Finite Group Databasebeta

← #34045862

Subgroups — #34045862

Order 19072.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#23750178C211yesmaximal, characteristic, complemented
2#23749643C211yesmaximal, characteristic
3C2×#18011837C211yesmaximal, characteristic
4#23749598C211yesmaximal, characteristic
5#23749397C211yesmaximal, characteristic, complemented
6#23749384C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10#18011910—21no—
11#18011902—21no—
12#18011888—22no—
13C4×Dic298—22no—
14#18011870C2211yescharacteristic
15C2×C4×Dic149C2211yescharacteristic
16#18011839—22no—
17#18011837—21no—
18#18011837—21no—
19#18011825—22no—
20C2×M16×C149C2211yescharacteristic
21#117×C149C2211yescharacteristic
22#117×C149C2211yescharacteristic
23#14558736—21no—
24#14558736—21no—
25#14558736—21no—
26#14558736—21no—
27C2×Dic298—22no—
28C2×Dic298Q811yescharacteristic, complemented
29C2×D596Q811yescharacteristic, complemented
30C2×C22⋊D149—21no—
31C22×Dic149—21no—
32C2×C4×D149—21no—
33#14558720—21no—
34#14558720—21no—
35C2×#11924746—21no—
36C4⋊Dic149—22no—
37C4⋊Dic149—21no—
38#14558715—22no—
39#14558715—22no—
40C22⋊Dic149D412yes—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C22×C4×C149C2311yescharacteristic
46M16×C149—21no—
47M16×C149—21no—
48C2×C8×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C22⋊C4×C149—21no—
52C22⋊C4×C149—21no—
53C42×C149—21no—
54C42×C149D412yes—
55C22×D149—21no—
56Dic298—21no—
57Dic298—21no—
58Dic298—44no—
59D596—21no—
60D596—21no—
61C22⋊D149—41no—
62C22⋊D149—41no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—22no—
66C2×Dic149—21no—
67C2×Dic149—42no—
68C4×D149—41no—
69C4×D149—41no—
70#11924746—41no—
71C23×C149C2×D411yescharacteristic
72C2×C4×C149—22no—
73C2×C4×C149—41no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×Q811yescharacteristic
77C2×C4×C149#4111yescharacteristic
78C2×C4×C149#4111yescharacteristic
79C2×C4×C149#4111yescharacteristic
80C8×C149—41no—
81C22×C149—41no—
82C22×C149#12011yescharacteristic
83C22×C149C22⋊Q811yescharacteristic
84C22×C149#12411yescharacteristic
85C2×D149—41no—
86C2×D149—81no—
87C4×C149—42no—
88C4×C149—81no—
89C4×C149C22⋊Q811yescharacteristic
90C4×C149C22⋊Q811yescharacteristic
91C4×C149#12411yescharacteristic
92C4×C149#12411yescharacteristic
93Dic149—22no—
94Dic149—41no—
95Dic149—42no—
96Dic149—41no—
97C2×C149—21no—
98C2×C149—21no—
99C2×C149—21no—
100C2×C149#39311yescharacteristic
101D149—81no—
102C149#203111yescharacteristic, complemented, Sylow
103#2031—1491nomaximal, Sylow
104#533—1491no—
105#421—1491no—
106C2×#104—1491no—
107#410—1491no—
108#344—1491no—
109#339—1491no—
110H(3,ℤ/4)D14911yescharacteristic, complemented
111C2×#41—1491no—
112C2×M16—1491no—
113C2×M16C2×D14911yescharacteristic
114C4⋊Q8—2981no—
115#125—2981no—
116C22⋊Q8—2982no—
117C4×Q8—2982no—
118#117—1491no—
119#117C2×D14911yescharacteristic
120#117C2×D14911yescharacteristic
121C2×C42—1491no—
122#104—2981no—
123#104—2981no—
124#104—2982no—
125#99—2982no—
126#41—2981no—
127#41—2981no—
128#41—2981no—
129#41—2981no—
130C2×Q8—2982no—
131C2×Q8—1491no—
132C2×D4—2981no—
133C2×D4—1491no—
134C22×C4—2981no—
135C22×C4—2981no—
136C22×C4C22×D14911yescharacteristic
137M16—21no—
138M16—21no—
139M16—2981no—
140M16—2981no—
141C2×C8—21no—
142C2×C8—2981no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2982no—
146C4⋊C4—2982no—
147C4⋊C4—2982no—
148C4⋊C4—2981no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—1492no—
152C42—21no—
153C42—2981no—
154C42—2981no—
155C42—1491no—
156C42—1491no—
157C42D59612yes—
158C23—2981no—
159C23D4×D14911yescharacteristic
160Q8—2981no—
161Q8—2981no—
162Q8—5964no—
163D4—2981no—
164D4—2981no—
165D4—5961no—
166D4—5961no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—2982no—
172C2×C4—2981no—
173C2×C4—5962no—
174C2×C4—5961no—
175C2×C4—5961no—
176C2×C4D4×D14911yescharacteristic
177C2×C4C2×D59611yescharacteristic
178C2×C4Q8×D14911yescharacteristic
179C2×C4#1455873511yescharacteristic
180C2×C4#1455873611yescharacteristic
181C2×C4#1455873611yescharacteristic
182C8—41no—
183C8—5961no—
184C22—41no—
185C22—5961no—
186C22—11921no—
187C22#1801188111yescharacteristic
188C22#1801188911yescharacteristic
189C22#1801189711yescharacteristic
190C4—42no—
191C4—81no—
192C4—2982no—
193C4—5961no—
194C4—5962no—
195C4—5961no—
196C4#1801188911yescharacteristic
197C4#1801189111yescharacteristic
198C4#1801189711yescharacteristic
199C4#1801189911yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—11921no—
204C2#2374953811yescharacteristic
subgroupG/H
centerC4#18011899
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingH(3,ℤ/4)×C149C2
socleC2×C149#393
prime radicalC2×#14558736C22
hypercenterH(3,ℤ/4)D149
hypocenterC149#2031
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #23750178C2semidirect
5. #23749397C2semidirect
6. #23749384C2semidirect
7. H(3,ℤ/4)×C149C2semidirect
28. C2×Dic298Q8semidirect
29. C2×D596Q8semidirect
102. C149#2031semidirect
110. H(3,ℤ/4)D149semidirect

Maximal subgroups

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

subgroupindex
#237501782
#237496432
C2×#180118372
#237495982
#237493972
#237493842
H(3,ℤ/4)×C1492
#2031149