Finite Group Databasebeta

← #34052871

Subgroups — #34052871

Order 19072.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C149⋊#401C212yesmaximal
2#23749567C212yesmaximal
3#23749565C212yesmaximal
4#23749564C211yesmaximal, characteristic
5#23749558C212yesmaximal
6#23749545C212yesmaximal
7#23749530C211yesmaximal, characteristic
8#23749511C212yesmaximal
9#398×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11C2×C4⋊Dic149C2212yes—
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×C4×Dic149C2211yescharacteristic
16#18011818C2212yes—
17#18011818C2212yes—
18#18011818C2212yes—
19#18011818C2212yes—
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2211yescharacteristic
26C2×C4⋊C4×C149C2212yes—
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2211yescharacteristic
29#95×C149C2212yes—
30#95×C149C2211yescharacteristic
31C2×Dic298—22no—
32C2×Dic298—41no—
33C2×Dic298—41no—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C4⋊Dic149—41no—
39C4⋊Dic149—42no—
40#14558715—42no—
41#14558715—42no—
42C4×Dic149—41no—
43C22×C4×C149C2312yes—
44C22×C4×C149C2311yescharacteristic
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2312yes—
47C22×C4×C149C2311yescharacteristic
48C4⋊C4×C149—24no—
49C4⋊C4×C149—41no—
50C4⋊C4×C149—41no—
51Dic298—44no—
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—24no—
62C2×Dic149—22no—
63C23×C149C2411yescharacteristic
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149—22no—
67C2×C4×C149—22no—
68C2×C4×C149—21no—
69C2×C4×C149—22no—
70C2×C4×C149—21no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149#4112yes—
77C22×C149C2×#4111yescharacteristic
78C22×C149H(5,𝔽2)11yescharacteristic
79C22×C149H(5,𝔽2)11yescharacteristic
80C22×C1492−1+412yes—
81C22×C1492−1+412yes—
82C4×C149—22no—
83C4×C149—42no—
84C4×C149—42no—
85C4×C149—41no—
86C4×C149—41no—
87Dic149—42no—
88Dic149—42no—
89Dic149—42no—
90Dic149—42no—
91C2×C149#53811yescharacteristic
92C2×C149#54112yes—
93C2×C149#56311yescharacteristic
94C2×C149#56311yescharacteristic
95C2×C149#56312yes—
96C149#283311yescharacteristic, complemented, Sylow
97#2833—1491nomaximal, Sylow
98#401—1492no—
99#400—1491no—
100#400—1492no—
101#400—1492no—
102#398—1492no—
103#398D14911yescharacteristic
104#395—1492no—
105#391—1491no—
106#387—1492no—
107C22×Q8—1491no—
108C2×C4⋊C4—1492no—
109C2×C4⋊C4—1492no—
110C2×C4⋊C4—1492no—
111C2×C4⋊C4—1491no—
112C2×C4⋊C4C2×D14912yes—
113C2×C4⋊C4C2×D14911yescharacteristic
114C2×C4⋊C4C2×D14911yescharacteristic
115C2×C42—1491no—
116#95—1492no—
117#95—1492no—
118#95—1492no—
119#95—1492no—
120#95—1492no—
121#95—1492no—
122#95—1492no—
123#95—1492no—
124#95—1492no—
125#95—1491no—
126#95C2×D14912yes—
127#95C2×D14911yescharacteristic
128C2×Q8—2982no—
129C2×Q8—5961no—
130C2×Q8—5961no—
131C22×C4—1492no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4—1492no—
135C22×C4C22×D14912yes—
136C22×C4C22×D14911yescharacteristic
137C22×C4C22×D14911yescharacteristic
138C22×C4C22×D14912yes—
139C22×C4C22×D14911yescharacteristic
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—5962no—
144C4⋊C4—5962no—
145C4⋊C4—5961no—
146C4⋊C4—5962no—
147C42—5961no—
148C23C23×D14911yescharacteristic
149Q8—5964no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2984no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4#1455873512yes—
174C22C2×#1455873511yescharacteristic
175C22#1801195611yescharacteristic
176C22#1801195711yescharacteristic
177C22#1801195812yes—
178C22#1801195912yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—5962no—
185C4—5962no—
186C4—5962no—
187C4—5962no—
188C2#2375021211yescharacteristic
189C2#2375023512yes—
190C2#2375037411yescharacteristic
191C2#2375037811yescharacteristic
192C2#2375037912yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#398×C149C2
hypercenter#398D149
hypocenterC149#2833
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
96. C149#2833semidirect

Maximal subgroups

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

subgroupindex
C149⋊#4012
#237495672
#237495652
#237495642
#237495582
#237495452
#237495302
#237495112
#398×C1492
#2833149