Finite Group Databasebeta

← #28378544

Subgroups — #28378544

Order 13952.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296029C211yesmaximal, characteristic, complemented
2C2×#16812766C211yesmaximal, characteristic, complemented
3#20295885C212yesmaximal, complemented
4#20295884C212yesmaximal, complemented
5#20295571C211yesmaximal, characteristic
6C2×#13182038—21no—
7C22×#11724786—21no—
8#16812766—21no—
9#16812766C2212yes—
10#16812766C2212yes—
11C4⋊#11724786—21no—
12C2×#13182028—21no—
13#16812698C2211yescharacteristic
14#16812695C2211yescharacteristic
15#16812685—21no—
16#16812673C411yescharacteristic
17#16812671—21no—
18D4×Dic109C411yescharacteristic
19#16812661C411yescharacteristic
20#16812659—21no—
21C2×C4×Dic109C2211yescharacteristic
22#121×C109C411yescharacteristic
23#13182038—42no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×#11724786—42no—
27#13182028—42no—
28#13182028—42no—
29C2×Dic218—21no—
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C22×Dic109—21no—
35C22×Dic109D411yescharacteristic
36C22×Dic109D411yescharacteristic
37C2×C4×D109—21no—
38C4⋊Dic109C2×C411yescharacteristic
39#13182008—21no—
40C22⋊Dic109—21no—
41#13182006—21no—
42#13182006—21no—
43C4×Dic109C2×C411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109D411yescharacteristic
46C4×Dic109C2311yescharacteristic
47C2×D4×C109—21no—
48C2×D4×C109C2×C411yescharacteristic
49C22×C4×C109C2×C411yescharacteristic
50C4⋊C4×C109C2×C411yescharacteristic
51C22⋊C4×C109—21no—
52C23×C109—21no—
53C23×C109C22⋊C411yescharacteristic
54C22×D109—21no—
55D4×C109—41no—
56D4×C109—42no—
57C2×C4×C109—21no—
58C2×C4×C109—41no—
59C2×C4×C109C22⋊C411yescharacteristic
60C2×C4×C109C22×C411yescharacteristic
61C22⋊D109—42no—
62C22⋊D109—41no—
63C22⋊D109—41no—
64C22⋊D109—41no—
65C22⋊D109—41no—
66C2×Dic109—21no—
67C2×Dic109—21no—
68C2×Dic109—21no—
69C2×Dic109—42no—
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C22⋊C411yescharacteristic
72C2×Dic109D812yes—
73C2×Dic109SD1612yes—
74C2×Dic109C2×D411yescharacteristic
75C2×Dic109C2×D411yescharacteristic
76D436—41no—
77C4×D109—42no—
78Dic218—41no—
79Dic218—41no—
80#11724786—42no—
81#11724786—42no—
82C22×C109—21no—
83C22×C109—21no—
84C22×C109—41no—
85C22×C109—41no—
86C22×C109—41no—
87C22×C109#10212yes—
88C22×C109C2×C22⋊C411yescharacteristic
89C2×D109—41no—
90C2×D109—41no—
91C2×D109—41no—
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—41no—
95Dic109—21no—
96Dic109—41no—
97Dic109#10212yes—
98Dic109C2×D811yescharacteristic
99Dic109C2×SD1611yescharacteristic
100Dic109AGL(1,ℤ/8)11yescharacteristic
101Dic109#13711yescharacteristic
102C2×C109—22no—
103C2×C109—81no—
104C2×C109#41311yescharacteristic
105C2×C109C2×#10211yescharacteristic
106C2×C109#41711yescharacteristic
107D109—81no—
108#1547—1091nomaximal, Sylow
109C109#154711yescharacteristic, complemented, Sylow
110#532—1091no—
111#423—1091no—
112C2×C4⋊C8—1091no—
113#332—1092no—
114#331—1092no—
115C2×#41—2181no—
116C2×M16—2181no—
117C22×C8—2181no—
118C4⋊Q8—1091no—
119#127—1091no—
120#124—2181no—
121#121—1091no—
122#121—2181no—
123#121#8913711yescharacteristic
124C4×D4—1091no—
125C4×D4—1091no—
126C4×D4—2181no—
127C2×C42—1091no—
128C4⋊C8—1092no—
129C4⋊C8—1092no—
130C4⋊C8—2181no—
131C4⋊C8—2181no—
132#41—4362no—
133#41—4362no—
134C2×Q8—2181no—
135C2×D4—21no—
136C2×D4—1091no—
137C2×D4—2181no—
138C2×D4—2181no—
139C2×D4—2181no—
140C2×D4C2×#8913711yescharacteristic
141C22×C4—1091no—
142C22×C4—1091no—
143C22×C4—2181no—
144C22×C4—2181no—
145C22×C4C2×#8913711yescharacteristic
146M16—4362no—
147C2×C8—4362no—
148C2×C8—2182no—
149C2×C8—2182no—
150C4⋊C4—1091no—
151C4⋊C4—2181no—
152C4⋊C4C2×#8913711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2181no—
155C22⋊C4—2181no—
156C22⋊C4—2181no—
157C42—1091no—
158C42—1091no—
159C42—1091no—
160C42—1091no—
161C23—21no—
162C23—2181no—
163C23C22⋊#8913711yescharacteristic
164Q8—4361no—
165Q8—4361no—
166D4—41no—
167D4—42no—
168D4—4361no—
169D4—4361no—
170D4—4361no—
171D4—4361no—
172D4—4361no—
173D4—4362no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—1092no—
177C2×C4—1092no—
178C2×C4—1091no—
179C2×C4—1091no—
180C2×C4—1091no—
181C2×C4—1091no—
182C2×C4—4362no—
183C2×C4—4362no—
184C2×C4—2181no—
185C2×C4—2181no—
186C2×C4—2181no—
187C2×C4C22⋊#8913711yescharacteristic
188C2×C4C22×#8913711yescharacteristic
189C8—4362no—
190C8—4362no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—4361no—
197C22—4361no—
198C22—4361no—
199C22#1681276112yes—
200C22C2×C22⋊#8913711yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—1091no—
205C4—1092no—
206C4—1091no—
207C4—1091no—
208C4—1091no—
209C4—4361no—
210C4—2181no—
211C2—22no—
212C2—81no—
213C2—8721no—
214C2#2029601311yescharacteristic
215C2C2×#1681276111yescharacteristic
216C2#2029601711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#121×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295571C2
cosocleC4×Dic109C23
hypercenter#121#89137
hypocenterC109#1547
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20296029C2semidirect
2. C2×#16812766C2semidirect
3. #20295885C2semidirect
4. #20295884C2semidirect
109. C109#1547semidirect

Maximal subgroups

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

subgroupindex
#202960292
C2×#168127662
#202958852
#202958842
#202955712
#1547109