Finite Group Databasebeta

← #487×D109 #28373340

Subgroups — #487×D109 #28373340

Order 13952.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D109C211yesmaximal, characteristic
2C4⋊Q8×D109C211yesmaximal, characteristic
3#20295378C211yesmaximal, characteristic, complemented
4#20295377C211yesmaximal, characteristic, complemented
5#20295376C211yesmaximal, characteristic, complemented
6#20295375C214yesmaximal, complemented
7#103×D109C214yesmaximal
8C4×C8×D109C211yesmaximal, characteristic
9#487×C109C211yesmaximal, characteristic, complemented
10C2×Q8×D109—21no—
11C2×Q8×D109C2212yes—
12C2×C8×D109C2212yes—
13#16812699C2211yescharacteristic
14#16812699C2211yescharacteristic
15#16812698—21no—
16#16812698—21no—
17#16812698—21no—
18#16812698C2212yes—
19#16812697—21no—
20#16812697C2212yes—
21C4⋊C4×D109—21no—
22C4⋊C4×D109—21no—
23C4⋊C4×D109—21no—
24C4⋊C4×D109C2212yes—
25C42×D109C2211yescharacteristic
26#16812624C2214yes—
27#16812623C2214yes—
28#16812622C2214yes—
29C4×#11724784C2211yescharacteristic
30C8×Dic109C2212yes—
31C4⋊Q8×C109C2211yescharacteristic
32C4⋊Q8×C109C2211yescharacteristic
33#103×C109C2214yes—
34C4×C8×C109C2211yescharacteristic
35C2×Dic218—21no—
36C2×Dic218—22no—
37C2×Dic218—22no—
38C2×Dic218C2312yes—
39Q8×D109—28no—
40Q8×D109—44no—
41C2×C4×D109—22no—
42C2×C4×D109—22no—
43C2×C4×D109D411yescharacteristic
44C2×C4×D109D411yescharacteristic
45C2×C4×D109C2311yescharacteristic
46C2×#11724784C2312yes—
47C8×D109—24no—
48C4⋊Dic109—21no—
49C4⋊Dic109—21no—
50C4⋊Dic109—21no—
51C4⋊Dic109C2312yes—
52#13182008—22no—
53#13182008—22no—
54#13182008—22no—
55#13182008—22no—
56C4×Dic109D411yescharacteristic
57C4×Dic109D411yescharacteristic
58C4×Dic109C2311yescharacteristic
59C2×Q8×C109—21no—
60C2×Q8×C109C2312yes—
61C2×C8×C109C2312yes—
62C4⋊C4×C109—21no—
63C4⋊C4×C109—21no—
64C4⋊C4×C109—21no—
65C4⋊C4×C109C2312yes—
66C42×C109C2311yescharacteristic
67C22×D109C2×D411yescharacteristic
68Q8×C109—24no—
69Q8×C109—42no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109C2411yescharacteristic
75C2×Dic109—22no—
76C2×Dic109—22no—
77C2×Dic109C2×D411yescharacteristic
78C2×Dic109C2×D411yescharacteristic
79C2×Dic109C2×D411yescharacteristic
80C4×D109—44no—
81C4×D109—44no—
82C4×D109SD1614yes—
83C4×D109Q1614yes—
84C4×D109#4114yes—
85Dic218—24no—
86Dic218—42no—
87Dic218—44no—
88Dic218—44no—
89C8×C109—22no—
90#11724784—22no—
91C22×C109C22×D411yescharacteristic
92C2×D109#12412yes—
93C2×D109C2×SD1612yes—
94C2×D109C2×Q1612yes—
95C4×C109—42no—
96C4×C109—42no—
97C4×C109C2×SD1612yes—
98C4×C109C2×Q1612yes—
99C4×C109C2×#4112yes—
100Dic109—42no—
101Dic109—42no—
102Dic109#12412yes—
103Dic109C2×SD1612yes—
104Dic109C2×Q1612yes—
105C2×C109C2×#12411yescharacteristic
106C2×C109C22×SD1611yescharacteristic
107C2×C109C22×Q1611yescharacteristic
108D109#48714yesdirect product factor
109C2×#487—1091nomaximal, Sylow
110C109C2×#48711yescharacteristic, complemented, Sylow
111C2×C4⋊Q8—1091no—
112C2×C4⋊Q8—1091no—
113#487—1091no—
114#487—1091no—
115#487—1094no—
116#487—1091no—
117#487D10911yescharacteristic, direct product factor
118C2×#103—1094no—
119C2×C4×C8—1091no—
120C22×Q8—1092no—
121C22×Q8—2181no—
122C22×C8—1092no—
123C4⋊Q8—1092no—
124C4⋊Q8—1092no—
125C4⋊Q8—1091no—
126C4⋊Q8—1091no—
127C4⋊Q8—2181no—
128C4⋊Q8—2181no—
129C4⋊Q8—2181no—
130C4⋊Q8—2181no—
131C4⋊Q8C2×D10911yescharacteristic
132C4⋊Q8C2×D10911yescharacteristic
133C2×C4⋊C4—1092no—
134C2×C4⋊C4—2181no—
135C2×C4⋊C4—2181no—
136C2×C4⋊C4—2181no—
137C2×C42—1091no—
138#103—1094no—
139#103—1094no—
140#103—1094no—
141#103C2×D10914yes—
142C4×C8—1092no—
143C4×C8—1091no—
144C4×C8C2×D10911yescharacteristic
145C2×Q8—21no—
146C2×Q8—1092no—
147C2×Q8—4364no—
148C2×Q8—2182no—
149C2×Q8—2182no—
150C2×Q8—2188no—
151C2×Q8—2181no—
152C2×Q8C22×D10912yes—
153C22×C4—1091no—
154C22×C4—1091no—
155C22×C4—1091no—
156C22×C4—2182no—
157C22×C4—2182no—
158C2×C8—1092no—
159C2×C8—2184no—
160C2×C8C22×D10912yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—1092no—
165C4⋊C4—2182no—
166C4⋊C4—2182no—
167C4⋊C4—2182no—
168C4⋊C4—2182no—
169C4⋊C4—2181no—
170C4⋊C4—2181no—
171C4⋊C4—2181no—
172C4⋊C4C22×D10912yes—
173C42—1091no—
174C42—1091no—
175C42—1091no—
176C42C22×D10911yescharacteristic
177C23—1091no—
178Q8—24no—
179Q8—42no—
180Q8—4364no—
181Q8—4364no—
182Q8—4362no—
183Q8—2184no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—1091no—
187C2×C4—1091no—
188C2×C4—1091no—
189C2×C4—1094no—
190C2×C4—1094no—
191C2×C4—1094no—
192C2×C4—4364no—
193C2×C4—4364no—
194C2×C4—2182no—
195C2×C4—2182no—
196C2×C4D4×D10911yescharacteristic
197C2×C4D4×D10911yescharacteristic
198C2×C4C23×D10911yescharacteristic
199C8—22no—
200C8—2182no—
201C22—1092no—
202C22—1092no—
203C22—1092no—
204C22C2×D4×D10911yescharacteristic
205C4—42no—
206C4—42no—
207C4—1092no—
208C4—1092no—
209C4—1092no—
210C4—4362no—
211C4—4362no—
212C4SD16×D10912yes—
213C4Q16×D10912yes—
214C4#41×D10912yes—
215C2—1094no—
216C2#124×D10911yescharacteristic
217C2C2×SD16×D10911yescharacteristic
218C2C2×Q16×D10911yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#487×C109C2
socleC22×C109C22×D4
prime radicalC22×D109C2×D4
hypercenter#487D109
hypocenterC109C2×#487
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #20295378C2semidirect
4. #20295377C2semidirect
5. #20295376C2semidirect
6. #20295375C2semidirect
9. #487×C109C2semidirect
108. D109#487direct (N × H)
110. C109C2×#487semidirect
117. #487D109direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1092
#202953782
#202953772
#202953762
#202953752
#103×D1092
C4×C8×D1092
#487×C1092
C2×#487109