Finite Group Databasebeta

← #34056127

Subgroups — #34056127

Order 19072.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750228C212yesmaximal, complemented
2#23749927C212yesmaximal, complemented
3#23749924C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic, complemented
5#23749859C212yesmaximal, complemented
6#23749819C212yesmaximal, complemented
7#23749818C212yesmaximal, complemented
8#23749653C211yesmaximal, characteristic, complemented
9#469×C149C211yesmaximal, characteristic, complemented
10C2×D1192C2211yescharacteristic
11C2×#14558721C2212yes—
12C22×#11924746C2211yescharacteristic
13#18011907C2212yes—
14#18011902C2212yes—
15#18011895—22no—
16#18011893—22no—
17#18011885C2212yes—
18#18011883—22no—
19#18011882—22no—
20D4×Dic149C2212yes—
21#18011873C2212yes—
22#18011870C2211yescharacteristic
23#18011844C2212yes—
24#18011843C2211yescharacteristic
25#18011840C2212yes—
26#18011840C2212yes—
27#18011833C2212yes—
28#18011832C2212yes—
29#18011831C2212yes—
30C2×D8×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32#121×C149C2212yes—
33#106×C149C2211yescharacteristic
34#102×C149C2212yes—
35C2×D596C2312yes—
36C2×C22⋊D149—22no—
37C2×C22⋊D149—22no—
38C2×C22⋊D149—22no—
39C22×Dic149—22no—
40C2×C4×D149—22no—
41D1192—41no—
42#14558721—42no—
43C2×#11924746—41no—
44C2×#11924746C2312yes—
45C4⋊Dic149—22no—
46C4⋊Dic149D412yes—
47C4⋊Dic149C2312yes—
48#14558715—22no—
49C22⋊Dic149—22no—
50C22⋊Dic149D411yescharacteristic
51C22⋊Dic149D411yescharacteristic
52#14558713—22no—
53#14558713—22no—
54C4×Dic149C2312yes—
55C2×D4×C149—22no—
56C2×D4×C149C2312yes—
57C22×C4×C149C2311yescharacteristic
58D8×C149—41no—
59M16×C149—41no—
60C2×C8×C149C2311yescharacteristic
61C2×C8×C149C2311yescharacteristic
62C4⋊C4×C149C2312yes—
63C22⋊C4×C149—22no—
64C22×D149—22no—
65D596—22no—
66D596—22no—
67C22⋊D149—82no—
68C22⋊D149—82no—
69C22⋊D149—82no—
70C2×Dic149—22no—
71C2×Dic149—82no—
72C2×Dic149C2×D412yes—
73C2×Dic149C2×D412yes—
74C4×D149—82no—
75#11924746—22no—
76C23×C149—22no—
77C23×C149C2×D411yescharacteristic
78D4×C149—22no—
79D4×C149—22no—
80D4×C149—82no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2411yescharacteristic
86C8×C149—21no—
87C8×C149—21no—
88C22×C149—21no—
89C22×C149—22no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149C22×D411yescharacteristic
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—42no—
97C4×C149—21no—
98C4×C149—42no—
99C4×C149H(5,𝔽2)11yescharacteristic
100C4×C1492−1+411yescharacteristic
101Dic149—22no—
102Dic149—22no—
103Dic149—42no—
104C2×C149—41no—
105C2×C149—82no—
106C2×C149#53711yescharacteristic
107C2×C149#57612yes—
108D149—82no—
109C149#325911yescharacteristic, complemented, Sylow
110#3259—1491nomaximal, Sylow
111#540—1492no—
112#478—1492no—
113#478—1492no—
114#469—1491no—
115#469D14911yescharacteristic, complemented
116#466—1492no—
117#459—1492no—
118#459—1492no—
119#424—1491no—
120C2×D8—1492no—
121C2×D8—1491no—
122C2×D8C2×D14911yescharacteristic
123C2×M16C2×D14911yescharacteristic
124C22×C8—1491no—
125#127—1492no—
126#125—1492no—
127#123—2982no—
128#123—2982no—
129#121—2982no—
130#121—2982no—
131#121—1492no—
132#121C2×D14912yes—
133C4×D4—1492no—
134C4×D4—1492no—
135#117—1491no—
136#107—1492no—
137#106—1491no—
138#106C2×D14911yescharacteristic
139C4⋊C8—1492no—
140C4⋊C8—1492no—
141#102—1492no—
142#102—1492no—
143#102—1492no—
144#102C2×D14912yes—
145C2×D4—22no—
146C2×D4—2982no—
147C2×D4—2982no—
148C2×D4—2982no—
149C2×D4—1492no—
150C2×D4C22×D14912yes—
151C22×C4—2982no—
152C22×C4—2982no—
153C22×C4C22×D14911yescharacteristic
154D8—41no—
155D8—5961no—
156D8—5962no—
157M16—41no—
158C2×C8—5961no—
159C2×C8—1492no—
160C2×C8C22×D14911yescharacteristic
161C2×C8C22×D14911yescharacteristic
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—1492no—
165C4⋊C4—1492no—
166C4⋊C4C22×D14912yes—
167C22⋊C4—22no—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C22⋊C4—1491no—
172C22⋊C4—1491no—
173C42—1492no—
174C23—22no—
175C23—2982no—
176C23D4×D14911yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—2982no—
181D4—2982no—
182D4—11922no—
183D4—11922no—
184D4—11922no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—2982no—
189C2×C4—1492no—
190C2×C4—1492no—
191C2×C4—11922no—
192C2×C4—11922no—
193C2×C4D4×D14911yescharacteristic
194C2×C4C23×D14911yescharacteristic
195C8—21no—
196C8—21no—
197C8—2982no—
198C22—22no—
199C22—21no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—5962no—
204C22—5962no—
205C22—5962no—
206C22C2×D4×D14911yescharacteristic
207C4—21no—
208C4—42no—
209C4—2982no—
210C4—2982no—
211C4—5962no—
212C4#1801195611yescharacteristic
213C4#1801195811yescharacteristic
214C2—41no—
215C2—82no—
216C2—11922no—
217C2#2375020211yescharacteristic
218C2#2375042912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3259
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750228C2semidirect
2. #23749927C2semidirect
3. #23749924C2semidirect
4. #23749878C2semidirect
5. #23749859C2semidirect
6. #23749819C2semidirect
7. #23749818C2semidirect
8. #23749653C2semidirect
9. #469×C149C2semidirect
109. C149#3259semidirect
115. #469D149semidirect

Maximal subgroups

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

subgroupindex
#237502282
#237499272
#237499242
#237498782
#237498592
#237498192
#237498182
#237496532
#469×C1492
#3259149