Finite Group Databasebeta

← #34053988

Subgroups — #34053988

Order 19072.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011958C211yesmaximal, characteristic
2C2×#18011944C211yesmaximal, characteristic, complemented
3C22×Dic596C211yesmaximal, characteristic, complemented
4#23750196C211yesmaximal, characteristic, complemented
5#23749789C214yesmaximal, complemented
6#23749783C214yesmaximal, complemented
7#23749635C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9#408×C149C211yesmaximal, characteristic, complemented
10#18011958—24no—
11#18011958—24no—
12C2×#14558736C2212yes—
13C2×#14558736C2211yescharacteristic
14C2×#14558735—22no—
15C2×#14558735—21no—
16C22×Dic298C2211yescharacteristic
17C22×Dic298C2212yes—
18C22×Dic298C2211yescharacteristic
19C2×Q8×D149—21no—
20#18011944—24no—
21C2×Dic596—24no—
22C2×Dic596C2214yes—
23C2×Dic596C2212yes—
24C2×#14558725C2212yes—
25#18011909—21no—
26#18011898—21no—
27#18011892—22no—
28#18011890C2214yes—
29#18011870C2211yescharacteristic
30#18011836C2214yes—
31#18011836C2212yes—
32#18011833C2212yes—
33C2×#41×C149C2211yescharacteristic
34C2×M16×C149C2211yescharacteristic
35C22×C8×C149C2211yescharacteristic
36C22⋊C8×C149C2214yes—
37#14558736—24no—
38#14558736—24no—
39#14558736—22no—
40#14558736D414yes—
41#14558735—216no—
42#14558735—28no—
43C2×Dic298—24no—
44C2×Dic298—24no—
45C2×Dic298—22no—
46C2×Dic298—21no—
47C2×Dic298—22no—
48C2×Dic298—21no—
49C2×Dic298—22no—
50C2×Dic298—22no—
51C2×Dic298D414yes—
52C2×Dic298C2312yes—
53C2×Dic298C2311yescharacteristic
54C2×Dic298C2312yes—
55Q8×D149—28no—
56C2×D596C2311yescharacteristic
57C2×C22⋊D149—22no—
58C2×C22⋊D149—21no—
59C22×Dic149—22no—
60C22×Dic149—21no—
61C22×Dic149—21no—
62C2×C4×D149—22no—
63C2×C4×D149—21no—
64Dic596—28no—
65Dic596—24no—
66#14558725—24no—
67C4⋊Dic149C2312yes—
68#14558715—24no—
69C22⋊Dic149—21no—
70C22⋊Dic149—24no—
71C4×Dic149—21no—
72#41×C149—22no—
73#41×C149—22no—
74C2×Q8×C149D411yescharacteristic
75C2×D4×C149D412yes—
76C2×D4×C149D411yescharacteristic
77C22×C4×C149C2312yes—
78C22×C4×C149C2311yescharacteristic
79M16×C149—22no—
80C2×C8×C149—22no—
81C2×C8×C149C2312yes—
82C2×C8×C149C2312yes—
83C22×D149—21no—
84Dic298—28no—
85Dic298—24no—
86Dic298—21no—
87Dic298—22no—
88Dic298—22no—
89Dic298—22no—
90Dic298—42no—
91Dic298C2×D412yes—
92Dic298C2×D414yes—
93D596—21no—
94D596C2×D412yes—
95C22⋊D149—28no—
96C22⋊D149—24no—
97C2×Dic149—28no—
98C2×Dic149—24no—
99C2×Dic149—22no—
100C2×Dic149—21no—
101C2×Dic149—22no—
102C2×Dic149—22no—
103C2×Dic149—42no—
104C4×D149—28no—
105C4×D149—24no—
106C23×C149C2×D412yes—
107C23×C149C2×D411yescharacteristic
108Q8×C149—22no—
109D4×C149—24no—
110D4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149C2×D412yes—
114C2×C4×C149C2×D412yes—
115C2×C4×C149C2×D412yes—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—22no—
119C8×C149—22no—
120C22×C149—22no—
121C22×C149—22no—
122C22×C149—24no—
123C22×C149#12012yes—
124C22×C149C22×D411yescharacteristic
125C2×D149—22no—
126C2×D149—42no—
127C4×C149—22no—
128C4×C149#12012yes—
129C4×C149C22×D411yescharacteristic
130C4×C149C22×D411yescharacteristic
131Dic149—24no—
132Dic149—22no—
133Dic149—42no—
134Dic149—42no—
135C2×C149—22no—
136C2×C149—42no—
137C2×C149C2×#12011yescharacteristic
138C2×C149#57812yes—
139D149—42no—
140C149#301111yescharacteristic, complemented, Sylow
141#3011—1491nomaximal, Sylow
142C2×2−1+4—1491no—
143C2×#137—1491no—
144C22×Q16—1491no—
145#536—1491no—
146#452—1494no—
147#451—1494no—
148#419—1491no—
149#416—1491no—
150#408D14911yescharacteristic, complemented
1512−1+4—2984no—
1522−1+4—2984no—
153C2×#41—2982no—
154C2×#41—2981no—
155C2×#41—1492no—
156C2×#41—1491no—
157C2×#41C2×D14911yescharacteristic
158C22×Q8—2981no—
159C22×Q8—1491no—
160C22×Q8—1492no—
161C22×Q8—1491no—
162#137—2984no—
163C2×Q16—2984no—
164C2×Q16—1494no—
165C2×Q16—1492no—
166C2×SD16—1492no—
167C2×M16C2×D14911yescharacteristic
168C22×C8C2×D14911yescharacteristic
169C4⋊Q8—2981no—
170#124—2981no—
171#123—2982no—
172C22⋊Q8—1494no—
173#117—1491no—
174#103—1492no—
175#103—1494no—
176#102—1492no—
177C22⋊C8C2×D14914yes—
178#41—22no—
179#41—22no—
180#41—2984no—
181#41—2984no—
182#41—29816no—
183#41—2988no—
184#41—2982no—
185#41—1494no—
186C2×Q8—2984no—
187C2×Q8—2984no—
188C2×Q8—2988no—
189C2×Q8—2982no—
190C2×Q8—2982no—
191C2×Q8—2981no—
192C2×Q8—2981no—
193C2×Q8—2982no—
194C2×Q8—2982no—
195C2×Q8—1494no—
196C2×Q8—1492no—
197C2×Q8—1491no—
198C2×Q8—1492no—
199C2×Q8D59611yescharacteristic
200C2×D4—2982no—
201C2×D4—2981no—
202C2×D4—1491no—
203C2×D4D59612yes—
204C2×D4D59611yescharacteristic
205C22×C4—2982no—
206C22×C4—2981no—
207C22×C4—2982no—
208C22×C4—2981no—
209C22×C4—2981no—
210C22×C4C22×D14912yes—
211C22×C4C22×D14911yescharacteristic
212Q16—2988no—
213Q16—2984no—
214SD16—2984no—
215M16—22no—
216C2×C8—22no—
217C2×C8C22×D14912yes—
218C2×C8C22×D14912yes—
219C4⋊C4—2984no—
220C4⋊C4—1492no—
221C22⋊C4—2981no—
222C22⋊C4—2984no—
223C42—2981no—
224C23—2981no—
225C23C2×D59612yes—
226C23C2×D59611yescharacteristic
227Q8—22no—
228Q8—2988no—
229Q8—2981no—
230Q8—2982no—
231Q8—2984no—
232Q8—2982no—
233Q8—2982no—
234Q8—5962no—
235Q8—1492no—
236Q8—1494no—
237D4—24no—
238D4—22no—
239D4—2988no—
240D4—2984no—
241D4—2981no—
242D4—1492no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—2988no—
246C2×C4—2988no—
247C2×C4—2982no—
248C2×C4—2981no—
249C2×C4—2984no—
250C2×C4—2984no—
251C2×C4—2982no—
252C2×C4—2982no—
253C2×C4—5962no—
254C2×C4D4×D14912yes—
255C2×C4D4×D14912yes—
256C2×C4C2×D59612yes—
257C2×C4C2×D59611yescharacteristic
258C2×C4C23×D14911yescharacteristic
259C8—22no—
260C8—22no—
261C22—22no—
262C22—24no—
263C22—22no—
264C22—2982no—
265C22—5962no—
266C22#1801188112yes—
267C22C22×D59611yescharacteristic
268C4—22no—
269C4—2984no—
270C4—2982no—
271C4—5962no—
272C4—5962no—
273C4#1801188112yes—
274C4C2×D4×D14911yescharacteristic
275C4C2×D4×D14911yescharacteristic
276C2—22no—
277C2—42no—
278C2—5962no—
279C2C2×#1801188111yescharacteristic
280C2#2375044212yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#408×C149C2
socleC22×C149C22×D4
prime radicalC2×#18011958C2
hypercenter#408D149
hypocenterC149#3011
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#18011944C2semidirect
3. C22×Dic596C2semidirect
4. #23750196C2semidirect
5. #23749789C2semidirect
6. #23749783C2semidirect
7. #23749635C2semidirect
8. #23749622C2semidirect
9. #408×C149C2semidirect
140. C149#3011semidirect
150. #408D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
C2×#180119442
C22×Dic5962
#237501962
#237497892
#237497832
#237496352
#237496222
#408×C1492
#3011149