Finite Group Databasebeta

← #34046050

Subgroups — #34046050

Order 19072.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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×#18011847C211yesmaximal, characteristic, complemented
2#23749668C211yesmaximal, characteristic, complemented
3#23749629C211yesmaximal, characteristic
4C2×#18011833C211yesmaximal, characteristic
5C2×#18011827C211yesmaximal, characteristic
6#23749393C211yesmaximal, characteristic, complemented
7#424×C149C211yesmaximal, characteristic, complemented
8C22×D596C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10C2×#14558720C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12#18011847—22no—
13#18011844—21no—
14#18011842—21no—
15#18011833—22no—
16#18011831—21no—
17#18011831—21no—
18#18011827—22no—
19C2×M16×C149C2211yescharacteristic
20C22×C8×C149C2211yescharacteristic
21#117×C149C2211yescharacteristic
22C4⋊C8×C149—22no—
23C23×D149—21no—
24C2×D596—21no—
25C2×D596—21no—
26C2×D596—21no—
27C2×D596—21no—
28C2×D596—21no—
29C2×D596Q812yes—
30C22×Dic149—21no—
31#14558720—21no—
32#14558720—21no—
33#14558720—21no—
34#14558720D412yes—
35C2×#11924746—21no—
36C2×#11924746—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C22×C4×C149C2311yescharacteristic
40M16×C149—21no—
41M16×C149—21no—
42C2×C8×C149—21no—
43C2×C8×C149—21no—
44C2×C8×C149—21no—
45C2×C8×C149D412yes—
46C4⋊C4×C149D411yescharacteristic
47C4⋊C4×C149D411yescharacteristic
48C22⋊C4×C149—21no—
49C42×C149—21no—
50C22×D149—22no—
51C22×D149—41no—
52C22×D149—41no—
53C22×D149—81no—
54C22×D149—81no—
55D596—22no—
56D596—22no—
57D596—41no—
58D596—41no—
59C2×Dic149—41no—
60C2×Dic149—81no—
61#11924746—22no—
62#11924746—41no—
63C23×C149#4111yescharacteristic
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149C2×D411yescharacteristic
67C2×C4×C149C2×D411yescharacteristic
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×Q811yescharacteristic
70C2×C4×C149#4111yescharacteristic
71C2×C4×C149#4111yescharacteristic
72C8×C149—22no—
73C8×C149—41no—
74C22×C149—21no—
75C22×C149—21no—
76C22×C149#12111yescharacteristic
77C22×C149C22⋊Q811yescharacteristic
78C22×C149#12611yescharacteristic
79C2×D149—42no—
80C2×D149—82no—
81C2×D149—81no—
82C2×D149—81no—
83C2×D149—82no—
84C4×C149—41no—
85C4×C149—41no—
86C4×C149#12111yescharacteristic
87C4×C149#12111yescharacteristic
88C4×C149C22⋊Q811yescharacteristic
89C4×C149C22⋊Q811yescharacteristic
90Dic149—81no—
91C2×C149—21no—
92C2×C149—21no—
93C2×C149#39611yescharacteristic
94C2×C149#47111yescharacteristic
95C2×C149#47211yescharacteristic
96D149—82no—
97C149#206311yescharacteristic, complemented, Sylow
98#2063—1491nomaximal, Sylow
99C2×#108—1491no—
100#428—1491no—
101#424D14911yescharacteristic, complemented
102#418—1491no—
103C2×#102—1491no—
104C2×#100—1491no—
105#343—1491no—
106C22×D4—1491no—
107C2×M16—1491no—
108C2×M16—1491no—
109C2×M16C2×D14911yescharacteristic
110C22×C8C2×D14911yescharacteristic
111#117C2×D14911yescharacteristic
112C2×C4⋊C4—1491no—
113#108—2982no—
114#107—2981no—
115#106—2981no—
116C4⋊C8—22no—
117#102—2982no—
118#102—2981no—
119#102—2981no—
120#100—2982no—
121C24—2981no—
122C2×D4—2981no—
123C2×D4—2981no—
124C2×D4—2981no—
125C2×D4—2981no—
126C2×D4—2981no—
127C2×D4—1492no—
128C22×C4—2981no—
129C22×C4C22×D14911yescharacteristic
130M16—21no—
131M16—21no—
132M16—2981no—
133M16—2981no—
134M16—2981no—
135M16—1492no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—2981no—
140C2×C8—2981no—
141C2×C8C22⋊D14912yes—
142C4⋊C4—2981no—
143C4⋊C4—2981no—
144C4⋊C4D59611yescharacteristic
145C4⋊C4D59611yescharacteristic
146C22⋊C4—21no—
147C42—21no—
148C23—2982no—
149C23—5961no—
150C23—5961no—
151C23—11921no—
152C23—11921no—
153C23#1455873611yescharacteristic
154D4—2982no—
155D4—2982no—
156D4—5961no—
157D4—5961no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—5961no—
161C2×C4—11921no—
162C2×C4D4×D14911yescharacteristic
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4C2×D59611yescharacteristic
165C2×C4Q8×D14911yescharacteristic
166C2×C4#1455873511yescharacteristic
167C2×C4#1455873711yescharacteristic
168C8—22no—
169C8—41no—
170C8—2982no—
171C8—5961no—
172C22—21no—
173C22—21no—
174C22—5962no—
175C22—11922no—
176C22—11922no—
177C22—11921no—
178C22—11921no—
179C22#1801188511yescharacteristic
180C22#1801188911yescharacteristic
181C22#1801190611yescharacteristic
182C4—41no—
183C4—41no—
184C4—11921no—
185C4#1801188311yescharacteristic
186C4#1801188611yescharacteristic
187C4#1801188711yescharacteristic
188C4#1801189111yescharacteristic
189C2—21no—
190C2—21no—
191C2—11922no—
192C2#2374954711yescharacteristic
193C2#2374988811yescharacteristic
194C2#2374989511yescharacteristic
subgroupG/H
centerC22#18011885
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#424×C149C2
socleC22×C149#121
prime radicalC22×D596C22
hypercenter#424D149
hypocenterC149#2063
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C2×#18011847C2semidirect
2. #23749668C2semidirect
6. #23749393C2semidirect
7. #424×C149C2semidirect
97. C149#2063semidirect
101. #424D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118472
#237496682
#237496292
C2×#180118332
C2×#180118272
#237493932
#424×C1492
#2063149