⋊#10597010—22no—
26C22⋊#10597010—24no—
27C22⋊#10597010—22no—
28C4×#10597010D414yescomplemented
29C23×D149D412yes—
30#14558737—22no—
31#14558737—22no—
32C2×D596—21no—
33C2×D596—22no—
34C2×D596C2×C411yescharacteristic
35C2×D596C2×C411yescharacteristic, complemented
36C2×C22⋊D149—22no—
37C2×C22⋊D149D412yes—
38D4×D149—22no—
39D4×D149—22no—
40C2×C4×D149—21no—
41C2×C4×D149C2311yescharacteristic
42#14558715—21no—
43#14558713—22no—
44#14558713—21no—
45C4×Dic149C2×C411yescharacteristic, complemented
46C2×Q8×C149C2×C411yescharacteristic, complemented
47C2×D4×C149C2×C411yescharacteristic
48C22⋊C4×C149—22no—
49C42×C149C2×C411yescharacteristic, complemented
50C2×#10597010—24no—
51C2×#10597010—84no—
52#11924753—42no—
53C22×D149—22no—
54C22×D149—22no—
55C22×D149—21no—
56C22×D149—82no—
57C22×D149C22⋊C412yes—
58C22×D149C2×D411yescharacteristic
59D596—22no—
60D596—22no—
61D596—41no—
62D596—41no—
63D596—82no—
64C22⋊D149—24no—
65C22⋊D149—82no—
66C2×Dic149—21no—
67C2×Dic149C2×D411yescharacteristic
68C4×D149—42no—
69C4×D149C2×D412yes—
70C4×D149#4112yes—
71C23×C149C22⋊C412yes—
72Q8×C149—22no—
73D4×C149—22no—
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149C22×C411yescharacteristic
77C22×C149—22no—
78C22×C149—42no—
79C22×C149C2×C22⋊C411yescharacteristic
80C2×D149—22no—
81C2×D149—41no—
82C2×D149—44no—
83C2×D149—42no—
84C2×D149—42no—
85C2×D149—41no—
86C2×D149—82no—
87C2×D149#12011yescharacteristic
88C2×D149#12311yescharacteristic
89#10597010—44no—
90C4×C149—41no—
91C4×C149—41no—
92C4×C149C4×D412yes—
93Dic149—41no—
94Dic149#12112yes—
95C2×C149—21no—
96C2×C149—42no—
97C2×C149#38611yescharacteristic
98D149—21no—
99D149—21no—
100D149—42no—
101D149—81no—
102C149#191111yescharacteristic, complemented, Sylow
103#1911—1491nomaximal, Sylow
104#535—1491no—
105#518—1491no—
106#421—1492no—
107C2×#100—1491no—
108H(3,ℤ/4)—1492no—
109C2×#41—1491no—
110C22×D4—1491no—
111C2×M16—1492no—
112#127—1491no—
113#127—1491no—
114#124—1491no—
115#124#1059701011yescharacteristic, complemented
116#121—2982no—
117#120—2982no—
118C4×D4—2984no—
119#117—1492no—
120#117—1491no—
121C2×C22⋊C4—2982no—
122#104—2984no—
123#100—2982no—
124C24—1492no—
125#41—2982no—
126#41—2982no—
127C2×Q8C2×#1059701011yescharacteristic, complemented
128C2×D4—2981no—
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—2982no—
132C2×D4—2982no—
133C2×D4—1492no—
134C2×D4—1491no—
135C2×D4—1491no—
136C2×D4C2×#1059701011yescharacteristic
137C22×C4—2981no—
138C22×C4—2984no—
139C22×C4—1491no—
140M16—2982no—
141M16—2982no—
142C2×C8—2982no—
143C4⋊C4—2981no—
144C4⋊C4—2982no—
145C22⋊C4—22no—
146C22⋊C4—2981no—
147C22⋊C4—2982no—
148C22⋊C4—2984no—
149C22⋊C4—2982no—
150C42—1494no—
151C42—1491no—
152C42C2×#1059701011yescharacteristic, complemented
153C23—2982no—
154C23—2982no—
155C23—2981no—
156C23—1492no—
157C23—1491no—
158C23—11922no—
159C23C22⋊#1059701012yes—
160Q8—22no—
161D4—22no—
162D4—2984no—
163D4—2982no—
164D4—2982no—
165D4—5961no—
166D4—5961no—
167D4—11922no—
168D4—11922no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—2984no—
172C2×C4—2981no—
173C2×C4—5962no—
174C2×C4—1491no—
175C2×C4—1492no—
176C2×C4—1492no—
177C2×C4—11924no—
178C2×C4C22×#1059701011yescharacteristic
179C8—5962no—
180C22—22no—
181C22—42no—
182C22—2982no—
183C22—5961no—
184C22—5962no—
185C22—5962no—
186C22—5964no—
187C22—5961no—
188C22—1491no—
189C22—1491no—
190C22—11922no—
191C22C2×C22⋊#1059701011yescharacteristic
192C4—41no—
193C4—41no—
194C4—5961no—
195C4—5964no—
196C4—1492no—
197C4D4×#1059701012yes—
198C2—21no—
199C2—42no—
200C2—2981no—
201C2—2981no—
202C2—5962no—
203C2—11921no—
204C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC2×C149#386
prime radical#23750193C2
cosocleC2×C4×D149C23
hypercenter#124#10597010
hypocenterC149#1911
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750692C2semidirect
2. #23750624C2semidirect
3. D149⋊#100C2semidirect
4. #23750492C2semidirect
14. #18011908C4semidirect
15. #18011907C4semidirect
16. #18011900C4semidirect
20. #124×C149C4semidirect
28. C4×#10597010D4semidirect
35. C2×D596C2×C4semidirect
45. C4×Dic149C2×C4semidirect
46. C2×Q8×C149C2×C4semidirect
49. C42×C149C2×C4semidirect
102. C149#1911semidirect
115. #124#10597010semidirect
127. C2×Q8C2×#10597010semidirect
152. C42C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506922
#237506242
D149⋊#1002
#237504922
#237501932
#1911149