Finite Group Databasebeta

← #34055050

Subgroups — #34055050

Order 19072.

404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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#23750194C211yesmaximal, characteristic
2#23749991C212yesmaximal, complemented
3#23749987C212yesmaximal, complemented
4#23749982C212yesmaximal, complemented
5#23749973C212yesmaximal, complemented
6#23749629C211yesmaximal, characteristic, complemented
7#23749624C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic, complemented
9C2×#18011831C211yesmaximal, characteristic, complemented
10#23749581C211yesmaximal, characteristic, complemented
11#544×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C22×D596C2211yescharacteristic
14C2×#14558720C2211yescharacteristic
15C22×#11924746C2211yescharacteristic
16#18011908C2212yes—
17#18011899C2212yes—
18#18011886—21no—
19#18011886—21no—
20#18011881—22no—
21#18011834C2211yescharacteristic, complemented
22#18011834C2212yescomplemented
23#18011834C2211yescharacteristic, complemented
24#18011831C2212yes—
25#18011831C2212yes—
26#18011831C2212yes—
27#18011831C2212yes—
28#18011831C2211yescharacteristic, complemented
29#18011831C2212yescomplemented
30#18011831C2211yescharacteristic, complemented
31#18011822C2212yescomplemented
32C4×#11924746C2212yescomplemented
33C4⋊Q8×C149—21no—
34C4⋊Q8×C149C2212yescomplemented
35#125×C149—21no—
36#125×C149C2212yescomplemented
37C22⋊Q8×C149—22no—
38#117×C149C2211yescharacteristic
39#117×C149C2211yescharacteristic
40C2×C4⋊C4×C149C2211yescharacteristic
41C23×D149—21no—
42#14558736—22no—
43#14558736—22no—
44C2×Dic298C2311yescharacteristic
45C2×D596—21no—
46C2×D596—22no—
47C2×D596—22no—
48C2×D596—22no—
49C2×D596—22no—
50C2×D596C2311yescharacteristic
51C2×D596C2312yes—
52C2×C22⋊D149—21no—
53C2×C4×D149—21no—
54#14558720—22no—
55C2×#11924746—22no—
56C2×#11924746C2311yescharacteristic
57C2×#11924746C2311yescharacteristic
58C2×#11924746C2312yes—
59#14558713—22no—
60#14558713—22no—
61C2×Q8×C149—22no—
62C22×C4×C149—21no—
63C22×C4×C149C2311yescharacteristic
64C4⋊C4×C149—21no—
65C4⋊C4×C149—22no—
66C4⋊C4×C149—22no—
67C4⋊C4×C149—22no—
68C4⋊C4×C149D411yescharacteristic
69C4⋊C4×C149D411yescharacteristic
70C4⋊C4×C149C2312yes—
71C4⋊C4×C149C2311yescharacteristic
72C4⋊C4×C149C2311yescharacteristic
73C22⋊C4×C149—21no—
74C22⋊C4×C149D412yes—
75C42×C149—21no—
76C42×C149C2312yes—
77C22×D149—21no—
78C22×D149—22no—
79C22×D149—42no—
80C22×D149—81no—
81C22×D149—81no—
82Dic298—21no—
83Dic298—21no—
84D596—22no—
85D596—22no—
86D596—21no—
87D596—21no—
88D596—42no—
89D596—82no—
90D596—82no—
91C22⋊D149—42no—
92C2×Dic149—21no—
93C4×D149—42no—
94#11924746—22no—
95#11924746—21no—
96#11924746—21no—
97C23×C149C2×D411yescharacteristic
98Q8×C149—82no—
99C2×C4×C149—21no—
100C2×C4×C149—21no—
101C2×C4×C149—22no—
102C2×C4×C149—81no—
103C2×C4×C149C2×D412yes—
104C2×C4×C149C2×D412yes—
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149#4112yes—
107C2×C4×C149#4112yes—
108C2×C4×C149C2411yescharacteristic
109C22×C149—21no—
110C22×C149—21no—
111C22×C149#12412yes—
112C22×C149C22×D411yescharacteristic
113C2×D149—41no—
114C2×D149—42no—
115C2×D149—41no—
116C2×D149—42no—
117C2×D149—41no—
118C2×D149—42no—
119C2×D149—84no—
120C4×C149—22no—
121C4×C149—22no—
122C4×C149—42no—
123C4×C149—41no—
124C4×C149—41no—
125C4×C149#12412yes—
126C4×C149C2×#4111yescharacteristic
127C4×C149C2×#4111yescharacteristic
128Dic149—41no—
129C2×C149—22no—
130C2×C149C2×#12411yescharacteristic
131C2×C149#57611yescharacteristic
132C2×C149#57711yescharacteristic
133D149—81no—
134D149—82no—
135C149#313611yescharacteristic, complemented, Sylow
136#3136—1491nomaximal, Sylow
137#544D14911yescharacteristic, complemented
138#535—1491no—
139#490—1492no—
140#489—1492no—
141#488—1492no—
142#486—1492no—
143#418—1491no—
144#417—1491no—
145#416—1491no—
146C2×#102—1491no—
147#405—1491no—
148C2×#41—1491no—
149C22×D4—1491no—
150C2×M16—1491no—
151C22×C8—1491no—
152C4⋊Q8—21no—
153C4⋊Q8C2×D14912yescomplemented
154#127—1492no—
155#125—21no—
156#125C2×D14912yescomplemented
157#124—1492no—
158C22⋊Q8—22no—
159#121—2981no—
160#121—2981no—
161#120—2982no—
162#117C2×D14911yescharacteristic
163#117C2×D14911yescharacteristic
164C2×C4⋊C4C2×D14911yescharacteristic
165#103—1491no—
166#103—1491no—
167#103—1492no—
168#102—1492no—
169#102—1492no—
170#102—1491no—
171#102—1491no—
172#102—1492no—
173#102—1492no—
174#102—1492no—
175#97—1492no—
176C4×C8—1492no—
177C24—2981no—
178#41—2982no—
179#41—2982no—
180C2×Q8—22no—
181C2×Q8—1491no—
182C2×D4—2981no—
183C2×D4—2981no—
184C2×D4—2982no—
185C2×D4—2982no—
186C2×D4—2982no—
187C2×D4—2982no—
188C2×D4—1492no—
189C2×D4—1491no—
190C22×C4—21no—
191C22×C4—2981no—
192C22×C4C22×D14911yescharacteristic
193M16—2982no—
194C2×C8—2982no—
195C2×C8—1491no—
196C2×C8—1492no—
197C2×C8—1491no—
198C4⋊C4—21no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4C22⋊D14911yescharacteristic
203C4⋊C4C22⋊D14911yescharacteristic
204C4⋊C4C22×D14912yes—
205C4⋊C4C22×D14911yescharacteristic
206C4⋊C4C22×D14911yescharacteristic
207C22⋊C4—21no—
208C22⋊C4—2982no—
209C22⋊C4—2982no—
210C22⋊C4C22⋊D14912yes—
211C42—21no—
212C42C22×D14912yes—
213C23—2982no—
214C23—2981no—
215C23—5962no—
216C23—11921no—
217C23—11921no—
218C23C2×C22⋊D14911yescharacteristic
219Q8—82no—
220Q8—2981no—
221Q8—2981no—
222D4—2982no—
223D4—2982no—
224D4—2981no—
225D4—2981no—
226D4—5962no—
227D4—5962no—
228D4—11922no—
229D4—11922no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—81no—
234C2×C4—2981no—
235C2×C4—5962no—
236C2×C4C2×C22⋊D14912yes—
237C2×C4C2×C22⋊D14912yes—
238C2×C4C2×C22⋊D14911yescharacteristic
239C2×C4#1455873712yes—
240C2×C4#1455873712yes—
241C2×C4C23×D14911yescharacteristic
242C8—2981no—
243C8—2981no—
244C8—2982no—
245C22—21no—
246C22—21no—
247C22—5961no—
248C22—5962no—
249C22—5961no—
250C22—5962no—
251C22—5961no—
252C22—5962no—
253C22—11924no—
254C22#1801190012yes—
255C22C22×C22⋊D14911yescharacteristic
256C4—22no—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—5961no—
262C4#1801190012yes—
263C4C2×#1455873711yescharacteristic
264C4C2×#1455873711yescharacteristic
265C2—22no—
266C2—11922no—
267C2—11921no—
268C2C2×#1801190011yescharacteristic
269C2#2375042811yescharacteristic
270C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#544×C149C2
socleC22×C149C22×D4
prime radical#23750194C2
hypercenter#544D149
hypocenterC149#3136
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #23749991C2semidirect
3. #23749987C2semidirect
4. #23749982C2semidirect
5. #23749973C2semidirect
6. #23749629C2semidirect
7. #23749624C2semidirect
8. #23749619C2semidirect
9. C2×#18011831C2semidirect
10. #23749581C2semidirect
11. #544×C149C2semidirect
21. #18011834C22semidirect
22. #18011834C22semidirect
23. #18011834C22semidirect
28. #18011831C22semidirect
29. #18011831C22semidirect
30. #18011831C22semidirect
31. #18011822C22semidirect
32. C4×#11924746C22semidirect
34. C4⋊Q8×C149C22semidirect
36. #125×C149C22semidirect
135. C149#3136semidirect
137. #544D149semidirect
153. C4⋊Q8C2×D149semidirect
156. #125C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501942
#237499912
#237499872
#237499822
#237499732
#237496292
#237496242
#237496192
C2×#180118312
#237495812
#544×C1492
#3136149