Finite Group Databasebeta

← #34043985

Subgroups — #34043985

Order 19072.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750369C211yesmaximal, characteristic, complemented
2#23750015C211yesmaximal, characteristic, complemented
3#23750014C211yesmaximal, characteristic, complemented
4#23749990C211yesmaximal, characteristic, complemented
5#23749366C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic, complemented
7#329×C149C211yesmaximal, characteristic, complemented
8C2×#14558725—21no—
9C2×#14558723—21no—
10C2×D1192—21no—
11C2×#14558721—21no—
12#18011908C2211yescharacteristic
13#18011903C2211yescharacteristic
14#18011899C2211yescharacteristic
15#18011895—21no—
16#18011893—21no—
17#18011888—21no—
18#18011887—21no—
19#18011884—21no—
20#18011883—21no—
21#18011833—21no—
22#18011833—21no—
23#18011822C2211yescharacteristic
24#124×C149C2211yescharacteristic
25#97×C149C2211yescharacteristic
26#97×C149C2211yescharacteristic
27C2×Dic298D411yescharacteristic
28C2×D596—21no—
29C2×D596—21no—
30C2×D596—21no—
31C2×D596D411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C22×Dic149—21no—
35C2×C4×D149—21no—
36#14558725—42no—
37#14558723—42no—
38D1192—42no—
39#14558721—42no—
40C2×#11924746—21no—
41C4⋊Dic149—21no—
42C4⋊Dic149D411yescharacteristic
43C4⋊Dic149D411yescharacteristic
44#14558715—21no—
45#14558715—21no—
46#14558715—21no—
47C22⋊Dic149—21no—
48#14558713—21no—
49#14558713—21no—
50#14558713—21no—
51C2×Q8×C149D411yescharacteristic
52C2×D4×C149D411yescharacteristic
53C2×C8×C149—21no—
54C2×C8×C149—21no—
55C22⋊C4×C149—21no—
56C22⋊C4×C149—21no—
57C42×C149C2311yescharacteristic
58C22×D149—21no—
59C22×D149—41no—
60Dic298—41no—
61D596—41no—
62D596—41no—
63D596—41no—
64D596—41no—
65D596—41no—
66D596—42no—
67C22⋊D149—81no—
68C22⋊D149—81no—
69C2×Dic149—21no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—81no—
73C4×D149—81no—
74#11924746—22no—
75C23×C149—21no—
76Q8×C149—41no—
77D4×C149—41no—
78C2×C4×C149—21no—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C8×C149—22no—
83C8×C149—41no—
84C22×C149—41no—
85C22×C149—41no—
86C22×C149—41no—
87C22×C149#12011yescharacteristic
88C2×D149—41no—
89C2×D149—41no—
90C2×D149—41no—
91C2×D149—81no—
92C2×D149—81no—
93C2×D149—81no—
94C4×C149—21no—
95C4×C149—21no—
96C4×C149—21no—
97C4×C149—41no—
98Dic149—41no—
99Dic149—41no—
100Dic149—41no—
101C2×C149—81no—
102C2×C149#45311yescharacteristic
103C2×C149#45311yescharacteristic
104C2×C149#45411yescharacteristic
105D149—81no—
106D149—161no—
107C149#165611yescharacteristic, complemented, Sylow
108#1656—1491nomaximal, Sylow
109#562—1491no—
110#496—1491no—
111#496—1491no—
112#490—1491no—
113#330—1491no—
114#329—1491no—
115#329D14911yescharacteristic, complemented
116C2×SD16—2981no—
117C2×SD16—2981no—
118C2×D8—2981no—
119C2×D8—2981no—
120#127—1491no—
121#125—1491no—
122#124—1491no—
123#124C2×D14911yescharacteristic
124#123—2981no—
125#123—2981no—
126C22⋊Q8—2981no—
127C22⋊Q8—2981no—
128#121—2981no—
129#121—2981no—
130#102—2981no—
131#102—2981no—
132#97—1491no—
133#97C2×D14911yescharacteristic
134#97C2×D14911yescharacteristic
135C2×Q8—1491no—
136C2×Q8D59611yescharacteristic
137C2×D4—2981no—
138C2×D4—2981no—
139C2×D4—2981no—
140C2×D4—2981no—
141C2×D4—2981no—
142C2×D4—1491no—
143C2×D4D59611yescharacteristic
144C22×C4—2981no—
145C22×C4—2981no—
146SD16—5962no—
147SD16—5962no—
148D8—5962no—
149D8—5962no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—2981no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—1491no—
158C4⋊C4—1491no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—2981no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C42C22×D14911yescharacteristic
166C23—21no—
167C23—2981no—
168C23—5961no—
169Q8—41no—
170Q8—5961no—
171D4—41no—
172D4—5961no—
173D4—5961no—
174D4—5961no—
175D4—5961no—
176D4—5961no—
177D4—5962no—
178D4—11921no—
179D4—11921no—
180C2×C4—21no—
181C2×C4—2981no—
182C2×C4—2981no—
183C2×C4—2981no—
184C2×C4—11921no—
185C2×C4—11921no—
186C2×C4D4×D14911yescharacteristic
187C2×C4D4×D14911yescharacteristic
188C2×C4C2×D59611yescharacteristic
189C8—22no—
190C8—41no—
191C8—2982no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—5961no—
196C22—5961no—
197C22—5961no—
198C22—11921no—
199C22—11921no—
200C22—11921no—
201C22#1801188111yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—5961no—
207C4—5961no—
208C4—5961no—
209C2—81no—
210C2—23841no—
211C2—11921no—
212C2#2374979411yescharacteristic
213C2#2374979511yescharacteristic
214C2#2374979911yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#329×C149C2
socleC22×C149#120
hypercenter#329D149
hypocenterC149#1656
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #23750369C2semidirect
2. #23750015C2semidirect
3. #23750014C2semidirect
4. #23749990C2semidirect
5. #23749366C2semidirect
6. #23749364C2semidirect
7. #329×C149C2semidirect
107. C149#1656semidirect
115. #329D149semidirect

Maximal subgroups

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

subgroupindex
#237503692
#237500152
#237500142
#237499902
#237493662
#237493642
#329×C1492
#1656149