Finite Group Databasebeta

← #34046643

Subgroups — #34046643

Order 19072.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#23750422C211yesmaximal, characteristic
2#23750068C211yesmaximal, characteristic, complemented
3#23750065C211yesmaximal, characteristic, complemented
4#23749884C211yesmaximal, characteristic, complemented
5#23749434C211yesmaximal, characteristic, complemented
6#23749406C211yesmaximal, characteristic, complemented
7#360×C149C211yesmaximal, characteristic, complemented
8#41×D149—21no—
9#18011943—21no—
10#18011940—21no—
11#18011938—21no—
12#18011935—21no—
13#18011933C2211yescharacteristic
14#18011931—21no—
15C2×Dic596C2211yescharacteristic, complemented
16C2×#14558719C2211yescharacteristic
17#18011891—21no—
18Dic1192—21no—
19#18011857—21no—
20#18011856—21no—
21#18011855—21no—
22#18011851C2211yescharacteristic, complemented
23#18011834—21no—
24#135×C149C2211yescharacteristic
25M32×C149C2211yescharacteristic, complemented
26#106×C149C2211yescharacteristic, complemented
27#14558737—21no—
28#14558736—21no—
29#14558736—41no—
30#14558735—21no—
31#14558735—41no—
32C2×Dic298—21no—
33Q8×D149—21no—
34D4×D149—21no—
35D4×D149—41no—
36C2×C4×D149—41no—
37C2×C4×D149D411yescharacteristic
38Dic596—21no—
39Dic596—21no—
40Dic596D411yescharacteristic
41#14558726—21no—
42#14558725—21no—
43#14558724—21no—
44#14558723—21no—
45D1192D411yescharacteristic
46#14558721—21no—
47#14558719—21no—
48#14558719—21no—
49C2×#11924746D411yescharacteristic
50C4⋊Dic149—41no—
51#14558713—41no—
52#14558711—21no—
53#41×C149—21no—
54Q16×C149D411yescharacteristic
55SD16×C149—21no—
56D8×C149D411yescharacteristic
57C2×C8×C149C2311yescharacteristic
58C4⋊C4×C149—21no—
59C16×C149—21no—
60C22×D149—41no—
61C22×D149D811yescharacteristic
62Dic298—21no—
63Dic298—41no—
64Dic298—41no—
65Dic298—41no—
66D596—21no—
67D596—41no—
68C22⋊D149—41no—
69C22⋊D149—41no—
70C22⋊D149—41no—
71C2×Dic149—41no—
72C2×Dic149—41no—
73C2×Dic149D811yescharacteristic
74C4×D149—21no—
75C4×D149—21no—
76C4×D149—41no—
77C4×D149—41no—
78C4×D149—41no—
79#11924746—21no—
80Q8×C149—21no—
81D4×C149—21no—
82D4×C149—41no—
83C2×C4×C149—41no—
84C2×C4×C149—41no—
85C2×C4×C149C2×D411yescharacteristic
86C8×C149C2×D411yescharacteristic
87C8×C149C2×D411yescharacteristic
88C22×C149—41no—
89C22×C149C2×D811yescharacteristic
90C2×D149—21no—
91C2×D149—41no—
92C2×D149—41no—
93C2×D149—82no—
94C4×C149—41no—
95C4×C149—81no—
96C4×C149#12011yescharacteristic
97C4×C149AGL(1,ℤ/8)11yescharacteristic
98Dic149—21no—
99Dic149—41no—
100Dic149—81no—
101C2×C149—21no—
102C2×C149—81no—
103C2×C149#44711yescharacteristic
104D149—41no—
105D149—81no—
106C149#219111yescharacteristic, complemented, Sylow
107#2191—1491nomaximal, Sylow
108#575—1491no—
109#510—1491no—
110#510—1491no—
111#470—1491no—
112#360—1491no—
113#360D14911yescharacteristic, complemented
114#349—1491no—
115C2×#41—2981no—
116#137—2981no—
117#137—2981no—
118AGL(1,ℤ/8)—2981no—
119AGL(1,ℤ/8)—2981no—
120#135—2981no—
121#135—1491no—
122#135C2×D14911yescharacteristic
123C2×Q16—1491no—
124C2×M16—1491no—
125C22⋊Q8—2981no—
126Q32—2981no—
127Q32—2981no—
128SD32—2981no—
129SD32—2981no—
130M32—1491no—
131M32C2×D14911yescharacteristic, complemented
132#106C2×D14911yescharacteristic, complemented
133#103—2981no—
134#41—21no—
135#41—2981no—
136#41—2981no—
137#41—2981no—
138#41—5961no—
139#41—5961no—
140C2×Q8—2981no—
141C2×Q8—2981no—
142C2×D4—2981no—
143C2×D4—5961no—
144C22×C4—5961no—
145C22×C4—1491no—
146Q16—2981no—
147Q16—2981no—
148Q16—2981no—
149Q16—1491no—
150Q16D59611yescharacteristic
151SD16—21no—
152SD16—2981no—
153SD16—2981no—
154SD16—2981no—
155D8—2981no—
156D8—1491no—
157D8D59611yescharacteristic
158M16—2981no—
159M16—2981no—
160C2×C8—1491no—
161C2×C8C22×D14911yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—5961no—
164C22⋊C4—5961no—
165C16—21no—
166C16—2981no—
167C23—5961no—
168C23—1491no—
169Q8—21no—
170Q8—2981no—
171Q8—5961no—
172Q8—5961no—
173Q8—5961no—
174D4—21no—
175D4—41no—
176D4—2981no—
177D4—5961no—
178D4—5961no—
179D4—5961no—
180D4—5961no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2981no—
184C2×C4—2981no—
185C2×C4—5961no—
186C2×C4—5961no—
187C2×C4—5961no—
188C2×C4—5961no—
189C2×C4—5961no—
190C2×C4—1491no—
191C2×C4D4×D14911yescharacteristic
192C8—2981no—
193C8D4×D14911yescharacteristic
194C8C2×D59611yescharacteristic
195C22—41no—
196C22—2981no—
197C22—5961no—
198C22—5961no—
199C22—11922no—
200C22D8×D14911yescharacteristic
201C4—41no—
202C4—81no—
203C4—2981no—
204C4—5961no—
205C4—11921no—
206C4#1801188111yescharacteristic
207C4#1801193811yescharacteristic
208C2—21no—
209C2—81no—
210C2—5961no—
211C2—11921no—
212C2#2374976011yescharacteristic
subgroupG/H
centerC2#23749760
commutator, cosocleC2×C8×C149C23
FrattiniC2×C8C22×D149
Fitting#360×C149C2
socleC2×C149#447
prime radical#23750422C2
hypercenter#360D149
hypocenterC149#2191
LCSG ▷ C2×C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #23750068C2semidirect
3. #23750065C2semidirect
4. #23749884C2semidirect
5. #23749434C2semidirect
6. #23749406C2semidirect
7. #360×C149C2semidirect
15. C2×Dic596C22semidirect
22. #18011851C22semidirect
25. M32×C149C22semidirect
26. #106×C149C22semidirect
106. C149#2191semidirect
113. #360D149semidirect
131. M32C2×D149semidirect
132. #106C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504222
#237500682
#237500652
#237498842
#237494342
#237494062
#360×C1492
#2191149