Finite Group Databasebeta

← #28378462

Subgroups — #28378462

Order 13952.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#20296045C211yesmaximal, characteristic, complemented
2#20295970C211yesmaximal, characteristic, complemented
3#20295878C212yesmaximal, complemented
4#20295877C212yesmaximal, complemented
5#20295573C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C4⋊#11724786—21no—
8#16812756C2212yes—
9C4×#11724786—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4C2212yes—
12C2×#13182029—21no—
13#16812698C411yescharacteristic, complemented
14#16812695C411yescharacteristic, complemented
15#16812685—21no—
16#16812674C2211yescharacteristic
17#16812672—21no—
18#16812670C2211yescharacteristic
19C4×D436C411yescharacteristic, complemented
20C4×C22⋊D109—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C4⋊#89137—42no—
26#13182029—42no—
27#13182029—42no—
28C2×Dic218—21no—
29C2×D436—21no—
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C2×C4×D109—21no—
35C2×C4×D109D411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C2×C4×D109C2311yescharacteristic
38C4⋊Dic109C2×C411yescharacteristic
39#13182008—21no—
40C22⋊Dic109—21no—
41#13182006—21no—
42#13182006—21no—
43C4×Dic109C2×C411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109D411yescharacteristic
46C2×D4×C109C2×C411yescharacteristic
47C22×C4×C109—21no—
48C4⋊C4×C109C2×C411yescharacteristic
49C22⋊C4×C109—21no—
50C42×C109C2×C411yescharacteristic
51C23×C109—21no—
52C22×D109—21no—
53C22×D109C2×D411yescharacteristic
54C2×#89137—42no—
55C2×#89137—42no—
56C2×#89137—42no—
57D4×C109—41no—
58C2×C4×C109—21no—
59C2×C4×C109—42no—
60C2×C4×C109C22⋊C411yescharacteristic
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22×C411yescharacteristic
63C22⋊D109—42no—
64C22⋊D109—41no—
65C22⋊D109—41no—
66C22⋊D109—42no—
67C2×Dic109—21no—
68C2×Dic109C22⋊C411yescharacteristic
69C2×Dic109C22⋊C411yescharacteristic
70C2×Dic109C2×D411yescharacteristic
71D436—41no—
72D436—41no—
73D436—41no—
74C4×D109—41no—
75C4×D109—41no—
76C4×D109—42no—
77C4×D109D812yes—
78C4×D109SD1612yes—
79Dic218—42no—
80#11724786—42no—
81C22×C109—41no—
82C22×C109—41no—
83C22×C109—41no—
84C22×C109C2×C22⋊C411yescharacteristic
85C2×D109—21no—
86C2×D109—21no—
87C2×D109—41no—
88C2×D109—41no—
89C2×D109—41no—
90C2×D109C2×D811yescharacteristic
91C2×D109C2×SD1611yescharacteristic
92#89137—82no—
93C4×C109—21no—
94C4×C109—21no—
95C4×C109—41no—
96C4×C109#10212yes—
97Dic109—21no—
98Dic109—21no—
99Dic109—41no—
100Dic109#10212yes—
101C2×C109—81no—
102C2×C109#41011yescharacteristic
103C2×C109C2×#10211yescharacteristic
104C2×C109#42111yescharacteristic
105D109—21no—
106D109—21no—
107D109—81no—
108#1517—1091nomaximal, Sylow
109C109#151711yescharacteristic, complemented, Sylow
110#532—1091no—
111#431—1091no—
112#382—1091no—
113#327—1092no—
114#327—1092no—
115C2×#41—2181no—
116C4⋊Q8—1091no—
117#127—1091no—
118#124—2181no—
119#121—1091no—
120#121—1091no—
121#121—2181no—
122C4×D4—1091no—
123C4×D4—2181no—
124C4×D4#8913711yescharacteristic, complemented
125C2×C4⋊C4—2181no—
126C2×C42—1091no—
127C4⋊C8—2181no—
128C22⋊C8—1092no—
129C4×C8—2181no—
130#95—1092no—
131#95—2181no—
132#41—4362no—
133#41—4362no—
134C2×Q8—2181no—
135C2×D4—1091no—
136C2×D4—2181no—
137C2×D4—2181no—
138C2×D4—2181no—
139C2×D4—2181no—
140C2×D4C2×#8913711yescharacteristic
141C22×C4—21no—
142C22×C4—1091no—
143C22×C4—1091no—
144C22×C4—1091no—
145C22×C4—2182no—
146C22×C4—2181no—
147C2×C8—2182no—
148C4⋊C4—1091no—
149C4⋊C4—4362no—
150C4⋊C4—2181no—
151C4⋊C4C2×#8913711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C22⋊C4—2181no—
156C42—1091no—
157C42—1091no—
158C42—1091no—
159C42C2×#8913711yescharacteristic
160C23—21no—
161C23—1091no—
162C23—2181no—
163Q8—4362no—
164D4—41no—
165D4—4361no—
166D4—4361no—
167D4—4361no—
168D4—4362no—
169D4—4361no—
170D4—4361no—
171D4—4362no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—1091no—
175C2×C4—1092no—
176C2×C4—1092no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—4361no—
180C2×C4—4361no—
181C2×C4—4362no—
182C2×C4—4362no—
183C2×C4—4362no—
184C2×C4—4362no—
185C2×C4—2181no—
186C2×C4C22⋊#8913711yescharacteristic
187C2×C4C22⋊#8913711yescharacteristic
188C2×C4C22×#8913711yescharacteristic
189C8—4362no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—1091no—
194C22—1091no—
195C22—4361no—
196C22—4361no—
197C22—4361no—
198C22—2181no—
199C22—2181no—
200C22C2×C22⋊#8913711yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—8722no—
205C4—1092no—
206C4—4361no—
207C4—2181no—
208C4—2181no—
209C4#1681276112yes—
210C2—81no—
211C2—8721no—
212C2—2181no—
213C2—2181no—
214C2#2029600511yescharacteristic
215C2C2×#1681276111yescharacteristic
216C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295573C2
cosocleC2×C4×D109C23
hypercenterC4×D4#89137
hypocenterC109#1517
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296045C2semidirect
2. #20295970C2semidirect
3. #20295878C2semidirect
4. #20295877C2semidirect
13. #16812698C4semidirect
14. #16812695C4semidirect
19. C4×D436C4semidirect
22. C4×D4×C109C4semidirect
109. C109#1517semidirect
124. C4×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202960452
#202959702
#202958782
#202958772
#202955732
#1517109