Finite Group Databasebeta

← #34055346

Subgroups — #34055346

Order 19072.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750233C212yesmaximal
2#23750026C211yesmaximal, characteristic, complemented
3#23750003C211yesmaximal, characteristic, complemented
4#23749992C212yesmaximal, complemented
5#23749882C212yesmaximal
6#23749867C211yesmaximal, characteristic
7#23749863C211yesmaximal, characteristic
8#23749730C212yesmaximal, complemented
9C4×Dic596C211yesmaximal, characteristic, complemented
10#23749579C211yesmaximal, characteristic
11C4×Q16×C149C211yesmaximal, characteristic, complemented
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14C2×#14558719C2211yescharacteristic
15C2×C8×D149C2211yescharacteristic
16#18011909C2212yes—
17#18011906—22no—
18#18011905—22no—
19#18011903—22no—
20#18011902C2212yes—
21#18011901—22no—
22#18011891C2212yes—
23#18011887C2212yes—
24C4×Dic298C2212yes—
25#18011868C2211yescharacteristic
26#18011845C2211yescharacteristic
27#18011842C2212yes—
28#18011836C2212yes—
29#18011835C2212yes—
30#18011834C2212yes—
31#18011822C2211yescharacteristic
32#18011821C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2212yes—
36#107×C149C2211yescharacteristic
37#103×C149C2212yes—
38C4×C8×C149C2211yescharacteristic
39C2×Dic298C2312yes—
40C2×C4×D149C2311yescharacteristic
41Dic596—22no—
42#14558726—24no—
43#14558719—22no—
44C2×#11924746C2311yescharacteristic
45C2×#11924746C2311yescharacteristic
46C8×D149—22no—
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558715D411yescharacteristic
56#14558715D411yescharacteristic
57#14558713—22no—
58#14558713—22no—
59#14558713D411yescharacteristic
60#14558713D411yescharacteristic
61C4×Dic149—22no—
62C4×Dic149C2311yescharacteristic
63C2×Q8×C149C2312yes—
64Q16×C149—22no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149—22no—
68C4⋊C4×C149C2312yes—
69C42×C149—22no—
70C42×C149C2311yescharacteristic
71C22×D149C2×D411yescharacteristic
72Dic298—22no—
73Dic298—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D411yescharacteristic
78C2×Dic149C2×D411yescharacteristic
79C4×D149—21no—
80C4×D149—21no—
81#11924746—21no—
82#11924746#4112yes—
83Q8×C149—22no—
84Q8×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C8×C149—21no—
91C8×C149#4112yes—
92C22×C149C22×D411yescharacteristic
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—42no—
99C4×C149—42no—
100C4×C149C2×#4111yescharacteristic
101C4×C149C2×#4111yescharacteristic
102Dic149—21no—
103Dic149—21no—
104Dic149—21no—
105Dic149—42no—
106Dic149—42no—
107C2×C149#53211yescharacteristic
108C2×C149#57811yescharacteristic
109C2×C149#57811yescharacteristic
110D149—41no—
111C149#317711yescharacteristic, complemented, Sylow
112#3177—1491nomaximal, Sylow
113#541—1492no—
114#499—1491no—
115#494—1491no—
116#491—1492no—
117#470—1492no—
118#467—1491no—
119#467—1491no—
120#441—1492no—
121C4×Q16—1491no—
122C4×Q16D14911yescharacteristic, complemented
123#405—1491no—
124C2×Q16—1492no—
125C2×Q16—1491no—
126C2×Q16C2×D14911yescharacteristic
127C2×M16—1491no—
128C22×C8—1491no—
129C4⋊Q8—1492no—
130#126—2982no—
131#126—2982no—
132#125—2982no—
133#125—2982no—
134#125—1492no—
135C22⋊Q8—1492no—
136C22⋊Q8—1492no—
137C4×Q8—1492no—
138C4×Q8C2×D14912yes—
139#117—1491no—
140#107—1491no—
141#107C2×D14911yescharacteristic
142#106—1492no—
143#103—1492no—
144#103—1492no—
145#103—1492no—
146#103C2×D14912yes—
147#97—1491no—
148#97—1491no—
149C4×C8—1491no—
150C4×C8C2×D14911yescharacteristic
151C2×Q8—1492no—
152C2×Q8C22×D14912yes—
153C22×C4—1491no—
154Q16—22no—
155Q16—2984no—
156Q16—2982no—
157M16—2982no—
158C2×C8—2982no—
159C2×C8—1491no—
160C2×C8—1491no—
161C2×C8C22×D14911yescharacteristic
162C2×C8C22×D14911yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—1492no—
172C4⋊C4—1491no—
173C4⋊C4—1491no—
174C4⋊C4C22×D14912yes—
175C22⋊C4—2982no—
176C22⋊C4—2982no—
177C22⋊C4—1491no—
178C22⋊C4—1491no—
179C42—22no—
180C42—2982no—
181C42—1491no—
182C42C22×D14911yescharacteristic
183C23—1491no—
184Q8—22no—
185Q8—22no—
186Q8—2982no—
187Q8—2982no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—1491no—
195C2×C4—1491no—
196C2×C4—1491no—
197C2×C4D4×D14911yescharacteristic
198C2×C4D4×D14911yescharacteristic
199C2×C4C23×D14911yescharacteristic
200C8—21no—
201C8—2981no—
202C8—1492no—
203C8#1455873612yes—
204C22—2981no—
205C22—2981no—
206C22—2981no—
207C22C2×D4×D14911yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—2981no—
213C4—2981no—
214C4—2981no—
215C4—5962no—
216C4—5962no—
217C4#41×D14911yescharacteristic
218C4C2×#1455873611yescharacteristic
219C2—5961no—
220C2#2375017211yescharacteristic
221C2#2375043811yescharacteristic
222C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×Q16×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenterC4×Q16D149
hypocenterC149#3177
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #23750026C2semidirect
3. #23750003C2semidirect
4. #23749992C2semidirect
8. #23749730C2semidirect
9. C4×Dic596C2semidirect
11. C4×Q16×C149C2semidirect
111. C149#3177semidirect
122. C4×Q16D149semidirect

Maximal subgroups

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

subgroupindex
#237502332
#237500262
#237500032
#237499922
#237498822
#237498672
#237498632
#237497302
C4×Dic5962
#237495792
C4×Q16×C1492
#3177149