Finite Group Databasebeta

← #28364045

Subgroups — #28364045

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×#16812724C211yesmaximal, characteristic, complemented
2C2×#16812695C211yesmaximal, characteristic, complemented
3C2×#16812626C211yesmaximal, characteristic, complemented
4#20295030C211yesmaximal, characteristic, complemented
5C2×#16812616C211yesmaximal, characteristic, complemented
6#20294785C211yesmaximal, characteristic, complemented
7#535×C109C211yesmaximal, characteristic, complemented
8C22×D436C2211yescharacteristic
9C22×C22⋊D109—22no—
10#16812724—22no—
11#16812724—22no—
12C2×#13182016—21no—
13C2×#13182014—21no—
14C2×#13182013C2211yescharacteristic
15C2×#13182013C2211yescharacteristic
16#16812695—22no—
17#16812695—22no—
18C2×C4×Dic109C2211yescharacteristic
19#16812626—22no—
20#16812619—22no—
21#16812616—22no—
22C2×#41×C109C2211yescharacteristic
23C22×D4×C109C2211yescharacteristic
24#127×C109—21no—
25#124×C109—21no—
26#121×C109—22no—
27#120×C109—22no—
28#117×C109C2211yescharacteristic
29C23×D109—21no—
30C2×D436—21no—
31C2×D436—21no—
32C2×D436—21no—
33C2×D436—21no—
34C2×D436—21no—
35C2×D436D412yescomplemented
36C2×C22⋊D109—28no—
37C2×C22⋊D109—48no—
38C22×Dic109—21no—
39#13182016—24no—
40#13182014—24no—
41#13182013—21no—
42#13182013—21no—
43#13182013—21no—
44#13182013D412yescomplemented
45C2×#11724784—21no—
46C2×#11724784—21no—
47C4×Dic109—21no—
48C4×Dic109D412yescomplemented
49C24×C109D412yes—
50#41×C109—21no—
51#41×C109—21no—
52#41×C109—21no—
53#41×C109—21no—
54C2×Q8×C109D411yescharacteristic, complemented
55C2×D4×C109—21no—
56C2×D4×C109—24no—
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×C109D411yescharacteristic, complemented
64C22×C4×C109—21no—
65C22×C4×C109C2311yescharacteristic
66C4⋊C4×C109D412yescomplemented
67C22⋊C4×C109—24no—
68C22⋊C4×C109—21no—
69C42×C109—21no—
70C23×C109—22no—
71C23×C109—21no—
72C23×C109—22no—
73C23×C109—22no—
74C23×C109—44no—
75C23×C109C2×D411yescharacteristic
76C22×D109—22no—
77C22×D109—44no—
78C22×D109—41no—
79C22×D109—41no—
80Q8×C109—21no—
81Q8×C109—21no—
82D4×C109—21no—
83D4×C109—21no—
84D4×C109—41no—
85D4×C109—41no—
86D4×C109—41no—
87D4×C109—41no—
88D4×C109—41no—
89D4×C109—41no—
90D4×C109—84no—
91C2×C4×C109—22no—
92C2×C4×C109—21no—
93C2×C4×C109—41no—
94C2×C4×C109—41no—
95C2×C4×C109C2×D411yescharacteristic
96C2×C4×C109C2×D411yescharacteristic
97C2×C4×C109C2×D411yescharacteristic
98C2×C4×C109C2×D411yescharacteristic
99C2×C4×C109C2×D411yescharacteristic
100C2×C4×C109#4111yescharacteristic
101C22⋊D109—416no—
102C2×Dic109—24no—
103C2×Dic109—22no—
104D436—22no—
105D436—22no—
106D436—41no—
107D436—41no—
108#11724784—22no—
109#11724784—41no—
110C22×C109—22no—
111C22×C109—44no—
112C22×C109—41no—
113C22×C109—42no—
114C22×C109—42no—
115C22×C109—44no—
116C22×C109—82no—
117C22×C109#12011yescharacteristic
118C22×C109#12011yescharacteristic
119C22×C109#12111yescharacteristic
120C2×D109—44no—
121C2×D109—42no—
122C2×D109—82no—
123C2×D109—82no—
124C4×C109—41no—
125C4×C109—42no—
126C4×C109#12011yescharacteristic
127C4×C109#12111yescharacteristic
128C4×C109#12111yescharacteristic
129C4×C109#12711yescharacteristic
130Dic109—24no—
131C2×C109—21no—
132C2×C109—21no—
133C2×C109—81no—
134C2×C109—82no—
135C2×C109#39211yescharacteristic
136C2×C109#45312yes—
137D109—82no—
138#2002—1091nomaximal, Sylow
139C109#200211yescharacteristic, complemented, Sylow
140C2×AGL(1,ℤ/8)—1091no—
141#535D10911yescharacteristic, complemented
142C2×#127—1091no—
143C2×#104—1091no—
144#418—1091no—
145C2×#100—1091no—
146#339—1091no—
147C2×#41C2×D10911yescharacteristic
148C22×D4—1091no—
149C22×D4—2182no—
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—21no—
158#127—2182no—
159#127—2182no—
160#124—21no—
161#121—22no—
162#120—22no—
163#117C2×D10911yescharacteristic
164C2×C42—1091no—
165#104—2182no—
166#102—2182no—
167#100—2182no—
168C24—2181no—
169C24C22⋊D10912yes—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D10911yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—24no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—1092no—
184C2×D4—4368no—
185C2×D4—2188no—
186C2×D4—2181no—
187C2×D4—2181no—
188C2×D4—2181no—
189C2×D4—2181no—
190C2×D4—2181no—
191C2×D4C22⋊D10911yescharacteristic, complemented
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⋊C4C22⋊D10912yescomplemented
204C22⋊C4—24no—
205C22⋊C4—21no—
206C42—21no—
207C42—1092no—
208C42—2181no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—44no—
214C23—4364no—
215C23—4361no—
216C23—4361no—
217C23—2182no—
218C23C2×C22⋊D10911yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—84no—
230D4—43616no—
231D4—4361no—
232D4—4361no—
233D4—2182no—
234D4—2182no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—2184no—
240C2×C4—2182no—
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—41no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—8722no—
257C22—8722no—
258C22—4364no—
259C22—4362no—
260C22#1681266711yescharacteristic
261C22#1681266811yescharacteristic
262C22#1681267111yescharacteristic
263C4—41no—
264C4—42no—
265C4—2184no—
266C4#1681266711yescharacteristic
267C4#1681267011yescharacteristic
268C4#1681267111yescharacteristic
269C4#1681269511yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—8722no—
275C2#2029493411yescharacteristic
276C2#2029519412yes—
subgroupG/H
centerC22#16812668
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#535×C109C2
socleC22×C109#120
hypercenter#535D109
hypocenterC109#2002
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16812724C2semidirect
2. C2×#16812695C2semidirect
3. C2×#16812626C2semidirect
4. #20295030C2semidirect
5. C2×#16812616C2semidirect
6. #20294785C2semidirect
7. #535×C109C2semidirect
35. C2×D436D4semidirect
44. #13182013D4semidirect
48. C4×Dic109D4semidirect
54. C2×Q8×C109D4semidirect
63. C2×D4×C109D4semidirect
66. C4⋊C4×C109D4semidirect
139. C109#2002semidirect
141. #535D109semidirect
174. C2×Q8C22⋊D109semidirect
191. C2×D4C22⋊D109semidirect
203. C4⋊C4C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127242
C2×#168126952
C2×#168126262
#202950302
C2×#168126162
#202947852
#535×C1092
#2002109