Finite Group Databasebeta

← #28375705

Subgroups — #28375705

Order 13952.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic218C211yesmaximal, characteristic
2#20295751C211yesmaximal, characteristic
3#20295376C211yesmaximal, characteristic
4#20295375C212yesmaximal
5#20295322C211yesmaximal, characteristic
6#20295319C212yesmaximal
7#20295234C212yesmaximal
8#20295150C211yesmaximal, characteristic
9Q16×Dic109C212yesmaximal
10C4×#13182019C211yesmaximal, characteristic
11#462×C109C211yesmaximal, characteristic
12C2×#13182019C2211yescharacteristic
13#16812699—21no—
14#16812699C2211yescharacteristic
15#16812698—22no—
16#16812698C2212yes—
17#16812697C2212yes—
18#16812690—21no—
19#16812689—22no—
20Q8×Dic109C2212yes—
21Q8×Dic109C2212yes—
22C4×Dic218—21no—
23C4×Dic218C2211yescharacteristic
24C4×Dic218C2211yescharacteristic
25#16812664—21no—
26#16812633C2212yes—
27#16812632C2211yescharacteristic
28#16812628C2212yes—
29#16812624C2212yes—
30#16812623C2212yes—
31#16812623C2211yescharacteristic
32#16812623C2212yes—
33#16812622C2211yescharacteristic
34C4×#11724784C2211yescharacteristic
35C8×Dic109C2212yes—
36C2×Q16×C109C2212yes—
37C4⋊Q8×C109C2211yescharacteristic
38C4×Q8×C109C2211yescharacteristic
39C4⋊C8×C109C2211yescharacteristic
40#103×C109C2212yes—
41C2×Dic218—21no—
42C2×Dic218—22no—
43C2×Dic218D411yescharacteristic
44C2×Dic218C2311yescharacteristic
45#13182019—22no—
46C2×#11724784C2311yescharacteristic
47C2×#11724784C2311yescharacteristic
48C4⋊Dic109—21no—
49C4⋊Dic109—22no—
50C4⋊Dic109—22no—
51C4⋊Dic109D411yescharacteristic
52C4⋊Dic109C2312yes—
53C4⋊Dic109C2311yescharacteristic
54#13182008—21no—
55#13182008—22no—
56#13182008—22no—
57#13182008—22no—
58#13182008D412yes—
59C4×Dic109—21no—
60C4×Dic109—22no—
61C4×Dic109—22no—
62C4×Dic109C2312yes—
63C2×Q8×C109C2312yes—
64C2×Q8×C109C2311yescharacteristic
65Q16×C109—24no—
66C2×C8×C109C2312yes—
67C4⋊C4×C109—21no—
68C4⋊C4×C109—21no—
69C4⋊C4×C109—21no—
70C4⋊C4×C109C2311yescharacteristic
71C42×C109—21no—
72C42×C109C2311yescharacteristic
73Q8×C109—21no—
74Q8×C109—22no—
75Q8×C109—22no—
76Q8×C109#4112yes—
77C2×C4×C109—21no—
78C2×C4×C109—21no—
79C2×C4×C109—22no—
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109C2×D411yescharacteristic
82C2×C4×C109C2411yescharacteristic
83C2×Dic109—21no—
84C2×Dic109—21no—
85C2×Dic109—22no—
86C2×Dic109C2×D412yes—
87C2×Dic109C2×D412yes—
88Dic218—21no—
89Dic218—21no—
90Dic218—82no—
91Dic218—81no—
92Dic218Q1614yescomplemented
93C8×C109—22no—
94#11724784—21no—
95#11724784—21no—
96C22×C109C22×D411yescharacteristic
97C4×C109—22no—
98C4×C109—21no—
99C4×C109—42no—
100C4×C109—41no—
101C4×C109C2×Q1612yes—
102C4×C109C2×#4111yescharacteristic
103C4×C1092−1+411yescharacteristic
104Dic109—22no—
105Dic109—41no—
106Dic109—42no—
107Dic109—41no—
108Dic109C2×Q1614yes—
109C2×C109#54811yescharacteristic
110C2×C109C22×Q1611yescharacteristic
111C2×C109#57711yescharacteristic
112#3363—1091nomaximal, Sylow
113C109#336311yescharacteristic, complemented, Sylow
114Q82—1091no—
115#557—1091no—
116#487—1091no—
117#487—1092no—
118#477—1091no—
119#477—1092no—
120#462—1092no—
121#462D10911yescharacteristic
122C8×Q8—1091no—
123C4×Q16—1092no—
124C4×Q16—1091no—
125C2×Q16—1091no—
126C2×Q16C2×D10912yes—
127C4⋊Q8—1092no—
128C4⋊Q8—1092no—
129C4⋊Q8—1091no—
130C4⋊Q8—2181no—
131C4⋊Q8—2182no—
132C4⋊Q8C2×D10911yescharacteristic
133#125—2182no—
134#125—2181no—
135C4×Q8—1091no—
136C4×Q8—1092no—
137C4×Q8—1092no—
138C4×Q8—1091no—
139C4×Q8—2181no—
140C4×Q8—2181no—
141C4×Q8C2×D10911yescharacteristic
142#107—1092no—
143#107—1091no—
144C4⋊C8—1092no—
145C4⋊C8C2×D10911yescharacteristic
146#103—1091no—
147#103—1092no—
148#103—1092no—
149#103—1092no—
150#103—1091no—
151#103C2×D10912yes—
152C4×C8—1092no—
153C4×C8—1091no—
154C2×Q8—1091no—
155C2×Q8—1091no—
156C2×Q8—2182no—
157C2×Q8—2181no—
158C2×Q8C22×D10912yes—
159C2×Q8C22×D10911yescharacteristic
160Q16—24no—
161Q16—2182no—
162C2×C8—1091no—
163C2×C8—1091no—
164C2×C8C22×D10912yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1092no—
169C4⋊C4—1091no—
170C4⋊C4—1092no—
171C4⋊C4—1091no—
172C4⋊C4—2182no—
173C4⋊C4—2182no—
174C4⋊C4—2182no—
175C4⋊C4—2182no—
176C4⋊C4—2182no—
177C4⋊C4—2181no—
178C4⋊C4—2181no—
179C4⋊C4C22×D10911yescharacteristic
180C42—21no—
181C42—1092no—
182C42—2182no—
183C42—2182no—
184C42—2181no—
185C42C22×D10911yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—8721no—
190Q8—8722no—
191Q8—1094no—
192Q8—2181no—
193Q8—2181no—
194Q8#1318202812yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—1092no—
199C2×C4—1092no—
200C2×C4—2181no—
201C2×C4—2182no—
202C2×C4—2181no—
203C2×C4D4×D10911yescharacteristic
204C2×C4D4×D10911yescharacteristic
205C2×C4C23×D10911yescharacteristic
206C8—22no—
207C8—2181no—
208C8—2181no—
209C22C2×D4×D10911yescharacteristic
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—1094no—
215C4—4361no—
216C4—4362no—
217C4—4361no—
218C4—2182no—
219C4Q16×D10912yes—
220C4C2×#1318202811yescharacteristic
221C4#1681274611yescharacteristic
222C2#2029568211yescharacteristic
223C2C2×Q16×D10911yescharacteristic
224C2#2029583511yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#462×C109C2
socle, prime radicalC22×C109C22×D4
hypercenter#462D109
hypocenterC109#3363
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
92. Dic218Q16semidirect
113. C109#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2182
#202957512
#202953762
#202953752
#202953222
#202953192
#202952342
#202951502
Q16×Dic1092
C4×#131820192
#462×C1092
#3363109