Finite Group Databasebeta

← #28378902

Subgroups — #28378902

Order 13952.

356 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D109⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#16812761C212yesmaximal
3#20295970C211yesmaximal, characteristic, complemented
4#20295899C212yesmaximal, complemented
5C4×D4×D109C211yesmaximal, characteristic
6C2×D109⋊C8C2212yes—
7C2×C4⋊#89137C2212yes—
8#16812766—21no—
9C4⋊#11724786—21no—
10#16812761—24no—
11(C2×#89137)⋊C4—21no—
12(C2×#89137)⋊C4—21no—
13C2×D4×D109C2211yescharacteristic
14C22×C4×D109—21no—
15C4×D436C411yescharacteristic, complemented
16D4×Dic109C411yescharacteristic, complemented
17#16812661C411yescharacteristic, complemented
18C4×C22⋊D109—21no—
19#16812659—21no—
20C4⋊C4×D109C2211yescharacteristic
21C22⋊C4×D109—21no—
22C42×D109C2211yescharacteristic
23C4×D4×C109C411yescharacteristic, complemented
24C22×#89137—22no—
25D109⋊C8—22no—
26D109⋊C8—22no—
27C2×#11724786—22no—
28C4⋊#89137—22no—
29C4⋊#89137—22no—
30C23×D109—21no—
31C2×D436C2×C411yescharacteristic
32C2×C22⋊D109—21no—
33D4×D109—21no—
34D4×D109—21no—
35D4×D109D412yes—
36D4×D109Q812yes—
37C22×Dic109—21no—
38C2×C4×D109—21no—
39C2×C4×D109—21no—
40C2×C4×D109—21no—
41C2×C4×D109—44no—
42C2×C4×D109D411yescharacteristic
43C2×C4×D109D411yescharacteristic
44C2×C4×D109C2311yescharacteristic
45C4⋊Dic109C2×C411yescharacteristic
46#13182008—21no—
47C22⋊Dic109—21no—
48#13182006—21no—
49#13182006—21no—
50C4×Dic109C2×C411yescharacteristic
51C4×Dic109D411yescharacteristic
52C4×Dic109D411yescharacteristic
53C2×D4×C109C2×C411yescharacteristic
54C22×C4×C109—21no—
55C4⋊C4×C109C2×C411yescharacteristic
56C22⋊C4×C109—21no—
57C42×C109C2×C411yescharacteristic
58C23×C109—21no—
59C22×D109—21no—
60C22×D109—22no—
61C22×D109—22no—
62C22×D109—42no—
63C22×D109—42no—
64C22×D109C2×D411yescharacteristic
65C2×#89137—42no—
66C2×#89137—42no—
67C2×#89137—42no—
68D4×C109—21no—
69D4×C109C4⋊C412yes—
70C2×C4×C109—21no—
71C2×C4×C109—42no—
72C2×C4×C109C22⋊C411yescharacteristic
73C2×C4×C109C22⋊C411yescharacteristic
74C2×C4×C109C22×C411yescharacteristic
75C22⋊D109—22no—
76C22⋊D109—22no—
77C2×Dic109—21no—
78C2×Dic109—42no—
79C2×Dic109C22⋊C411yescharacteristic
80C2×Dic109C22⋊C411yescharacteristic
81C2×Dic109C2×D411yescharacteristic
82D436—21no—
83D436C4⋊C412yes—
84C4×D109—22no—
85C4×D109—22no—
86C4×D109—42no—
87C4×D109—42no—
88C4×D109—42no—
89C4×D109C2×D411yescharacteristic
90C4×D109C2×Q811yescharacteristic
91C4×D109#4111yescharacteristic
92C4×D109#4111yescharacteristic
93#11724786—42no—
94C22×C109—22no—
95C22×C109—41no—
96C22×C109—41no—
97C22×C109C2×C22⋊C411yescharacteristic
98C2×D109—22no—
99C2×D109—41no—
100C2×D109—41no—
101C2×D109—44no—
102C2×D109—44no—
103C2×D109#12111yescharacteristic
104C2×D109C22⋊Q811yescharacteristic
105C2×D109#13512yes—
106C2×D109AGL(1,ℤ/8)12yes—
107#89137—82no—
108C4×C109—21no—
109C4×C109—21no—
110C4×C109—41no—
111C4×C109C2×C4⋊C411yescharacteristic
112C4×C109#11711yescharacteristic
113Dic109—21no—
114Dic109—21no—
115Dic109—41no—
116Dic109#12111yescharacteristic
117Dic109C22⋊Q811yescharacteristic
118C2×C109—42no—
119C2×C109#38011yescharacteristic
120C2×C109#41611yescharacteristic
121C2×C109#41811yescharacteristic
122D109—42no—
123D109#46312yes—
124D109#47812yes—
125#1804—1091nomaximal, Sylow
126C109#180411yescharacteristic, complemented, Sylow
127C2×C4×D4—1091no—
128C2×C4⋊C8—1091no—
129C2×#102—1092no—
130#382—1091no—
131#340—1092no—
132C22×D4—1091no—
133C23×C4—2181no—
134C22×C8—1092no—
135C4×D4—1091no—
136C4×D4—1091no—
137C4×D4—1091no—
138C4×D4—2181no—
139C4×D4—2181no—
140C4×D4#8913711yescharacteristic, complemented
141C2×C4⋊C4—1091no—
142C2×C4⋊C4—1092no—
143C2×C22⋊C4—2181no—
144C2×C42—1091no—
145C4⋊C8—2181no—
146C4⋊C8—2181no—
147#102—2184no—
148#95—2181no—
149#95—2181no—
150C24—2181no—
151C2×D4—1092no—
152C2×D4—1092no—
153C2×D4—1091no—
154C2×D4—2181no—
155C2×D4—2181no—
156C2×D4—2181no—
157C2×D4C2×#8913711yescharacteristic
158C22×C4—21no—
159C22×C4—1091no—
160C22×C4—1091no—
161C22×C4—1091no—
162C22×C4—4364no—
163C22×C4—2181no—
164C22×C4—2181no—
165C22×C4—2181no—
166C22×C4—2182no—
167C22×C4—2181no—
168C2×C8—2182no—
169C2×C8—2182no—
170C2×C8—2182no—
171C4⋊C4—1091no—
172C4⋊C4—2181no—
173C4⋊C4—2182no—
174C4⋊C4—2182no—
175C4⋊C4C2×#8913711yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—2181no—
178C22⋊C4—2181no—
179C22⋊C4—2181no—
180C42—1091no—
181C42—1091no—
182C42—1091no—
183C42C2×#8913711yescharacteristic
184C23—21no—
185C23—1091no—
186C23—4362no—
187C23—4362no—
188C23—2182no—
189C23—2182no—
190C23—2181no—
191D4—21no—
192D4—1092no—
193D4—2182no—
194D4—2182no—
195D4—2181no—
196D4C4⋊#8913712yes—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—1091no—
200C2×C4—1091no—
201C2×C4—1091no—
202C2×C4—1091no—
203C2×C4—1091no—
204C2×C4—1091no—
205C2×C4—1091no—
206C2×C4—4362no—
207C2×C4—4362no—
208C2×C4—4362no—
209C2×C4—4362no—
210C2×C4—4362no—
211C2×C4—4362no—
212C2×C4—4362no—
213C2×C4—2182no—
214C2×C4—2182no—
215C2×C4—2181no—
216C2×C4C22⋊#8913711yescharacteristic
217C2×C4C22⋊#8913711yescharacteristic
218C2×C4C22×#8913711yescharacteristic
219C8—4362no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—1091no—
224C22—1091no—
225C22—1092no—
226C22—1092no—
227C22—4364no—
228C22—4364no—
229C22—4361no—
230C22—4361no—
231C22—2182no—
232C22C2×C22⋊#8913711yescharacteristic
233C4—21no—
234C4—21no—
235C4—41no—
236C4—8722no—
237C4—1091no—
238C4—1091no—
239C4—4361no—
240C4—2181no—
241C4—2181no—
242C4C2×C4⋊#8913711yescharacteristic
243C4#1681277811yescharacteristic
244C2—42no—
245C2—1092no—
246C2—1092no—
247C2—4362no—
248C2#2029596811yescharacteristic
249C2#2029601611yescharacteristic
250C2#2029601811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×D4×D109C22
cosocleC2×C4×D109C23
hypercenterC4×D4#89137
hypocenterC109#1804
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D109⋊(C4⋊C8)C2semidirect
3. #20295970C2semidirect
4. #20295899C2semidirect
15. C4×D436C4semidirect
16. D4×Dic109C4semidirect
17. #16812661C4semidirect
23. C4×D4×C109C4semidirect
126. C109#1804semidirect
140. C4×D4#89137semidirect

Maximal subgroups

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

subgroupindex
D109⋊(C4⋊C8)2
C2×#168127612
#202959702
#202958992
C4×D4×D1092
#1804109