Finite Group Databasebeta

← #34057782

Subgroups — #34057782

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#23750357C212yesmaximal, complemented
2#23750011C212yesmaximal, complemented
3#23749849C212yesmaximal, complemented
4#23749837C212yesmaximal, complemented
5#23749818C212yesmaximal, complemented
6#23749755C211yesmaximal, characteristic, complemented
7#23749726C212yesmaximal, complemented
8C4×D1192C211yesmaximal, characteristic, complemented
9#495×C149C211yesmaximal, characteristic, complemented
10C2×#14558723C2212yes—
11C2×D1192C2211yescharacteristic
12C2×#14558721C2212yes—
13#18011907C2212yes—
14#18011900C2212yes—
15#18011897—22no—
16#18011895—22no—
17#18011893—22no—
18Q8×Dic149C2212yes—
19C4×Dic298C2211yescharacteristic
20C4×D596C2212yes—
21D4×Dic149C2212yes—
22#18011871—22no—
23#18011845C2211yescharacteristic
24C4⋊#11924746C2211yescharacteristic
25#18011840C2212yes—
26#18011835C2212yes—
27#18011833C2212yes—
28#18011832C2212yes—
29#18011821C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C2×SD16×C149C2212yes—
32C2×D8×C149C2211yescharacteristic
33#124×C149C2212yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298D411yescharacteristic
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C22⋊D149—22no—
39C22×Dic149—22no—
40C2×C4×D149—22no—
41#14558723—42no—
42D1192—22no—
43#14558721—42no—
44C2×#11924746C2312yes—
45C4⋊Dic149—22no—
46C4⋊Dic149D411yescharacteristic
47C4⋊Dic149C2312yes—
48#14558715D412yes—
49C22⋊Dic149—22no—
50#14558713—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C4×Dic149C2312yes—
55C2×Q8×C149C2312yes—
56C2×D4×C149C2312yes—
57Q16×C149—41no—
58SD16×C149—24no—
59D8×C149—41no—
60C2×C8×C149C2311yescharacteristic
61C2×C8×C149C2311yescharacteristic
62C22⋊C4×C149—22no—
63C22⋊C4×C149—22no—
64C42×C149C2311yescharacteristic
65C22×D149—22no—
66Dic298—41no—
67D596—22no—
68D596—22no—
69C22⋊D149—44no—
70C22⋊D149—82no—
71C2×Dic149—22no—
72C2×Dic149—82no—
73C2×Dic149C2×D412yes—
74C2×Dic149C2×D412yes—
75C4×D149—82no—
76#11924746—22no—
77C23×C149—22no—
78Q8×C149—22no—
79Q8×C149—22no—
80D4×C149—22no—
81D4×C149—22no—
82C2×C4×C149—22no—
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#495D14911yescharacteristic, complemented
113#464—1492no—
114#463—1492no—
115#459—1492no—
116#446—1491no—
117#440—1492no—
118C4×D8—1491no—
119C2×Q16C2×D14911yescharacteristic
120C2×SD16—1492no—
121C2×SD16C2×D14912yes—
122C2×D8—1492no—
123C2×D8—1491no—
124C2×D8C2×D14911yescharacteristic
125#127—1492no—
126#124—2982no—
127#124—1492no—
128#124C2×D14912yes—
129#123—2982no—
130#123—2982no—
131C4×Q8—1492no—
132C4×Q8—1491no—
133C4×D4—2982no—
134C4×D4—1492no—
135C4×D4—1492no—
136#107—1491no—
137C4⋊C8—1492no—
138C4⋊C8—1491no—
139#103—1492no—
140#102—1492no—
141#102—1492no—
142#97—1492no—
143C4×C8C2×D14911yescharacteristic
144C2×Q8—1491no—
145C2×Q8C22×D14912yes—
146C2×D4—2982no—
147C2×D4—2982no—
148C2×D4—1492no—
149C2×D4C22×D14912yes—
150C22×C4—2982no—
151C22×C4—2982no—
152Q16—41no—
153SD16—24no—
154SD16—5962no—
155D8—41no—
156D8—2982no—
157D8—5962no—
158C2×C8—1492no—
159C2×C8C22×D14911yescharacteristic
160C2×C8C22×D14911yescharacteristic
161C4⋊C4—2982no—
162C4⋊C4—1492no—
163C4⋊C4—1492no—
164C4⋊C4—1491no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—2982no—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C42—2982no—
172C42—1492no—
173C42C22×D14911yescharacteristic
174C23—22no—
175C23—2982no—
176Q8—22no—
177Q8—22no—
178Q8—5961no—
179D4—22no—
180D4—22no—
181D4—2982no—
182D4—2982no—
183D4—5964no—
184D4—11922no—
185C2×C4—22no—
186C2×C4—2982no—
187C2×C4—1492no—
188C2×C4—1492no—
189C2×C4—11922no—
190C2×C4—11922no—
191C2×C4D4×D14911yescharacteristic
192C2×C4D4×D14911yescharacteristic
193C2×C4C23×D14911yescharacteristic
194C8—21no—
195C8—2982no—
196C8#1455873512yes—
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×#1455873511yescharacteristic
211C4#1801195611yescharacteristic
212C2—82no—
213C2—11922no—
214C2#2375029511yescharacteristic
215C2#2375042211yescharacteristic
216C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3403
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23750357C2semidirect
2. #23750011C2semidirect
3. #23749849C2semidirect
4. #23749837C2semidirect
5. #23749818C2semidirect
6. #23749755C2semidirect
7. #23749726C2semidirect
8. C4×D1192C2semidirect
9. #495×C149C2semidirect
108. C149#3403semidirect
112. #495D149semidirect

Maximal subgroups

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

subgroupindex
#237503572
#237500112
#237498492
#237498372
#237498182
#237497552
#237497262
C4×D11922
#495×C1492
#3403149