Finite Group Databasebeta

← #34045182

Subgroups — #34045182

Order 19072.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#18011941C211yesmaximal, characteristic
2#23750102C211yesmaximal, characteristic, complemented
3#23749635C211yesmaximal, characteristic, complemented
4#23749599C211yesmaximal, characteristic
5#23749397C211yesmaximal, characteristic, complemented
6#23749381C211yesmaximal, characteristic, complemented
7#421×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9#18011941—22no—
10#18011941—22no—
11C2×#14558726C412yescomplemented
12C2×#14558724C412yescomplemented
13C2×#14558720C2211yescharacteristic
14C4×Dic298—22no—
15#18011876—22no—
16#18011870C2211yescharacteristic
17#18011870C2211yescharacteristic
18#18011867—22no—
19#18011836—22no—
20#18011826—22no—
21C2×#41×C149C2211yescharacteristic
22C2×M16×C149C2211yescharacteristic
23#117×C149C2211yescharacteristic
24#104×C149—22no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298C2×C412yes—
29C2×Dic298D412yes—
30C2×Dic298D412yes—
31C22×Dic149—21no—
32#14558726—24no—
33#14558724—24no—
34#14558720—21no—
35#14558720—21no—
36C2×#11924746C2×C412yes—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39#14558715—24no—
40C22⋊Dic149—21no—
41C22⋊Dic149D412yes—
42C4×Dic149—24no—
43C4×Dic149—21no—
44C4×Dic149—21no—
45#41×C149—21no—
46#41×C149—21no—
47#41×C149—21no—
48#41×C149—21no—
49C2×Q8×C149C2×C411yescharacteristic
50C2×D4×C149—21no—
51C2×D4×C149C2×C411yescharacteristic
52C22×C4×C149—21no—
53C22×C4×C149C2311yescharacteristic
54M16×C149—21no—
55M16×C149—21no—
56C2×C8×C149—21no—
57C4⋊C4×C149—21no—
58C22⋊C4×C149—21no—
59C42×C149D412yes—
60Dic298—22no—
61Dic298—22no—
62Dic298—22no—
63Dic298C22⋊C414yes—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—41no—
69#11924746—22no—
70C23×C149—21no—
71C23×C149C2×D411yescharacteristic
72Q8×C149—21no—
73Q8×C149—21no—
74D4×C149—21no—
75D4×C149—21no—
76D4×C149—41no—
77D4×C149—41no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—41no—
81C2×C4×C149—41no—
82C2×C4×C149C22×C411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149#4111yescharacteristic
87C2×C4×C149#4111yescharacteristic
88C8×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149—81no—
92C22×C149C4×D411yescharacteristic
93C22×C149#12011yescharacteristic
94C22×C149#12111yescharacteristic
95C4×C149—42no—
96C4×C149—41no—
97C4×C149C2×C22⋊C411yescharacteristic
98C4×C149C4×D411yescharacteristic
99C4×C149#12111yescharacteristic
100C4×C149#12311yescharacteristic
101Dic149—24no—
102Dic149—42no—
103Dic149—81no—
104C2×C149—21no—
105C2×C149—21no—
106C2×C149—21no—
107C2×C149—81no—
108C2×C149#38611yescharacteristic
109C149#190511yescharacteristic, complemented, Sylow
110#1905—1491nomaximal, Sylow
111C2×#137—1491no—
112#519—1491no—
113#421D14911yescharacteristic
114#419—1491no—
115#410—1491no—
116#344—1491no—
117H(3,ℤ/4)—1491no—
118C2×#41C2×D14911yescharacteristic
119C22×Q8—1491no—
120#137—2982no—
121#137—2982no—
122C2×Q16—1492no—
123C2×SD16—1492no—
124C2×M16—1491no—
125C2×M16C2×D14911yescharacteristic
126C4×Q8—2982no—
127C4×Q8—2982no—
128#117—2982no—
129#117—1491no—
130#117—1491no—
131#117C2×D14911yescharacteristic
132#104—22no—
133#103—2982no—
134#99—2982no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—2981no—
140C2×Q8—2981no—
141C2×Q8—2981no—
142C2×Q8—1492no—
143C2×Q8—1492no—
144C2×Q8—1492no—
145C2×Q8C4×D14911yescharacteristic
146C2×D4—21no—
147C2×D4C4×D14911yescharacteristic
148C22×C4—21no—
149C22×C4—2981no—
150C22×C4C22×D14911yescharacteristic
151Q16—2984no—
152SD16—2984no—
153M16—21no—
154M16—21no—
155M16—2981no—
156M16—2981no—
157C2×C8—21no—
158C2×C8—1492no—
159C4⋊C4—21no—
160C4⋊C4—2984no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C22⋊C4—21no—
164C22⋊C4—2981no—
165C22⋊C4—1492no—
166C42—2984no—
167C42—2981no—
168C42—2981no—
169C42C22⋊D14912yes—
170C23—21no—
171C23D4×D14911yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—2982no—
175Q8—2982no—
176Q8—2982no—
177Q8—1494no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—5961no—
191C2×C4C2×C4×D14911yescharacteristic
192C2×C4D4×D14911yescharacteristic
193C2×C4D4×D14911yescharacteristic
194C2×C4C2×C22⋊D14911yescharacteristic
195C2×C4#1455873511yescharacteristic
196C2×C4#1455873611yescharacteristic
197C8—41no—
198C8—2982no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22#1801187111yescharacteristic
203C22#1801187911yescharacteristic
204C22#1801188411yescharacteristic
205C4—42no—
206C4—41no—
207C4—2984no—
208C4—5962no—
209C4—11921no—
210C4C22⋊C4×D14911yescharacteristic
211C4C4×C22⋊D14911yescharacteristic
212C4#1801188211yescharacteristic
213C4#1801189311yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#2374950111yescharacteristic
subgroupG/H
centerC2#23749501
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#421×C149C2
socleC2×C149#386
prime radicalC2×#41×C149C22
cosocleC22×C4×C149C23
hypercenter#421D149
hypocenterC149#1905
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #23750102C2semidirect
3. #23749635C2semidirect
5. #23749397C2semidirect
6. #23749381C2semidirect
11. C2×#14558726C4semidirect
12. C2×#14558724C4semidirect
109. C149#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#180119412
#237501022
#237496352
#237495992
#237493972
#237493812
#421×C1492
#1905149