Finite Group Databasebeta

← #34043158

Subgroups — #34043158

Order 19072.

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

normal subgroups only

This group has 246 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#23750172C211yesmaximal, characteristic
2#23749681C211yesmaximal, characteristic, complemented
3#23749676C211yesmaximal, characteristic, complemented
4#23749354C211yesmaximal, characteristic, complemented
5D4⋊#11924746C211yesmaximal, characteristic, complemented
6#23749352C211yesmaximal, characteristic, complemented
7D4⋊C8×C149C211yesmaximal, characteristic, complemented
8C2×#14558736—21no—
9#18011910C411yescharacteristic
10#18011907C411yescharacteristic
11#18011897—21no—
12#18011886C411yescharacteristic
13#18011884—21no—
14#18011882C411yescharacteristic
15C4×D596C2211yescharacteristic
16C4×C22⋊D149—21no—
17C42×D149C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011840—21no—
20#18011823—21no—
21#18011823—21no—
22#18011821—21no—
23C4×#11924746C2211yescharacteristic
24C4×D4×C149C2211yescharacteristic
25C4⋊C8×C149C2211yescharacteristic
26C4×C8×C149C2211yescharacteristic
27#14558736—42no—
28#14558736—42no—
29C2×Dic298—21no—
30C2×D596—21no—
31C2×D596C2×C411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35C2×C4×D149—21no—
36C2×C4×D149C2×C411yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×#11924746—21no—
40C2×#11924746—21no—
41C4⋊Dic149C2×C411yescharacteristic
42#14558715—21no—
43C22⋊Dic149—21no—
44#14558713—21no—
45#14558713—21no—
46C4×Dic149C2×C411yescharacteristic
47C4×Dic149D411yescharacteristic
48C4×Dic149D411yescharacteristic
49C2×D4×C149C2×C411yescharacteristic
50C22×C4×C149—21no—
51C2×C8×C149—21no—
52C2×C8×C149—21no—
53C4⋊C4×C149C2×C411yescharacteristic
54C22⋊C4×C149—21no—
55C42×C149C2311yescharacteristic
56C22×D149—21no—
57C22×D149C22⋊C411yescharacteristic
58Dic298—42no—
59D596—21no—
60D596—21no—
61D596—42no—
62C22⋊D149—42no—
63C22⋊D149—42no—
64C22⋊D149—42no—
65C2×Dic149—21no—
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C22⋊C411yescharacteristic
69C4×D149—21no—
70C4×D149—21no—
71C4×D149—21no—
72C4×D149—21no—
73C4×D149—41no—
74C4×D149—41no—
75C4×D149—41no—
76#11924746—41no—
77#11924746—41no—
78C23×C149—21no—
79D4×C149—21no—
80D4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—41no—
83C2×C4×C149—41no—
84C2×C4×C149C22×C411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C8×C149—41no—
88C8×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149—41no—
92C22×C149C2×C22⋊C411yescharacteristic
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149—41no—
97C2×D149—41no—
98C2×D149—41no—
99C4×C149—21no—
100C4×C149—41no—
101C4×C149#13111yescharacteristic
102C4×C149#13111yescharacteristic
103C4×C149AGL(1,ℤ/8)11yescharacteristic
104C4×C149AGL(1,ℤ/8)11yescharacteristic
105Dic149—21no—
106Dic149—21no—
107Dic149—21no—
108Dic149—41no—
109C2×C149—81no—
110C2×C149#40811yescharacteristic
111C2×C149#41811yescharacteristic
112C2×C149#42111yescharacteristic
113D149—41no—
114D149—81no—
115C149#149611yescharacteristic, complemented, Sylow
116#1496—1491nomaximal, Sylow
117#532—1491no—
118#432—1491no—
119#431—1491no—
120D4⋊C8—1491no—
121D4⋊C8—1491no—
122D4⋊C8—1491no—
123D4⋊C8D14911yescharacteristic, complemented
124C2×#41—2981no—
125C4⋊Q8—1491no—
126#127—1491no—
127#124—2981no—
128#121—2981no—
129#121—1491no—
130#121—1491no—
131C4×D4—2981no—
132C4×D4—1491no—
133C4×D4C2×D14911yescharacteristic
134C2×C42—1491no—
135C4⋊C8—2981no—
136C4⋊C8—1491no—
137C4⋊C8C2×D14911yescharacteristic
138C22⋊C8—2981no—
139C22⋊C8—2981no—
140#97—2981no—
141C4×C8—1491no—
142C4×C8C2×D14911yescharacteristic
143#41—5962no—
144#41—5962no—
145C2×Q8—2981no—
146C2×D4—2981no—
147C2×D4—2981no—
148C2×D4—2981no—
149C2×D4—2981no—
150C2×D4—1491no—
151C2×D4C4×D14911yescharacteristic
152C22×C4—21no—
153C22×C4—2981no—
154C22×C4—1491no—
155C22×C4—1491no—
156C22×C4—1491no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—2981no—
160C2×C8—2981no—
161C4⋊C4—2981no—
162C4⋊C4—1491no—
163C4⋊C4C4×D14911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C42—1491no—
169C42—1491no—
170C42—1491no—
171C42C22×D14911yescharacteristic
172C23—21no—
173C23—2981no—
174C23—1491no—
175Q8—5962no—
176D4—21no—
177D4—21no—
178D4—2981no—
179D4—2981no—
180D4—5962no—
181D4—5962no—
182D4—5962no—
183D4—5962no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2981no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—5961no—
193C2×C4—5961no—
194C2×C4—5961no—
195C2×C4—1491no—
196C2×C4—1491no—
197C2×C4—1491no—
198C2×C4C2×C4×D14911yescharacteristic
199C2×C4D4×D14911yescharacteristic
200C2×C4D4×D14911yescharacteristic
201C8—41no—
202C8—41no—
203C8—5961no—
204C8—5961no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—2981no—
209C22—2981no—
210C22—2981no—
211C22—5961no—
212C22—5961no—
213C22—5961no—
214C22C22⋊C4×D14911yescharacteristic
215C4—21no—
216C4—41no—
217C4—2981no—
218C4—2981no—
219C4—2981no—
220C4—5961no—
221C4#1801191711yescharacteristic
222C4#1801191911yescharacteristic
223C4#1801193511yescharacteristic
224C4#1801193811yescharacteristic
225C2—81no—
226C2—5961no—
227C2—11921no—
228C2#2374959011yescharacteristic
229C2#2374962811yescharacteristic
230C2#2374964011yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
FittingD4⋊C8×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750172C2
cosocleC42×C149C23
hypercenterD4⋊C8D149
hypocenterC149#1496
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23749681C2semidirect
3. #23749676C2semidirect
4. #23749354C2semidirect
5. D4⋊#11924746C2semidirect
6. #23749352C2semidirect
7. D4⋊C8×C149C2semidirect
115. C149#1496semidirect
123. D4⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
#237501722
#237496812
#237496762
#237493542
D4⋊#119247462
#237493522
D4⋊C8×C1492
#1496149