Finite Group Databasebeta

← #34052839

Subgroups — #34052839

Order 19072.

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

normal subgroups only

This group has 408 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
1#23749555C211yesmaximal, characteristic, complemented
2#23749554C212yesmaximal, complemented
3#23749551C212yesmaximal, complemented
4#23749547C212yesmaximal, complemented
5#23749543C212yesmaximal
6#23749536C212yesmaximal, complemented
7#23749526C211yesmaximal, characteristic
8#23749507C212yesmaximal, complemented
9#395×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715C2212yes—
13C2×#14558715C2212yes—
14C2×#14558713C2212yes—
15C2×#14558713C2212yes—
16C2×#14558713C2212yes—
17C2×#14558713C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20C2×C4×Dic149C2211yescharacteristic
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2211yescharacteristic
26C22×Q8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2212yes—
29#95×C149C2212yes—
30#95×C149C2211yescharacteristic
31C23×D149C2312yes—
32C2×D596—22no—
33C2×D596—41no—
34C2×D596—41no—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C4⋊Dic149—41no—
39#14558715—24no—
40#14558715—42no—
41#14558713—42no—
42#14558713—42no—
43#14558713—42no—
44#14558713—42no—
45#14558713—42no—
46#14558713—42no—
47C4×Dic149—41no—
48C2×Q8×C149—41no—
49C2×Q8×C149—42no—
50C22×C4×C149C2312yes—
51C22×C4×C149C2312yes—
52C22×C4×C149C2311yescharacteristic
53C22×C4×C149C2311yescharacteristic
54C22×C4×C149C2311yescharacteristic
55C4⋊C4×C149—41no—
56C4⋊C4×C149—42no—
57C22×D149—22no—
58C22×D149—22no—
59C22×D149—22no—
60C22×D149—22no—
61C22×D149—22no—
62C22×D149—22no—
63C22×D149—22no—
64D596—44no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C23×C149C2411yescharacteristic
75Q8×C149—44no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149—22no—
88C2×C4×C149#4112yes—
89C22×C149C2×#4111yescharacteristic
90C22×C149H(5,𝔽2)11yescharacteristic
91C22×C149H(5,𝔽2)12yes—
92C22×C149H(5,𝔽2)11yescharacteristic
93C22×C1492−1+412yes—
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—42no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C2×D149—42no—
101C4×C149—22no—
102C4×C149—41no—
103C4×C149—41no—
104C4×C149—42no—
105C4×C149—42no—
106Dic149—42no—
107Dic149—42no—
108Dic149—42no—
109C2×C149#53811yescharacteristic
110C2×C149#54212yes—
111C2×C149#56011yescharacteristic
112C2×C149#56212yes—
113C2×C149#56311yescharacteristic
114D149—82no—
115C149#283011yescharacteristic, complemented, Sylow
116#2830—1491nomaximal, Sylow
117#398—1491no—
118#397—1492no—
119#397—1492no—
120#396—1492no—
121#395D14911yescharacteristic, complemented
122#394—1492no—
123#393—1492no—
124#390—1491no—
125#387—1492no—
126C22×Q8C2×D14911yescharacteristic
127C22×D4—1491no—
128C2×C4⋊C4—1492no—
129C2×C4⋊C4—1492no—
130C2×C4⋊C4—1491no—
131C2×C4⋊C4C2×D14911yescharacteristic
132C2×C4⋊C4C2×D14912yes—
133C2×C22⋊C4—1492no—
134C2×C22⋊C4—1492no—
135C2×C22⋊C4—1492no—
136C2×C22⋊C4—1492no—
137C2×C22⋊C4—1492no—
138C2×C22⋊C4—1492no—
139C2×C42—1491no—
140#95—1492no—
141#95—1492no—
142#95—1492no—
143#95—1492no—
144#95—1491no—
145#95C2×D14912yes—
146#95C2×D14911yescharacteristic
147C24—1492no—
148C2×Q8—41no—
149C2×Q8—42no—
150C2×D4—2982no—
151C2×D4—5961no—
152C2×D4—5961no—
153C22×C4—1492no—
154C22×C4—1492no—
155C22×C4—1492no—
156C22×C4C22×D14912yes—
157C22×C4C22×D14911yescharacteristic
158C22×C4C22×D14912yes—
159C22×C4C22×D14911yescharacteristic
160C22×C4C22×D14911yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—42no—
163C4⋊C4—2984no—
164C4⋊C4—5962no—
165C4⋊C4—5961no—
166C22⋊C4—5962no—
167C22⋊C4—5962no—
168C22⋊C4—5962no—
169C22⋊C4—5962no—
170C22⋊C4—5962no—
171C22⋊C4—5962no—
172C42—5961no—
173C23—2982no—
174C23—2982no—
175C23—2982no—
176C23—2982no—
177C23—2982no—
178C23—2982no—
179C23—2982no—
180C23C23×D14911yescharacteristic
181Q8—44no—
182D4—5964no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4#1455873712yes—
205C22—5962no—
206C22—5962no—
207C22—5962no—
208C22—5962no—
209C22—5962no—
210C22—5962no—
211C22—5962no—
212C22C2×#1455873711yescharacteristic
213C22#1801195611yescharacteristic
214C22#1801195612yes—
215C22#1801195711yescharacteristic
216C22#1801195912yes—
217C4—22no—
218C4—42no—
219C4—41no—
220C4—41no—
221C4—42no—
222C4—5962no—
223C4—5962no—
224C4—5962no—
225C2—11922no—
226C2#2375021511yescharacteristic
227C2#2375024912yes—
228C2#2375036411yescharacteristic
229C2#2375037112yes—
230C2#2375037411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#395×C149C2
prime radicalC22×D596C22
hypercenter#395D149
hypocenterC149#2830
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #23749555C2semidirect
2. #23749554C2semidirect
3. #23749551C2semidirect
4. #23749547C2semidirect
6. #23749536C2semidirect
8. #23749507C2semidirect
9. #395×C149C2semidirect
115. C149#2830semidirect
121. #395D149semidirect

Maximal subgroups

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

subgroupindex
#237495552
#237495542
#237495512
#237495472
#237495432
#237495362
#237495262
#237495072
#395×C1492
#2830149