Finite Group Databasebeta

← #34054222

Subgroups — #34054222

Order 19072.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18011944C211yesmaximal, characteristic
2C22×Dic596C211yesmaximal, characteristic, complemented
3#23750201C211yesmaximal, characteristic
4#23750102C211yesmaximal, characteristic, complemented
5#23749848C214yesmaximal, complemented
6#23749836C214yesmaximal, complemented
7#23749635C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic
9#424×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×Dic298C2211yescharacteristic
12C22×Dic298C2211yescharacteristic
13#18011944—24no—
14C2×Dic596—24no—
15C2×Dic596C2214yes—
16C2×Dic596C2212yes—
17C2×#14558725C2212yes—
18#18011911C2212yes—
19#18011899C2212yes—
20#18011895—22no—
21#18011891—22no—
22C4×Dic298C2214yes—
23#18011876—22no—
24#18011870C2211yescharacteristic
25#18011867—22no—
26#18011836C2214yes—
27#18011836C2212yes—
28#18011833C2212yes—
29C2×M16×C149C2211yescharacteristic
30C22×C8×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32C4⋊C8×C149C2214yes—
33#14558736—22no—
34#14558736—22no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298—22no—
38C2×Dic298—22no—
39C2×Dic298—22no—
40C2×Dic298D414yes—
41C2×Dic298C2311yescharacteristic
42C2×Dic298C2312yes—
43C2×Dic298C2312yes—
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C22×Dic149—21no—
47C22×Dic149—21no—
48C2×C4×D149—21no—
49Dic596—28no—
50Dic596—24no—
51#14558725—24no—
52C4⋊Dic149—24no—
53C4⋊Dic149C2312yes—
54#14558715—24no—
55C22⋊Dic149—21no—
56#14558713—24no—
57C4×Dic149—24no—
58C4×Dic149—21no—
59C22×C4×C149C2311yescharacteristic
60M16×C149—22no—
61C2×C8×C149—22no—
62C2×C8×C149C2312yes—
63C2×C8×C149C2312yes—
64C4⋊C4×C149D412yes—
65C22⋊C4×C149D412yes—
66C42×C149C2312yes—
67C22×D149—21no—
68Dic298—24no—
69Dic298—22no—
70Dic298—22no—
71Dic298—21no—
72Dic298—22no—
73Dic298—21no—
74Dic298—42no—
75Dic298C2×D414yes—
76D596—21no—
77D596—21no—
78C22⋊D149—42no—
79C2×Dic149—24no—
80C2×Dic149—22no—
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—42no—
85C4×D149—42no—
86C23×C149C2×D411yescharacteristic
87C2×C4×C149C2×D412yes—
88C2×C4×C149C2×D414yes—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149#4112yes—
91C2×C4×C149C2411yescharacteristic
92C8×C149—22no—
93C8×C149—22no—
94C22×C149—22no—
95C22×C149#12112yes—
96C22×C149C22×D411yescharacteristic
97C2×D149—41no—
98C2×D149—42no—
99C4×C149—24no—
100C4×C149#12112yes—
101C4×C149C22×D411yescharacteristic
102C4×C149C2×#4111yescharacteristic
103Dic149—24no—
104Dic149—41no—
105Dic149—42no—
106Dic149—42no—
107C2×C149—22no—
108C2×C149C2×#12111yescharacteristic
109C2×C149#57812yes—
110D149—81no—
111C149#304411yescharacteristic, complemented, Sylow
112#3044—1491nomaximal, Sylow
113C2×#137—1491no—
114C22×Q16—1491no—
115#536—1491no—
116#519—1491no—
117#464—1494no—
118#462—1494no—
119#424D14911yescharacteristic, complemented
120#419—1491no—
121#416—1491no—
122C2×#41—1491no—
123C22×Q8—1491no—
124C22×Q8—1491no—
125#137—2984no—
126C2×Q16—2984no—
127C2×Q16—1494no—
128C2×Q16—1492no—
129C2×SD16—1492no—
130C2×M16C2×D14911yescharacteristic
131C22×C8C2×D14911yescharacteristic
132C4⋊Q8—1492no—
133#124—1492no—
134#123—2982no—
135C22⋊Q8—2982no—
136C4×Q8—2982no—
137C4×Q8—1494no—
138#117—2982no—
139#117—1491no—
140#117C2×D14911yescharacteristic
141C4⋊C8C2×D14914yes—
142#103—1492no—
143#103—1494no—
144#102—1492no—
145#41—2982no—
146#41—2982no—
147C2×Q8—2981no—
148C2×Q8—2981no—
149C2×Q8—2982no—
150C2×Q8—2982no—
151C2×Q8—2982no—
152C2×Q8—1494no—
153C2×Q8—1492no—
154C2×Q8—1491no—
155C2×Q8—1492no—
156C2×D4—2981no—
157C2×D4—1491no—
158C22×C4—2981no—
159C22×C4—2981no—
160C22×C4—2981no—
161C22×C4C22×D14911yescharacteristic
162Q16—2988no—
163Q16—2984no—
164SD16—2984no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D14912yes—
168C2×C8C22×D14912yes—
169C4⋊C4—2984no—
170C4⋊C4—2984no—
171C4⋊C4—1492no—
172C4⋊C4D59612yes—
173C22⋊C4—2981no—
174C22⋊C4—2984no—
175C22⋊C4D59612yes—
176C42—2984no—
177C42—2981no—
178C42C22×D14912yes—
179C23—2981no—
180C23C2×D59611yescharacteristic
181Q8—2982no—
182Q8—2984no—
183Q8—2982no—
184Q8—2981no—
185Q8—2982no—
186Q8—2981no—
187Q8—5962no—
188Q8—1494no—
189D4—2981no—
190D4—2981no—
191D4—5962no—
192C2×C4—2982no—
193C2×C4—2984no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2981no—
197C2×C4—5962no—
198C2×C4—5962no—
199C2×C4D4×D14912yes—
200C2×C4C2×D59614yes—
201C2×C4C2×D59611yescharacteristic
202C2×C4#1455873712yes—
203C2×C4C23×D14911yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—5962no—
208C22—5961no—
209C22#1801188612yes—
210C22C22×D59611yescharacteristic
211C4—24no—
212C4—2984no—
213C4—5962no—
214C4—5961no—
215C4—5962no—
216C4#1801188612yes—
217C4C2×D4×D14911yescharacteristic
218C4C2×#1455873711yescharacteristic
219C2—22no—
220C2—11921no—
221C2C2×#1801188611yescharacteristic
222C2#2375044212yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#424×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#424D149
hypocenterC149#3044
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic596C2semidirect
4. #23750102C2semidirect
5. #23749848C2semidirect
6. #23749836C2semidirect
7. #23749635C2semidirect
9. #424×C149C2semidirect
111. C149#3044semidirect
119. #424D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C22×Dic5962
#237502012
#237501022
#237498482
#237498362
#237496352
#237496222
#424×C1492
#3044149