Finite Group Databasebeta

← #34060561

Subgroups — #34060561

Order 19072.

356 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D149⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#18011973C212yesmaximal
3#23750569C211yesmaximal, characteristic, complemented
4#23750498C212yesmaximal, complemented
5C4×D4×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010C2212yes—
8#18011978—21no—
9C4⋊#11924753—21no—
10#18011973—24no—
11(C2×#10597010)⋊C4—21no—
12(C2×#10597010)⋊C4—21no—
13C2×D4×D149C2211yescharacteristic
14C22×C4×D149—21no—
15C4×D596C411yescharacteristic, complemented
16D4×Dic149C411yescharacteristic, complemented
17#18011873C411yescharacteristic, complemented
18C4×C22⋊D149—21no—
19#18011871—21no—
20C4⋊C4×D149C2211yescharacteristic
21C22⋊C4×D149—21no—
22C42×D149C2211yescharacteristic
23C4×D4×C149C411yescharacteristic, complemented
24C22×#10597010—22no—
25D149⋊C8—22no—
26D149⋊C8—22no—
27C2×#11924753—22no—
28C4⋊#10597010—22no—
29C4⋊#10597010—22no—
30C23×D149—21no—
31C2×D596C2×C411yescharacteristic
32C2×C22⋊D149—21no—
33D4×D149—21no—
34D4×D149—21no—
35D4×D149D412yes—
36D4×D149Q812yes—
37C22×Dic149—21no—
38C2×C4×D149—21no—
39C2×C4×D149—21no—
40C2×C4×D149—21no—
41C2×C4×D149—44no—
42C2×C4×D149D411yescharacteristic
43C2×C4×D149D411yescharacteristic
44C2×C4×D149C2311yescharacteristic
45C4⋊Dic149C2×C411yescharacteristic
46#14558715—21no—
47C22⋊Dic149—21no—
48#14558713—21no—
49#14558713—21no—
50C4×Dic149C2×C411yescharacteristic
51C4×Dic149D411yescharacteristic
52C4×Dic149D411yescharacteristic
53C2×D4×C149C2×C411yescharacteristic
54C22×C4×C149—21no—
55C4⋊C4×C149C2×C411yescharacteristic
56C22⋊C4×C149—21no—
57C42×C149C2×C411yescharacteristic
58C2×#10597010—42no—
59C2×#10597010—42no—
60C2×#10597010—42no—
61#11924753—42no—
62C22×D149—21no—
63C22×D149—22no—
64C22×D149—22no—
65C22×D149—42no—
66C22×D149—42no—
67C22×D149C2×D411yescharacteristic
68D596—21no—
69D596C4⋊C412yes—
70C22⋊D149—22no—
71C22⋊D149—22no—
72C2×Dic149—21no—
73C2×Dic149—42no—
74C2×Dic149C22⋊C411yescharacteristic
75C2×Dic149C22⋊C411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C4×D149—22no—
78C4×D149—22no—
79C4×D149—42no—
80C4×D149—42no—
81C4×D149—42no—
82C4×D149C2×D411yescharacteristic
83C4×D149C2×Q811yescharacteristic
84C4×D149#4111yescharacteristic
85C4×D149#4111yescharacteristic
86C23×C149—21no—
87D4×C149—21no—
88D4×C149C4⋊C412yes—
89C2×C4×C149—21no—
90C2×C4×C149—42no—
91C2×C4×C149C22⋊C411yescharacteristic
92C2×C4×C149C22⋊C411yescharacteristic
93C2×C4×C149C22×C411yescharacteristic
94C22×C149—22no—
95C22×C149—41no—
96C22×C149—41no—
97C22×C149C2×C22⋊C411yescharacteristic
98C2×D149—22no—
99C2×D149—41no—
100C2×D149—41no—
101C2×D149—44no—
102C2×D149—44no—
103C2×D149#12111yescharacteristic
104C2×D149C22⋊Q811yescharacteristic
105C2×D149#13512yes—
106C2×D149AGL(1,ℤ/8)12yes—
107#10597010—82no—
108C4×C149—21no—
109C4×C149—21no—
110C4×C149—41no—
111C4×C149C2×C4⋊C411yescharacteristic
112C4×C149#11711yescharacteristic
113Dic149—21no—
114Dic149—21no—
115Dic149—41no—
116Dic149#12111yescharacteristic
117Dic149C22⋊Q811yescharacteristic
118C2×C149—42no—
119C2×C149#38011yescharacteristic
120C2×C149#41611yescharacteristic
121C2×C149#41811yescharacteristic
122D149—42no—
123D149#46312yes—
124D149#47812yes—
125C149#180411yescharacteristic, complemented, Sylow
126#1804—1491nomaximal, Sylow
127C2×C4×D4—1491no—
128C2×C4⋊C8—1491no—
129C2×#102—1492no—
130#382—1491no—
131#340—1492no—
132C22×D4—1491no—
133C23×C4—2981no—
134C22×C8—1492no—
135C4×D4—2981no—
136C4×D4—2981no—
137C4×D4—1491no—
138C4×D4—1491no—
139C4×D4—1491no—
140C4×D4#1059701011yescharacteristic, complemented
141C2×C4⋊C4—1492no—
142C2×C4⋊C4—1491no—
143C2×C22⋊C4—2981no—
144C2×C42—1491no—
145C4⋊C8—2981no—
146C4⋊C8—2981no—
147#102—2984no—
148#95—2981no—
149#95—2981no—
150C24—2981no—
151C2×D4—2981no—
152C2×D4—2981no—
153C2×D4—2981no—
154C2×D4—1492no—
155C2×D4—1492no—
156C2×D4—1491no—
157C2×D4C2×#1059701011yescharacteristic
158C22×C4—21no—
159C22×C4—2981no—
160C22×C4—2981no—
161C22×C4—2981no—
162C22×C4—2981no—
163C22×C4—2982no—
164C22×C4—5964no—
165C22×C4—1491no—
166C22×C4—1491no—
167C22×C4—1491no—
168C2×C8—2982no—
169C2×C8—2982no—
170C2×C8—2982no—
171C4⋊C4—2981no—
172C4⋊C4—2982no—
173C4⋊C4—2982no—
174C4⋊C4—1491no—
175C4⋊C4C2×#1059701011yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—2981no—
178C22⋊C4—2981no—
179C22⋊C4—2981no—
180C42—1491no—
181C42—1491no—
182C42—1491no—
183C42C2×#1059701011yescharacteristic
184C23—21no—
185C23—2982no—
186C23—2982no—
187C23—2981no—
188C23—5962no—
189C23—5962no—
190C23—1491no—
191D4—21no—
192D4—2982no—
193D4—2982no—
194D4—2981no—
195D4—1492no—
196D4C4⋊#1059701012yes—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2981no—
202C2×C4—5962no—
203C2×C4—5962no—
204C2×C4—5962no—
205C2×C4—5962no—
206C2×C4—5962no—
207C2×C4—5962no—
208C2×C4—5962no—
209C2×C4—1491no—
210C2×C4—1491no—
211C2×C4—1491no—
212C2×C4—1491no—
213C2×C4—1491no—
214C2×C4—1491no—
215C2×C4—1491no—
216C2×C4C22⋊#1059701011yescharacteristic
217C2×C4C22⋊#1059701011yescharacteristic
218C2×C4C22×#1059701011yescharacteristic
219C8—5962no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—2982no—
224C22—5964no—
225C22—5964no—
226C22—5961no—
227C22—5961no—
228C22—1491no—
229C22—1491no—
230C22—1492no—
231C22—1492no—
232C22C2×C22⋊#1059701011yescharacteristic
233C4—21no—
234C4—21no—
235C4—41no—
236C4—2981no—
237C4—2981no—
238C4—5961no—
239C4—1491no—
240C4—1491no—
241C4—11922no—
242C4C2×C4⋊#1059701011yescharacteristic
243C4#1801199011yescharacteristic
244C2—42no—
245C2—5962no—
246C2—1492no—
247C2—1492no—
248C2#2375056711yescharacteristic
249C2#2375061511yescharacteristic
250C2#2375061711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×D4×D149C22
cosocleC2×C4×D149C23
hypercenterC4×D4#10597010
hypocenterC149#1804
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D149⋊(C4⋊C8)C2semidirect
3. #23750569C2semidirect
4. #23750498C2semidirect
15. C4×D596C4semidirect
16. D4×Dic149C4semidirect
17. #18011873C4semidirect
23. C4×D4×C149C4semidirect
125. C149#1804semidirect
140. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C4⋊C8)2
C2×#180119732
#237505692
#237504982
C4×D4×D1492
#1804149