Finite Group Databasebeta

← #34060704

Subgroups — #34060704

Order 19072.

380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×D149⋊C8C211yesmaximal, characteristic
2C2×#18011974C212yesmaximal, complemented
3#23750567C211yesmaximal, characteristic
4#23750498C212yesmaximal, complemented
5C22⋊Q8×D149C211yesmaximal, characteristic
6C2×D149⋊C8—24no—
7C2×D149⋊C8—21no—
8C2×D149⋊C8C2212yes—
9C22×#11924753—21no—
10C2×C4⋊#10597010C2212yes—
11C2×C22⋊#10597010—21no—
12#18011974—24no—
13(C2×#10597010)⋊C4—21no—
14C2×Q8×D149C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16#18011891C411yescharacteristic, complemented
17#18011890C411yescharacteristic, complemented
18#18011889—21no—
19#18011888—21no—
20#18011887C411yescharacteristic, complemented
21C4⋊C4×D149—21no—
22C4⋊C4×D149C2211yescharacteristic
23C22⋊C4×D149—21no—
24C22⋊Q8×C149C411yescharacteristic, complemented
25C22×#10597010—22no—
26D149⋊C8—24no—
27D149⋊C8—22no—
28D149⋊C8D414yes—
29C2×#11924753—24no—
30C2×#11924753—22no—
31C4⋊#10597010—22no—
32C4⋊#10597010—22no—
33C22⋊#10597010—42no—
34C23×D149D411yescharacteristic
35C2×Dic298—21no—
36C2×Dic298C2×C411yescharacteristic
37Q8×D149—22no—
38Q8×D149—22no—
39C22×Dic149D411yescharacteristic
40C2×C4×D149—22no—
41C2×C4×D149—22no—
42C2×C4×D149—21no—
43C2×C4×D149—21no—
44C2×C4×D149C2×C411yescharacteristic
45C2×C4×D149D411yescharacteristic
46C2×C4×D149D411yescharacteristic
47C2×C4×D149C2311yescharacteristic
48C4⋊Dic149—21no—
49C4⋊Dic149C2×C411yescharacteristic
50#14558715—21no—
51#14558715—21no—
52#14558715—21no—
53C22⋊Dic149—21no—
54#14558713—21no—
55#14558713—21no—
56C2×Q8×C149C2×C411yescharacteristic
57C22×C4×C149C2×C411yescharacteristic
58C4⋊C4×C149—21no—
59C4⋊C4×C149C2×C411yescharacteristic
60C22⋊C4×C149—21no—
61C2×#10597010—42no—
62C2×#10597010—42no—
63C2×#10597010—42no—
64#11924753—24no—
65C22×D149—22no—
66C22×D149—22no—
67C22×D149C22⋊C411yescharacteristic
68C22×D149SD1612yes—
69C22×D149Q1612yes—
70C22×D149C2×D411yescharacteristic
71Dic298—22no—
72Dic298—41no—
73Dic298—41no—
74C2×Dic149—21no—
75C2×Dic149—21no—
76C2×Dic149—21no—
77C2×Dic149—21no—
78C2×Dic149C22⋊C411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—21no—
83C4×D149—21no—
84C4×D149—42no—
85C4×D149—42no—
86C4×D149C2×D412yes—
87C4×D149#4112yes—
88C23×C149C22⋊C411yescharacteristic
89Q8×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149C22⋊C411yescharacteristic
94C2×C4×C149C22×C411yescharacteristic
95C22×C149—21no—
96C22×C149—21no—
97C22×C149#10312yescomplemented
98C22×C149C2×C22⋊C411yescharacteristic
99C2×D149—21no—
100C2×D149—21no—
101C2×D149—24no—
102C2×D149—24no—
103C2×D149#10312yescomplemented
104C2×D149#12112yes—
105C2×D149C2×SD1611yescharacteristic
106C2×D149C2×Q1611yescharacteristic
107C2×D149#13512yes—
108#10597010—82no—
109C4×C149—21no—
110C4×C149—41no—
111C4×C149—41no—
112C4×C149C4×D412yes—
113Dic149—21no—
114Dic149—41no—
115Dic149—41no—
116Dic149#12011yescharacteristic
117Dic149#12311yescharacteristic
118C2×C149—22no—
119C2×C149#38611yescharacteristic
120C2×C149C2×#10311yescharacteristic
121C2×C149#41611yescharacteristic
122D149—22no—
123D149#46512yes—
124D149#46712yes—
125C149#189211yescharacteristic, complemented, Sylow
126#1892—1491nomaximal, Sylow
127C23×C8—1491no—
128C2×C22⋊Q8—1491no—
129C2×#103—1492no—
130#380—1491no—
131#340—1492no—
132C22×Q8—1491no—
133C23×C4—1491no—
134C22×C8—2981no—
135C22×C8—2981no—
136C22×C8—2984no—
137C22×C8—1492no—
138C22⋊Q8—2981no—
139C22⋊Q8—2981no—
140C22⋊Q8—1491no—
141C22⋊Q8—1491no—
142C22⋊Q8—1491no—
143C22⋊Q8#1059701011yescharacteristic, complemented
144C2×C4⋊C4—2981no—
145C2×C4⋊C4—1492no—
146C2×C4⋊C4—1491no—
147C2×C22⋊C4—2981no—
148C2×C22⋊C4—2981no—
149#103—2984no—
150#95—2981no—
151C24—1491no—
152C2×Q8—2981no—
153C2×Q8—2982no—
154C2×Q8—2982no—
155C2×Q8—1491no—
156C2×Q8C2×#1059701011yescharacteristic
157C22×C4—2982no—
158C22×C4—2982no—
159C22×C4—2981no—
160C22×C4—2981no—
161C22×C4—2982no—
162C22×C4—1491no—
163C22×C4—1491no—
164C22×C4—1491no—
165C22×C4—1491no—
166C22×C4—1491no—
167C22×C4C2×#1059701011yescharacteristic
168C2×C8—2984no—
169C2×C8—2984no—
170C2×C8—2982no—
171C2×C8—2982no—
172C2×C8—1494no—
173C4⋊C4—21no—
174C4⋊C4—2981no—
175C4⋊C4—2981no—
176C4⋊C4—2981no—
177C4⋊C4—2981no—
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—1491no—
181C4⋊C4C2×#1059701011yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—2981no—
184C22⋊C4—2981no—
185C22⋊C4—2981no—
186C22⋊C4—5962no—
187C23—2982no—
188C23—2982no—
189C23—1492no—
190C23—1492no—
191C23—1491no—
192C23—1491no—
193C23C22⋊#1059701011yescharacteristic
194Q8—22no—
195Q8—2982no—
196Q8—5961no—
197Q8—5961no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—2982no—
202C2×C4—2981no—
203C2×C4—2981no—
204C2×C4—2981no—
205C2×C4—2981no—
206C2×C4—2982no—
207C2×C4—2981no—
208C2×C4—2981no—
209C2×C4—5962no—
210C2×C4—5962no—
211C2×C4—5962no—
212C2×C4—5962no—
213C2×C4—5962no—
214C2×C4—1491no—
215C2×C4—1491no—
216C2×C4—1492no—
217C2×C4—1492no—
218C2×C4C22⋊#1059701011yescharacteristic
219C2×C4C22×#1059701011yescharacteristic
220C8—2984no—
221C22—21no—
222C22—21no—
223C22—2984no—
224C22—2984no—
225C22—2981no—
226C22—2981no—
227C22—1492no—
228C22—1492no—
229C22—1491no—
230C22—1491no—
231C22—1492no—
232C22#1801197412yescomplemented
233C22C2×C22⋊#1059701011yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—2981no—
238C4—5961no—
239C4—5961no—
240C4—1491no—
241C4—1491no—
242C4—11922no—
243C4D4×#1059701012yes—
244C2—22no—
245C2—2982no—
246C2—1492no—
247C2—1492no—
248C2#2375057311yescharacteristic
249C2C2×#1801197411yescharacteristic
250C2#2375061511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1892
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#18011974C2semidirect
4. #23750498C2semidirect
16. #18011891C4semidirect
17. #18011890C4semidirect
20. #18011887C4semidirect
24. C22⋊Q8×C149C4semidirect
97. C22×C149#103semidirect
103. C2×D149#103semidirect
125. C149#1892semidirect
143. C22⋊Q8#10597010semidirect
232. C22#18011974semidirect

Maximal subgroups

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

subgroupindex
C22×D149⋊C82
C2×#180119742
#237505672
#237504982
C22⋊Q8×D1492
#1892149