Finite Group Databasebeta

← #34054221

Subgroups — #34054221

Order 19072.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011942C211yesmaximal, characteristic
2C22×#14558726C211yesmaximal, characteristic, complemented
3#23750201C211yesmaximal, characteristic
4#23749847C214yesmaximal, complemented
5#23749835C214yesmaximal, complemented
6#23749652C211yesmaximal, characteristic, complemented
7#23749633C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic
9#519×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×Dic298C2211yescharacteristic
12#18011942—24no—
13C2×#14558726—24no—
14C2×#14558726C2214yes—
15C2×#14558726C2212yes—
16C2×#14558723C2212yes—
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011911C2212yes—
20#18011899C2212yes—
21#18011895—22no—
22#18011891—22no—
23C4⋊#11924746C2214yes—
24#18011834C2214yes—
25#18011834C2212yes—
26#18011831C2212yes—
27C22×Q8×C149C2211yescharacteristic
28C4×Q8×C149—22no—
29C4×Q8×C149C2214yes—
30#117×C149—22no—
31#117×C149C2211yescharacteristic
32#117×C149C2211yescharacteristic
33#14558736—22no—
34#14558736—22no—
35C2×Dic298—21no—
36C2×Dic298—22no—
37C2×Dic298—22no—
38C2×Dic298C2311yescharacteristic
39C2×Dic298C2312yes—
40C2×D596C2311yescharacteristic
41C2×C22⋊D149—21no—
42C22×Dic149—21no—
43C2×C4×D149—21no—
44#14558726—28no—
45#14558726—24no—
46#14558723—24no—
47#14558720—22no—
48C2×#11924746—22no—
49C2×#11924746C2312yes—
50C2×#11924746C2312yes—
51C4⋊Dic149—24no—
52#14558713—24no—
53C2×Q8×C149—21no—
54C2×Q8×C149—22no—
55C2×Q8×C149D414yes—
56C2×Q8×C149C2312yes—
57C22×C4×C149—21no—
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—24no—
60C4⋊C4×C149D412yes—
61C4⋊C4×C149C2312yes—
62C22⋊C4×C149—21no—
63C22⋊C4×C149D412yes—
64C42×C149—24no—
65C42×C149—21no—
66C42×C149C2312yes—
67C22×D149—21no—
68Dic298—22no—
69Dic298—21no—
70Dic298—22no—
71Dic298—21no—
72Dic298—42no—
73D596—21no—
74D596—21no—
75C22⋊D149—42no—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C2×Dic149—42no—
79C4×D149—42no—
80#11924746—22no—
81#11924746—22no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—24no—
84Q8×C149—22no—
85Q8×C149C2×D414yes—
86C2×C4×C149—24no—
87C2×C4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D414yes—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2×D412yes—
92C2×C4×C149#4112yes—
93C2×C4×C149C2411yescharacteristic
94C22×C149—22no—
95C22×C149#12112yes—
96C22×C149C22×D411yescharacteristic
97C2×D149—41no—
98C2×D149—42no—
99C4×C149—24no—
100C4×C149—24no—
101C4×C149—42no—
102C4×C149#12112yes—
103C4×C149C22×D411yescharacteristic
104C4×C149C2×#4111yescharacteristic
105Dic149—41no—
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#519D14911yescharacteristic, complemented
117#464—1494no—
118#462—1494no—
119#424—1491no—
120#419—1491no—
121#416—1491no—
122C2×#41—1491no—
123C22×Q8—1491no—
124C22×Q8C2×D14911yescharacteristic
125#137—2984no—
126C2×Q16—2984no—
127C2×Q16—1494no—
128C2×Q16—1492no—
129C2×SD16—1492no—
130C2×M16—1491no—
131C22×C8—1491no—
132C4⋊Q8—1492no—
133#124—1492no—
134#123—2982no—
135C22⋊Q8—2982no—
136C4×Q8—22no—
137C4×Q8C2×D14914yes—
138#117—22no—
139#117C2×D14911yescharacteristic
140#117C2×D14911yescharacteristic
141C4⋊C8—1494no—
142#103—1492no—
143#103—1494no—
144#102—1492no—
145#41—2982no—
146#41—2982no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—2981no—
150C2×Q8—2982no—
151C2×Q8—2982no—
152C2×Q8—1492no—
153C2×Q8—1491no—
154C2×Q8D59614yes—
155C2×Q8C22×D14912yes—
156C2×D4—2981no—
157C2×D4—1491no—
158C22×C4—21no—
159C22×C4—2981no—
160C22×C4—2981no—
161C22×C4C22×D14911yescharacteristic
162Q16—2988no—
163Q16—2984no—
164SD16—2984no—
165M16—2982no—
166C2×C8—2982no—
167C2×C8—1492no—
168C2×C8—1492no—
169C4⋊C4—24no—
170C4⋊C4—2984no—
171C4⋊C4C22⋊D14912yes—
172C4⋊C4C22×D14912yes—
173C22⋊C4—21no—
174C22⋊C4—2984no—
175C22⋊C4C22⋊D14912yes—
176C42—24no—
177C42—21no—
178C42C22×D14912yes—
179C23—2981no—
180C23C2×C22⋊D14911yescharacteristic
181Q8—22no—
182Q8—24no—
183Q8—2982no—
184Q8—2981no—
185Q8—2982no—
186Q8—2981no—
187Q8—5962no—
188Q8C2×D59614yes—
189D4—2981no—
190D4—2981no—
191D4—5962no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—2982no—
196C2×C4—2981no—
197C2×C4—5962no—
198C2×C4—5962no—
199C2×C4C2×C22⋊D14914yes—
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C2×D59612yes—
202C2×C4#1455873612yes—
203C2×C4C23×D14911yescharacteristic
204C8—2982no—
205C8—2982no—
206C22—22no—
207C22—5962no—
208C22—5961no—
209C22#1801188512yes—
210C22C22×C22⋊D14911yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—5961no—
215C4—5962no—
216C4#1801188512yes—
217C4C22×D59611yescharacteristic
218C4C2×#1455873611yescharacteristic
219C2—22no—
220C2—11921no—
221C2C2×#1801188511yescharacteristic
222C2#2375044012yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#519×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#519D149
hypocenterC149#3044
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#14558726C2semidirect
4. #23749847C2semidirect
5. #23749835C2semidirect
6. #23749652C2semidirect
7. #23749633C2semidirect
9. #519×C149C2semidirect
111. C149#3044semidirect
116. #519D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C22×#145587262
#237502012
#237498472
#237498352
#237496522
#237496332
#237496192
#519×C1492
#3044149