Finite Group Databasebeta

← #34052858

Subgroups — #34052858

Order 19072.

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

normal subgroups only

This group has 416 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#23749566C212yesmaximal, complemented
2#23749554C212yesmaximal, complemented
3#23749545C211yesmaximal, characteristic, complemented
4#23749543C212yesmaximal
5#23749542C211yesmaximal, characteristic
6#23749538C212yesmaximal, complemented
7#23749536C212yesmaximal, complemented
8#23749516C212yesmaximal, complemented
9#391×C149C211yesmaximal, characteristic, complemented
10C22×Dic298C2211yescharacteristic
11C22×D596C2211yescharacteristic
12C2×#14558715C2212yes—
13C2×#14558715C2212yes—
14C2×#14558713C2212yes—
15C2×#14558713C2212yes—
16C2×#14558713C2212yes—
17C2×#14558713C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2211yescharacteristic
25#18011818C2211yescharacteristic
26C22×Q8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C42×C149C2211yescharacteristic
29#95×C149C2212yes—
30#95×C149C2212yes—
31C23×D149C2312yes—
32C2×Dic298—41no—
33C2×Dic298—42no—
34C2×D596—41no—
35C2×D596—42no—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C22×Dic149C2312yes—
39#14558715—42no—
40#14558715—42no—
41#14558713—24no—
42#14558713—42no—
43#14558713—42no—
44#14558713—42no—
45#14558713—42no—
46#14558713—42no—
47C2×Q8×C149—22no—
48C2×Q8×C149—41no—
49C2×Q8×C149—41no—
50C22×C4×C149C2311yescharacteristic
51C22×C4×C149C2311yescharacteristic
52C22×C4×C149C2312yes—
53C22×C4×C149C2312yes—
54C22×C4×C149C2311yescharacteristic
55C4⋊C4×C149—41no—
56C42×C149—41no—
57C22×D149—22no—
58C22×D149—22no—
59C22×D149—22no—
60C22×D149—22no—
61C22×D149—22no—
62C22×D149—22no—
63C22×D149—22no—
64Dic298—44no—
65D596—44no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C23×C149C2411yescharacteristic
76Q8×C149—44no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—21no—
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—22no—
89C2×C4×C149#4112yes—
90C22×C149C2×#4111yescharacteristic
91C22×C149H(5,𝔽2)11yescharacteristic
92C22×C149H(5,𝔽2)11yescharacteristic
93C22×C149H(5,𝔽2)12yes—
94C22×C1492−1+412yes—
95C2×D149—42no—
96C2×D149—42no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—42no—
100C2×D149—42no—
101C2×D149—42no—
102C4×C149—22no—
103C4×C149—42no—
104C4×C149—41no—
105C4×C149—41no—
106C4×C149—42no—
107Dic149—42no—
108Dic149—42no—
109Dic149—42no—
110C2×C149#53811yescharacteristic
111C2×C149#54212yes—
112C2×C149H(3,𝔽4)11yescharacteristic
113C2×C149#56212yes—
114C2×C149#56311yescharacteristic
115D149—82no—
116C149#283211yescharacteristic, complemented, Sylow
117#2832—1491nomaximal, Sylow
118#400—1492no—
119#397—1492no—
120#395—1491no—
121#394—1491no—
122#394—1492no—
123#393—1492no—
124#393—1492no—
125#391D14911yescharacteristic, complemented
126#388—1492no—
127C22×Q8—1491no—
128C22×Q8C2×D14911yescharacteristic
129C22×D4—1491no—
130C2×C4⋊C4—1492no—
131C2×C4⋊C4—1492no—
132C2×C4⋊C4C2×D14911yescharacteristic
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×C42C2×D14911yescharacteristic
140#95—1492no—
141#95—1492no—
142#95—1492no—
143#95—1492no—
144#95—1491no—
145#95—1491no—
146#95C2×D14912yes—
147#95C2×D14912yes—
148C24—1492no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—5961no—
153C2×Q8—5962no—
154C2×D4—5961no—
155C2×D4—5962no—
156C22×C4—1492no—
157C22×C4—1492no—
158C22×C4—1492no—
159C22×C4C22×D14912yes—
160C22×C4C22×D14912yes—
161C22×C4C22×D14911yescharacteristic
162C22×C4C22×D14911yescharacteristic
163C22×C4C22×D14911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—5962no—
166C4⋊C4—5962no—
167C22⋊C4—2984no—
168C22⋊C4—5962no—
169C22⋊C4—5962no—
170C22⋊C4—5962no—
171C22⋊C4—5962no—
172C22⋊C4—5962no—
173C42—41no—
174C23—2982no—
175C23—2982no—
176C23—2982no—
177C23—2982no—
178C23—2982no—
179C23—2982no—
180C23—2982no—
181C23C23×D14911yescharacteristic
182Q8—44no—
183Q8—5964no—
184D4—5964no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4#1455873612yes—
207C22—5962no—
208C22—5962no—
209C22—5962no—
210C22—5962no—
211C22—5962no—
212C22—5962no—
213C22—5962no—
214C22C2×#1455873611yescharacteristic
215C22#1801195611yescharacteristic
216C22#1801195611yescharacteristic
217C22#1801195712yes—
218C22#1801195912yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—5962no—
225C4—5962no—
226C4—5962no—
227C2—11922no—
228C2#2375021311yescharacteristic
229C2#2375024712yes—
230C2#2375036711yescharacteristic
231C2#2375037112yes—
232C2#2375037411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#391×C149C2
prime radicalC22×D596C22
hypercenter#391D149
hypocenterC149#2832
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #23749566C2semidirect
2. #23749554C2semidirect
3. #23749545C2semidirect
6. #23749538C2semidirect
7. #23749536C2semidirect
8. #23749516C2semidirect
9. #391×C149C2semidirect
116. C149#2832semidirect
125. #391D149semidirect

Maximal subgroups

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

subgroupindex
#237495662
#237495542
#237495452
#237495432
#237495422
#237495382
#237495362
#237495162
#391×C1492
#2832149