Finite Group Databasebeta

← #28378411

Subgroups — #28378411

Order 13952.

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

normal subgroups only

This group has 284 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#20296044C211yesmaximal, characteristic, complemented
2C4×C4⋊#89137C211yesmaximal, characteristic, complemented
3#20295878C212yesmaximal, complemented
4#20295877C212yesmaximal, complemented
5#20295573C211yesmaximal, characteristic
6C2×C4⋊#89137—21no—
7C2×C4×#89137—21no—
8#16812766—21no—
9#16812756C2212yes—
10C4×#11724786—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—24no—
26C4×#89137—42no—
27#13182029—42no—
28#13182029—42no—
29C2×Dic218—21no—
30C2×D436—21no—
31C2×D436C2×C411yescharacteristic
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C2×C22⋊D109—21no—
35C2×C4×D109—21no—
36C2×C4×D109D411yescharacteristic
37C2×C4×D109D411yescharacteristic
38C2×C4×D109C2311yescharacteristic
39C4⋊Dic109C2×C411yescharacteristic
40#13182008—21no—
41C22⋊Dic109—21no—
42#13182006—21no—
43#13182006—21no—
44C4×Dic109C2×C411yescharacteristic
45C4×Dic109D411yescharacteristic
46C4×Dic109D411yescharacteristic
47C2×D4×C109C2×C411yescharacteristic
48C22×C4×C109—21no—
49C4⋊C4×C109C2×C411yescharacteristic
50C22⋊C4×C109—21no—
51C42×C109C2×C411yescharacteristic
52C23×C109—21no—
53C22×D109—21no—
54C22×D109C2×D411yescharacteristic
55C2×#89137—24no—
56C2×#89137—42no—
57C2×#89137—42no—
58D4×C109—41no—
59C2×C4×C109—21no—
60C2×C4×C109—42no—
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22⋊C411yescharacteristic
63C2×C4×C109C22×C411yescharacteristic
64C22⋊D109—41no—
65C22⋊D109—41no—
66C22⋊D109—42no—
67C22⋊D109—42no—
68C2×Dic109—21no—
69C2×Dic109C22⋊C411yescharacteristic
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C2×D411yescharacteristic
72D436—41no—
73D436—41no—
74D436—41no—
75C4×D109—22no—
76C4×D109—41no—
77C4×D109—42no—
78C4×D109D812yes—
79C4×D109SD1612yes—
80Dic218—42no—
81#11724786—42no—
82C22×C109—41no—
83C22×C109—41no—
84C22×C109—41no—
85C22×C109C2×C22⋊C411yescharacteristic
86C2×D109—21no—
87C2×D109—21no—
88C2×D109—41no—
89C2×D109—41no—
90C2×D109—41no—
91C2×D109C2×D811yescharacteristic
92C2×D109C2×SD1611yescharacteristic
93#89137—44no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—41no—
97C4×C109#10212yes—
98Dic109—21no—
99Dic109—41no—
100Dic109#10212yes—
101Dic109#10412yes—
102C2×C109—81no—
103C2×C109#41011yescharacteristic
104C2×C109C2×#10211yescharacteristic
105C2×C109C2×#10411yescharacteristic
106D109—21no—
107D109—21no—
108D109—81no—
109#1502—1091nomaximal, Sylow
110C109#150211yescharacteristic, complemented, Sylow
111#532—1091no—
112#431—1091no—
113C4×C4⋊C4—1091no—
114#327—1092no—
115#327—1092no—
116C2×#41—2181no—
117C4⋊Q8—1091no—
118#127—1091no—
119#124—2181no—
120#121—1091no—
121#121—1091no—
122#121—2181no—
123C4×D4—1091no—
124C4×D4—2181no—
125C4×D4#8913711yescharacteristic, complemented
126C2×C4⋊C4—2181no—
127C2×C42—1091no—
128C2×C42—2181no—
129C4⋊C8—2181no—
130C22⋊C8—1092no—
131C4×C8—2181no—
132#95—1092no—
133#41—4362no—
134#41—4362no—
135C2×Q8—2181no—
136C2×D4—1091no—
137C2×D4—2181no—
138C2×D4—2181no—
139C2×D4—2181no—
140C2×D4—2181no—
141C2×D4C2×#8913711yescharacteristic
142C22×C4—21no—
143C22×C4—1091no—
144C22×C4—1091no—
145C22×C4—1091no—
146C22×C4—2182no—
147C22×C4—2181no—
148C2×C8—2182no—
149C4⋊C4—1091no—
150C4⋊C4—2181no—
151C4⋊C4—2184no—
152C4⋊C4C2×#8913711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2181no—
155C22⋊C4—2181no—
156C22⋊C4—2181no—
157C42—1091no—
158C42—1091no—
159C42—1091no—
160C42—4362no—
161C42C2×#8913711yescharacteristic
162C23—21no—
163C23—1091no—
164C23—2181no—
165Q8—4362no—
166D4—41no—
167D4—4361no—
168D4—4361no—
169D4—4361no—
170D4—4362no—
171D4—4362no—
172D4—4361no—
173D4—4361no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—1092no—
179C2×C4—1092no—
180C2×C4—1091no—
181C2×C4—4361no—
182C2×C4—4362no—
183C2×C4—4362no—
184C2×C4—4362no—
185C2×C4—2182no—
186C2×C4—2184no—
187C2×C4—2181no—
188C2×C4C22⋊#8913711yescharacteristic
189C2×C4C22⋊#8913711yescharacteristic
190C2×C4C22×#8913711yescharacteristic
191C8—4362no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—1091no—
196C22—1091no—
197C22—4361no—
198C22—4361no—
199C22—4361no—
200C22—2181no—
201C22—2181no—
202C22C2×C22⋊#8913711yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1092no—
207C4—1092no—
208C4—4364no—
209C4—4361no—
210C4—2181no—
211C4#1681276112yes—
212C2—81no—
213C2—8721no—
214C2—2181no—
215C2—2181no—
216C2#2029600511yescharacteristic
217C2C2×#1681276111yescharacteristic
218C2D109⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1502
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296044C2semidirect
2. C4×C4⋊#89137C2semidirect
3. #20295878C2semidirect
4. #20295877C2semidirect
13. #16812698C4semidirect
14. #16812695C4semidirect
19. C4×D436C4semidirect
22. C4×D4×C109C4semidirect
110. C109#1502semidirect
125. C4×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202960442
C4×C4⋊#891372
#202958782
#202958772
#202955732
#1502109