Finite Group Databasebeta

← #28378903

Subgroups — #28378903

Order 13952.

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

normal subgroups only

This group has 292 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
2C2×#16812762C212yesmaximal
3#20295970C211yesmaximal, characteristic
4#20295899C212yesmaximal
5C4×Q8×D109C211yesmaximal, characteristic
6C2×D109⋊C8C2212yes—
7C2×C4⋊#89137C2212yes—
8#16812766—21no—
9C4⋊#11724786—21no—
10#16812762—24no—
11(C2×#89137)⋊C4—21no—
12(C2×#89137)⋊C4—21no—
13C2×Q8×D109C2211yescharacteristic
14Q8×Dic109C411yescharacteristic, complemented
15C4×Dic218—21no—
16C4×Dic218C411yescharacteristic, complemented
17#16812664—21no—
18#16812664C411yescharacteristic, complemented
19C4⋊C4×D109—21no—
20C4⋊C4×D109C2211yescharacteristic
21C42×D109—21no—
22C42×D109C2211yescharacteristic
23C4×Q8×C109C411yescharacteristic, complemented
24C22×#89137—22no—
25D109⋊C8—22no—
26D109⋊C8—22no—
27C2×#11724786—22no—
28C4⋊#89137—22no—
29C4⋊#89137—22no—
30C2×Dic218—21no—
31C2×Dic218C2×C411yescharacteristic
32Q8×D109—21no—
33Q8×D109—21no—
34Q8×D109D412yes—
35Q8×D109Q812yes—
36C2×C4×D109—21no—
37C2×C4×D109—21no—
38C2×C4×D109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40C2×C4×D109C2311yescharacteristic
41C4⋊Dic109—21no—
42C4⋊Dic109C2×C411yescharacteristic
43#13182008—21no—
44#13182008—21no—
45#13182008—21no—
46C4×Dic109—21no—
47C4×Dic109—21no—
48C4×Dic109—21no—
49C4×Dic109C2×C411yescharacteristic
50C4×Dic109D411yescharacteristic
51C4×Dic109D411yescharacteristic
52C2×Q8×C109C2×C411yescharacteristic
53C4⋊C4×C109—21no—
54C4⋊C4×C109C2×C411yescharacteristic
55C42×C109—21no—
56C42×C109C2×C411yescharacteristic
57C22×D109C2×D411yescharacteristic
58C2×#89137—42no—
59C2×#89137—42no—
60C2×#89137—42no—
61Q8×C109—21no—
62Q8×C109C4⋊C412yes—
63C2×C4×C109—21no—
64C2×C4×C109—21no—
65C2×C4×C109C22⋊C411yescharacteristic
66C2×C4×C109C22⋊C411yescharacteristic
67C2×C4×C109C22×C411yescharacteristic
68C2×Dic109—21no—
69C2×Dic109—21no—
70C2×Dic109C22⋊C411yescharacteristic
71C2×Dic109C22⋊C411yescharacteristic
72C2×Dic109C2×D411yescharacteristic
73C4×D109—22no—
74C4×D109—22no—
75C4×D109—22no—
76C4×D109—22no—
77C4×D109—42no—
78C4×D109C2×D411yescharacteristic
79C4×D109C2×Q811yescharacteristic
80C4×D109#4111yescharacteristic
81C4×D109#4111yescharacteristic
82Dic218—21no—
83Dic218—22no—
84Dic218—22no—
85Dic218C4⋊C412yes—
86#11724786—42no—
87C22×C109C2×C22⋊C411yescharacteristic
88C2×D109#12111yescharacteristic
89C2×D109C22⋊Q811yescharacteristic
90C2×D109#13512yes—
91C2×D109#13712yes—
92#89137—82no—
93C4×C109—22no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—41no—
97C4×C109C2×C4⋊C411yescharacteristic
98C4×C109#11711yescharacteristic
99Dic109—22no—
100Dic109—21no—
101Dic109—21no—
102Dic109—41no—
103Dic109#12111yescharacteristic
104Dic109C22⋊Q811yescharacteristic
105C2×C109#38011yescharacteristic
106C2×C109#41611yescharacteristic
107C2×C109#41911yescharacteristic
108D109#46412yes—
109D109#47912yes—
110#1805—1091nomaximal, Sylow
111C109#180511yescharacteristic, complemented, Sylow
112C2×C4×Q8—1091no—
113C2×C4⋊C8—1091no—
114C2×#103—1092no—
115#382—1091no—
116#340—1092no—
117C22×Q8—1091no—
118C22×C8—1092no—
119C4×Q8—1091no—
120C4×Q8—1091no—
121C4×Q8—1091no—
122C4×Q8—2181no—
123C4×Q8—2181no—
124C4×Q8#8913711yescharacteristic, complemented
125C2×C4⋊C4—1091no—
126C2×C4⋊C4—1092no—
127C2×C4⋊C4—2181no—
128C2×C42—1091no—
129C2×C42—2181no—
130C4⋊C8—2181no—
131C4⋊C8—2181no—
132#103—2184no—
133#95—2181no—
134#95—2181no—
135C2×Q8—1092no—
136C2×Q8—1092no—
137C2×Q8—1091no—
138C2×Q8—2181no—
139C2×Q8—2181no—
140C2×Q8—2181no—
141C2×Q8C2×#8913711yescharacteristic
142C22×C4—1091no—
143C22×C4—1091no—
144C22×C4—1091no—
145C22×C4—2181no—
146C22×C4—2181no—
147C22×C4—2182no—
148C2×C8—2182no—
149C2×C8—2182no—
150C2×C8—2182no—
151C4⋊C4—21no—
152C4⋊C4—1091no—
153C4⋊C4—2181no—
154C4⋊C4—2181no—
155C4⋊C4—2181no—
156C4⋊C4—2182no—
157C4⋊C4—2182no—
158C4⋊C4—2181no—
159C4⋊C4C2×#8913711yescharacteristic
160C42—21no—
161C42—1091no—
162C42—1091no—
163C42—1091no—
164C42—2181no—
165C42—2181no—
166C42—2181no—
167C42C2×#8913711yescharacteristic
168C23—1091no—
169Q8—21no—
170Q8—1092no—
171Q8—2182no—
172Q8—2182no—
173Q8—2181no—
174Q8C4⋊#8913712yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—1091no—
180C2×C4—1091no—
181C2×C4—1091no—
182C2×C4—1091no—
183C2×C4—1091no—
184C2×C4—4362no—
185C2×C4—4362no—
186C2×C4—4362no—
187C2×C4—4362no—
188C2×C4—2182no—
189C2×C4—2182no—
190C2×C4—2182no—
191C2×C4—2182no—
192C2×C4—2181no—
193C2×C4—2181no—
194C2×C4C22⋊#8913711yescharacteristic
195C2×C4C22⋊#8913711yescharacteristic
196C2×C4C22×#8913711yescharacteristic
197C8—4362no—
198C22—1091no—
199C22—1091no—
200C22—1092no—
201C22—1092no—
202C22C2×C22⋊#8913711yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—8722no—
208C4—1091no—
209C4—1091no—
210C4—4361no—
211C4—2182no—
212C4—2181no—
213C4—2181no—
214C4C2×C4⋊#8913711yescharacteristic
215C4#1681277811yescharacteristic
216C2—1092no—
217C2—1092no—
218C2#2029596811yescharacteristic
219C2#2029601611yescharacteristic
220C2#2029601911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C2×D4
cosocleC2×C4×D109C23
hypercenterC4×Q8#89137
hypocenterC109#1805
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic109C4semidirect
16. C4×Dic218C4semidirect
18. #16812664C4semidirect
23. C4×Q8×C109C4semidirect
111. C109#1805semidirect
124. C4×Q8#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×#168127622
#202959702
#202958992
C4×Q8×D1092
#1805109