Finite Group Databasebeta

← #34060646

Subgroups — #34060646

Order 19072.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750692C211yesmaximal, characteristic
2#23750636C212yesmaximal, complemented
3#23750577C211yesmaximal, characteristic
4#23750497C212yesmaximal, complemented
5#100×D149C211yesmaximal, characteristic
6D4×#10597010—22no—
7D4×#10597010—22no—
8#18011990C2212yes—
9C2×C4⋊#10597010C2211yescharacteristic
10C2×C22⋊#10597010—22no—
11C2×C22⋊#10597010—22no—
12C2×C4×#10597010C2211yescharacteristic
13#18011980—22no—
14#18011979—22no—
15C2×D4×D149C2211yescharacteristic
16M16×D149C2212yes—
17#18011828C411yescharacteristic, complemented
18#18011827C412yescomplemented
19#100×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C22×#10597010—22no—
22C22×#10597010—21no—
23C22×#10597010—21no—
24C4⋊#10597010—22no—
25C4⋊#10597010D412yes—
26C4⋊#10597010D412yes—
27C22⋊#10597010—24no—
28C22⋊#10597010—22no—
29C22⋊#10597010—44no—
30C4×#10597010—22no—
31C4×#10597010—22no—
32C23×D149D412yes—
33C2×D596C2×C411yescharacteristic
34C2×C22⋊D149Q812yes—
35D4×D149—22no—
36D4×D149—22no—
37C2×C4×D149C2311yescharacteristic
38#14558720C2×C412yescomplemented
39#14558719—22no—
40C8×D149—22no—
41C2×D4×C149C2×C411yescharacteristic
42M16×C149C2×C412yescomplemented
43C2×#10597010—22no—
44C2×#10597010—22no—
45C2×#10597010—22no—
46C2×#10597010—41no—
47C2×#10597010—41no—
48C2×#10597010—42no—
49C2×#10597010—41no—
50C2×#10597010—82no—
51C2×#10597010—82no—
52C22×D149—22no—
53C22×D149—22no—
54C22×D149—42no—
55C22×D149—42no—
56C22×D149C4⋊C412yes—
57C22×D149C2×D411yescharacteristic
58D596—22no—
59C22⋊D149—24no—
60C2×Dic149C2×Q811yescharacteristic
61C4×D149C2×D412yes—
62C4×D149#4112yes—
63#11924746—22no—
64C23×C149C4⋊C412yes—
65D4×C149—22no—
66C2×C4×C149C22×C411yescharacteristic
67C8×C149—22no—
68C22×C149—22no—
69C22×C149—42no—
70C22×C149C2×C4⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—22no—
74C2×D149—42no—
75C2×D149—42no—
76C2×D149—42no—
77C2×D149—82no—
78C2×D149#12011yescharacteristic
79C2×D149#12311yescharacteristic
80#10597010—42no—
81#10597010—42no—
82#10597010—42no—
83#10597010—81no—
84C4×C149C4×D412yes—
85Dic149C22⋊Q812yes—
86C2×C149—21no—
87C2×C149—42no—
88C2×C149#38511yescharacteristic
89D149—21no—
90D149—42no—
91D149#45311yescharacteristic
92D149#45511yescharacteristic
93C149#185611yescharacteristic, complemented, Sylow
94#1856—1491nomaximal, Sylow
95#518—1491no—
96#428—1492no—
97C2×#100—1491no—
98#390—1491no—
99#339—1492no—
100C22×D4—1491no—
101C2×M16—1492no—
102C4×D4—2982no—
103C4×D4—2982no—
104#117—1492no—
105C2×C4⋊C4—1491no—
106C2×C22⋊C4—2982no—
107C2×C22⋊C4—2982no—
108C2×C42—1491no—
109#107—2982no—
110#106—2982no—
111#100—1491no—
112#100—1492no—
113#100#1059701011yescharacteristic, complemented
114C24—1492no—
115C2×D4—2982no—
116C2×D4—2982no—
117C2×D4—1492no—
118C2×D4—1491no—
119C2×D4C2×#1059701011yescharacteristic
120C22×C4—2981no—
121C22×C4—2982no—
122C22×C4—2982no—
123C22×C4—2981no—
124C22×C4—1491no—
125M16—2982no—
126M16—1492no—
127M16C2×#1059701012yescomplemented
128C2×C8—2982no—
129C4⋊C4—2982no—
130C4⋊C4—1492no—
131C4⋊C4—1492no—
132C22⋊C4—2984no—
133C22⋊C4—2982no—
134C22⋊C4—5964no—
135C42—2982no—
136C42—2982no—
137C23—2982no—
138C23—2982no—
139C23—5962no—
140C23—5962no—
141C23—1491no—
142C23—1492no—
143C23C4⋊#1059701012yes—
144D4—22no—
145D4—2984no—
146D4—2982no—
147C2×C4—2982no—
148C2×C4—2982no—
149C2×C4—2982no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—5962no—
153C2×C4—5961no—
154C2×C4—1491no—
155C2×C4—1492no—
156C2×C4—1492no—
157C2×C4—11922no—
158C2×C4—11922no—
159C2×C4C22×#1059701011yescharacteristic
160C8—22no—
161C8—2982no—
162C22—22no—
163C22—42no—
164C22—2981no—
165C22—2981no—
166C22—2982no—
167C22—5962no—
168C22—5962no—
169C22—5962no—
170C22—1491no—
171C22—1491no—
172C22—11922no—
173C22C2×C4⋊#1059701011yescharacteristic
174C4—5962no—
175C4—5962no—
176C4—5962no—
177C4—1492no—
178C4—11921no—
179C4D4×#1059701012yes—
180C2—21no—
181C2—42no—
182C2—2981no—
183C2—5962no—
184C2—1491no—
185C2—1491no—
186C2#2375057211yescharacteristic
subgroupG/H
centerC2#23750572
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#100×C149C4
socleC2×C149#385
prime radicalC2×D4×D149C22
cosocleC2×C4×D149C23
hypercenter#100#10597010
hypocenterC149#1856
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. #23750636C2semidirect
4. #23750497C2semidirect
17. #18011828C4semidirect
18. #18011827C4semidirect
19. #100×C149C4semidirect
38. #14558720C2×C4semidirect
42. M16×C149C2×C4semidirect
93. C149#1856semidirect
113. #100#10597010semidirect
127. M16C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506922
#237506362
#237505772
#237504972
#100×D1492
#1856149