Finite Group Databasebeta

← #34060741

Subgroups — #34060741

Order 19072.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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, complemented
2C2×#18011970C212yesmaximal, complemented
3D149⋊#99C211yesmaximal, characteristic, complemented
4#23750502C212yesmaximal, complemented
5#23750186C211yesmaximal, characteristic
6D4×#10597010—24no—
7#18011990—21no—
8C2×C22⋊#10597010—21no—
9C2×C22⋊#10597010C2212yes—
10C2×C22⋊#10597010C2212yes—
11#18011970—24no—
12#18011970—21no—
13#18011969—21no—
14C22×D596C2211yescharacteristic
15C2×D4×D149C2211yescharacteristic
16#18011896—21no—
17#18011894C411yescharacteristic, complemented
18#18011886—21no—
19#18011884—21no—
20#18011881—21no—
21#18011881C411yescharacteristic, complemented
22#18011879C411yescharacteristic, complemented
23C22⋊C4×D149C2211yescharacteristic
24#123×C149C411yescharacteristic, complemented
25C22×#10597010—22no—
26C22×#10597010—22no—
27C22×#10597010—22no—
28C4⋊#10597010—22no—
29C22⋊#10597010—22no—
30C22⋊#10597010—22no—
31C22⋊#10597010—22no—
32C22⋊#10597010—22no—
33C22⋊#10597010D414yescomplemented
34C4×#10597010—22no—
35C23×D149C2×C411yescharacteristic, complemented
36C23×D149D411yescharacteristic
37C23×D149C2311yescharacteristic
38C2×D596—22no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596—22no—
42C2×D596—21no—
43C2×D596D411yescharacteristic
44C2×C22⋊D149—21no—
45C2×C22⋊D149C2×C411yescharacteristic
46C2×C22⋊D149D411yescharacteristic
47D4×D149—22no—
48D4×D149—22no—
49C2×C4×D149—21no—
50C2×C4×D149D411yescharacteristic
51#14558715—21no—
52C22⋊Dic149C2×C411yescharacteristic, complemented
53#14558713—21no—
54#14558713—21no—
55#14558713—21no—
56#14558713—21no—
57C2×D4×C149C2×C411yescharacteristic
58C22×C4×C149C2×C411yescharacteristic, complemented
59C4⋊C4×C149—21no—
60C22⋊C4×C149—21no—
61C22⋊C4×C149C2×C411yescharacteristic, complemented
62C2×#10597010—24no—
63C2×#10597010—42no—
64C2×#10597010—82no—
65C2×#10597010—82no—
66C2×#10597010—82no—
67C22×D149—21no—
68C22×D149—21no—
69C22×D149—21no—
70C22×D149—22no—
71C22×D149—81no—
72C22×D149—81no—
73C22×D149—81no—
74C22×D149C22⋊C411yescharacteristic
75C22×D149C2×D412yes—
76C22×D149C2×D411yescharacteristic
77C22×D149C2×D411yescharacteristic
78C22×D149#4112yes—
79D596—22no—
80D596—41no—
81D596—42no—
82D596—41no—
83D596—81no—
84C22⋊D149—22no—
85C22⋊D149—22no—
86C22⋊D149—81no—
87C2×Dic149—21no—
88C2×Dic149C22⋊C411yescharacteristic
89C4×D149—21no—
90C4×D149—21no—
91C4×D149—81no—
92C23×C149C22⋊C411yescharacteristic
93C23×C149C22×C411yescharacteristic
94D4×C149—22no—
95C2×C4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149—22no—
98C2×C4×C149C22⋊C411yescharacteristic
99C22×C149—21no—
100C22×C149—41no—
101C22×C149—41no—
102C22×C149C2×C22⋊C411yescharacteristic
103C22×C149C4×D412yes—
104C2×D149—21no—
105C2×D149—41no—
106C2×D149—41no—
107C2×D149—42no—
108C2×D149—42no—
109C2×D149—42no—
110C2×D149—41no—
111C2×D149—41no—
112C2×D149—41no—
113C2×D149—41no—
114C2×D149—81no—
115C2×D149—82no—
116C2×D149#12011yescharacteristic
117C2×D149#12112yes—
118C2×D149#12311yescharacteristic
119#10597010—44no—
120#10597010—82no—
121C4×C149—21no—
122C4×C149—41no—
123C4×C149—41no—
124Dic149—21no—
125Dic149—41no—
126C2×C149—21no—
127C2×C149—22no—
128C2×C149—41no—
129C2×C149#38611yescharacteristic
130D149—21no—
131D149—22no—
132D149—21no—
133D149—41no—
134D149—81no—
135C149#191311yescharacteristic, complemented, Sylow
136#1913—1491nomaximal, Sylow
137#534—1491no—
138#518—1491no—
139C2×#99—1491no—
140C2×#99—1492no—
141#342—1492no—
142C22×D4—1491no—
143C22×D4—1491no—
144#123—2981no—
145#123—1491no—
146#123#1059701011yescharacteristic, complemented
147#121—2981no—
148#121—2981no—
149#120—2981no—
150#120—1491no—
151#120—1491no—
152C4×D4—2984no—
153#117—2981no—
154C2×C22⋊C4—2981no—
155C2×C22⋊C4—1492no—
156C2×C22⋊C4—1492no—
157C2×C22⋊C4—1491no—
158#99—2981no—
159#99—2981no—
160#99—2984no—
161C24—1491no—
162C24—1491no—
163C24—1491no—
164C2×D4—2982no—
165C2×D4—2981no—
166C2×D4—2981no—
167C2×D4—2982no—
168C2×D4—2981no—
169C2×D4—2982no—
170C2×D4—2982no—
171C2×D4—2981no—
172C2×D4—1491no—
173C2×D4—1491no—
174C2×D4—1491no—
175C2×D4C2×#1059701011yescharacteristic
176C22×C4—2981no—
177C22×C4—2982no—
178C22×C4—2982no—
179C22×C4—2982no—
180C22×C4—1491no—
181C22×C4C2×#1059701011yescharacteristic, complemented
182C4⋊C4—21no—
183C4⋊C4—2981no—
184C4⋊C4—2982no—
185C22⋊C4—21no—
186C22⋊C4—2981no—
187C22⋊C4—2981no—
188C22⋊C4—2981no—
189C22⋊C4—2982no—
190C22⋊C4—2982no—
191C22⋊C4—2981no—
192C22⋊C4—2982no—
193C22⋊C4—2982no—
194C22⋊C4—1494no—
195C22⋊C4—1491no—
196C22⋊C4C2×#1059701011yescharacteristic, complemented
197C42—2982no—
198C23—2981no—
199C23—2981no—
200C23—2981no—
201C23—2982no—
202C23—1491no—
203C23—1491no—
204C23—1491no—
205C23—1492no—
206C23—1492no—
207C23—11921no—
208C23—11921no—
209C23—11921no—
210C23C22⋊#1059701011yescharacteristic
211C23C22×#1059701011yescharacteristic
212D4—22no—
213D4—2982no—
214D4—2982no—
215D4—2982no—
216D4—5961no—
217D4—5961no—
218D4—5962no—
219D4—11921no—
220D4—11921no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—2984no—
227C2×C4—2981no—
228C2×C4—5962no—
229C2×C4—1491no—
230C2×C4—11921no—
231C2×C4—11922no—
232C2×C4—11922no—
233C2×C4—11922no—
234C2×C4C22⋊#1059701011yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—2981no—
239C22—5961no—
240C22—5962no—
241C22—5962no—
242C22—5961no—
243C22—5961no—
244C22—5961no—
245C22—5961no—
246C22—5962no—
247C22—5961no—
248C22—1491no—
249C22—1491no—
250C22—1492no—
251C22—11922no—
252C22—11921no—
253C22C2×C22⋊#1059701011yescharacteristic
254C22D4×#1059701012yes—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—2981no—
259C4—5961no—
260C4—5964no—
261C4—11922no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—2981no—
266C2—2982no—
267C2—2981no—
268C2—5961no—
269C2—11921no—
270C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#123×C149C4
socleC2×C149#386
prime radical#23750186C2
cosocleC23×D149C23
hypercenter#123#10597010
hypocenterC149#1913
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #23750692C2semidirect
2. C2×#18011970C2semidirect
3. D149⋊#99C2semidirect
4. #23750502C2semidirect
17. #18011894C4semidirect
21. #18011881C4semidirect
22. #18011879C4semidirect
24. #123×C149C4semidirect
33. C22⋊#10597010D4semidirect
35. C23×D149C2×C4semidirect
52. C22⋊Dic149C2×C4semidirect
58. C22×C4×C149C2×C4semidirect
61. C22⋊C4×C149C2×C4semidirect
135. C149#1913semidirect
146. #123#10597010semidirect
181. C22×C4C2×#10597010semidirect
196. C22⋊C4C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506922
C2×#180119702
D149⋊#992
#237505022
#237501862
#1913149