Finite Group Databasebeta

← #28364047

Subgroups — #28364047

Order 13952.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#16812725C211yesmaximal, characteristic, complemented
2#20295593C211yesmaximal, characteristic, complemented
3C2×#16812627C211yesmaximal, characteristic, complemented
4#20295031C211yesmaximal, characteristic, complemented
5C2×#16812616C211yesmaximal, characteristic, complemented
6#20294786C211yesmaximal, characteristic, complemented
7C2×#127×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9#16812725—22no—
10#16812725—22no—
11C2×#13182017—21no—
12C2×#13182014—21no—
13C2×#13182013C2211yescharacteristic
14C2×#13182013C2211yescharacteristic
15#16812695—21no—
16#16812686—21no—
17#16812670—22no—
18#16812668—22no—
19#16812658C2211yescharacteristic
20#16812627—22no—
21#16812620—22no—
22#16812616—22no—
23C22×D4×C109—22no—
24C22×D4×C109C2211yescharacteristic
25C22×D4×C109C2211yescharacteristic
26#127×C109—22no—
27#127×C109—22no—
28C2×C42×C109C2211yescharacteristic
29#13182029—21no—
30#13182029—21no—
31#13182029—21no—
32#13182029—21no—
33C2×Dic218D411yescharacteristic, complemented
34C2×D436D411yescharacteristic, complemented
35C2×C22⋊D109—21no—
36C2×C22⋊D109—24no—
37C2×C4×D109—21no—
38#13182017—24no—
39#13182014—24no—
40#13182013—21no—
41#13182013—21no—
42#13182013—21no—
43#13182013D412yescomplemented
44C2×#11724784—21no—
45C2×#11724784—21no—
46C4⋊Dic109D412yescomplemented
47C22⋊Dic109—24no—
48C22⋊Dic109—21no—
49C4×Dic109—21no—
50C24×C109—21no—
51C24×C109D412yes—
52C2×D4×C109—28no—
53C2×D4×C109—21no—
54C2×D4×C109—21no—
55C2×D4×C109—21no—
56C2×D4×C109—21no—
57C2×D4×C109—21no—
58C2×D4×C109—21no—
59C2×D4×C109—21no—
60C2×D4×C109—21no—
61C2×D4×C109—21no—
62C2×D4×C109—21no—
63C2×D4×C109—21no—
64C2×D4×C109—48no—
65C2×D4×C109D412yescomplemented
66C22×C4×C109—21no—
67C22×C4×C109C2311yescharacteristic
68C42×C109—21no—
69C42×C109D412yescomplemented
70C23×C109—22no—
71C23×C109—22no—
72C23×C109—22no—
73C23×C109—22no—
74C23×C109—44no—
75C23×C109—44no—
76C23×C109—41no—
77C23×C109—41no—
78C23×C109C2×D411yescharacteristic
79C22×D109—21no—
80D4×C109—22no—
81D4×C109—22no—
82D4×C109—416no—
83D4×C109—41no—
84D4×C109—41no—
85D4×C109—41no—
86D4×C109—41no—
87D4×C109—41no—
88D4×C109—41no—
89C2×C4×C109—24no—
90C2×C4×C109—22no—
91C2×C4×C109C2×D411yescharacteristic
92C2×C4×C109C2×D411yescharacteristic
93C2×C4×C109C2×D411yescharacteristic
94C2×C4×C109C2×D411yescharacteristic
95C2×C4×C109C2×D411yescharacteristic
96C2×C4×C109#4111yescharacteristic
97C22⋊D109—41no—
98C22⋊D109—41no—
99C22⋊D109—84no—
100C2×Dic109—22no—
101C2×Dic109—21no—
102D436—21no—
103D436—21no—
104C4×D109—41no—
105C4×D109—41no—
106Dic218—21no—
107Dic218—21no—
108#11724784—22no—
109#11724784—41no—
110C22×C109—22no—
111C22×C109—44no—
112C22×C109—44no—
113C22×C109—42no—
114C22×C109—42no—
115C22×C109—44no—
116C22×C109—82no—
117C22×C109—82no—
118C22×C109—82no—
119C22×C109#12011yescharacteristic
120C22×C109#12011yescharacteristic
121C22×C109#12111yescharacteristic
122C2×D109—41no—
123C2×D109—42no—
124C4×C109—24no—
125C4×C109#12011yescharacteristic
126C4×C109#12111yescharacteristic
127C4×C109#12111yescharacteristic
128C4×C109#12711yescharacteristic
129Dic109—41no—
130Dic109—42no—
131C2×C109—21no—
132C2×C109—21no—
133C2×C109—82no—
134C2×C109—82no—
135C2×C109#39211yescharacteristic
136C2×C109#45312yes—
137D109—81no—
138#2002—1091nomaximal, Sylow
139C109#200211yescharacteristic, complemented, Sylow
140C2×AGL(1,ℤ/8)—1091no—
141#535—1091no—
142C2×#127D10911yescharacteristic, complemented
143C2×#104—1091no—
144#418—1091no—
145C2×#100—1091no—
146#339—1091no—
147C2×#41—1091no—
148C22×D4—22no—
149C22×D4C2×D10911yescharacteristic
150C22×D4C2×D10911yescharacteristic
151AGL(1,ℤ/8)—2182no—
152AGL(1,ℤ/8)—2182no—
153C2×SD16—2181no—
154C2×D8—2181no—
155C2×M16—1091no—
156C2×M16—1091no—
157#127—22no—
158#127—22no—
159#127—2181no—
160#124—2181no—
161#121—2182no—
162#120—2182no—
163#117—1091no—
164C2×C42C2×D10911yescharacteristic
165#104—2182no—
166#102—2182no—
167#100—2182no—
168C24—21no—
169C24C22⋊D10912yes—
170#41—2181no—
171#41—2181no—
172#41—2181no—
173#41—2181no—
174C2×Q8—1091no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—1091no—
189C2×D4—2184no—
190C2×D4—2181no—
191C2×D4C22⋊D10912yescomplemented
192C22×C4—21no—
193C22×C4—2181no—
194C22×C4C22×D10911yescharacteristic
195SD16—2184no—
196D8—2184no—
197M16—1092no—
198M16—2181no—
199M16—2181no—
200M16—2181no—
201C2×C8—2181no—
202C2×C8—2181no—
203C4⋊C4—1092no—
204C22⋊C4—2184no—
205C22⋊C4—2181no—
206C42—21no—
207C42—2181no—
208C42C22⋊D10912yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—2181no—
218C23C2×C22⋊D10911yescharacteristic
219Q8—2181no—
220Q8—2181no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—8724no—
231D4—4361no—
232D4—4361no—
233D4—2181no—
234D4—2181no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—4361no—
238C2×C4—4361no—
239C2×C4—2182no—
240C2×C4—2181no—
241C2×C4D4×D10911yescharacteristic
242C2×C4D4×D10911yescharacteristic
243C2×C4D4×D10911yescharacteristic
244C2×C4C2×C22⋊D10911yescharacteristic
245C2×C4C2×C22⋊D10911yescharacteristic
246C2×C4#1318202811yescharacteristic
247C8—4361no—
248C8—2182no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—4361no—
259C22—4362no—
260C22#1681266711yescharacteristic
261C22#1681266811yescharacteristic
262C22#1681267111yescharacteristic
263C4—24no—
264C4—4361no—
265C4—4362no—
266C4#1681266711yescharacteristic
267C4#1681267011yescharacteristic
268C4#1681267111yescharacteristic
269C4#1681269511yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—8721no—
275C2#2029493411yescharacteristic
276C2#2029519312yes—
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
FittingC2×#127×C109C2
socleC22×C109#120
hypercenterC2×#127D109
hypocenterC109#2002
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16812725C2semidirect
2. #20295593C2semidirect
3. C2×#16812627C2semidirect
4. #20295031C2semidirect
5. C2×#16812616C2semidirect
6. #20294786C2semidirect
7. C2×#127×C109C2semidirect
33. C2×Dic218D4semidirect
34. C2×D436D4semidirect
43. #13182013D4semidirect
46. C4⋊Dic109D4semidirect
65. C2×D4×C109D4semidirect
69. C42×C109D4semidirect
139. C109#2002semidirect
142. C2×#127D109semidirect
191. C2×D4C22⋊D109semidirect
208. C42C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127252
#202955932
C2×#168126272
#202950312
C2×#168126162
#202947862
C2×#127×C1092
#2002109