Finite Group Databasebeta

← #34060715

Subgroups — #34060715

Order 19072.

378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 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×#18011990C211yesmaximal, characteristic, complemented
2C2×#18011970C212yesmaximal
3#23750568C211yesmaximal, characteristic, complemented
4#23750503C212yesmaximal, complemented
5C2×#18011896C211yesmaximal, characteristic
6#18011990—24no—
7C2×C4⋊#10597010—21no—
8C2×C22⋊#10597010C2212yes—
9C2×C22⋊#10597010C2212yes—
10C2×C4×#10597010—21no—
11#18011970—24no—
12(C2×#10597010)⋊C4—21no—
13(C2×#10597010)⋊C4—21no—
14C22×D596C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16#18011896—21no—
17#18011896—21no—
18#18011896—21no—
19#18011896—21no—
20C2×#14558715C411yescharacteristic, complemented
21C2×#14558713C411yescharacteristic, complemented
22C2×#14558713C411yescharacteristic, complemented
23C2×#14558713C2211yescharacteristic
24C2×C4⋊C4×C149C411yescharacteristic, complemented
25C22×#10597010—22no—
26C22×#10597010—22no—
27C4⋊#10597010—24no—
28C22⋊#10597010—22no—
29C22⋊#10597010—22no—
30C22⋊#10597010—22no—
31C22⋊#10597010D414yes—
32C4×#10597010—24no—
33C23×D149C2×C411yescharacteristic
34C23×D149C2311yescharacteristic
35C2×D596—22no—
36C2×D596—21no—
37C2×D596—21no—
38C2×D596—22no—
39C22×Dic149C2×C411yescharacteristic
40C22×Dic149C2×C411yescharacteristic
41C2×C4×D149—22no—
42C2×C4×D149—22no—
43C2×C4×D149D411yescharacteristic
44C2×C4×D149D411yescharacteristic
45C2×C4×D149D411yescharacteristic
46C2×C4×D149D411yescharacteristic
47#14558715—21no—
48#14558715—21no—
49#14558713—21no—
50#14558713—21no—
51#14558713—21no—
52#14558713—21no—
53#14558713—21no—
54#14558713—21no—
55C22×C4×C149C2×C411yescharacteristic
56C22×C4×C149C2×C411yescharacteristic
57C22×C4×C149C2×C411yescharacteristic
58C4⋊C4×C149—21no—
59C4⋊C4×C149—21no—
60C2×#10597010—24no—
61C2×#10597010—42no—
62C2×#10597010—42no—
63C2×#10597010—42no—
64C2×#10597010—42no—
65C2×#10597010—42no—
66C22×D149—21no—
67C22×D149—22no—
68C22×D149—41no—
69C22×D149—41no—
70C22×D149—41no—
71C22×D149—41no—
72C22×D149C2×D411yescharacteristic
73C22×D149C2×D411yescharacteristic
74C22×D149C2×D412yes—
75C22×D149#4112yes—
76D596—41no—
77D596—42no—
78D596—41no—
79C2×Dic149—22no—
80C2×Dic149—21no—
81C2×Dic149—41no—
82C2×Dic149C22⋊C411yescharacteristic
83C2×Dic149C22⋊C411yescharacteristic
84C4×D149—21no—
85C4×D149—21no—
86C4×D149—22no—
87C4×D149—22no—
88C4×D149—21no—
89C4×D149—21no—
90C23×C149C22×C411yescharacteristic
91C2×C4×C149—22no—
92C2×C4×C149—21no—
93C2×C4×C149—21no—
94C2×C4×C149—22no—
95C2×C4×C149—41no—
96C2×C4×C149C22⋊C411yescharacteristic
97C2×C4×C149C22⋊C411yescharacteristic
98C22×C149—21no—
99C22×C149—21no—
100C22×C149C2×C22⋊C411yescharacteristic
101C22×C149C4×D412yes—
102C2×D149—21no—
103C2×D149—21no—
104C2×D149—21no—
105C2×D149—21no—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—41no—
109C2×D149—41no—
110C2×D149—41no—
111C2×D149—82no—
112C2×D149#12011yescharacteristic
113C2×D149#12112yes—
114C2×D149#12311yescharacteristic
115#10597010—44no—
116#10597010—82no—
117C4×C149—21no—
118C4×C149—21no—
119C4×C149—41no—
120C4×C149—41no—
121Dic149—21no—
122Dic149—21no—
123Dic149—41no—
124C2×C149—22no—
125C2×C149#38611yescharacteristic
126C2×C149#41011yescharacteristic
127C2×C149#41011yescharacteristic
128D149—21no—
129D149—22no—
130D149—21no—
131D149—81no—
132C149#189911yescharacteristic, complemented, Sylow
133#1899—1491nomaximal, Sylow
134C2×#123—1491no—
135C2×#117—1491no—
136C2×#99—1492no—
137#381—1491no—
138#342—1492no—
139C22×D4—1491no—
140C23×C4—1491no—
141#123—2981no—
142#123—2981no—
143#123—2981no—
144#123—2981no—
145#117—2984no—
146C2×C4⋊C4—2981no—
147C2×C4⋊C4—1491no—
148C2×C4⋊C4#1059701011yescharacteristic, complemented
149C2×C22⋊C4—1492no—
150C2×C22⋊C4—1491no—
151C2×C22⋊C4—1491no—
152C2×C22⋊C4—1491no—
153C2×C22⋊C4—1492no—
154C2×C42—2981no—
155#99—2984no—
156#95—2981no—
157#95—2981no—
158C24—1491no—
159C24—1491no—
160C2×D4—2982no—
161C2×D4—2981no—
162C2×D4—2981no—
163C2×D4—2982no—
164C22×C4—2982no—
165C22×C4—2982no—
166C22×C4—2982no—
167C22×C4—2982no—
168C22×C4—1491no—
169C22×C4—1491no—
170C22×C4—1491no—
171C22×C4—1491no—
172C22×C4—1491no—
173C22×C4—1491no—
174C22×C4C2×#1059701011yescharacteristic
175C22×C4C2×#1059701011yescharacteristic
176C22×C4C2×#1059701011yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—2981no—
180C4⋊C4—2981no—
181C4⋊C4—2984no—
182C22⋊C4—2981no—
183C22⋊C4—2981no—
184C22⋊C4—2981no—
185C22⋊C4—2981no—
186C22⋊C4—2982no—
187C22⋊C4—2981no—
188C22⋊C4—2981no—
189C22⋊C4—2982no—
190C22⋊C4—2982no—
191C22⋊C4—1494no—
192C42—2984no—
193C23—2981no—
194C23—2982no—
195C23—5961no—
196C23—5961no—
197C23—5961no—
198C23—5961no—
199C23—1491no—
200C23—1491no—
201C23—1492no—
202C23—1492no—
203C23C22×#1059701011yescharacteristic
204D4—5961no—
205D4—5962no—
206D4—5961no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—2981no—
213C2×C4—2981no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4—2981no—
217C2×C4—2981no—
218C2×C4—2982no—
219C2×C4—2984no—
220C2×C4—2981no—
221C2×C4—5962no—
222C2×C4—5962no—
223C2×C4—5961no—
224C2×C4—5962no—
225C2×C4—5962no—
226C2×C4—5962no—
227C2×C4—1491no—
228C2×C4—1491no—
229C2×C4C22⋊#1059701011yescharacteristic
230C2×C4C22⋊#1059701011yescharacteristic
231C22—21no—
232C22—21no—
233C22—2981no—
234C22—2981no—
235C22—2981no—
236C22—2981no—
237C22—5962no—
238C22—5962no—
239C22—5961no—
240C22—5961no—
241C22—5961no—
242C22—1491no—
243C22—1492no—
244C22—1491no—
245C22—11922no—
246C22C2×C22⋊#1059701011yescharacteristic
247C22D4×#1059701012yes—
248C4—21no—
249C4—21no—
250C4—41no—
251C4—41no—
252C4—2981no—
253C4—2981no—
254C4—5964no—
255C4—5961no—
256C4—11922no—
257C2—22no—
258C2—2981no—
259C2—2982no—
260C2—2981no—
261C2—11921no—
262C2#2375057311yescharacteristic
263C2#2375060411yescharacteristic
264C2#2375060611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C22
cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1899
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#18011990C2semidirect
3. #23750568C2semidirect
4. #23750503C2semidirect
20. C2×#14558715C4semidirect
21. C2×#14558713C4semidirect
22. C2×#14558713C4semidirect
24. C2×C4⋊C4×C149C4semidirect
132. C149#1899semidirect
148. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119902
C2×#180119702
#237505682
#237505032
C2×#180118962
#1899149