Finite Group Databasebeta

← #34046331

Subgroups — #34046331

Order 19072.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750133C211yesmaximal, characteristic
2#23749606C211yesmaximal, characteristic, complemented
3#23749597C211yesmaximal, characteristic, complemented
4#23749415C211yesmaximal, characteristic, complemented
5#23749413C211yesmaximal, characteristic, complemented
6#23749411C211yesmaximal, characteristic, complemented
7#352×C149C211yesmaximal, characteristic, complemented
8C2×#14558735C2211yescharacteristic
9C22×C4×D149C411yescharacteristic, complemented
10M16×D149—21no—
11#18011894C411yescharacteristic, complemented
12#18011889—21no—
13#18011884—21no—
14#18011881C411yescharacteristic, complemented
15#18011879C2211yescharacteristic
16#18011873—21no—
17#18011871—21no—
18#18011867—21no—
19#18011867C411yescharacteristic, complemented
20#18011829—21no—
21#18011828C2211yescharacteristic
22#18011826C2211yescharacteristic
23#18011825—21no—
24#123×C149C2211yescharacteristic
25#100×C149C2211yescharacteristic
26#99×C149C2211yescharacteristic
27C23×D149C2×C411yescharacteristic
28#14558735—41no—
29#14558735—41no—
30C2×Dic298D411yescharacteristic
31C2×D596—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149C2×C411yescharacteristic
34C2×C22⋊D149D411yescharacteristic
35C22×Dic149C2×C411yescharacteristic
36C22×Dic149D411yescharacteristic
37C2×C4×D149—21no—
38C2×C4×D149—21no—
39C2×C4×D149—41no—
40C2×C4×D149—41no—
41C2×C4×D149D411yescharacteristic
42#14558720—21no—
43#14558719—41no—
44C8×D149—41no—
45#14558715—21no—
46#14558715—21no—
47#14558715—41no—
48C22⋊Dic149—21no—
49C22⋊Dic149C2×C411yescharacteristic
50#14558713—21no—
51#14558713—21no—
52#14558713—21no—
53C4×Dic149—21no—
54C4×Dic149—41no—
55C2×D4×C149C2311yescharacteristic
56C22×C4×C149C2×C411yescharacteristic
57M16×C149—21no—
58C4⋊C4×C149—21no—
59C22⋊C4×C149—21no—
60C22⋊C4×C149—21no—
61C22⋊C4×C149C2×C411yescharacteristic
62C22×D149—21no—
63C22×D149—42no—
64C22×D149—41no—
65C22×D149C22⋊C411yescharacteristic
66Dic298—41no—
67D596—42no—
68C22⋊D149—41no—
69C22⋊D149—41no—
70C22⋊D149—42no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—21no—
76C2×Dic149—41no—
77C2×Dic149C22⋊C411yescharacteristic
78C2×Dic149C22⋊C411yescharacteristic
79C2×Dic149C22⋊C411yescharacteristic
80C4×D149—21no—
81C4×D149—21no—
82C4×D149—42no—
83C4×D149—41no—
84C4×D149—41no—
85#11924746—41no—
86C23×C149C22×C411yescharacteristic
87C23×C149C2×D411yescharacteristic
88D4×C149—41no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149—41no—
92C2×C4×C149—41no—
93C2×C4×C149C2×D411yescharacteristic
94C8×C149—41no—
95C22×C149—21no—
96C22×C149—21no—
97C22×C149—41no—
98C22×C149—41no—
99C22×C149C2×C22⋊C411yescharacteristic
100C2×D149—22no—
101C2×D149—21no—
102C2×D149—41no—
103C2×D149—42no—
104C2×D149—41no—
105C2×D149—41no—
106C2×D149—42no—
107C4×C149—21no—
108C4×C149—41no—
109C4×C149—41no—
110C4×C149—81no—
111Dic149—21no—
112Dic149—21no—
113Dic149—41no—
114Dic149—81no—
115Dic149#9911yescharacteristic
116Dic149#9911yescharacteristic
117C2×C149—21no—
118C2×C149—41no—
119C2×C149—41no—
120C2×C149C2×#9911yescharacteristic
121D149—41no—
122D149—42no—
123C149#212011yescharacteristic, complemented, Sylow
124#2120—1491nomaximal, Sylow
125#525—1491no—
126#413—1491no—
127#410—1491no—
128#352—1491no—
129#352D14911yescharacteristic, complemented
130AΣL(1,𝔽16)—1491no—
131AΣL(1,𝔽16)—1491no—
132C2×#41—1491no—
133C23×C4—1491no—
134C2×M16—2981no—
135#123—1491no—
136#123C2×D14911yescharacteristic
137C22⋊Q8—2981no—
138#121—2981no—
139#120—1491no—
140#120—1491no—
141C4×D4—2981no—
142C4×D4—2981no—
143#117—2981no—
144#117—1491no—
145#101—2981no—
146#100—1491no—
147#100C2×D14911yescharacteristic
148#99—2981no—
149#99—1491no—
150#99C2×D14911yescharacteristic
151C24—1491no—
152#41—5961no—
153#41—5961no—
154C2×Q8—1491no—
155C2×D4—2981no—
156C2×D4—2981no—
157C2×D4—1491no—
158C2×D4—1491no—
159C2×D4C22×D14911yescharacteristic
160C22×C4—2981no—
161C22×C4—2981no—
162C22×C4—5961no—
163C22×C4—5961no—
164C22×C4—1491no—
165C22×C4—1491no—
166C22×C4—1491no—
167C22×C4C4×D14911yescharacteristic
168M16—21no—
169M16—2981no—
170M16—5961no—
171C2×C8—5961no—
172C4⋊C4—21no—
173C4⋊C4—2981no—
174C4⋊C4—2981no—
175C4⋊C4—5961no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—2981no—
179C22⋊C4—2981no—
180C22⋊C4—2981no—
181C22⋊C4—2981no—
182C22⋊C4—1491no—
183C22⋊C4C4×D14911yescharacteristic
184C42—2981no—
185C42—5961no—
186C23—2981no—
187C23—5961no—
188C23—5962no—
189C23—1491no—
190C23C2×C4×D14911yescharacteristic
191C23D4×D14911yescharacteristic
192Q8—5961no—
193D4—41no—
194D4—5962no—
195D4—5961no—
196D4—5961no—
197D4—5962no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—2981no—
203C2×C4—2981no—
204C2×C4—2981no—
205C2×C4—2981no—
206C2×C4—2981no—
207C2×C4—2981no—
208C2×C4—2981no—
209C2×C4—5962no—
210C2×C4—5961no—
211C2×C4—5961no—
212C2×C4—5961no—
213C2×C4—1491no—
214C2×C4—1491no—
215C2×C4—1491no—
216C2×C4D4×D14911yescharacteristic
217C8—41no—
218C8—5961no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—2982no—
224C22—2981no—
225C22—5961no—
226C22—5961no—
227C22—5962no—
228C22—5962no—
229C22—5961no—
230C22C22⋊C4×D14911yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—2981no—
236C4—2981no—
237C4—5961no—
238C4—1491no—
239C4—1491no—
240C4—11921no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—5962no—
245C2—5961no—
246C2#99×D14911yescharacteristic
subgroupG/H
centerC2#99×D149
commutatorC23×C149C22×C4
FrattiniC2×D4C22×D149
Fitting#352×C149C2
socleC2×C149C2×#99
prime radical#23750133C2
cosocleC2×D4×C149C23
hypercenter#352D149
hypocenterC149#2120
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #23749606C2semidirect
3. #23749597C2semidirect
4. #23749415C2semidirect
5. #23749413C2semidirect
6. #23749411C2semidirect
7. #352×C149C2semidirect
9. C22×C4×D149C4semidirect
11. #18011894C4semidirect
14. #18011881C4semidirect
19. #18011867C4semidirect
123. C149#2120semidirect
129. #352D149semidirect

Maximal subgroups

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

subgroupindex
#237501332
#237496062
#237495972
#237494152
#237494132
#237494112
#352×C1492
#2120149