Finite Group Databasebeta

← #34046340

Subgroups — #34046340

Order 19072.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#23750189C211yesmaximal, characteristic
2#23749609C211yesmaximal, characteristic, complemented
3#23749411C214yesmaximal, complemented
4#410×C149C211yesmaximal, characteristic, complemented
5C22×D596C411yescharacteristic, complemented
6C2×#14558720—21no—
7#18011907—21no—
8#18011900—21no—
9#18011885—21no—
10#18011885—21no—
11#18011879C412yescomplemented
12#18011879C2212yes—
13#18011870C411yescharacteristic, complemented
14#18011830—21no—
15#18011828C2212yes—
16C2×#41×C149C2211yescharacteristic
17#117×C149—21no—
18#99×C149—21no—
19#99×C149C2212yes—
20C23×D149C2×C412yes—
21C2×D596—21no—
22C2×D596—21no—
23C2×D596—41no—
24C2×D596—41no—
25C2×C22⋊D149—22no—
26C2×C22⋊D149—22no—
27#14558720—22no—
28#14558720—41no—
29C2×#11924746—41no—
30C4⋊Dic149—21no—
31C22⋊Dic149C2×C412yes—
32#14558713—22no—
33#14558713—22no—
34C4×Dic149—21no—
35#41×C149—41no—
36#41×C149—41no—
37C2×Q8×C149D411yescharacteristic
38C2×D4×C149C2×C411yescharacteristic
39C2×D4×C149D411yescharacteristic
40C2×D4×C149C2311yescharacteristic
41C22×C4×C149C2×C411yescharacteristic
42C22×C4×C149D411yescharacteristic
43C22×C4×C149D411yescharacteristic
44C4⋊C4×C149—41no—
45C22⋊C4×C149—22no—
46C42×C149—41no—
47C22×D149—22no—
48C22×D149—42no—
49C22×D149—82no—
50D596—42no—
51D596—41no—
52D596—41no—
53C22⋊D149—82no—
54C22⋊D149—82no—
55C2×Dic149—22no—
56#11924746—42no—
57C23×C149C22⋊C411yescharacteristic
58C23×C149C22×C411yescharacteristic
59C23×C149C2×D411yescharacteristic
60Q8×C149—41no—
61D4×C149—41no—
62D4×C149—41no—
63D4×C149—41no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—42no—
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C22×C149—21no—
76C22×C149—21no—
77C22×C149—21no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—42no—
83C2×D149—42no—
84C2×D149—42no—
85C2×D149—84no—
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—82no—
90C4×C149#9911yescharacteristic
91C4×C149#9911yescharacteristic
92Dic149—42no—
93C2×C149—21no—
94C2×C149—41no—
95C2×C149—41no—
96C2×C149—41no—
97C2×C149C2×#9911yescharacteristic
98D149—82no—
99C149#212211yescharacteristic, complemented, Sylow
100#2122—1491nomaximal, Sylow
101#535—1491no—
102#413—1491no—
103#410D14911yescharacteristic, complemented
104AΣL(1,𝔽16)—1494no—
105C2×#41C2×D14911yescharacteristic
106C22×D4—1491no—
107C2×M16—2981no—
108#127—2981no—
109#124—2981no—
110#121—2981no—
111#121—2981no—
112#120—1492no—
113#120—1492no—
114#117—21no—
115#117—1491no—
116#101—2981no—
117#100—1492no—
118#99—21no—
119#99C2×D14912yes—
120C24—1492no—
121#41—41no—
122#41—41no—
123C2×Q8D59611yescharacteristic
124C2×D4—2982no—
125C2×D4—2982no—
126C2×D4—2981no—
127C2×D4—2981no—
128C2×D4—5961no—
129C2×D4—5961no—
130C2×D4C4×D14911yescharacteristic
131C2×D4C22⋊D14911yescharacteristic
132C2×D4C22×D14911yescharacteristic
133C22×C4C4×D14911yescharacteristic
134C22×C4C22⋊D14911yescharacteristic
135C22×C4D59611yescharacteristic
136M16—2982no—
137M16—5961no—
138C2×C8—5961no—
139C4⋊C4—41no—
140C4⋊C4—2981no—
141C22⋊C4—22no—
142C22⋊C4—2982no—
143C22⋊C4—2982no—
144C22⋊C4—1492no—
145C42—41no—
146C42—2981no—
147C23—2982no—
148C23—5962no—
149C23—11922no—
150C23#1455871311yescharacteristic
151C23C2×C4×D14911yescharacteristic
152C23C2×C22⋊D14911yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—5962no—
158D4—5961no—
159D4—5961no—
160D4—11922no—
161D4—11922no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—2982no—
170C2×C4#1455871311yescharacteristic
171C2×C4#1455871311yescharacteristic
172C2×C4#1455871311yescharacteristic
173C2×C4C2×D59611yescharacteristic
174C8—5962no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—5962no—
182C22—5962no—
183C22—5962no—
184C22—11924no—
185C22C2×#1455871311yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—82no—
190C4—5962no—
191C4#1801182511yescharacteristic
192C4#1801182511yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—11922no—
198C2C2×#1801182511yescharacteristic
subgroupG/H
centerC2C2×#18011825
commutatorC23×C149C22×C4
FrattiniC2×D4C22×D149
Fitting#410×C149C2
socleC2×C149C2×#99
prime radical#23750189C2
cosocleC2×D4×C149C23
hypercenter#410D149
hypocenterC149#2122
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #23749609C2semidirect
3. #23749411C2semidirect
4. #410×C149C2semidirect
5. C22×D596C4semidirect
11. #18011879C4semidirect
13. #18011870C4semidirect
99. C149#2122semidirect
103. #410D149semidirect

Maximal subgroups

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

subgroupindex
#237501892
#237496092
#237494112
#410×C1492
#2122149