Finite Group Databasebeta

← #28373155

Subgroups — #28373155

Order 13952.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#20295576C211yesmaximal, characteristic
2C2×C4×Dic218C211yesmaximal, characteristic, complemented
3#20295340C212yesmaximal, complemented
4#20295322C212yesmaximal, complemented
5#20295227C212yesmaximal, complemented
6#20295167C212yesmaximal, complemented
7#20295128C214yesmaximal, complemented
8#432×C109C211yesmaximal, characteristic, complemented
9C2×#13182029—21no—
10C22×Dic218C2211yescharacteristic
11C2×#13182018C2214yes—
12#16812699C2211yescharacteristic
13#16812696C2211yescharacteristic
14#16812687—21no—
15#16812673—21no—
16#16812673C2212yes—
17C4×Dic218—21no—
18C4×Dic218—21no—
19C4×Dic218C2212yes—
20C4×Dic218C2212yes—
21C4×D436—21no—
22C4×D436C2212yes—
23C2×C4⋊Dic109C2211yescharacteristic
24C2×#13182008—21no—
25C2×C4×Dic109—21no—
26#16812633C2214yes—
27#16812624C2214yes—
28#16812621C2214yes—
29C2×C42×C109C2211yescharacteristic
30C4⋊C8×C109C2212yes—
31C22⋊C8×C109C2212yes—
32#97×C109C2212yes—
33#13182029—44no—
34C2×Dic218—21no—
35C2×Dic218—24no—
36C2×Dic218—21no—
37C2×Dic218C2312yes—
38C2×D436—21no—
39C2×D436—21no—
40C2×D436C2312yes—
41C2×C22⋊D109—22no—
42C22×Dic109—21no—
43C22×Dic109—21no—
44C2×C4×D109—22no—
45#13182018—28no—
46C4⋊Dic109—21no—
47C4⋊Dic109—21no—
48C4⋊Dic109C2312yes—
49C4⋊Dic109C2312yes—
50#13182008—22no—
51#13182008—22no—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109—22no—
55C4×Dic109—22no—
56C22×C4×C109D411yescharacteristic
57C22×C4×C109D411yescharacteristic
58C22×C4×C109C2311yescharacteristic
59C2×C8×C109C2314yes—
60C42×C109D411yescharacteristic
61C42×C109D411yescharacteristic
62C42×C109C2311yescharacteristic
63C42×C109C2311yescharacteristic
64C23×C109C2×D411yescharacteristic
65C22×D109—22no—
66C2×C4×C109—22no—
67C2×C4×C109—22no—
68C2×C4×C109—22no—
69C2×C4×C109C2×D411yescharacteristic
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109C2411yescharacteristic
75C22⋊D109—44no—
76C2×Dic109—24no—
77C2×Dic109—22no—
78C2×Dic109—22no—
79C2×Dic109—22no—
80C2×Dic109—42no—
81D436—24no—
82D436—42no—
83D436—42no—
84C4×D109—44no—
85Dic218—24no—
86Dic218—22no—
87Dic218—42no—
88Dic218#4114yescomplemented
89C8×C109—24no—
90C22×C109—21no—
91C22×C109—21no—
92C22×C109AGL(1,ℤ/8)12yes—
93C22×C109C22×D411yescharacteristic
94C2×D109—42no—
95C2×D109—42no—
96C2×D109—42no—
97C4×C109—21no—
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—21no—
101C4×C109#13712yes—
102C4×C109C2×#4112yes—
103Dic109—24no—
104Dic109—42no—
105Dic109—42no—
106C2×C109—22no—
107C2×C109#52511yescharacteristic
108C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C109C2×#13711yescharacteristic
110D109—82no—
111#3112—1091nomaximal, Sylow
112C109#311211yescharacteristic, complemented, Sylow
113#532—1091no—
114C2×C4×Q8—1091no—
115#480—1092no—
116#477—1092no—
117#460—1092no—
118#448—1092no—
119#440—1094no—
120#432D10911yescharacteristic, complemented
121C2×#41—2181no—
122C22×Q8—1091no—
123C2×SD16—1094no—
124C4⋊Q8—1091no—
125#127—1091no—
126#124—2181no—
127#121—1092no—
128#121—2181no—
129C4×Q8—1092no—
130C4×Q8—1092no—
131C4×Q8—2181no—
132C4×Q8—2181no—
133C4×D4—1092no—
134C4×D4—2181no—
135C2×C4⋊C4—1091no—
136C2×C4⋊C4—2181no—
137C2×C42—2181no—
138C2×C42C2×D10911yescharacteristic
139#107—1094no—
140C4⋊C8C2×D10912yes—
141#103—1094no—
142#102—1094no—
143C22⋊C8C2×D10912yes—
144#97C2×D10912yes—
145#41—4364no—
146C2×Q8—1092no—
147C2×Q8—2184no—
148C2×Q8—2181no—
149C2×Q8—2181no—
150C2×D4—1092no—
151C2×D4—2182no—
152C2×D4—2181no—
153C2×D4—2181no—
154C22×C4—2181no—
155C22×C4—2182no—
156C22×C4—2181no—
157C22×C4D43611yescharacteristic
158C22×C4D43611yescharacteristic
159C22×C4C22×D10911yescharacteristic
160SD16—2188no—
161C2×C8C22×D10914yes—
162C4⋊C4—1092no—
163C4⋊C4—1092no—
164C4⋊C4—2182no—
165C4⋊C4—2182no—
166C4⋊C4—2181no—
167C4⋊C4—2181no—
168C22⋊C4—2182no—
169C22⋊C4—2182no—
170C42—2182no—
171C42—2182no—
172C42D43611yescharacteristic
173C42D43611yescharacteristic
174C42C22×D10911yescharacteristic
175C42C22×D10911yescharacteristic
176C23—2182no—
177C23C2×D43611yescharacteristic
178Q8—1094no—
179Q8—4362no—
180Q8—2184no—
181Q8—2182no—
182D4—4362no—
183D4—4364no—
184D4—4362no—
185D4—2184no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—4364no—
190C2×C4—4362no—
191C2×C4—2182no—
192C2×C4—2182no—
193C2×C4—2184no—
194C2×C4—2182no—
195C2×C4C2×D43611yescharacteristic
196C2×C4C2×D43611yescharacteristic
197C2×C4C2×D43611yescharacteristic
198C2×C4C2×D43611yescharacteristic
199C2×C4C2×D43611yescharacteristic
200C2×C4C23×D10911yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—4362no—
205C22—4362no—
206C22—4362no—
207C22#1681272712yes—
208C22C22×D43611yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—4362no—
214C4—4362no—
215C4—2184no—
216C4#1681273212yes—
217C4#41×D10912yes—
218C2—22no—
219C2—8722no—
220C2#2029553811yescharacteristic
221C2C2×#1681272711yescharacteristic
222C2C2×#1681273211yescharacteristic
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#432×C109C2
socleC22×C109C22×D4
prime radical#20295576C2
hypercenter#432D109
hypocenterC109#3112
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic218C2semidirect
3. #20295340C2semidirect
4. #20295322C2semidirect
5. #20295227C2semidirect
6. #20295167C2semidirect
7. #20295128C2semidirect
8. #432×C109C2semidirect
88. Dic218#41semidirect
112. C109#3112semidirect
120. #432D109semidirect

Maximal subgroups

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

subgroupindex
#202955762
C2×C4×Dic2182
#202953402
#202953222
#202952272
#202951672
#202951282
#432×C1092
#3112109