Finite Group Databasebeta

← #34054935

Subgroups — #34054935

Order 19072.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750230C211yesmaximal, characteristic, complemented
2#23750099C211yesmaximal, characteristic, complemented
3#23749950C212yesmaximal, complemented
4#23749926C212yesmaximal, complemented
5#23749821C212yesmaximal, complemented
6#23749761C212yesmaximal, complemented
7#23749738C212yesmaximal, complemented
8C4×D1192C212yesmaximal, complemented
9#433×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C2×D1192C2212yes—
12C2×D1192C2212yes—
13#18011908C2211yescharacteristic, complemented
14#18011903C2211yescharacteristic, complemented
15#18011896—22no—
16#18011885C2212yes—
17#18011884—22no—
18C4×D596C2212yes—
19C4×D596C2212yes—
20C4×D596C2212yescomplemented
21#18011873—22no—
22#18011870C2211yescharacteristic
23C22⋊C4×D149—22no—
24#18011845C2212yescomplemented
25#18011843C2212yescomplemented
26#18011833C2212yes—
27#18011833C2212yes—
28#18011833C2212yescomplemented
29#18011833C2212yescomplemented
30#117×C149C2211yescharacteristic
31C4⋊C8×C149C2212yescomplemented
32C22⋊C8×C149C2212yes—
33#97×C149C2211yescharacteristic, complemented
34C4×C8×C149C2211yescharacteristic, complemented
35C23×D149—21no—
36C2×D596—24no—
37C2×D596—21no—
38C2×D596—22no—
39C2×D596C2312yes—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C2×C4×D149—22no—
43C2×C4×D149—22no—
44C2×C4×D149—22no—
45D1192—24no—
46D1192—24no—
47C4⋊Dic149C2312yes—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50C22⋊Dic149—21no—
51#14558713—22no—
52#14558713—22no—
53#14558713—22no—
54#14558713—22no—
55C4×Dic149—21no—
56C22×C4×C149C2311yescharacteristic
57C2×C8×C149C2312yes—
58C2×C8×C149C2312yes—
59C4⋊C4×C149D412yes—
60C22⋊C4×C149D412yes—
61C42×C149C2311yescharacteristic
62C42×C149C2311yescharacteristic
63C22×D149—22no—
64C22×D149—24no—
65C22×D149—22no—
66C22×D149—82no—
67D596—24no—
68D596—22no—
69D596—22no—
70D596—22no—
71D596—82no—
72D596#4114yes—
73C22⋊D149—82no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C4×D149—82no—
77C4×D149—82no—
78C4×D149—82no—
79C23×C149C2×D411yescharacteristic
80C2×C4×C149—22no—
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2×D412yes—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2411yescharacteristic
85C8×C149—22no—
86C8×C149—22no—
87C22×C149—21no—
88C22×C149—22no—
89C22×C149C22×D411yescharacteristic
90C2×D149—24no—
91C2×D149—42no—
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—84no—
97C4×C149—21no—
98C4×C149—22no—
99C4×C149—22no—
100C4×C149C2×#4112yes—
101Dic149—42no—
102Dic149—42no—
103C2×C149—41no—
104C2×C149#52511yescharacteristic
105C2×C149#57612yes—
106D149—44no—
107D149—82no—
108C149#312211yescharacteristic, complemented, Sylow
109#3122—1491nomaximal, Sylow
110#540—1491no—
111#518—1491no—
112#482—1492no—
113#478—1492no—
114#459—1492no—
115#447—1492no—
116#442—1492no—
117C4×D8—1492no—
118#433D14911yescharacteristic, complemented
119C22×D4—1491no—
120C2×D8—1492no—
121C2×D8—1492no—
122#127—1491no—
123#125—1491no—
124#123—2982no—
125#121—2982no—
126#121—1492no—
127C4×D4—2982no—
128C4×D4—1492no—
129C4×D4—1492no—
130C4×D4—1492no—
131#117—1491no—
132#117C2×D14911yescharacteristic
133C2×C22⋊C4—2982no—
134#107—1492no—
135#106—1492no—
136C4⋊C8C2×D14912yescomplemented
137#102—1492no—
138#102—1492no—
139#102—1492no—
140#102—1492no—
141C22⋊C8C2×D14912yes—
142#97C2×D14911yescharacteristic, complemented
143C4×C8C2×D14911yescharacteristic, complemented
144C24—2981no—
145C2×D4—2984no—
146C2×D4—2982no—
147C2×D4—2981no—
148C2×D4—2982no—
149C2×D4—1492no—
150C2×D4—1492no—
151C22×C4—2982no—
152C22×C4—2982no—
153C22×C4—2982no—
154C22×C4C22×D14911yescharacteristic
155D8—2984no—
156D8—2984no—
157C2×C8C22×D14912yes—
158C2×C8C22×D14912yes—
159C4⋊C4—2982no—
160C4⋊C4—1492no—
161C4⋊C4—1492no—
162C4⋊C4D59612yes—
163C22⋊C4—2981no—
164C22⋊C4—2982no—
165C22⋊C4—2982no—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C22⋊C4D59612yes—
169C42—2981no—
170C42C22×D14911yescharacteristic
171C42C22×D14911yescharacteristic
172C23—2984no—
173C23—2982no—
174C23—2982no—
175C23—11922no—
176C23C2×D59611yescharacteristic
177D4—2984no—
178D4—2982no—
179D4—2982no—
180D4—2982no—
181D4—1494no—
182D4—11922no—
183D4—11922no—
184C2×C4—22no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—11922no—
188C2×C4—11922no—
189C2×C4—11922no—
190C2×C4C2×D59611yescharacteristic
191C2×C4C2×D59612yes—
192C2×C4C2×D59612yes—
193C2×C4C23×D14911yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—2984no—
199C22—5962no—
200C22—5962no—
201C22—5962no—
202C22—5962no—
203C22—5962no—
204C22—11924no—
205C22C22×D59611yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—5962no—
210C4—5962no—
211C4#41×D14912yes—
212C2—41no—
213C2—5964no—
214C2—11922no—
215C2#2375013711yescharacteristic
216C2#2375043012yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
hypercenter#433D149
hypocenterC149#3122
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750230C2semidirect
2. #23750099C2semidirect
3. #23749950C2semidirect
4. #23749926C2semidirect
5. #23749821C2semidirect
6. #23749761C2semidirect
7. #23749738C2semidirect
8. C4×D1192C2semidirect
9. #433×C149C2semidirect
13. #18011908C22semidirect
14. #18011903C22semidirect
20. C4×D596C22semidirect
24. #18011845C22semidirect
25. #18011843C22semidirect
28. #18011833C22semidirect
29. #18011833C22semidirect
31. C4⋊C8×C149C22semidirect
33. #97×C149C22semidirect
34. C4×C8×C149C22semidirect
108. C149#3122semidirect
118. #433D149semidirect
136. C4⋊C8C2×D149semidirect
142. #97C2×D149semidirect
143. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502302
#237500992
#237499502
#237499262
#237498212
#237497612
#237497382
C4×D11922
#433×C1492
#3122149