Finite Group Databasebeta

← #34043663

Subgroups — #34043663

Order 19072.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#23750254C211yesmaximal, characteristic
2#23749781C211yesmaximal, characteristic
3#23749544C211yesmaximal, characteristic
4#23749363C211yesmaximal, characteristic
5#23749362C211yesmaximal, characteristic
6#23749350C211yesmaximal, characteristic
7#451×C149C211yesmaximal, characteristic
8C2×#14558726—21no—
9#18011910—21no—
10#18011909—21no—
11#18011901—21no—
12#18011901—21no—
13#18011890C2211yescharacteristic
14#18011888—21no—
15#18011867—21no—
16C2×#14558715—21no—
17C2×#14558715C2211yescharacteristic
18#18011835—21no—
19C22⋊#11924746C2211yescharacteristic
20#18011818—21no—
21#18011818C2211yescharacteristic
22C22×Q8×C149C2211yescharacteristic
23C2×Q16×C149—21no—
24C22⋊Q8×C149C2211yescharacteristic
25#103×C149—21no—
26C22⋊C8×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C22×Dic149D411yescharacteristic
32#14558726—42no—
33C2×#11924746—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149D411yescharacteristic
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43#14558715—42no—
44C22⋊Dic149—21no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—42no—
50C2×Q8×C149D411yescharacteristic
51C22×C4×C149—21no—
52C22×C4×C149C2311yescharacteristic
53Q16×C149—42no—
54C2×C8×C149—21no—
55C4⋊C4×C149—21no—
56C4⋊C4×C149D411yescharacteristic
57C22⋊C4×C149—21no—
58Dic298—41no—
59Dic298—81no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—22no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—41no—
67C2×Dic149—41no—
68C2×Dic149—41no—
69C2×Dic149Q1612yescomplemented
70#11924746—41no—
71C23×C149C2×D411yescharacteristic
72Q8×C149—22no—
73Q8×C149—22no—
74Q8×C149—41no—
75Q8×C149—41no—
76Q8×C149—41no—
77C2×C4×C149—22no—
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—41no—
81C2×C4×C149—41no—
82C2×C4×C149—41no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C8×C149—41no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149#12011yescharacteristic
89C22×C149C2×Q1611yescharacteristic
90C22×C149#13711yescharacteristic
91C4×C149—21no—
92C4×C149—21no—
93C4×C149—41no—
94C4×C149—42no—
95C4×C149—41no—
96Dic149—22no—
97Dic149—42no—
98Dic149—41no—
99Dic149—41no—
100Dic149—41no—
101C2×C149—21no—
102C2×C149—21no—
103C2×C149#45111yescharacteristic
104C2×C149#45611yescharacteristic
105C2×C149B(4,𝔽2)11yescharacteristic
106C149#160511yescharacteristic, complemented, Sylow
107#1605—1491nomaximal, Sylow
108#544—1491no—
109#451—1491no—
110#451D14911yescharacteristic
111#395—1491no—
112#328—1491no—
113#328—1491no—
114#324—1491no—
115C22×Q8C2×D14911yescharacteristic
116C2×Q16—21no—
117C2×Q16—2981no—
118C4⋊Q8—2981no—
119C4⋊Q8—2981no—
120#125—2981no—
121#125—2981no—
122C22⋊Q8—2981no—
123C22⋊Q8—1491no—
124C22⋊Q8C2×D14911yescharacteristic
125#117—2981no—
126C2×C4⋊C4—2981no—
127C2×C4⋊C4—1491no—
128#103—21no—
129#103—2981no—
130C22⋊C8—1491no—
131C22⋊C8C2×D14911yescharacteristic
132#95—2981no—
133#95—1491no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—2981no—
138C2×Q8—1491no—
139C2×Q8C22⋊D14911yescharacteristic
140C22×C4—21no—
141C22×C4—2981no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4C22×D14911yescharacteristic
145Q16—42no—
146Q16—5962no—
147C2×C8—21no—
148C2×C8—2981no—
149C4⋊C4—21no—
150C4⋊C4—2981no—
151C4⋊C4—2981no—
152C4⋊C4—2981no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—5962no—
159C4⋊C4—1491no—
160C4⋊C4C22⋊D14911yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2981no—
163C42—2981no—
164C42—2981no—
165C23D4×D14911yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
171Q8—5961no—
172Q8—11921no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2981no—
180C2×C4—2981no—
181C2×C4—2982no—
182C2×C4—2981no—
183C2×C4—2981no—
184C2×C4—2981no—
185C2×C4—5961no—
186C2×C4—5961no—
187C2×C4—5961no—
188C2×C4—1492no—
189C2×C4D4×D14911yescharacteristic
190C2×C4C2×C22⋊D14911yescharacteristic
191C8—41no—
192C8—5961no—
193C22—21no—
194C22—21no—
195C22#1801187911yescharacteristic
196C22Q16×D14911yescharacteristic
197C22#1801194311yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—2982no—
204C4—5962no—
205C4—5961no—
206C4—5961no—
207C4—5961no—
208C2—21no—
209C2—21no—
210C2#2374977911yescharacteristic
211C2#2374980611yescharacteristic
212C2#2374981111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#451×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#451D149
hypocenterC149#1605
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
69. C2×Dic149Q16semidirect
106. C149#1605semidirect

Maximal subgroups

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

subgroupindex
#237502542
#237497812
#237495442
#237493632
#237493622
#237493502
#451×C1492
#1605149