Finite Group Databasebeta

← #28361978

Subgroups — #28361978

Order 13952.

320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#20295176C211yesmaximal, characteristic, complemented
2#20295159C211yesmaximal, characteristic, complemented
3#20294935C211yesmaximal, characteristic, complemented
4#20294763C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294750C211yesmaximal, characteristic, complemented
7#538×C109C211yesmaximal, characteristic, complemented
8C22×D436C2211yescharacteristic
9C22×C22⋊D109—21no—
10C2×#13182016—21no—
11C2×#13182014—21no—
12C2×#13182006—21no—
13#16812619—21no—
14#16812619—21no—
15C22⋊#11724784C2211yescharacteristic
16C22⋊#11724784C2211yescharacteristic
17#16812606C2211yescharacteristic
18#126×C109—21no—
19#124×C109—21no—
20#123×C109—21no—
21C22⋊Q8×C109C2211yescharacteristic
22#121×C109—21no—
23#121×C109C2211yescharacteristic
24#120×C109—21no—
25C4×D4×C109—21no—
26C2×C22⋊C4×C109C2211yescharacteristic
27C23×D109—21no—
28C2×D436—21no—
29C2×D436—21no—
30C2×D436—42no—
31C2×C22⋊D109—42no—
32C2×C22⋊D109—42no—
33C2×C22⋊D109—42no—
34C22×Dic109—21no—
35#13182016—42no—
36#13182014—42no—
37C2×#11724784—21no—
38C2×#11724784—21no—
39#13182006—42no—
40C24×C109D411yescharacteristic
41C2×Q8×C109D411yescharacteristic, complemented
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—21no—
45C2×D4×C109D411yescharacteristic, complemented
46C22×C4×C109—21no—
47C22×C4×C109D411yescharacteristic
48C22×C4×C109C2311yescharacteristic
49C4⋊C4×C109—21no—
50C4⋊C4×C109—21no—
51C4⋊C4×C109D411yescharacteristic, complemented
52C4⋊C4×C109D411yescharacteristic, complemented
53C22⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C22⋊C4×C109—21no—
56C22⋊C4×C109—21no—
57C22⋊C4×C109—21no—
58C22⋊C4×C109—21no—
59C22⋊C4×C109—21no—
60C42×C109—21no—
61C23×C109—21no—
62C23×C109—21no—
63C23×C109—21no—
64C23×C109—21no—
65C23×C109—41no—
66C23×C109—41no—
67C23×C109C2×D411yescharacteristic
68C22×D109—22no—
69C22×D109—41no—
70C22×D109—41no—
71C22×D109—41no—
72C22×D109—41no—
73C22×D109—41no—
74C22×D109—41no—
75Q8×C109—41no—
76D4×C109—41no—
77D4×C109—41no—
78D4×C109—41no—
79D4×C109—81no—
80D4×C109—81no—
81C2×C4×C109—21no—
82C2×C4×C109—21no—
83C2×C4×C109—21no—
84C2×C4×C109—21no—
85C2×C4×C109—41no—
86C2×C4×C109—41no—
87C2×C4×C109—81no—
88C2×C4×C109C2×D411yescharacteristic
89C2×C4×C109C2×D411yescharacteristic
90C22⋊D109—48no—
91C2×Dic109—22no—
92C2×Dic109—41no—
93C2×Dic109—41no—
94D436—22no—
95D436—22no—
96D436—41no—
97D436—41no—
98#11724784—41no—
99#11724784—41no—
100C22×C109—21no—
101C22×C109—21no—
102C22×C109—42no—
103C22×C109—41no—
104C22×C109—41no—
105C22×C109—41no—
106C22×C109—41no—
107C22×C109—41no—
108C22×C109—41no—
109C22×C109—81no—
110C22×C109#12011yescharacteristic
111C22×C109#13511yescharacteristic
112C22×C109AGL(1,ℤ/8)11yescharacteristic
113C2×D109—42no—
114C2×D109—42no—
115C2×D109—42no—
116C2×D109—81no—
117C2×D109—81no—
118C2×D109—81no—
119C2×D109—81no—
120C4×C109—21no—
121C4×C109—21no—
122C4×C109—41no—
123C4×C109—41no—
124C4×C109—41no—
125C4×C109—41no—
126Dic109—42no—
127C2×C109—21no—
128C2×C109—21no—
129C2×C109—81no—
130C2×C109—81no—
131C2×C109#44911yescharacteristic
132C2×C109#45311yescharacteristic
133C2×C109B(4,𝔽2)11yescharacteristic
134D109—82no—
135#1600—1091nomaximal, Sylow
136C109#160011yescharacteristic, complemented, Sylow
137#538D10911yescharacteristic, complemented
138#450—1091no—
139#447—1091no—
140#392—1091no—
141#328—1091no—
142#327—1091no—
143#323—1091no—
144C22×D4—1091no—
145C22×D4—2181no—
146C2×SD16—2181no—
147C2×D8—2181no—
148#126—21no—
149#124—21no—
150#123—21no—
151C22⋊Q8C2×D10911yescharacteristic
152#121—21no—
153#121C2×D10911yescharacteristic
154#120—21no—
155C4×D4—21no—
156C2×C22⋊C4—2181no—
157C2×C22⋊C4C2×D10911yescharacteristic
158#102—2181no—
159#102—2181no—
160C22⋊C8—1091no—
161C22⋊C8—1091no—
162#95—1091no—
163C24—2181no—
164C24C22⋊D10911yescharacteristic
165C2×Q8C22⋊D10911yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—4362no—
170C2×D4—4362no—
171C2×D4—4362no—
172C2×D4—4362no—
173C2×D4—2181no—
174C2×D4—2181no—
175C2×D4C22⋊D10911yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—2181no—
178C22×C4C22⋊D10911yescharacteristic
179C22×C4C22×D10911yescharacteristic
180SD16—4362no—
181D8—4362no—
182C2×C8—2181no—
183C2×C8—2181no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4C22⋊D10911yescharacteristic, complemented
187C4⋊C4C22⋊D10911yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—21no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—4362no—
196C42—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23—4361no—
204C23—4361no—
205C23—4361no—
206C23—4361no—
207C23—4361no—
208C23—4361no—
209C23—2182no—
210C23C2×C22⋊D10911yescharacteristic
211Q8—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—4361no—
218D4—4361no—
219D4—4368no—
220D4—2182no—
221D4—2182no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—81no—
229C2×C4—4361no—
230C2×C4—4361no—
231C2×C4—2182no—
232C2×C4C2×C22⋊D10911yescharacteristic
233C2×C4C2×C22⋊D10911yescharacteristic
234C8—4361no—
235C8—4361no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—8721no—
247C22—8721no—
248C22—8721no—
249C22—8721no—
250C22—4362no—
251C22—4362no—
252C22—4362no—
253C22#1681266811yescharacteristic
254C22#1681271911yescharacteristic
255C22#1681272411yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—4362no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—81no—
267C2—8722no—
268C2#2029517111yescharacteristic
269C2#2029519411yescharacteristic
270C2#2029521311yescharacteristic
subgroupG/H
centerC22#16812668
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#538×C109C2
socleC22×C109#120
hypercenter#538D109
hypocenterC109#1600
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #20295176C2semidirect
2. #20295159C2semidirect
3. #20294935C2semidirect
4. #20294763C2semidirect
5. #20294760C2semidirect
6. #20294750C2semidirect
7. #538×C109C2semidirect
41. C2×Q8×C109D4semidirect
45. C2×D4×C109D4semidirect
51. C4⋊C4×C109D4semidirect
52. C4⋊C4×C109D4semidirect
136. C109#1600semidirect
137. #538D109semidirect
165. C2×Q8C22⋊D109semidirect
175. C2×D4C22⋊D109semidirect
186. C4⋊C4C22⋊D109semidirect
187. C4⋊C4C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202951762
#202951592
#202949352
#202947632
#202947602
#202947502
#538×C1092
#1600109