Finite Group Databasebeta

← #28362033

Subgroups — #28362033

Order 13952.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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#20295603C211yesmaximal, characteristic
2#20295339C211yesmaximal, characteristic, complemented
3#20294957C211yesmaximal, characteristic, complemented
4#20294761C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294751C211yesmaximal, characteristic, complemented
7#480×C109C211yesmaximal, characteristic, complemented
8C2×#13182028—21no—
9#16812677—21no—
10#16812676—21no—
11#16812673C2211yescharacteristic
12#16812672—21no—
13#16812671—21no—
14#16812671—21no—
15C2×#13182008—21no—
16C2×#13182008C2211yescharacteristic
17#16812632—21no—
18#16812619—21no—
19C22⋊#11724784C2211yescharacteristic
20#16812606—21no—
21#16812606C2211yescharacteristic
22#121×C109C2211yescharacteristic
23C2×C4⋊C4×C109C2211yescharacteristic
24#107×C109—21no—
25#102×C109—21no—
26C22⋊C8×C109C2211yescharacteristic
27#13182028—42no—
28#13182028—42no—
29C2×Dic218—21no—
30C2×D436D411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C22×Dic109—21no—
35C22×Dic109—21no—
36C22×Dic109D411yescharacteristic
37C22×Dic109D411yescharacteristic
38C2×C4×D109—21no—
39C2×#11724784—21no—
40C4⋊Dic109D411yescharacteristic
41#13182008—21no—
42#13182008—21no—
43#13182008—21no—
44#13182008—42no—
45C22⋊Dic109—21no—
46#13182006—21no—
47#13182006—21no—
48C2×D4×C109—21no—
49C2×D4×C109D411yescharacteristic
50C22×C4×C109—21no—
51C22×C4×C109C2311yescharacteristic
52C2×C8×C109—21no—
53C4⋊C4×C109—21no—
54C4⋊C4×C109—21no—
55C4⋊C4×C109D411yescharacteristic
56C22⋊C4×C109—21no—
57C23×C109—21no—
58C23×C109C2×D411yescharacteristic
59C22×D109—21no—
60D4×C109—41no—
61D4×C109—41no—
62D4×C109—41no—
63C2×C4×C109—21no—
64C2×C4×C109—41no—
65C2×C4×C109—41no—
66C2×C4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109C2×D411yescharacteristic
70C22⋊D109—42no—
71C22⋊D109—41no—
72C22⋊D109—41no—
73C22⋊D109—81no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—22no—
77C2×Dic109—21no—
78C2×Dic109—21no—
79C2×Dic109—42no—
80C2×Dic109—41no—
81C2×Dic109—41no—
82C2×Dic109—41no—
83C2×Dic109D812yes—
84D436—41no—
85C4×D109—42no—
86Dic218—42no—
87C8×C109—41no—
88#11724784—41no—
89C22×C109—21no—
90C22×C109—21no—
91C22×C109—41no—
92C22×C109—41no—
93C22×C109—41no—
94C22×C109#12011yescharacteristic
95C22×C109C2×D811yescharacteristic
96C22×C109AGL(1,ℤ/8)11yescharacteristic
97C2×D109—41no—
98C2×D109—41no—
99C2×D109—41no—
100C4×C109—21no—
101C4×C109—21no—
102C4×C109—41no—
103C4×C109—81no—
104Dic109—22no—
105Dic109—42no—
106Dic109—41no—
107Dic109—41no—
108C2×C109—21no—
109C2×C109—21no—
110C2×C109—81no—
111C2×C109#44711yescharacteristic
112C2×C109#45611yescharacteristic
113C2×C109#45811yescharacteristic
114D109—81no—
115#1610—1091nomaximal, Sylow
116C109#161011yescharacteristic, complemented, Sylow
117#537—1091no—
118#480—1091no—
119#480D10911yescharacteristic, complemented
120#398—1091no—
121#327—1091no—
122#327—1091no—
123#324—1091no—
124C2×#41—2181no—
125C22⋊Q8—2181no—
126C22⋊Q8—2181no—
127#121—1091no—
128#121—2181no—
129#121—2181no—
130#121—2181no—
131#121C2×D10911yescharacteristic
132C2×C4⋊C4—1091no—
133C2×C4⋊C4—2181no—
134C2×C4⋊C4C2×D10911yescharacteristic
135#107—21no—
136#107—2181no—
137#102—21no—
138#102—2181no—
139C22⋊C8—1091no—
140C22⋊C8C2×D10911yescharacteristic
141#95—1091no—
142#95—2181no—
143#41—4362no—
144#41—4362no—
145C2×Q8—2181no—
146C2×D4—21no—
147C2×D4—1091no—
148C2×D4—2181no—
149C2×D4—2181no—
150C2×D4—2181no—
151C2×D4C22⋊D10911yescharacteristic
152C22×C4—21no—
153C22×C4—1091no—
154C22×C4—1091no—
155C22×C4—2181no—
156C22×C4—2181no—
157C22×C4—2181no—
158C22×C4C22×D10911yescharacteristic
159C2×C8—21no—
160C2×C8—2181no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—1091no—
164C4⋊C4—4362no—
165C4⋊C4—2181no—
166C4⋊C4—2181no—
167C4⋊C4—2181no—
168C4⋊C4C22⋊D10911yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—2181no—
171C22⋊C4—2181no—
172C22⋊C4—2181no—
173C23—21no—
174C23—2181no—
175C23D4×D10911yescharacteristic
176Q8—4362no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—8721no—
181D4—4361no—
182D4—4361no—
183D4—4361no—
184D4—4362no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—1092no—
191C2×C4—4362no—
192C2×C4—4361no—
193C2×C4—4361no—
194C2×C4—4362no—
195C2×C4—4361no—
196C2×C4—2182no—
197C2×C4—2181no—
198C2×C4—2181no—
199C2×C4—2181no—
200C2×C4—2181no—
201C2×C4D4×D10911yescharacteristic
202C2×C4C2×C22⋊D10911yescharacteristic
203C8—41no—
204C8—4361no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—4361no—
211C22—4361no—
212C22—4361no—
213C22#1681266711yescharacteristic
214C22D8×D10911yescharacteristic
215C22#1681272311yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—81no—
220C4—4362no—
221C4—4361no—
222C4—4361no—
223C4—2182no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—8721no—
228C2#2029515811yescharacteristic
229C2#2029520711yescharacteristic
230C2#2029521511yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#480×C109C2
socleC22×C109#120
prime radical#20295603C2
hypercenter#480D109
hypocenterC109#1610
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20295339C2semidirect
3. #20294957C2semidirect
4. #20294761C2semidirect
5. #20294760C2semidirect
6. #20294751C2semidirect
7. #480×C109C2semidirect
116. C109#1610semidirect
119. #480D109semidirect

Maximal subgroups

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

subgroupindex
#202956032
#202953392
#202949572
#202947612
#202947602
#202947512
#480×C1092
#1610109