Finite Group Databasebeta

← #34057777

Subgroups — #34057777

Order 19072.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750358C212yesmaximal, complemented
2#23750013C212yesmaximal, complemented
3#23750009C211yesmaximal, characteristic, complemented
4#23749846C212yesmaximal, complemented
5#23749840C212yesmaximal, complemented
6#23749819C212yesmaximal, complemented
7#23749755C211yesmaximal, characteristic, complemented
8#23749724C212yesmaximal, complemented
9C4×D8×C149C211yesmaximal, characteristic, complemented
10C2×Dic596C2211yescharacteristic
11C2×#14558725C2212yes—
12C2×#14558724C2212yes—
13C2×D1192C2211yescharacteristic
14C2×#14558721C2212yes—
15#18011907C2212yes—
16#18011899C2212yes—
17#18011898C2212yes—
18#18011897—22no—
19#18011894—22no—
20#18011893—22no—
21C4×Dic298C2211yescharacteristic
22#18011876C2212yes—
23#18011873C2212yes—
24C4×C22⋊D149—22no—
25C4⋊#11924746C2211yescharacteristic
26#18011840C2212yes—
27#18011834C2212yes—
28#18011831C2212yes—
29#18011821C2212yes—
30C2×D8×C149C2211yescharacteristic
31C4×D4×C149C2212yes—
32#107×C149C2211yescharacteristic
33#102×C149C2212yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298D411yescharacteristic
36C2×Dic298C2312yes—
37C2×D596C2312yes—
38C2×C22⋊D149—22no—
39C2×C22⋊D149—22no—
40C2×C4×D149—22no—
41Dic596—41no—
42#14558725—24no—
43#14558724—42no—
44D1192—41no—
45#14558721—42no—
46C2×#11924746C2312yes—
47C4⋊Dic149D411yescharacteristic
48#14558715—22no—
49#14558715D412yes—
50C22⋊Dic149—22no—
51C22⋊Dic149—22no—
52#14558713—22no—
53#14558713—22no—
54#14558713—22no—
55C4×Dic149—22no—
56C4×Dic149C2312yes—
57C2×D4×C149C2312yes—
58C22×C4×C149—22no—
59D8×C149—22no—
60C2×C8×C149C2311yescharacteristic
61C2×C8×C149C2311yescharacteristic
62C4⋊C4×C149C2312yes—
63C22⋊C4×C149—22no—
64C42×C149C2311yescharacteristic
65C22×D149—22no—
66Dic298—22no—
67Dic298—22no—
68Dic298—41no—
69D596—22no—
70D596—22no—
71C22⋊D149—44no—
72C22⋊D149—82no—
73C2×Dic149—22no—
74C2×Dic149C2×D412yes—
75C2×Dic149C2×D412yes—
76C4×D149—82no—
77#11924746—22no—
78C23×C149—22no—
79D4×C149—22no—
80D4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—82no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2411yescharacteristic
86C8×C149—21no—
87C8×C149#4112yes—
88C22×C149—42no—
89C22×C149—42no—
90C22×C149—42no—
91C22×C149C22×D411yescharacteristic
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—42no—
95C4×C149—21no—
96C4×C149—21no—
97C4×C149—42no—
98C4×C149C2×#4111yescharacteristic
99C4×C149H(5,𝔽2)11yescharacteristic
100Dic149—22no—
101Dic149—22no—
102Dic149—42no—
103C2×C149—82no—
104C2×C149#55011yescharacteristic
105C2×C149#57511yescharacteristic
106C2×C149#57611yescharacteristic
107D149—82no—
108C149#340311yescharacteristic, complemented, Sylow
109#3403—1491nomaximal, Sylow
110#559—1492no—
111#496—1492no—
112#495—1491no—
113#464—1492no—
114#463—1492no—
115#459—1492no—
116#446—1491no—
117#440—1492no—
118C4×D8D14911yescharacteristic, complemented
119C2×Q16—1491no—
120C2×SD16—1492no—
121C2×SD16—1492no—
122C2×D8—1492no—
123C2×D8—1491no—
124C2×D8C2×D14911yescharacteristic
125#127—1492no—
126#124—2982no—
127#124—1492no—
128#124—1492no—
129#123—2982no—
130#123—2982no—
131C4×Q8—1492no—
132C4×Q8—1491no—
133C4×D4—2982no—
134C4×D4—1492no—
135C4×D4C2×D14912yes—
136#107C2×D14911yescharacteristic
137C4⋊C8—1492no—
138C4⋊C8—1491no—
139#103—1492no—
140#102—1492no—
141#102C2×D14912yes—
142#97—1492no—
143C4×C8C2×D14911yescharacteristic
144C2×Q8—1492no—
145C2×Q8—1491no—
146C2×D4—2982no—
147C2×D4—2982no—
148C2×D4—1492no—
149C2×D4C22×D14912yes—
150C22×C4—22no—
151C22×C4—2982no—
152Q16—5961no—
153SD16—2984no—
154SD16—5962no—
155D8—22no—
156D8—5961no—
157D8—5962no—
158C2×C8—1492no—
159C2×C8C22×D14911yescharacteristic
160C2×C8C22×D14911yescharacteristic
161C4⋊C4—2982no—
162C4⋊C4—1492no—
163C4⋊C4—1491no—
164C4⋊C4C22×D14912yes—
165C22⋊C4—22no—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C42—2982no—
172C42—1492no—
173C42C22×D14911yescharacteristic
174C23—22no—
175C23—2982no—
176Q8—2982no—
177Q8—2982no—
178Q8—5961no—
179D4—22no—
180D4—22no—
181D4—2982no—
182D4—2982no—
183D4—5964no—
184D4—11922no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—2982no—
188C2×C4—1492no—
189C2×C4—1492no—
190C2×C4—11922no—
191C2×C4D4×D14911yescharacteristic
192C2×C4D4×D14911yescharacteristic
193C2×C4C23×D14911yescharacteristic
194C8—21no—
195C8—2982no—
196C8#1455873612yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—5962no—
201C22—5962no—
202C22—5962no—
203C22C2×D4×D14911yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—2982no—
208C4—2982no—
209C4—5962no—
210C4C2×#1455873611yescharacteristic
211C4#1801195711yescharacteristic
212C2—82no—
213C2—11922no—
214C2#2375029611yescharacteristic
215C2#2375042211yescharacteristic
216C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750358C2semidirect
2. #23750013C2semidirect
3. #23750009C2semidirect
4. #23749846C2semidirect
5. #23749840C2semidirect
6. #23749819C2semidirect
7. #23749755C2semidirect
8. #23749724C2semidirect
9. C4×D8×C149C2semidirect
108. C149#3403semidirect
118. C4×D8D149semidirect

Maximal subgroups

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

subgroupindex
#237503582
#237500132
#237500092
#237498462
#237498402
#237498192
#237497552
#237497242
C4×D8×C1492
#3403149