Finite Group Databasebeta

← #49131505

Subgroups — #49131505

Order 36224.

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#31827070C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic, complemented
3#31826790C212yesmaximal, complemented
4#31826766C212yesmaximal, complemented
5#31826661C212yesmaximal, complemented
6#31826601C212yesmaximal, complemented
7#31826578C212yesmaximal, complemented
8C4×D2264C212yesmaximal, complemented
9#433×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×D2264C2212yes—
12C2×D2264C2212yes—
13#22583607C2211yescharacteristic, complemented
14#22583602C2211yescharacteristic, complemented
15#22583595—22no—
16#22583584C2212yes—
17#22583583—22no—
18C4×D1132C2212yes—
19C4×D1132C2212yes—
20C4×D1132C2212yescomplemented
21#22583572—22no—
22#22583569C2211yescharacteristic
23C22⋊C4×D283—22no—
24#22583544C2212yescomplemented
25#22583542C2212yescomplemented
26#22583532C2212yes—
27#22583532C2212yes—
28#22583532C2212yescomplemented
29#22583532C2212yescomplemented
30#117×C283C2211yescharacteristic
31C4⋊C8×C283C2212yescomplemented
32C22⋊C8×C283C2212yes—
33#97×C283C2211yescharacteristic, complemented
34C4×C8×C283C2211yescharacteristic, complemented
35C23×D283—21no—
36C2×D1132—24no—
37C2×D1132—21no—
38C2×D1132—22no—
39C2×D1132C2312yes—
40C2×D1132C2312yes—
41C2×C22⋊D283—22no—
42C2×C4×D283—22no—
43C2×C4×D283—22no—
44C2×C4×D283—22no—
45D2264—24no—
46D2264—24no—
47C4⋊Dic283C2312yes—
48C4⋊Dic283C2312yes—
49Dic283⋊C4—22no—
50C22⋊Dic283—21no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54(C2×D283)⋊C4—22no—
55C4×Dic283—21no—
56C22×C4×C283C2311yescharacteristic
57C2×C8×C283C2312yes—
58C2×C8×C283C2312yes—
59C4⋊C4×C283D412yes—
60C22⋊C4×C283D412yes—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64C22×D283—24no—
65C22×D283—22no—
66C22×D283—82no—
67D1132—24no—
68D1132—22no—
69D1132—22no—
70D1132—22no—
71D1132—82no—
72D1132#4114yes—
73C22⋊D283—82no—
74C2×Dic283—22no—
75C2×Dic283—22no—
76C4×D283—82no—
77C4×D283—82no—
78C4×D283—82no—
79C23×C283C2×D411yescharacteristic
80C2×C4×C283—22no—
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D412yes—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2411yescharacteristic
85C8×C283—22no—
86C8×C283—22no—
87C22×C283—21no—
88C22×C283—22no—
89C22×C283C22×D411yescharacteristic
90C2×D283—24no—
91C2×D283—42no—
92C2×D283—42no—
93C2×D283—42no—
94C2×D283—42no—
95C2×D283—42no—
96C2×D283—84no—
97C4×C283—21no—
98C4×C283—22no—
99C4×C283—22no—
100C4×C283C2×#4112yes—
101Dic283—42no—
102Dic283—42no—
103C2×C283—41no—
104C2×C283#52511yescharacteristic
105C2×C283#57612yes—
106D283—44no—
107D283—82no—
108C283#312211yescharacteristic, complemented, Sylow
109#3122—2831nomaximal, Sylow
110#540—2831no—
111#518—2831no—
112#482—2832no—
113#478—2832no—
114#459—2832no—
115#447—2832no—
116#442—2832no—
117C4×D8—2832no—
118#433D28311yescharacteristic, complemented
119C22×D4—2831no—
120C2×D8—2832no—
121C2×D8—2832no—
122#127—2831no—
123#125—2831no—
124#123—5662no—
125#121—2832no—
126#121—5662no—
127C4×D4—2832no—
128C4×D4—2832no—
129C4×D4—2832no—
130C4×D4—5662no—
131#117—2831no—
132#117C2×D28311yescharacteristic
133C2×C22⋊C4—5662no—
134#107—2832no—
135#106—2832no—
136C4⋊C8C2×D28312yescomplemented
137#102—2832no—
138#102—2832no—
139#102—2832no—
140#102—2832no—
141C22⋊C8C2×D28312yes—
142#97C2×D28311yescharacteristic, complemented
143C4×C8C2×D28311yescharacteristic, complemented
144C24—5661no—
145C2×D4—2832no—
146C2×D4—2832no—
147C2×D4—5664no—
148C2×D4—5662no—
149C2×D4—5661no—
150C2×D4—5662no—
151C22×C4—5662no—
152C22×C4—5662no—
153C22×C4—5662no—
154C22×C4C22×D28311yescharacteristic
155D8—5664no—
156D8—5664no—
157C2×C8C22×D28312yes—
158C2×C8C22×D28312yes—
159C4⋊C4—2832no—
160C4⋊C4—2832no—
161C4⋊C4—5662no—
162C4⋊C4D113212yes—
163C22⋊C4—5661no—
164C22⋊C4—5662no—
165C22⋊C4—5662no—
166C22⋊C4—5662no—
167C22⋊C4—5662no—
168C22⋊C4D113212yes—
169C42—5661no—
170C42C22×D28311yescharacteristic
171C42C22×D28311yescharacteristic
172C23—5664no—
173C23—5662no—
174C23—5662no—
175C23—22642no—
176C23C2×D113211yescharacteristic
177D4—2834no—
178D4—5664no—
179D4—5662no—
180D4—5662no—
181D4—5662no—
182D4—22642no—
183D4—22642no—
184C2×C4—22no—
185C2×C4—5662no—
186C2×C4—5662no—
187C2×C4—22642no—
188C2×C4—22642no—
189C2×C4—22642no—
190C2×C4C2×D113211yescharacteristic
191C2×C4C2×D113212yes—
192C2×C4C2×D113212yes—
193C2×C4C23×D28311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—5664no—
199C22—11322no—
200C22—11322no—
201C22—11322no—
202C22—11322no—
203C22—11322no—
204C22—22644no—
205C22C22×D113211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—11322no—
210C4—11322no—
211C4#41×D28312yes—
212C2—41no—
213C2—11324no—
214C2—22642no—
215C2#3182697711yescharacteristic
216C2#3182727012yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
hypercenter#433D283
hypocenterC283#3122
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31827070C2semidirect
2. #31826939C2semidirect
3. #31826790C2semidirect
4. #31826766C2semidirect
5. #31826661C2semidirect
6. #31826601C2semidirect
7. #31826578C2semidirect
8. C4×D2264C2semidirect
9. #433×C283C2semidirect
13. #22583607C22semidirect
14. #22583602C22semidirect
20. C4×D1132C22semidirect
24. #22583544C22semidirect
25. #22583542C22semidirect
28. #22583532C22semidirect
29. #22583532C22semidirect
31. C4⋊C8×C283C22semidirect
33. #97×C283C22semidirect
34. C4×C8×C283C22semidirect
108. C283#3122semidirect
118. #433D283semidirect
136. C4⋊C8C2×D283semidirect
142. #97C2×D283semidirect
143. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318269392
#318267902
#318267662
#318266612
#318266012
#318265782
C4×D22642
#433×C2832
#3122283