Finite Group Databasebeta

← #34045000

Subgroups — #34045000

Order 19072.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#18011887C211yesmaximal, characteristic
2C2×#18011869C211yesmaximal, characteristic
3C2×#18011835C211yesmaximal, characteristic, complemented
4C2×#18011823C211yesmaximal, characteristic
5#23749388C211yesmaximal, characteristic, complemented
6#23749387C211yesmaximal, characteristic, complemented
7C2×#103×C149C211yesmaximal, characteristic, complemented
8C22×C4×D149C2211yescharacteristic
9C22×#11924746C2211yescharacteristic
10#18011887—22no—
11#18011887C414yescomplemented
12#18011869—22no—
13#18011869—22no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558715—21no—
17C2×#14558713—21no—
18C2×#14558713—21no—
19C2×C4×Dic149—21no—
20#18011835—22no—
21#18011823—22no—
22C22×Q8×C149C2211yescharacteristic
23C22×C8×C149C2211yescharacteristic
24C2×C4⋊C4×C149C2211yescharacteristic
25#103×C149—22no—
26C23×D149D411yescharacteristic
27C22×Dic149—21no—
28C22×Dic149—21no—
29C22×Dic149D411yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—21no—
34C2×C4×D149C2×C412yes—
35C2×C4×D149D412yes—
36C2×#11924746—21no—
37C2×#11924746—21no—
38C2×#11924746—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149C2×C412yes—
42C4⋊Dic149D412yes—
43#14558715—24no—
44#14558713—24no—
45#14558713—24no—
46C4×Dic149—24no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—21no—
50C2×Q8×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149C2×C412yes—
53C22×C4×C149—21no—
54C22×C4×C149—21no—
55C22×C4×C149C2311yescharacteristic
56C2×C8×C149—21no—
57C2×C8×C149—21no—
58C2×C8×C149—21no—
59C4⋊C4×C149—21no—
60C4⋊C4×C149D412yes—
61C22×D149—21no—
62C22×D149—21no—
63C22×D149—21no—
64C22×D149—21no—
65C22×D149—21no—
66C22×D149—21no—
67C22×D149C22⋊C412yes—
68C2×Dic149—21no—
69C2×Dic149—21no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—41no—
73C2×Dic149—41no—
74C2×Dic149—41no—
75C2×Dic149—41no—
76C2×Dic149C22⋊C412yes—
77C4×D149—22no—
78C4×D149—22no—
79C4×D149—22no—
80C4×D149—22no—
81#11924746—41no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—22no—
84Q8×C149—22no—
85Q8×C149—41no—
86Q8×C149—41no—
87C2×C4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149—41no—
90C2×C4×C149—41no—
91C2×C4×C149—41no—
92C2×C4×C149—41no—
93C2×C4×C149C22×C411yescharacteristic
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149#4111yescharacteristic
98C2×C4×C149#4111yescharacteristic
99C8×C149—41no—
100C22×C149C2×C22⋊C411yescharacteristic
101C22×C149#12011yescharacteristic
102C22×C149#12311yescharacteristic
103C22×C149#13511yescharacteristic
104C22×C149#13511yescharacteristic
105C22×C149#13711yescharacteristic
106C22×C149#13711yescharacteristic
107C2×D149—22no—
108C2×D149—22no—
109C2×D149—22no—
110C2×D149—41no—
111C2×D149—41no—
112C2×D149—41no—
113C2×D149—41no—
114C4×C149—42no—
115C4×C149—42no—
116C4×C149C4×D411yescharacteristic
117C4×C149C4×D411yescharacteristic
118C4×C149#12111yescharacteristic
119C4×C149#12111yescharacteristic
120Dic149—22no—
121Dic149—42no—
122Dic149—42no—
123C2×C149#38611yescharacteristic
124C2×C149#41611yescharacteristic
125C2×C149#41911yescharacteristic
126C2×C149#45211yescharacteristic
127C2×C149#45211yescharacteristic
128C2×C149#48511yescharacteristic
129C2×C149#48511yescharacteristic
130D149—42no—
131C149#187311yescharacteristic, complemented, Sylow
132#1873—1491nomaximal, Sylow
133C2×C22⋊Q8—1491no—
134C2×#117—1491no—
135C2×#103—1491no—
136C2×#103D14911yescharacteristic, complemented
137C2×C22⋊C8—1491no—
138#340—1491no—
139#340—1491no—
140C22×Q8C2×D14911yescharacteristic
141C23×C4—1491no—
142C22×C8—1491no—
143C22×C8C2×D14911yescharacteristic
144C22⋊Q8—2982no—
145C22⋊Q8—1494no—
146#117—2982no—
147#117—2982no—
148C2×C4⋊C4—2981no—
149C2×C4⋊C4—1491no—
150C2×C4⋊C4—1491no—
151C2×C4⋊C4C2×D14911yescharacteristic
152C2×C22⋊C4—2981no—
153C2×C22⋊C4—2981no—
154C2×C42—2981no—
155#103—22no—
156#103—2982no—
157C22⋊C8—2982no—
158C24—1491no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D14912yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—2981no—
168C22×C4—2981no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—2981no—
172C22×C4—2981no—
173C22×C4—1491no—
174C22×C4—1492no—
175C22×C4—1492no—
176C22×C4C22×D14911yescharacteristic
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—2981no—
181C2×C8—2981no—
182C2×C8—2981no—
183C4⋊C4—21no—
184C4⋊C4—2984no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—1492no—
188C4⋊C4—1492no—
189C4⋊C4C22⋊D14912yes—
190C22⋊C4—2984no—
191C22⋊C4—2984no—
192C42—2984no—
193C23—2981no—
194C23—2981no—
195C23—2981no—
196C23—2981no—
197C23—2981no—
198C23—2981no—
199C23—1492no—
200C23D4×D14911yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2981no—
212C2×C4—2981no—
213C2×C4—2982no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—5961no—
220C2×C4—5961no—
221C2×C4—5961no—
222C2×C4—5961no—
223C2×C4—1492no—
224C2×C4C2×C4×D14911yescharacteristic
225C2×C4D4×D14911yescharacteristic
226C2×C4D4×D14911yescharacteristic
227C2×C4C2×C22⋊D14911yescharacteristic
228C2×C4#1455873511yescharacteristic
229C2×C4#1455873611yescharacteristic
230C8—41no—
231C8—5961no—
232C22—2982no—
233C22—2982no—
234C22—2982no—
235C22—5961no—
236C22—5961no—
237C22—5961no—
238C22—5961no—
239C22C22⋊C4×D14911yescharacteristic
240C22#1801187911yescharacteristic
241C22#1801189311yescharacteristic
242C22#1801193211yescharacteristic
243C22#1801193411yescharacteristic
244C22#1801194011yescharacteristic
245C22#1801194311yescharacteristic
246C4—42no—
247C4—42no—
248C4—2982no—
249C4—5962no—
250C4—5962no—
251C4#1801187111yescharacteristic
252C4C4×C22⋊D14911yescharacteristic
253C4#1801188211yescharacteristic
254C4#1801188411yescharacteristic
255C2—5962no—
256C2#2374950111yescharacteristic
257C2#2374962011yescharacteristic
258C2#2374963211yescharacteristic
259C2#2374978411yescharacteristic
260C2#2374978611yescharacteristic
261C2#2374996411yescharacteristic
262C2#2374996511yescharacteristic
subgroupG/H
centerC23D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
cosocleC22×C4×C149C23
hypercenterC2×#103D149
hypocenterC149#1873
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#18011835C2semidirect
5. #23749388C2semidirect
6. #23749387C2semidirect
7. C2×#103×C149C2semidirect
11. #18011887C4semidirect
131. C149#1873semidirect
136. C2×#103D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118872
C2×#180118692
C2×#180118352
C2×#180118232
#237493882
#237493872
C2×#103×C1492
#1873149