Finite Group Databasebeta

← #34055698

Subgroups — #34055698

Order 19072.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750175C211yesmaximal, characteristic
2#23750017C212yesmaximal, complemented
3#23749987C212yesmaximal, complemented
4#23749835C212yesmaximal, complemented
5#23749825C212yesmaximal, complemented
6#23749785C214yesmaximal, complemented
7#23749682C211yesmaximal, characteristic, complemented
8#533×C149C211yesmaximal, characteristic, complemented
9C2×#14558736C2212yes—
10C2×#14558726C2214yes—
11C2×#14558723C2214yes—
12#18011911C2211yescharacteristic
13#18011908C2211yescharacteristic
14#18011899C2212yes—
15#18011885—21no—
16#18011885—21no—
17C4×D596—21no—
18C4×D596—21no—
19C4⋊#11924746C2212yes—
20#18011834C2214yes—
21#18011831C2214yes—
22C22⋊#11924746C2212yes—
23#18011822C2212yes—
24C4⋊Q8×C149C2211yescharacteristic
25C4⋊Q8×C149C2211yescharacteristic
26#125×C149—21no—
27C22⋊Q8×C149—21no—
28C22⋊Q8×C149C2212yes—
29C4×Q8×C149—21no—
30C4×Q8×C149C2212yes—
31#117×C149—21no—
32C2×C42×C149C2211yescharacteristic
33#14558736—44no—
34C2×Dic298C2312yes—
35C2×D596—21no—
36C2×D596—21no—
37C2×D596C2312yes—
38C2×C22⋊D149—22no—
39C2×C4×D149—22no—
40#14558726—44no—
41#14558723—44no—
42C2×#11924746C2314yes—
43C4⋊Dic149—21no—
44C4⋊Dic149—21no—
45#14558713—22no—
46#14558713—22no—
47C2×Q8×C149—21no—
48C2×Q8×C149C2312yes—
49C22×C4×C149D411yescharacteristic
50C22×C4×C149D411yescharacteristic
51C22×C4×C149C2311yescharacteristic
52C4⋊C4×C149—21no—
53C4⋊C4×C149—21no—
54C4⋊C4×C149—21no—
55C4⋊C4×C149—22no—
56C4⋊C4×C149—22no—
57C4⋊C4×C149C2312yes—
58C22⋊C4×C149—22no—
59C42×C149—22no—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64C22×D149—22no—
65Dic298—24no—
66D596—24no—
67D596—42no—
68D596—42no—
69C22⋊D149—44no—
70C2×Dic149—22no—
71C4×D149—44no—
72#11924746—24no—
73C23×C149C2×D411yescharacteristic
74Q8×C149—22no—
75Q8×C149—22no—
76Q8×C149—42no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—41no—
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2411yescharacteristic
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—21no—
91C22×C149C22×D411yescharacteristic
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—42no—
95C4×C149—21no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—42no—
100C4×C149—42no—
101C4×C149#13712yes—
102C4×C149H(5,𝔽2)12yes—
103Dic149—42no—
104C2×C149—41no—
105C2×C149#53511yescharacteristic
106C2×C149C2×#13711yescharacteristic
107C2×C149#57511yescharacteristic
108D149—82no—
109C149#321611yescharacteristic, complemented, Sylow
110#3216—1491nomaximal, Sylow
111#533D14911yescharacteristic, complemented
112#532—1491no—
113#497—1492no—
114#489—1492no—
115#462—1492no—
116#460—1492no—
117#452—1494no—
118#432—1491no—
119C2×#41—1492no—
120C2×Q16—1494no—
121C2×SD16—1494no—
122C4⋊Q8—1491no—
123C4⋊Q8C2×D14911yescharacteristic
124C4⋊Q8C2×D14911yescharacteristic
125#127—1491no—
126#125—21no—
127#124—1492no—
128C22⋊Q8—21no—
129C22⋊Q8C2×D14912yes—
130#121—2981no—
131#121—2981no—
132C4×Q8—21no—
133C4×Q8C2×D14912yes—
134C4×D4—2981no—
135C4×D4—2981no—
136#117—21no—
137C2×C42C2×D14911yescharacteristic
138C4⋊C8—1492no—
139#103—1494no—
140#102—1494no—
141C22⋊C8—1492no—
142#97—1492no—
143#41—5964no—
144C2×Q8—21no—
145C2×Q8—1492no—
146C2×Q8C22×D14912yes—
147C2×D4—2982no—
148C2×D4—2981no—
149C2×D4—2981no—
150C2×D4—1492no—
151C22×C4—2982no—
152C22×C4C22⋊D14911yescharacteristic
153C22×C4C22⋊D14911yescharacteristic
154C22×C4C22×D14911yescharacteristic
155Q16—5964no—
156SD16—5964no—
157C2×C8—1494no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4C22×D14912yes—
166C22⋊C4—22no—
167C22⋊C4—2982no—
168C22⋊C4—2982no—
169C42—22no—
170C42C22⋊D14911yescharacteristic
171C42C22⋊D14911yescharacteristic
172C42C22×D14911yescharacteristic
173C42C22×D14911yescharacteristic
174C23—2982no—
175C23C2×C22⋊D14911yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—42no—
179Q8—2984no—
180D4—2984no—
181D4—5962no—
182D4—5964no—
183D4—5962no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—2982no—
190C2×C4—5964no—
191C2×C4C2×C22⋊D14911yescharacteristic
192C2×C4C2×C22⋊D14911yescharacteristic
193C2×C4C2×C22⋊D14911yescharacteristic
194C2×C4C2×C22⋊D14911yescharacteristic
195C2×C4C2×C22⋊D14911yescharacteristic
196C2×C4C23×D14911yescharacteristic
197C8—2984no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—5962no—
202C22—5962no—
203C22—5962no—
204C22C22×C22⋊D14911yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—42no—
210C4—42no—
211C4—5962no—
212C4#1801194212yes—
213C4#1801195712yes—
214C2—41no—
215C2—11922no—
216C2#2375018911yescharacteristic
217C2C2×#1801194211yescharacteristic
218C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#533D149
hypocenterC149#3216
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750017C2semidirect
3. #23749987C2semidirect
4. #23749835C2semidirect
5. #23749825C2semidirect
6. #23749785C2semidirect
7. #23749682C2semidirect
8. #533×C149C2semidirect
109. C149#3216semidirect
111. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501752
#237500172
#237499872
#237498352
#237498252
#237497852
#237496822
#533×C1492
#3216149