Finite Group Databasebeta

← #34056043

Subgroups — #34056043

Order 19072.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750159C212yesmaximal, complemented
2#23749933C212yesmaximal, complemented
3#23749926C212yesmaximal, complemented
4#23749866C211yesmaximal, characteristic, complemented
5#23749861C211yesmaximal, characteristic
6#23749854C212yesmaximal, complemented
7#23749848C212yesmaximal, complemented
8#23749841C212yesmaximal, complemented
9C2×C4⋊C8×C149C211yesmaximal, characteristic, complemented
10C2×Dic596C2211yescharacteristic
11C2×#14558725C2212yes—
12C2×D1192C2211yescharacteristic
13#18011905—22no—
14#18011903C2212yes—
15#18011899C2212yes—
16#18011894—22no—
17#18011890C2212yes—
18#18011885C2212yes—
19C4×Dic298C2212yes—
20C4×D596C2212yes—
21C4×C22⋊D149—22no—
22#18011868—22no—
23#18011845C2211yescharacteristic
24#18011845C2211yescharacteristic
25#18011843C2212yes—
26#18011836C2212yes—
27#18011836C2212yes—
28#18011833C2212yes—
29#18011833C2212yes—
30C22×C8×C149C2211yescharacteristic
31C22×C8×C149C2211yescharacteristic
32C2×C42×C149C2211yescharacteristic
33C4⋊C8×C149C2212yes—
34C4⋊C8×C149C2212yes—
35C2×Dic298C2312yes—
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C4×D149—22no—
39Dic596—41no—
40#14558725—42no—
41D1192—41no—
42C4⋊Dic149C2312yes—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
46#14558715—22no—
47#14558715—22no—
48C22⋊Dic149—22no—
49#14558713—22no—
50#14558713—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C22×C4×C149D411yescharacteristic
55C22×C4×C149D411yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C2×C8×C149—41no—
58C2×C8×C149—41no—
59C2×C8×C149C2311yescharacteristic
60C2×C8×C149C2312yes—
61C2×C8×C149C2311yescharacteristic
62C42×C149D412yes—
63C42×C149C2312yes—
64C22×D149—22no—
65Dic298—22no—
66Dic298—22no—
67D596—22no—
68D596—22no—
69C22⋊D149—44no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C4×D149—44no—
74C23×C149C2×D411yescharacteristic
75C2×C4×C149—22no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149—41no—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2411yescharacteristic
83C8×C149—21no—
84C8×C149—22no—
85C8×C149—21no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149#13512yes—
89C22×C149C22×D411yescharacteristic
90C2×D149—42no—
91C2×D149—42no—
92C2×D149—42no—
93C4×C149—21no—
94C4×C149—22no—
95C4×C149—22no—
96C4×C149H(5,𝔽2)11yescharacteristic
97C4×C1492−1+411yescharacteristic
98Dic149—42no—
99Dic149—42no—
100Dic149—42no—
101C2×C149—22no—
102C2×C149#53711yescharacteristic
103C2×C149C2×#13511yescharacteristic
104C2×C149#57511yescharacteristic
105D149—82no—
106C149#325011yescharacteristic, complemented, Sylow
107#3250—1491nomaximal, Sylow
108#529—1492no—
109#479—1492no—
110#478—1492no—
111#467—1491no—
112#466—1491no—
113#465—1492no—
114#464—1492no—
115#463—1492no—
116C2×C4⋊C8D14911yescharacteristic, complemented
117C2×Q16—1491no—
118C2×SD16—1492no—
119C2×D8—1491no—
120C22×C8C2×D14911yescharacteristic
121C22×C8C2×D14911yescharacteristic
122#126—2982no—
123#125—1492no—
124#124—1492no—
125#123—2982no—
126C22⋊Q8—1492no—
127#121—1492no—
128C4×Q8—1492no—
129C4×D4—2982no—
130C4×D4—1492no—
131#117—2982no—
132C2×C42C2×D14911yescharacteristic
133#107—1491no—
134#107—1491no—
135#106—1492no—
136C4⋊C8C2×D14912yes—
137C4⋊C8C2×D14912yes—
138#103—1492no—
139#103—1492no—
140#102—1492no—
141#102—1492no—
142C2×Q8—1492no—
143C2×D4—2982no—
144C2×D4—1492no—
145C22×C4—2982no—
146C22×C4D59611yescharacteristic
147C22×C4D59611yescharacteristic
148C22×C4C22×D14911yescharacteristic
149Q16—5961no—
150SD16—5962no—
151D8—5961no—
152C2×C8—41no—
153C2×C8—41no—
154C2×C8C22×D14911yescharacteristic
155C2×C8C22×D14912yes—
156C2×C8C22×D14911yescharacteristic
157C4⋊C4—2982no—
158C4⋊C4—2982no—
159C4⋊C4—2982no—
160C4⋊C4—2982no—
161C4⋊C4—1492no—
162C4⋊C4—1492no—
163C22⋊C4—2982no—
164C22⋊C4—2982no—
165C22⋊C4—2982no—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C42—2982no—
169C42D59612yes—
170C42C22×D14912yes—
171C23—2982no—
172C23C2×D59611yescharacteristic
173Q8—2982no—
174Q8—2982no—
175D4—2982no—
176D4—2982no—
177D4—5964no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4—5964no—
186C2×C4C2×D59612yes—
187C2×C4C2×D59611yescharacteristic
188C2×C4C2×D59612yes—
189C2×C4C23×D14911yescharacteristic
190C8—21no—
191C8—22no—
192C8—21no—
193C22—21no—
194C22—21no—
195C22—5962no—
196C22—5962no—
197C22—5962no—
198C22#1801193312yes—
199C22C22×D59611yescharacteristic
200C4—22no—
201C4—22no—
202C4—21no—
203C4—5962no—
204C4—5962no—
205C4—5962no—
206C4#1801195611yescharacteristic
207C4#1801195911yescharacteristic
208C2—22no—
209C2—11922no—
210C2#2375020611yescharacteristic
211C2C2×#1801193311yescharacteristic
212C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4⋊C8×C149C2
socleC22×C149C22×D4
prime radical#23749861C2
hypercenterC2×C4⋊C8D149
hypocenterC149#3250
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #23750159C2semidirect
2. #23749933C2semidirect
3. #23749926C2semidirect
4. #23749866C2semidirect
6. #23749854C2semidirect
7. #23749848C2semidirect
8. #23749841C2semidirect
9. C2×C4⋊C8×C149C2semidirect
106. C149#3250semidirect
116. C2×C4⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237499332
#237499262
#237498662
#237498612
#237498542
#237498482
#237498412
C2×C4⋊C8×C1492
#3250149