Finite Group Databasebeta

← #34044641

Subgroups — #34044641

Order 19072.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#23750461C211yesmaximal, characteristic
2#23749609C211yesmaximal, characteristic, complemented
3#23749607C212yesmaximal, complemented
4#23749591C212yesmaximal, complemented
5#408×C149C211yesmaximal, characteristic, complemented
6#18011959—21no—
7#18011958—22no—
8#18011957—22no—
9#18011956—21no—
10#18011956C414yes—
11C2×#14558736—22no—
12C2×#14558736C2212yes—
13#41×D149—24no—
14C2×#14558720C2212yescomplemented
15#18011830—21no—
16#18011829—22no—
17#18011828—21no—
18#18011827—22no—
19#18011823—24no—
20C2×#41×C149C2211yescharacteristic
21C2×M16×C149C2211yescharacteristic, complemented
22C22×C8×C149C2211yescharacteristic, complemented
23C22⋊C8×C149—22no—
24#14558737—24no—
25#14558736—24no—
26#14558736—24no—
27#14558736—24no—
28#14558736—22no—
29#14558736—22no—
30#14558736—22no—
31#14558736—22no—
32#14558735—24no—
33#14558735—28no—
34C2×Dic298—22no—
35C2×Dic298D412yes—
36Q8×D149—24no—
37C2×D596—22no—
38C2×D596D412yes—
39C2×C22⋊D149—24no—
40C2×C22⋊D149C2×C414yes—
41D4×D149—24no—
42D4×D149—28no—
43C2×C4×D149—24no—
44C2×C4×D149D414yes—
45#14558720—22no—
46#14558720—22no—
47C2×#11924746—22no—
48#41×C149—22no—
49#41×C149—22no—
50C2×Q8×C149D411yescharacteristic
51C2×D4×C149C2×C412yes—
52C2×D4×C149D411yescharacteristic
53C22×C4×C149D412yes—
54C22×C4×C149C2311yescharacteristic
55M16×C149—22no—
56C2×C8×C149—21no—
57C2×C8×C149—21no—
58C2×C8×C149—22no—
59C22×D149—24no—
60C22×D149C22⋊C414yes—
61Dic298—24no—
62Dic298—22no—
63Dic298—22no—
64D596—24no—
65D596—22no—
66D596—22no—
67C22⋊D149—28no—
68C22⋊D149—24no—
69C22⋊D149—24no—
70C2×Dic149—24no—
71C2×Dic149C22⋊C414yes—
72C4×D149—28no—
73C4×D149—24no—
74C4×D149—24no—
75#11924746—42no—
76C23×C149C22⋊C412yes—
77C23×C149C22×C411yescharacteristic
78Q8×C149—22no—
79D4×C149—24no—
80D4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149C22⋊C412yes—
84C2×C4×C149C2×D412yes—
85C2×C4×C149C2×D412yes—
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C8×C149—41no—
89C8×C149—41no—
90C22×C149—22no—
91C22×C149—41no—
92C22×C149—42no—
93C22×C149C2×C22⋊C412yes—
94C22×C149C2×C22⋊C411yescharacteristic
95C2×D149—24no—
96C2×D149—44no—
97C2×D149—84no—
98C4×C149—22no—
99C4×C149#12011yescharacteristic
100C4×C149#12011yescharacteristic
101C4×C149#12012yes—
102Dic149—24no—
103C2×C149—22no—
104C2×C149—21no—
105C2×C149—42no—
106C2×C149#37911yescharacteristic
107D149—44no—
108C149#179111yescharacteristic, complemented, Sylow
109#1791—1491nomaximal, Sylow
110#585—1491no—
111#413—1491no—
112#413—1492no—
113#408—1492no—
114#408D14911yescharacteristic, complemented
1152−1+4—2982no—
1162−1+4—2981no—
117H(5,𝔽2)—2982no—
118H(5,𝔽2)—2981no—
119H(5,𝔽2)—1494no—
120C2×#41—2984no—
121C2×#41—2982no—
122C2×#41—1492no—
123C2×#41C2×D14911yescharacteristic
124C2×M16—1492no—
125C2×M16C2×D14911yescharacteristic, complemented
126C22×C8C2×D14911yescharacteristic, complemented
127#101—2982no—
128#101—2981no—
129#100—2982no—
130#100—2981no—
131C22⋊C8—22no—
132C22⋊C8—2984no—
133#41—22no—
134#41—22no—
135#41—2984no—
136#41—2984no—
137#41—2984no—
138#41—2984no—
139#41—2988no—
140#41—2982no—
141#41—2982no—
142#41—2982no—
143#41—2982no—
144#41—2984no—
145C2×Q8—2982no—
146C2×Q8—2984no—
147C2×Q8—1492no—
148C2×Q8D59611yescharacteristic
149C2×D4—2982no—
150C2×D4—2984no—
151C2×D4—2988no—
152C2×D4—2984no—
153C2×D4—1494no—
154C2×D4—1492no—
155C2×D4C4×D14912yes—
156C2×D4D59611yescharacteristic
157C22×C4—2984no—
158C22×C4—1494no—
159C22×C4C22⋊D14912yes—
160C22×C4C22×D14911yescharacteristic
161M16—22no—
162M16—2982no—
163M16—2982no—
164C2×C8—22no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—2982no—
168C23—2984no—
169C23—1494no—
170C23#1455871312yes—
171C23C2×C4×D14911yescharacteristic
172Q8—22no—
173Q8—2984no—
174Q8—2982no—
175Q8—2982no—
176D4—24no—
177D4—22no—
178D4—2984no—
179D4—2988no—
180D4—2984no—
181D4—2984no—
182D4—2982no—
183D4—2982no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2988no—
187C2×C4—2984no—
188C2×C4—2984no—
189C2×C4—2984no—
190C2×C4—1494no—
191C2×C4#1455871312yes—
192C2×C4D4×D14912yes—
193C2×C4D4×D14912yes—
194C2×C4C2×C22⋊D14911yescharacteristic
195C2×C4C2×D59611yescharacteristic
196C8—41no—
197C8—41no—
198C8—5962no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—2984no—
203C22—5964no—
204C22—11924no—
205C22C22⋊C4×D14912yes—
206C22C2×#1455871311yescharacteristic
207C4—22no—
208C4—2984no—
209C4#1801187911yescharacteristic
210C4#1801187911yescharacteristic
211C4#1801188112yes—
212C2—21no—
213C2—22no—
214C2—42no—
215C2—5964no—
216C2#2374948011yescharacteristic
subgroupG/H
centerC4#18011879
commutatorC23×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#408×C149C2
socleC2×C149#379
prime radical#23750461C2
cosocleC22×C4×C149C23
hypercenter#408D149
hypocenterC149#1791
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23749609C2semidirect
3. #23749607C2semidirect
4. #23749591C2semidirect
5. #408×C149C2semidirect
14. C2×#14558720C22semidirect
21. C2×M16×C149C22semidirect
22. C22×C8×C149C22semidirect
108. C149#1791semidirect
114. #408D149semidirect
125. C2×M16C2×D149semidirect
126. C22×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504612
#237496092
#237496072
#237495912
#408×C1492
#1791149