Finite Group Databasebeta

← #34055392

Subgroups — #34055392

Order 19072.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750176C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic, complemented
3#23750031C211yesmaximal, characteristic, complemented
4#23750015C211yesmaximal, characteristic, complemented
5#23749990C211yesmaximal, characteristic, complemented
6#23749860C212yesmaximal, complemented
7#23749857C212yesmaximal, complemented
8#23749734C212yesmaximal, complemented
9#23749728C212yesmaximal, complemented
10#97×D149C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—21no—
13C2×#14558723C2212yes—
14C2×#14558721C2212yes—
15C2×C8×D149C2212yes—
16#18011908C2211yescharacteristic
17#18011904—21no—
18#18011903C2211yescharacteristic
19#18011900—21no—
20#18011893—21no—
21#18011887C2211yescharacteristic
22#18011886—21no—
23#18011886C2212yes—
24#18011882C2211yescharacteristic
25Q8×Dic149C2211yescharacteristic
26D4×Dic149C2211yescharacteristic
27#18011873—21no—
28#18011873C2212yes—
29#18011871—21no—
30#18011867—21no—
31C42×D149C2211yescharacteristic
32#18011844C2212yes—
33#18011842C2212yes—
34#18011833C2212yes—
35#18011833C2212yes—
36#18011822C2211yescharacteristic
37#18011821C2212yes—
38C4⋊Q8×C149C2211yescharacteristic
39#124×C149C2211yescharacteristic
40#103×C149C2212yes—
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic
43#14558737—44no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596C2312yes—
48C2×C22⋊D149—21no—
49C22×Dic149—21no—
50C2×C4×D149—22no—
51C2×C4×D149D411yescharacteristic
52C2×C4×D149D411yescharacteristic
53C2×C4×D149C2311yescharacteristic
54#14558723—24no—
55#14558721—24no—
56C2×#11924746C2312yes—
57C8×D149—24no—
58C4⋊Dic149—21no—
59C4⋊Dic149C2311yescharacteristic
60C4⋊Dic149C2311yescharacteristic
61#14558715—21no—
62#14558715—21no—
63#14558715—21no—
64C22⋊Dic149—21no—
65C22⋊Dic149—21no—
66#14558713—21no—
67#14558713—22no—
68#14558713—22no—
69C4×Dic149—21no—
70C4×Dic149D411yescharacteristic
71C4×Dic149D411yescharacteristic
72C4×Dic149C2311yescharacteristic
73C2×Q8×C149—21no—
74C2×Q8×C149C2311yescharacteristic
75C2×D4×C149C2311yescharacteristic
76C2×C8×C149C2312yes—
77C4⋊C4×C149—21no—
78C4⋊C4×C149C2312yes—
79C22⋊C4×C149—21no—
80C22⋊C4×C149—21no—
81C42×C149C2311yescharacteristic
82C22×D149—22no—
83C22×D149C2×D411yescharacteristic
84D596—22no—
85D596—22no—
86D596—42no—
87D596—42no—
88D596—44no—
89C22⋊D149—42no—
90C2×Dic149—21no—
91C2×Dic149—21no—
92C2×Dic149—42no—
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—22no—
97C4×D149—22no—
98C4×D149—41no—
99C4×D149—44no—
100#11924746#4114yescomplemented
101C23×C149—21no—
102Q8×C149—22no—
103Q8×C149—42no—
104D4×C149—22no—
105C2×C4×C149—22no—
106C2×C4×C149—21no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C8×C149—22no—
111C22×C149—41no—
112C22×C149—41no—
113C22×C149—41no—
114C22×C149C22×D411yescharacteristic
115C2×D149—21no—
116C2×D149—21no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—42no—
120C2×D149AGL(1,ℤ/8)12yes—
121C4×C149—21no—
122C4×C149—21no—
123C4×C149—41no—
124C4×C149—42no—
125C4×C149C2×#4112yes—
126Dic149—21no—
127Dic149—21no—
128Dic149—21no—
129Dic149—41no—
130Dic149—41no—
131C2×C149—81no—
132C2×C149#53211yescharacteristic
133C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C149#57511yescharacteristic
135D149—22no—
136D149—82no—
137C149#318011yescharacteristic, complemented, Sylow
138#3180—1491nomaximal, Sylow
139#532—1491no—
140#529—1491no—
141#501—1491no—
142#496—1491no—
143#490—1491no—
144#489D14911yescharacteristic, complemented
145#466—1492no—
146#465—1492no—
147#442—1492no—
148#440—1492no—
149C2×#97—1491no—
150C2×#41—2981no—
151C2×SD16—1492no—
152C2×D8—1492no—
153C22×C8—1492no—
154C4⋊Q8C2×D14911yescharacteristic
155#127—1491no—
156#126—2981no—
157#125—1491no—
158#124—2981no—
159#124C2×D14911yescharacteristic
160#123—2981no—
161C22⋊Q8—1491no—
162#121—2981no—
163#121—1491no—
164#121—1492no—
165C4×Q8—1491no—
166C4×D4—2981no—
167C4×D4—2981no—
168C4×D4—1491no—
169C4×D4—1492no—
170#117—2981no—
171C2×C42—1491no—
172#107—1492no—
173#106—1492no—
174#103C2×D14912yes—
175#102—1492no—
176#102—1492no—
177#102C2×D14912yes—
178#97—1492no—
179#97—1491no—
180#97C2×D14911yescharacteristic
181#41—5964no—
182C2×Q8—21no—
183C2×Q8C22×D14911yescharacteristic
184C2×D4—2982no—
185C2×D4—2981no—
186C2×D4—2981no—
187C2×D4—2981no—
188C2×D4—1492no—
189C2×D4C22×D14911yescharacteristic
190C22×C4—2982no—
191C22×C4—2981no—
192C22×C4—1491no—
193C22×C4—1491no—
194C22×C4—1491no—
195SD16—2984no—
196D8—2984no—
197C2×C8—2984no—
198C2×C8—1492no—
199C2×C8C22×D14912yes—
200C4⋊C4—21no—
201C4⋊C4—2981no—
202C4⋊C4—2981no—
203C4⋊C4—2981no—
204C4⋊C4—2981no—
205C4⋊C4—1491no—
206C4⋊C4—1491no—
207C4⋊C4C22×D14912yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—2981no—
211C22⋊C4—2982no—
212C22⋊C4—2982no—
213C22⋊C4—2981no—
214C22⋊C4—2981no—
215C42—2981no—
216C42—1491no—
217C42—1491no—
218C42—1491no—
219C42C22×D14911yescharacteristic
220C23—21no—
221C23—2982no—
222C23—1491no—
223Q8—22no—
224Q8—42no—
225D4—22no—
226D4—2982no—
227D4—2982no—
228D4—5962no—
229D4—5962no—
230D4—5964no—
231D4—5962no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—2982no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—2981no—
238C2×C4—5961no—
239C2×C4—5964no—
240C2×C4—5962no—
241C2×C4—1491no—
242C2×C4—1491no—
243C2×C4—1491no—
244C2×C4D4×D14911yescharacteristic
245C2×C4D4×D14911yescharacteristic
246C2×C4C23×D14911yescharacteristic
247C8—22no—
248C8—1494no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—2981no—
253C22—2981no—
254C22—5962no—
255C22—5962no—
256C22—5962no—
257C22—1492no—
258C22C2×D4×D14911yescharacteristic
259C4—21no—
260C4—21no—
261C4—42no—
262C4—41no—
263C4—2981no—
264C4—2981no—
265C4—2981no—
266C4—5961no—
267C4—5961no—
268C4#41×D14912yes—
269C2—81no—
270C2—2982no—
271C2—11922no—
272C2#2375017411yescharacteristic
273C2AGL(1,ℤ/8)×D14911yescharacteristic
274C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
hypercenter#489D149
hypocenterC149#3180
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23750176C2semidirect
2. #23750154C2semidirect
3. #23750031C2semidirect
4. #23750015C2semidirect
5. #23749990C2semidirect
6. #23749860C2semidirect
7. #23749857C2semidirect
8. #23749734C2semidirect
9. #23749728C2semidirect
10. #97×D149C2semidirect
11. #489×C149C2semidirect
100. #11924746#41semidirect
137. C149#3180semidirect
144. #489D149semidirect

Maximal subgroups

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

subgroupindex
#237501762
#237501542
#237500312
#237500152
#237499902
#237498602
#237498572
#237497342
#237497282
#97×D1492
#489×C1492
#3180149