Finite Group Databasebeta

← #34052951

Subgroups — #34052951

Order 19072.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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#23749565C212yesmaximal, complemented
2#23749561C211yesmaximal, characteristic
3#23749559C212yesmaximal, complemented
4#23749559C212yesmaximal, complemented
5#23749548C212yesmaximal
6#23749544C212yesmaximal, complemented
7#23749486C211yesmaximal, characteristic
8#23749483C212yesmaximal
9#393×C149C211yesmaximal, characteristic
10C23×Dic149C2211yescharacteristic
11C2×C4⋊Dic149C2212yes—
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×C22⋊Dic149C2212yes—
19C2×C22⋊Dic149C2211yescharacteristic
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2211yescharacteristic
26C22×Q8×C149C2211yescharacteristic
27C2×C22⋊C4×C149C2212yes—
28C2×C22⋊C4×C149C2211yescharacteristic
29#95×C149C2211yescharacteristic
30#95×C149C2212yes—
31C22×Dic149—41no—
32C22×Dic149—41no—
33C22×Dic149Q814yescomplemented
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C4⋊Dic149—41no—
39C4⋊Dic149—42no—
40#14558715—42no—
41#14558715—42no—
42#14558715—42no—
43#14558715—42no—
44#14558715—42no—
45C22⋊Dic149—41no—
46C22⋊Dic149—42no—
47C24×C149C2311yescharacteristic
48C2×Q8×C149—41no—
49C2×Q8×C149—42no—
50C22×C4×C149C2311yescharacteristic
51C22×C4×C149C2312yes—
52C22×C4×C149C2311yescharacteristic
53C22×C4×C149C2312yes—
54C22⋊C4×C149—42no—
55C22⋊C4×C149—41no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—44no—
68C2×Dic149C2×Q814yes—
69C23×C149—21no—
70C23×C149—21no—
71C23×C149—22no—
72C23×C149—22no—
73C23×C149C2×Q812yes—
74C23×C149C2411yescharacteristic
75Q8×C149—44no—
76C2×C4×C149—21no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—21no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C22×C149—22no—
87C22×C149—24no—
88C22×C149—41no—
89C22×C149—42no—
90C22×C149—41no—
91C22×C149C22×Q811yescharacteristic
92C22×C149H(5,𝔽2)11yescharacteristic
93C22×C149H(5,𝔽2)12yes—
94C22×C149H(5,𝔽2)11yescharacteristic
95C22×C1492−1+412yes—
96C4×C149—41no—
97C4×C149—42no—
98C4×C149—42no—
99C4×C149—41no—
100Dic149—24no—
101Dic149—42no—
102Dic149—42no—
103Dic149—42no—
104C2×C149—42no—
105C2×C149#54311yescharacteristic
106C2×C149#54412yes—
107C2×C149#56011yescharacteristic
108C2×C149#56212yes—
109C2×C149#56311yescharacteristic
110C149#284111yescharacteristic, complemented, Sylow
111#2841—1491nomaximal, Sylow
112#400—1492no—
113#399—1491no—
114#398—1492no—
115#398—1492no—
116#396—1492no—
117#395—1492no—
118#393D14911yescharacteristic
119#381—1491no—
120#380—1492no—
121C22×Q8C2×D14911yescharacteristic
122C23×C4—1491no—
123C2×C4⋊C4—1492no—
124C2×C4⋊C4—1492no—
125C2×C4⋊C4—1492no—
126C2×C4⋊C4—1492no—
127C2×C4⋊C4—1492no—
128C2×C4⋊C4—1492no—
129C2×C4⋊C4—1491no—
130C2×C22⋊C4—1492no—
131C2×C22⋊C4—1491no—
132C2×C22⋊C4C2×D14912yes—
133C2×C22⋊C4C2×D14911yescharacteristic
134#95—1492no—
135#95—1492no—
136#95—1492no—
137#95—1492no—
138#95—1492no—
139#95—1491no—
140#95C2×D14911yescharacteristic
141#95C2×D14912yes—
142C24C22×D14911yescharacteristic
143C2×Q8—41no—
144C2×Q8—42no—
145C22×C4—5961no—
146C22×C4—5961no—
147C22×C4—1492no—
148C22×C4—1492no—
149C22×C4—1492no—
150C22×C4—1492no—
151C22×C4—1494no—
152C22×C4C22×D14911yescharacteristic
153C22×C4C22×D14912yes—
154C22×C4C22×D14911yescharacteristic
155C22×C4C22×D14912yes—
156C4⋊C4—5962no—
157C4⋊C4—5962no—
158C4⋊C4—5962no—
159C4⋊C4—5962no—
160C4⋊C4—5962no—
161C4⋊C4—5961no—
162C4⋊C4—5962no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—5962no—
166C22⋊C4—5961no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D14912yes—
172C23C23×D14911yescharacteristic
173Q8—44no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—5964no—
196C2×C4—1494no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C2×Q8×D14911yescharacteristic
203C22#1801195611yescharacteristic
204C22#1801195612yes—
205C22#1801195711yescharacteristic
206C22#1801195812yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—2984no—
212C4—5962no—
213C4—5962no—
214C4—5962no—
215C2—42no—
216C2#2375025011yescharacteristic
217C2#2375025412yes—
218C2#2375036411yescharacteristic
219C2#2375036912yes—
220C2#2375037511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#393×C149C2
prime radicalC24×C149C23
hypercenter#393D149
hypocenterC149#2841
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #23749565C2semidirect
3. #23749559C2semidirect
4. #23749559C2semidirect
6. #23749544C2semidirect
33. C22×Dic149Q8semidirect
110. C149#2841semidirect

Maximal subgroups

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

subgroupindex
#237495652
#237495612
#237495592
#237495482
#237495442
#237494862
#237494832
#393×C1492
#2841149