Finite Group Databasebeta

← #34044793

Subgroups — #34044793

Order 19072.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#23750093C211yesmaximal, characteristic
2#23749607C211yesmaximal, characteristic
3#23749598C211yesmaximal, characteristic
4#23749386C211yesmaximal, characteristic, complemented
5#23749384C211yesmaximal, characteristic, complemented
6#23749381C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C2×#14558720C2211yescharacteristic
10#18011876—21no—
11#18011873—21no—
12#18011871—22no—
13#18011870C2211yescharacteristic
14#18011868C412yescomplemented
15C2×C4×Dic149C2211yescharacteristic
16C42×D149C412yescomplemented
17#18011829—21no—
18#18011827—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×Dic298D411yescharacteristic
28C2×D596D411yescharacteristic
29C2×C22⋊D149D412yes—
30C22×Dic149—21no—
31C2×C4×D149—22no—
32C2×C4×D149C2×C412yes—
33#14558720—21no—
34#14558720—21no—
35C2×#11924746—21no—
36C4⋊Dic149—21no—
37#14558715—22no—
38C22⋊Dic149—21no—
39#14558713—22no—
40C4×Dic149—22no—
41C4×Dic149—21no—
42C4×Dic149—21no—
43C4×Dic149C2×C411yescharacteristic
44C4×Dic149C2×C411yescharacteristic
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×C149C2×C412yes—
55C22×D149C22⋊C412yes—
56Dic298—21no—
57Dic298—21no—
58D596—21no—
59D596—21no—
60C22⋊D149—22no—
61C22⋊D149—22no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—42no—
65C2×Dic149—41no—
66C2×Dic149C22⋊C412yes—
67C4×D149—22no—
68C4×D149—22no—
69C4×D149—44no—
70#11924746—41no—
71C23×C149C2×D411yescharacteristic
72C2×C4×C149—22no—
73C2×C4×C149—41no—
74C2×C4×C149C22×C411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149#4111yescharacteristic
77C2×C4×C149#4111yescharacteristic
78C2×C4×C149#4111yescharacteristic
79C2×C4×C149#4111yescharacteristic
80C8×C149—41no—
81C22×C149—41no—
82C22×C149C2×C22⋊C411yescharacteristic
83C22×C149#12311yescharacteristic
84C22×C149#12311yescharacteristic
85C2×D149—22no—
86C2×D149—42no—
87C4×C149—42no—
88C4×C149—81no—
89C4×C149#11711yescharacteristic
90C4×C149#11711yescharacteristic
91C4×C149#12311yescharacteristic
92C4×C149#12311yescharacteristic
93Dic149—22no—
94Dic149—22no—
95Dic149—41no—
96Dic149—81no—
97C2×C149—21no—
98C2×C149—21no—
99C2×C149—21no—
100C2×C149#38111yescharacteristic
101D149—42no—
102C149#182711yescharacteristic, complemented, Sylow
103#1827—1491nomaximal, Sylow
104C4×#41—1491no—
105#413—1491no—
106#410—1491no—
107#339—1491no—
108#339—1491no—
109H(3,ℤ/4)—1491no—
110H(3,ℤ/4)D14911yescharacteristic, complemented
111C2×#41—1491no—
112C2×M16—1491no—
113C2×M16C2×D14911yescharacteristic
114C4×Q8—2981no—
115C4×D4—2982no—
116C4×D4—2981no—
117#117—1491no—
118#117—1492no—
119#117C2×D14911yescharacteristic
120#117C2×D14911yescharacteristic
121C2×C42—1491no—
122C2×C42—1492no—
123#101—2981no—
124#100—2981no—
125#99—2982no—
126#41—2981no—
127#41—2981no—
128#41—2981no—
129#41—2981no—
130C2×Q8—1491no—
131C2×D4—1492no—
132C2×D4—1491no—
133C22×C4—2982no—
134C22×C4—2981no—
135C22×C4—1492no—
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—2981no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2982no—
150C22⋊C4—2981no—
151C42—21no—
152C42—2982no—
153C42—2981no—
154C42—2981no—
155C42—1491no—
156C42—1491no—
157C42C4×D14912yes—
158C23—1492no—
159C23D4×D14911yescharacteristic
160Q8—2981no—
161Q8—2981no—
162D4—2982no—
163D4—2982no—
164D4—2981no—
165D4—2981no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—2981no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2981no—
172C2×C4—5964no—
173C2×C4—5962no—
174C2×C4—5961no—
175C2×C4—1492no—
176C2×C4C2×C4×D14911yescharacteristic
177C2×C4D4×D14911yescharacteristic
178C2×C4#1455873511yescharacteristic
179C2×C4#1455873611yescharacteristic
180C2×C4#1455873611yescharacteristic
181C2×C4#1455873711yescharacteristic
182C8—41no—
183C8—5961no—
184C22—41no—
185C22—2982no—
186C22—5962no—
187C22C22⋊C4×D14911yescharacteristic
188C22#1801189311yescharacteristic
189C22#1801189611yescharacteristic
190C4—42no—
191C4—81no—
192C4—2982no—
193C4—2982no—
194C4—5961no—
195C4—11921no—
196C4#1801186811yescharacteristic
197C4#1801186911yescharacteristic
198C4#1801189311yescharacteristic
199C4#1801189611yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—5962no—
204C2#2374948711yescharacteristic
subgroupG/H
centerC4#18011868
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingH(3,ℤ/4)×C149C2
socleC2×C149#381
prime radicalC2×#14558736C22
cosocleC22×C4×C149C23
hypercenterH(3,ℤ/4)D149
hypocenterC149#1827
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #23749386C2semidirect
5. #23749384C2semidirect
6. #23749381C2semidirect
7. H(3,ℤ/4)×C149C2semidirect
14. #18011868C4semidirect
16. C42×D149C4semidirect
102. C149#1827semidirect
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
#237500932
#237496072
#237495982
#237493862
#237493842
#237493812
H(3,ℤ/4)×C1492
#1827149