Finite Group Databasebeta

← #34055089

Subgroups — #34055089

Order 19072.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#23750171C211yesmaximal, characteristic
2C2×#18011902C211yesmaximal, characteristic, complemented
3#23749992C212yesmaximal, complemented
4#23749988C212yesmaximal, complemented
5#23749981C212yesmaximal, complemented
6#23749978C212yesmaximal, complemented
7#23749627C211yesmaximal, characteristic, complemented
8#23749626C211yesmaximal, characteristic, complemented
9#23749624C211yesmaximal, characteristic, complemented
10M16×Dic149C211yesmaximal, characteristic, complemented
11#417×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C2×#14558720C2211yescharacteristic
14#18011909C2211yescharacteristic
15#18011907C2211yescharacteristic
16#18011902—21no—
17#18011902—21no—
18#18011902C2212yes—
19#18011902C2212yes—
20#18011900C2211yescharacteristic
21#18011898C2211yescharacteristic
22#18011883—21no—
23#18011883—21no—
24C4×C22⋊D149—21no—
25C4×C22⋊D149—21no—
26C2×C4⋊Dic149—21no—
27C2×C4⋊Dic149C2211yescharacteristic
28C2×#14558715—21no—
29C2×C4×Dic149C2211yescharacteristic
30#18011836C2212yes—
31#18011835C2212yes—
32#18011834C2212yes—
33#18011833C2212yes—
34#18011832C2212yes—
35#18011831C2212yes—
36#18011821C2212yes—
37C8×Dic149C2212yes—
38C2×#41×C149C2211yescharacteristic
39C2×M16×C149C2211yescharacteristic
40C2×C4⋊C4×C149C2211yescharacteristic
41#103×C149C2212yes—
42#102×C149C2212yes—
43#14558736—22no—
44#14558736—22no—
45C2×Dic298C2311yescharacteristic
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—21no—
48C2×C22⋊D149—21no—
49C2×C22⋊D149—21no—
50C22×Dic149—21no—
51C22×Dic149D411yescharacteristic
52C22×Dic149D411yescharacteristic
53C2×C4×D149—21no—
54#14558720—22no—
55C2×#11924746C2312yes—
56C4⋊Dic149—22no—
57C4⋊Dic149—22no—
58C4⋊Dic149—21no—
59C4⋊Dic149C2312yes—
60#14558715—21no—
61#14558715—21no—
62#14558715—22no—
63#14558715—22no—
64C22⋊Dic149—21no—
65C22⋊Dic149—21no—
66#14558713—21no—
67#14558713—21no—
68C4×Dic149D411yescharacteristic
69C4×Dic149D411yescharacteristic
70C4×Dic149C2311yescharacteristic
71C4×Dic149C2311yescharacteristic
72#41×C149—22no—
73#41×C149—22no—
74C2×Q8×C149C2311yescharacteristic
75C2×D4×C149—21no—
76C2×D4×C149C2311yescharacteristic
77C22×C4×C149—21no—
78C22×C4×C149—21no—
79C22×C4×C149C2311yescharacteristic
80M16×C149—22no—
81C2×C8×C149C2312yes—
82C4⋊C4×C149—21no—
83C4⋊C4×C149C2312yes—
84C22×D149—21no—
85Dic298—21no—
86Dic298—21no—
87D596—21no—
88D596—21no—
89C22⋊D149—42no—
90C22⋊D149—42no—
91C22⋊D149—42no—
92C2×Dic149—21no—
93C2×Dic149—22no—
94C2×Dic149—41no—
95C2×Dic149—41no—
96C2×Dic149—42no—
97C2×Dic149C2×D411yescharacteristic
98C2×Dic149C2×D411yescharacteristic
99C2×Dic149C2×D411yescharacteristic
100C2×Dic149C2×D411yescharacteristic
101C4×D149—42no—
102#11924746—22no—
103C23×C149—21no—
104C23×C149C2×D411yescharacteristic
105Q8×C149—21no—
106Q8×C149—21no—
107D4×C149—21no—
108D4×C149—21no—
109D4×C149—42no—
110C2×C4×C149—22no—
111C2×C4×C149—21no—
112C2×C4×C149—42no—
113C2×C4×C149—42no—
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149#4112yes—
116C2×C4×C149#4112yes—
117C2×C4×C149C2411yescharacteristic
118C8×C149—22no—
119C22×C149—21no—
120C22×C149—21no—
121C22×C149—41no—
122C22×C149—41no—
123C22×C149—41no—
124C22×C149#12412yes—
125C22×C149C22×D411yescharacteristic
126C2×D149—41no—
127C2×D149—41no—
128C2×D149—41no—
129C4×C149—41no—
130C4×C149—42no—
131C4×C149#12412yes—
132C4×C149C2×#4111yescharacteristic
133C4×C149C2×#4111yescharacteristic
134Dic149—21no—
135Dic149—21no—
136Dic149—21no—
137Dic149—21no—
138Dic149—41no—
139Dic149—42no—
140C2×C149—22no—
141C2×C149—81no—
142C2×C149C2×#12411yescharacteristic
143C2×C149#57511yescharacteristic
144C2×C149#57511yescharacteristic
145D149—81no—
146C149#314211yescharacteristic, complemented, Sylow
147#3142—1491nomaximal, Sylow
148#532—1491no—
149C2×#125—1491no—
150#491—1492no—
151#490—1492no—
152#488—1492no—
153#488—1492no—
154#417—1491no—
155#417—1491no—
156#417—1491no—
157#417D14911yescharacteristic, complemented
158C4×M16—1491no—
159C2×#41—1491no—
160C2×#41C2×D14911yescharacteristic
161C2×M16—1491no—
162C2×M16C2×D14911yescharacteristic
163C4⋊Q8—1491no—
164#127—1491no—
165#125—2981no—
166#125—2981no—
167#125—1492no—
168#125—1492no—
169#124—1491no—
170#124—1491no—
171#121—2981no—
172#121—2981no—
173C4×D4—2981no—
174C4×D4—2981no—
175C2×C4⋊C4—2981no—
176C2×C4⋊C4—2981no—
177C2×C4⋊C4—1491no—
178C2×C4⋊C4C2×D14911yescharacteristic
179C2×C42—1491no—
180#103—1492no—
181#103—1492no—
182#103—1492no—
183#103C2×D14912yes—
184#102—1492no—
185#102—1492no—
186#102—1492no—
187#102C2×D14912yes—
188#97—1492no—
189C4×C8—1492no—
190#41—22no—
191#41—22no—
192#41—2982no—
193#41—2982no—
194C2×Q8—1491no—
195C2×Q8C22×D14911yescharacteristic
196C2×D4—21no—
197C2×D4—2981no—
198C2×D4—2981no—
199C2×D4—2981no—
200C2×D4—1491no—
201C2×D4C22×D14911yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—2981no—
205C22×C4—2981no—
206C22×C4—1491no—
207C22×C4—1491no—
208C22×C4C22×D14911yescharacteristic
209M16—22no—
210M16—2982no—
211C2×C8—1492no—
212C2×C8C22×D14912yes—
213C4⋊C4—21no—
214C4⋊C4—2982no—
215C4⋊C4—2982no—
216C4⋊C4—2982no—
217C4⋊C4—2982no—
218C4⋊C4—2981no—
219C4⋊C4—2981no—
220C4⋊C4—2981no—
221C4⋊C4—1492no—
222C4⋊C4C22×D14912yes—
223C22⋊C4—2981no—
224C22⋊C4—2981no—
225C22⋊C4—2981no—
226C22⋊C4—2981no—
227C42—1491no—
228C42—1491no—
229C42—1491no—
230C42—1491no—
231C23—21no—
232C23—2981no—
233C23D4×D14911yescharacteristic
234Q8—21no—
235Q8—21no—
236Q8—2981no—
237Q8—2981no—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—2981no—
242D4—2981no—
243D4—5962no—
244D4—5962no—
245D4—5962no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—2981no—
251C2×C4—2982no—
252C2×C4—5961no—
253C2×C4—5961no—
254C2×C4—5962no—
255C2×C4—5962no—
256C2×C4—1491no—
257C2×C4—1491no—
258C2×C4—1491no—
259C2×C4—1491no—
260C2×C4D4×D14911yescharacteristic
261C2×C4#1455873512yes—
262C2×C4#1455873612yes—
263C2×C4C23×D14911yescharacteristic
264C8—22no—
265C8—2982no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—5961no—
272C22—5961no—
273C22—5961no—
274C22#1801189712yes—
275C22C2×D4×D14911yescharacteristic
276C4—42no—
277C4—41no—
278C4—2981no—
279C4—2981no—
280C4—2981no—
281C4—2981no—
282C4—5962no—
283C4—5961no—
284C4#1801189712yes—
285C4C2×#1455873511yescharacteristic
286C4C2×#1455873611yescharacteristic
287C2—22no—
288C2—81no—
289C2—11921no—
290C2C2×#1801189711yescharacteristic
291C2#2375042111yescharacteristic
292C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#417×C149C2
socleC22×C149C22×D4
prime radical#23750171C2
hypercenter#417D149
hypocenterC149#3142
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#18011902C2semidirect
3. #23749992C2semidirect
4. #23749988C2semidirect
5. #23749981C2semidirect
6. #23749978C2semidirect
7. #23749627C2semidirect
8. #23749626C2semidirect
9. #23749624C2semidirect
10. M16×Dic149C2semidirect
11. #417×C149C2semidirect
146. C149#3142semidirect
157. #417D149semidirect

Maximal subgroups

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

subgroupindex
#237501712
C2×#180119022
#237499922
#237499882
#237499812
#237499782
#237496272
#237496262
#237496242
M16×Dic1492
#417×C1492
#3142149