Finite Group Databasebeta

← #44401417

Subgroups — #44401417

Order 29056.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#28409578C211yesmaximal, characteristic
2#28409016C211yesmaximal, characteristic, complemented
3#28408830C212yesmaximal, complemented
4#28408828C212yesmaximal, complemented
5#413×C227C211yesmaximal, characteristic, complemented
6C2×#16813884C411yescharacteristic
7C2×#16813868—21no—
8#20300286C2211yescharacteristic
9#20300284C411yescharacteristic
10#20300277C2211yescharacteristic
11#20300275C411yescharacteristic
12#20300260—21no—
13#20300260—21no—
14C4×C22⋊D227—21no—
15C4×C22⋊D227—21no—
16C2×C4×Dic227C411yescharacteristic
17#20300207C2212yes—
18#20300205—21no—
19C2×#41×C227C2211yescharacteristic
20C2×M16×C227—21no—
21#101×C227C2212yes—
22#100×C227—21no—
23#16813884—41no—
24#16813884—41no—
25C2×Dic454C2×C411yescharacteristic
26C2×D908C2×C411yescharacteristic
27C2×C22⋊D227—21no—
28C2×C22⋊D227—21no—
29C2×C22⋊D227—21no—
30C22×Dic227—21no—
31C2×C4×D227—21no—
32#16813868—22no—
33#16813868—41no—
34C2×C227⋊C8—41no—
35Dic227⋊C4—21no—
36Dic227⋊C4—21no—
37C22⋊Dic227—21no—
38C22⋊Dic227—21no—
39(C2×D227)⋊C4—21no—
40(C2×D227)⋊C4—21no—
41C4×Dic227—21no—
42C4×Dic227C2×C411yescharacteristic
43C4×Dic227C2×C411yescharacteristic
44#41×C227—41no—
45#41×C227—41no—
46C2×Q8×C227C2311yescharacteristic
47C2×D4×C227C2×C411yescharacteristic
48C2×D4×C227D411yescharacteristic
49C2×D4×C227D411yescharacteristic
50C22×C4×C227C2×C411yescharacteristic
51C22×C4×C227D411yescharacteristic
52C22×C4×C227D411yescharacteristic
53M16×C227—22no—
54M16×C227—41no—
55C2×C8×C227—41no—
56C22×D227—21no—
57Dic454—41no—
58D908—41no—
59C22⋊D227—42no—
60C22⋊D227—42no—
61C22⋊D227—42no—
62C2×Dic227—21no—
63C2×Dic227—21no—
64C2×Dic227—21no—
65C2×Dic227—42no—
66C4×D227—41no—
67C4×D227—41no—
68C227⋊C8—42no—
69C23×C227C22⋊C411yescharacteristic
70C23×C227C22⋊C411yescharacteristic
71C23×C227C22⋊C411yescharacteristic
72Q8×C227—41no—
73D4×C227—41no—
74D4×C227—41no—
75D4×C227—41no—
76C2×C4×C227—21no—
77C2×C4×C227—21no—
78C2×C4×C227—21no—
79C2×C4×C227—21no—
80C2×C4×C227—21no—
81C2×C4×C227—21no—
82C2×C4×C227C22⋊C411yescharacteristic
83C2×C4×C227C22×C411yescharacteristic
84C2×C4×C227C2×D411yescharacteristic
85C2×C4×C227C2×D411yescharacteristic
86C8×C227—42no—
87C22×C227—21no—
88C22×C227—21no—
89C22×C227—21no—
90C22×C227—41no—
91C22×C227—41no—
92C22×C227—41no—
93C22×C227C2×C22⋊C411yescharacteristic
94C2×D227—41no—
95C2×D227—41no—
96C2×D227—41no—
97C4×C227—21no—
98C4×C227—21no—
99C4×C227—21no—
100C4×C227#9911yescharacteristic
101C4×C227#9911yescharacteristic
102Dic227—22no—
103Dic227—41no—
104Dic227—41no—
105C2×C227—21no—
106C2×C227—41no—
107C2×C227—41no—
108C2×C227—41no—
109C2×C227C2×#9911yescharacteristic
110D227—81no—
111C227#213211yescharacteristic, complemented, Sylow
112#2132—2271nomaximal, Sylow
113#532—2271no—
114#413—2271no—
115#413D22711yescharacteristic, complemented
116#356—2272no—
117#355—2272no—
118C2×#41—2271no—
119C2×#41C2×D22711yescharacteristic
120C2×M16—21no—
121C2×M16—4541no—
122C4⋊Q8—2271no—
123#127—2271no—
124#124—2271no—
125#124—2271no—
126#121—4541no—
127#121—4541no—
128C4×D4—4541no—
129C4×D4—4541no—
130C2×C42—2271no—
131#101—2272no—
132#101C2×D22712yes—
133#100—21no—
134#100—4541no—
135#41—41no—
136#41—41no—
137#41—9081no—
138#41—9081no—
139C2×Q8—2271no—
140C2×Q8C22×D22711yescharacteristic
141C2×D4—4541no—
142C2×D4—4541no—
143C2×D4—4541no—
144C2×D4—2271no—
145C2×D4C4×D22711yescharacteristic
146C2×D4C22⋊D22711yescharacteristic
147C2×D4D90811yescharacteristic
148C22×C4—4541no—
149C22×C4—4541no—
150C22×C4C4×D22711yescharacteristic
151C22×C4C22⋊D22711yescharacteristic
152C22×C4D90811yescharacteristic
153M16—22no—
154M16—41no—
155M16—9081no—
156M16—4542no—
157C2×C8—41no—
158C2×C8—9081no—
159C4⋊C4—4541no—
160C4⋊C4—4541no—
161C22⋊C4—4541no—
162C22⋊C4—4541no—
163C22⋊C4—4541no—
164C22⋊C4—4541no—
165C42—4541no—
166C42—2271no—
167C42—2271no—
168C23—4541no—
169C23(C2×D227)⋊C411yescharacteristic
170C23(C2×D227)⋊C411yescharacteristic
171C23(C2×D227)⋊C411yescharacteristic
172Q8—41no—
173Q8—9081no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—9081no—
178D4—9082no—
179D4—9082no—
180D4—9082no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—9082no—
188C2×C4—9081no—
189C2×C4—9081no—
190C2×C4—4541no—
191C2×C4—4541no—
192C2×C4—4541no—
193C2×C4(C2×D227)⋊C411yescharacteristic
194C2×C4C2×C4×D22711yescharacteristic
195C2×C4C2×C22⋊D22711yescharacteristic
196C2×C4C2×D90811yescharacteristic
197C8—42no—
198C8—9082no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—9081no—
206C22—9081no—
207C22—9081no—
208C22C2×(C2×D227)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—9081no—
213C4—9081no—
214C4—4542no—
215C4#2030020211yescharacteristic
216C4#2030020211yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—18161no—
222C2C2×#2030020211yescharacteristic
subgroupG/H
centerC4#20300202
commutatorC2×C4×C227C22×C4
FrattiniC2×Q8C22×D227
Fitting#413×C227C2
socleC2×C227C2×#99
prime radical#28409578C2
cosocleC2×Q8×C227C23
hypercenter#413D227
hypocenterC227#2132
LCSG ▷ C2×C4×C227 ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #28409016C2semidirect
3. #28408830C2semidirect
4. #28408828C2semidirect
5. #413×C227C2semidirect
111. C227#2132semidirect
115. #413D227semidirect

Maximal subgroups

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

subgroupindex
#284095782
#284090162
#284088302
#284088282
#413×C2272
#2132227