Finite Group Databasebeta

← #34056093

Subgroups — #34056093

Order 19072.

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

normal subgroups only

This group has 354 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#23750161C212yesmaximal, complemented
2#23749930C212yesmaximal, complemented
3#23749924C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic
5#23749873C212yesmaximal, complemented
6#23749849C212yesmaximal, complemented
7#23749843C212yesmaximal, complemented
8#23749648C211yesmaximal, characteristic, complemented
9#470×C149C211yesmaximal, characteristic, complemented
10C2×#14558723C2212yes—
11C2×D1192C2211yescharacteristic
12C2×#14558720C2211yescharacteristic
13#18011906—22no—
14#18011902C2212yes—
15#18011900C2212yes—
16#18011895—22no—
17#18011885C2212yes—
18Q8×Dic149C2212yes—
19#18011873C2212yes—
20#18011871—22no—
21#18011869—22no—
22C2×C4×Dic149C2211yescharacteristic
23#18011844C2212yes—
24#18011843C2211yescharacteristic
25#18011840C2212yes—
26#18011840C2212yes—
27#18011835C2212yes—
28#18011833C2212yes—
29#18011831C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#106×C149C2211yescharacteristic
34#103×C149C2212yes—
35C2×D596C2312yes—
36C2×C22⋊D149—22no—
37C22×Dic149D412yes—
38C2×C4×D149—22no—
39#14558723—42no—
40D1192—41no—
41#14558720—41no—
42C2×#11924746C2312yes—
43C4⋊Dic149—22no—
44C4⋊Dic149—22no—
45C4⋊Dic149C2312yes—
46#14558715—22no—
47#14558713—22no—
48#14558713—22no—
49#14558713—22no—
50#14558713—22no—
51C4×Dic149—22no—
52C4×Dic149D411yescharacteristic
53C4×Dic149D411yescharacteristic
54C4×Dic149C2312yes—
55C2×Q8×C149C2312yes—
56C22×C4×C149C2311yescharacteristic
57Q16×C149—41no—
58M16×C149—41no—
59C2×C8×C149C2311yescharacteristic
60C2×C8×C149C2311yescharacteristic
61C4⋊C4×C149—22no—
62C4⋊C4×C149C2312yes—
63C22⋊C4×C149—22no—
64C22×D149—22no—
65D596—22no—
66D596—22no—
67C22⋊D149—44no—
68C2×Dic149—22no—
69C2×Dic149—42no—
70C2×Dic149C2×D412yes—
71C2×Dic149C2×D412yes—
72C4×D149—44no—
73#11924746—22no—
74C23×C149C2×D411yescharacteristic
75Q8×C149—22no—
76Q8×C149—22no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2411yescharacteristic
83C8×C149—21no—
84C8×C149—21no—
85C22×C149—21no—
86C22×C149—22no—
87C22×C149C22×D411yescharacteristic
88C2×D149—42no—
89C2×D149—42no—
90C2×D149—42no—
91C4×C149—21no—
92C4×C149—42no—
93C4×C149—42no—
94C4×C149H(5,𝔽2)11yescharacteristic
95C4×C1492−1+411yescharacteristic
96Dic149—22no—
97Dic149—22no—
98Dic149—42no—
99C2×C149—41no—
100C2×C149#53711yescharacteristic
101C2×C149#57512yes—
102D149—82no—
103C149#325611yescharacteristic, complemented, Sylow
104#3256—1491nomaximal, Sylow
105#529—1492no—
106#479—1492no—
107#478—1492no—
108#470D14911yescharacteristic, complemented
109#469—1491no—
110#468—1492no—
111#464—1492no—
112#463—1492no—
113#423—1491no—
114C2×Q16C2×D14911yescharacteristic
115C2×SD16—1492no—
116C2×D8—1491no—
117C2×M16—1491no—
118C2×M16C2×D14911yescharacteristic
119#126—2982no—
120#125—1492no—
121#124—1492no—
122#123—2982no—
123C22⋊Q8C2×D14912yes—
124#121—1492no—
125C4×Q8—1492no—
126C4×D4—2982no—
127C4×D4—1492no—
128#117—2982no—
129C2×C42—1491no—
130#107—1492no—
131#106—1491no—
132#106C2×D14911yescharacteristic
133C4⋊C8—1492no—
134C4⋊C8—1492no—
135#103—1492no—
136#103C2×D14912yes—
137#102—1492no—
138#102—1492no—
139C2×Q8C22×D14912yes—
140C2×D4—2982no—
141C2×D4—1492no—
142C22×C4—2982no—
143C22×C4—1492no—
144C22×C4C22×D14911yescharacteristic
145Q16—41no—
146SD16—5962no—
147D8—5961no—
148M16—41no—
149M16—5961no—
150C2×C8—1492no—
151C2×C8C22×D14911yescharacteristic
152C2×C8C22×D14911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2982no—
157C4⋊C4—1492no—
158C4⋊C4C22×D14912yes—
159C22⋊C4—22no—
160C22⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C22⋊C4—2982no—
164C42—2982no—
165C42—1491no—
166C42—1491no—
167C42—1492no—
168C23—2982no—
169C23D4×D14911yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—2982no—
173D4—2982no—
174D4—5964no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2982no—
180C2×C4—5964no—
181C2×C4—5962no—
182C2×C4—1492no—
183C2×C4—1492no—
184C2×C4D4×D14911yescharacteristic
185C2×C4C23×D14911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2982no—
189C22—22no—
190C22—21no—
191C22—5962no—
192C22—5962no—
193C22—5962no—
194C22C2×D4×D14911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—2982no—
199C4—2982no—
200C4—5962no—
201C4#1801195611yescharacteristic
202C4#1801195811yescharacteristic
203C2—41no—
204C2—11922no—
205C2#2375020211yescharacteristic
206C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
prime radical#23749878C2
hypercenter#470D149
hypocenterC149#3256
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23750161C2semidirect
2. #23749930C2semidirect
3. #23749924C2semidirect
5. #23749873C2semidirect
6. #23749849C2semidirect
7. #23749843C2semidirect
8. #23749648C2semidirect
9. #470×C149C2semidirect
103. C149#3256semidirect
108. #470D149semidirect

Maximal subgroups

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

subgroupindex
#237501612
#237499302
#237499242
#237498782
#237498732
#237498492
#237498432
#237496482
#470×C1492
#3256149