Finite Group Databasebeta

← #34059876

Subgroups — #34059876

Order 19072.

564 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 140 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×C4⋊#10597010C211yesmaximal, characteristic
2C2×(C2×#10597010)⋊C4C212yesmaximal
3C2×(C2×#10597010)⋊C4C211yesmaximal, characteristic
4C2×(C2×#10597010)⋊C4C212yesmaximal
5C2×C4⋊C4×D149C211yesmaximal, characteristic
6C23×#10597010C2212yes—
7C23×#10597010C2212yes—
8C2×C4⋊#10597010—24no—
9C2×C4⋊#10597010—22no—
10(C2×#10597010)⋊C4—24no—
11(C2×#10597010)⋊C4—22no—
12(C2×#10597010)⋊C4—24no—
13C22×C4×D149C2211yescharacteristic
14C22×C4×D149C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16C2×C4⋊Dic149C411yescharacteristic, complemented
17C2×#14558715C411yescharacteristic, complemented
18C2×#14558715C411yescharacteristic, complemented
19C4⋊C4×D149—22no—
20C4⋊C4×D149—22no—
21C2×C4⋊C4×C149C411yescharacteristic, complemented
22C22×#10597010—22no—
23C22×#10597010—22no—
24C22×#10597010—22no—
25C22×#10597010—22no—
26C22×#10597010—22no—
27C22×#10597010—22no—
28C22×#10597010—22no—
29C22×#10597010—22no—
30C22×#10597010—22no—
31C22×#10597010—22no—
32C22×#10597010—22no—
33C22×#10597010—22no—
34C22×#10597010D414yes—
35C22×#10597010Q814yes—
36C4⋊#10597010—28no—
37C23×D149C2311yescharacteristic
38C22×Dic149C2×C411yescharacteristic
39C22×Dic149C2×C411yescharacteristic
40C22×Dic149C2×C411yescharacteristic
41C2×C4×D149—22no—
42C2×C4×D149—21no—
43C2×C4×D149—21no—
44C2×C4×D149—21no—
45C2×C4×D149—21no—
46C2×C4×D149—22no—
47C2×C4×D149—22no—
48C2×C4×D149—21no—
49C2×C4×D149—21no—
50C2×C4×D149—22no—
51C2×C4×D149D412yes—
52C2×C4×D149D412yes—
53C2×C4×D149D412yes—
54C2×C4×D149Q812yes—
55C4⋊Dic149—22no—
56#14558715—22no—
57#14558715—22no—
58C22×C4×C149C2×C411yescharacteristic
59C22×C4×C149C2×C411yescharacteristic
60C22×C4×C149C2×C411yescharacteristic
61C4⋊C4×C149—22no—
62C2×#10597010—24no—
63C2×#10597010—24no—
64C2×#10597010—24no—
65C2×#10597010—24no—
66C2×#10597010—24no—
67C2×#10597010—24no—
68C2×#10597010—42no—
69C2×#10597010—42no—
70C2×#10597010—42no—
71C2×#10597010—42no—
72C2×#10597010—42no—
73C2×#10597010—42no—
74C2×#10597010—42no—
75C2×#10597010—42no—
76C22×D149C2×D412yes—
77C22×D149C2×D411yescharacteristic
78C22×D149C2×D411yescharacteristic
79C22×D149C2×D411yescharacteristic
80C22×D149C2×Q812yes—
81C22×D149C2×Q811yescharacteristic
82C22×D149#4111yescharacteristic
83C22×D149#4111yescharacteristic
84C22×D149#4112yes—
85C22×D149#4112yes—
86C2×Dic149—21no—
87C2×Dic149—21no—
88C2×Dic149—22no—
89C2×Dic149—21no—
90C2×Dic149—22no—
91C2×Dic149C22⋊C412yes—
92C2×Dic149C4⋊C412yescomplemented
93C4×D149—22no—
94C4×D149—22no—
95C4×D149—22no—
96C4×D149—24no—
97C4×D149—22no—
98C4×D149—22no—
99C4×D149—22no—
100C4×D149—41no—
101C4×D149—42no—
102C4×D149—41no—
103C23×C149C22×C411yescharacteristic
104C2×C4×C149—21no—
105C2×C4×C149—21no—
106C2×C4×C149—22no—
107C2×C4×C149—21no—
108C2×C4×C149—22no—
109C2×C4×C149C22⋊C412yes—
110C2×C4×C149C4⋊C412yescomplemented
111C22×C149C2×C22⋊C411yescharacteristic
112C22×C149C2×C4⋊C411yescharacteristic
113C22×C149#11711yescharacteristic
114C22×C149C4×D412yes—
115C22×C149C4×Q812yes—
116C2×D149#12011yescharacteristic
117C2×D149#12112yes—
118C2×D149#12111yescharacteristic
119C2×D149#12111yescharacteristic
120C2×D149#12112yes—
121C2×D149C22⋊Q812yes—
122C2×D149C22⋊Q811yescharacteristic
123C2×D149C22⋊Q812yes—
124C2×D149C22⋊Q812yes—
125C2×D149C22⋊Q811yescharacteristic
126C2×D149#12312yes—
127C2×D149#12311yescharacteristic
128C2×D149#12411yescharacteristic
129C2×D149#12512yes—
130C2×D149#12512yes—
131C2×D149#12612yes—
132C2×D149C4⋊Q812yes—
133C2×D149C4⋊Q811yescharacteristic
134#10597010—44no—
135#10597010—44no—
136C4×C149—22no—
137C4×C149—22no—
138C4×C149—41no—
139Dic149—22no—
140Dic149—22no—
141Dic149—41no—
142C2×C149#38011yescharacteristic
143C2×C149#38611yescharacteristic
144C2×C149#38712yes—
145C2×C149#38912yes—
146C2×C149#39111yescharacteristic
147D149#39411yescharacteristic
148D149#39511yescharacteristic
149D149#39612yes—
150D149#39811yescharacteristic
151D149#39812yes—
152D149#40011yescharacteristic
153C149#144111yescharacteristic, complemented, Sylow
154#1441—1491nomaximal, Sylow
155C22×C4⋊C4—1491no—
156C22×C4⋊C4—1491no—
157C2×#95—1492no—
158C2×#95—1492no—
159C2×#95—1491no—
160C23×C4—1492no—
161C23×C4—1492no—
162C23×C4—1491no—
163C23×C4—1491no—
164C23×C4—1491no—
165C2×C4⋊C4—2982no—
166C2×C4⋊C4—2982no—
167C2×C4⋊C4—2984no—
168C2×C4⋊C4—2982no—
169C2×C4⋊C4—1491no—
170C2×C4⋊C4—1491no—
171C2×C4⋊C4—1491no—
172C2×C4⋊C4#1059701011yescharacteristic, complemented
173#95—2984no—
174#95—2982no—
175#95—2984no—
176C24—1491no—
177C22×C4—2981no—
178C22×C4—2981no—
179C22×C4—2982no—
180C22×C4—2981no—
181C22×C4—2981no—
182C22×C4—2982no—
183C22×C4—2982no—
184C22×C4—2981no—
185C22×C4—2981no—
186C22×C4—2982no—
187C22×C4—2982no—
188C22×C4—2982no—
189C22×C4—2982no—
190C22×C4—2982no—
191C22×C4—2982no—
192C22×C4—2982no—
193C22×C4—2982no—
194C22×C4—2982no—
195C22×C4—2982no—
196C22×C4—2982no—
197C22×C4—2982no—
198C22×C4—2982no—
199C22×C4—1494no—
200C22×C4—1494no—
201C22×C4—1491no—
202C22×C4—1491no—
203C22×C4—1491no—
204C22×C4—1492no—
205C22×C4—1492no—
206C22×C4—1492no—
207C22×C4—1492no—
208C22×C4C2×#1059701011yescharacteristic
209C22×C4C2×#1059701011yescharacteristic
210C22×C4C2×#1059701011yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—2982no—
213C4⋊C4—2982no—
214C4⋊C4—2988no—
215C4⋊C4—2982no—
216C23—1491no—
217C23—1491no—
218C23—1491no—
219C23—1491no—
220C23—1491no—
221C23—1491no—
222C23—1492no—
223C23—1492no—
224C23—1492no—
225C23—1492no—
226C23C22×#1059701011yescharacteristic
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—2982no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4—2982no—
236C2×C4—2982no—
237C2×C4—2984no—
238C2×C4—2982no—
239C2×C4—2981no—
240C2×C4—2981no—
241C2×C4—2982no—
242C2×C4—2984no—
243C2×C4—2984no—
244C2×C4—2984no—
245C2×C4—2984no—
246C2×C4—2984no—
247C2×C4—2984no—
248C2×C4—2981no—
249C2×C4—2982no—
250C2×C4—5961no—
251C2×C4—5962no—
252C2×C4—5961no—
253C2×C4—5962no—
254C2×C4—5962no—
255C2×C4—5962no—
256C2×C4—5962no—
257C2×C4—5962no—
258C2×C4—5962no—
259C2×C4—5962no—
260C2×C4—5962no—
261C2×C4—1492no—
262C2×C4—1492no—
263C2×C4C22⋊#1059701012yes—
264C2×C4C4⋊#1059701012yescomplemented
265C22—1491no—
266C22—1491no—
267C22—1491no—
268C22—1491no—
269C22—1491no—
270C22—1492no—
271C22—1491no—
272C22—1492no—
273C22—1492no—
274C22—1492no—
275C22—1492no—
276C22—1492no—
277C22—1492no—
278C22—1492no—
279C22—1492no—
280C22—1492no—
281C22—1491no—
282C22—1491no—
283C22C2×C22⋊#1059701011yescharacteristic
284C22C2×C4⋊#1059701011yescharacteristic
285C22#1801199011yescharacteristic
286C22D4×#1059701012yes—
287C22Q8×#1059701012yes—
288C4—22no—
289C4—22no—
290C4—41no—
291C4—2982no—
292C4—2982no—
293C4—5964no—
294C4—5964no—
295C4—5961no—
296C2—1491no—
297C2—1492no—
298C2—1491no—
299C2—1491no—
300C2—1492no—
301C2—1491no—
302C2#2375056711yescharacteristic
303C2#2375057311yescharacteristic
304C2#2375057412yes—
305C2#2375057612yes—
306C2(C2×#10597010)⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C22×#10597010
commutator, socleC23×C149C22×C4
FittingC2×C4⋊C4×C149C4
prime radical, cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1441
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic149C4semidirect
17. C2×#14558715C4semidirect
18. C2×#14558715C4semidirect
21. C2×C4⋊C4×C149C4semidirect
92. C2×Dic149C4⋊C4semidirect
110. C2×C4×C149C4⋊C4semidirect
153. C149#1441semidirect
172. C2×C4⋊C4#10597010semidirect
264. C2×C4C4⋊#10597010semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#105970102
C2×(C2×#10597010)⋊C42
C2×C4⋊C4×D1492
#1441149