Finite Group Databasebeta

← #34047983

Subgroups — #34047983

Order 19072.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#18011876C211yesmaximal, characteristic
2C2×#18011876C211yesmaximal, characteristic
3#23749559C212yesmaximal
4#23749556C211yesmaximal, characteristic
5#23749546C211yesmaximal, characteristic
6#23749545C212yesmaximal
7#23749545C211yesmaximal, characteristic
8C4⋊C4×Dic149C212yesmaximal
9#23749476C212yesmaximal
10#23749470C211yesmaximal, characteristic
11#398×C149C211yesmaximal, characteristic
12C22×Dic298C2211yescharacteristic
13C22×Dic298C2211yescharacteristic
14#18011876—24no—
15#18011876—24no—
16C2×C4⋊Dic149C2212yes—
17C2×#14558715C2212yes—
18C2×#14558715C2212yes—
19C2×#14558715C2212yes—
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×C4×Dic149C2211yescharacteristic
23C2×C4×Dic149C2212yes—
24C2×C4×Dic149C2211yescharacteristic
25C2×C4×Dic149C2211yescharacteristic
26C2×C4×Dic149C2212yes—
27#18011818C2211yescharacteristic
28#18011818C2212yes—
29#18011818C2212yes—
30#18011818C2212yes—
31#18011818C2212yes—
32C2×C4⋊C4×C149C2212yes—
33C2×C4⋊C4×C149C2211yescharacteristic
34C2×C4⋊C4×C149C2211yescharacteristic
35#95×C149C2211yescharacteristic
36#95×C149C2212yes—
37C2×Dic298—22no—
38C2×Dic298—22no—
39C2×Dic298—24no—
40C2×Dic298—22no—
41C2×Dic298—22no—
42C22×Dic149C2311yescharacteristic
43C22×Dic149C2311yescharacteristic
44C22×Dic149C2312yes—
45C22×Dic149C2311yescharacteristic
46C22×Dic149C2312yes—
47C22×Dic149C2311yescharacteristic
48C4⋊Dic149—24no—
49#14558715—24no—
50#14558715—22no—
51#14558715—24no—
52#14558715—24no—
53#14558715—22no—
54C4×Dic149—22no—
55C4×Dic149—22no—
56C4×Dic149—24no—
57C4×Dic149D414yes—
58C4×Dic149Q818yescomplemented
59C22×C4×C149C2311yescharacteristic
60C22×C4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62C22×C4×C149C2312yes—
63C22×C4×C149C2311yescharacteristic
64C4⋊C4×C149—22no—
65C4⋊C4×C149—22no—
66C4⋊C4×C149—24no—
67Dic298—28no—
68Dic298—28no—
69C2×Dic149—21no—
70C2×Dic149—22no—
71C2×Dic149—21no—
72C2×Dic149—22no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—21no—
78C2×Dic149—22no—
79C2×Dic149C2×D412yes—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×Q814yes—
82C2×Dic149C2×Q814yes—
83C2×Dic149#4112yes—
84C2×Dic149#4114yes—
85C23×C149C2411yescharacteristic
86C2×C4×C149—21no—
87C2×C4×C149—22no—
88C2×C4×C149—21no—
89C2×C4×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149—21no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149C2×D412yes—
97C2×C4×C149C2×Q814yes—
98C2×C4×C149#4112yes—
99C22×C149C22×D411yescharacteristic
100C22×C149C22×Q812yes—
101C22×C149C2×#4112yes—
102C22×C149C2×#4111yescharacteristic
103C22×C149C2×#4111yescharacteristic
104C4×C149—22no—
105C4×C149—22no—
106C4×C149—24no—
107C4×C149—41no—
108C4×C149—42no—
109Dic149—22no—
110Dic149—24no—
111Dic149—22no—
112Dic149—24no—
113Dic149—41no—
114Dic149C4⋊Q814yes—
115C2×C149#52511yescharacteristic
116C2×C149#52511yescharacteristic
117C2×C149C2×C4⋊Q811yescharacteristic
118C2×C149#53312yes—
119C2×C149#53312yes—
120C149#239911yescharacteristic, complemented, Sylow
121#2399—1491nomaximal, Sylow
122C2×C4×Q8—1491no—
123C2×C4×Q8—1491no—
124#398—1491no—
125#398—1492no—
126#398D14911yescharacteristic
127#395—1492no—
128#395—1491no—
129#395—1491no—
130C4×C4⋊C4—1492no—
131C4×C4⋊C4—1492no—
132#376—1491no—
133C22×Q8—1491no—
134C22×Q8—1491no—
135C4×Q8—2984no—
136C4×Q8—2984no—
137C2×C4⋊C4—1492no—
138C2×C4⋊C4—1491no—
139C2×C4⋊C4—1491no—
140C2×C4⋊C4—1492no—
141C2×C4⋊C4—1492no—
142C2×C4⋊C4—1492no—
143C2×C4⋊C4C2×D14911yescharacteristic
144C2×C4⋊C4C2×D14911yescharacteristic
145C2×C4⋊C4C2×D14912yes—
146C2×C42—1491no—
147C2×C42—1492no—
148C2×C42—1491no—
149C2×C42—1491no—
150C2×C42—1492no—
151#95—1491no—
152#95—1492no—
153#95—1492no—
154#95—1492no—
155#95—1492no—
156#95C2×D14911yescharacteristic
157#95C2×D14912yes—
158C2×Q8—2982no—
159C2×Q8—2984no—
160C2×Q8—2982no—
161C2×Q8—2982no—
162C2×Q8—2982no—
163C22×C4—1491no—
164C22×C4—1492no—
165C22×C4—1492no—
166C22×C4—1491no—
167C22×C4—1491no—
168C22×C4—1491no—
169C22×C4C22×D14912yes—
170C22×C4C22×D14911yescharacteristic
171C22×C4C22×D14911yescharacteristic
172C22×C4C22×D14912yes—
173C22×C4C22×D14911yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—2984no—
178C4⋊C4—2982no—
179C4⋊C4—2984no—
180C4⋊C4—2984no—
181C4⋊C4—2984no—
182C4⋊C4—2982no—
183C42—2982no—
184C42—2982no—
185C42—2984no—
186C42—1494no—
187C42—1498no—
188C23C23×D14911yescharacteristic
189Q8—2988no—
190Q8—2988no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—2982no—
202C2×C4—2981no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—2981no—
207C2×C4—2981no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2982no—
211C2×C4—1492no—
212C2×C4—1494no—
213C2×C4—1494no—
214C2×C4—1492no—
215C2×C4—1492no—
216C2×C4—1494no—
217C2×C4D4×D14912yes—
218C2×C4Q8×D14914yes—
219C2×C4#1455873512yes—
220C22C2×D4×D14911yescharacteristic
221C22C2×Q8×D14912yes—
222C22#41×D14912yes—
223C22#41×D14911yescharacteristic
224C22C2×#1455873511yescharacteristic
225C4—24no—
226C4—22no—
227C4—22no—
228C4—41no—
229C4—42no—
230C4—2984no—
231C4—2984no—
232C4—2982no—
233C4—2982no—
234C4—5961no—
235C4—1494no—
236C2#2375013311yescharacteristic
237C2#2375013511yescharacteristic
238C2C4⋊Q8×D14911yescharacteristic
239C2#2375017712yes—
240C2#2375018112yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#398×C149C2
hypercenter#398D149
hypocenterC149#2399
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic149Q8semidirect
120. C149#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#180118762
#237495592
#237495562
#237495462
#237495452
C4⋊C4×Dic1492
#237494762
#237494702
#398×C1492
#2399149