Finite Group Databasebeta

← #27170065

Subgroups — #27170065

Order 12928.

310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 51 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#20265754C211yesmaximal, characteristic, complemented
2#20265311C211yesmaximal, characteristic, complemented
3#20265091C211yesmaximal, characteristic, complemented
4#20264912C211yesmaximal, characteristic, complemented
5#20264911C211yesmaximal, characteristic, complemented
6#20264902C211yesmaximal, characteristic, complemented
7#447×C101C211yesmaximal, characteristic, complemented
8C2×#13108073—21no—
9C2×#13108059—21no—
10#15692233—21no—
11#15692232—21no—
12#15692229C2211yescharacteristic
13#15692228—21no—
14#15692227—21no—
15#15692227—21no—
16C2×#13108053C2211yescharacteristic
17C2×C22⋊Dic101—21no—
18C2×C22⋊Dic101—21no—
19#15692176—21no—
20C22⋊#11717579C2211yescharacteristic
21#15692162C2211yescharacteristic
22C22×D4×C101C2211yescharacteristic
23C2×D8×C101—21no—
24#121×C101C2211yescharacteristic
25#102×C101—21no—
26C22⋊C8×C101C2211yescharacteristic
27#13108073—42no—
28#13108073—42no—
29C2×Dic202—21no—
30C2×D404D411yescharacteristic
31C2×C22⋊D101—21no—
32C2×C22⋊D101—21no—
33C2×C22⋊D101—21no—
34C22×Dic101—21no—
35C22×Dic101—21no—
36C22×Dic101D411yescharacteristic
37C22×Dic101D411yescharacteristic
38C2×C4×D101—21no—
39#13108059—42no—
40C2×#11717579—21no—
41C4⋊Dic101D411yescharacteristic
42#13108053—21no—
43#13108053—21no—
44#13108053—21no—
45C22⋊Dic101—21no—
46C22⋊Dic101—42no—
47C22⋊Dic101—42no—
48#13108051—21no—
49#13108051—21no—
50C24×C101—21no—
51C2×D4×C101—21no—
52C2×D4×C101—21no—
53C2×D4×C101—21no—
54C2×D4×C101—42no—
55C2×D4×C101D411yescharacteristic
56C22×C4×C101C2311yescharacteristic
57D8×C101—42no—
58C2×C8×C101—21no—
59C4⋊C4×C101D411yescharacteristic
60C22⋊C4×C101—21no—
61C23×C101—22no—
62C23×C101—21no—
63C23×C101—41no—
64C23×C101—41no—
65C23×C101—41no—
66C23×C101—41no—
67C23×C101—41no—
68C23×C101—41no—
69C23×C101C2×D411yescharacteristic
70C22×D101—21no—
71D4×C101—22no—
72D4×C101—22no—
73D4×C101—41no—
74D4×C101—41no—
75D4×C101—41no—
76D4×C101—41no—
77D4×C101—41no—
78C2×C4×C101—21no—
79C2×C4×C101—41no—
80C2×C4×C101C2×D411yescharacteristic
81C2×C4×C101C2×D411yescharacteristic
82C22⋊D101—42no—
83C22⋊D101—41no—
84C22⋊D101—41no—
85C22⋊D101—81no—
86C2×Dic101—21no—
87C2×Dic101—21no—
88C2×Dic101—21no—
89C2×Dic101—21no—
90C2×Dic101—42no—
91C2×Dic101—41no—
92C2×Dic101—41no—
93C2×Dic101—41no—
94C2×Dic101—41no—
95C2×Dic101D812yescomplemented
96D404—41no—
97C4×D101—42no—
98Dic202—42no—
99C8×C101—41no—
100#11717579—41no—
101C22×C101—21no—
102C22×C101—21no—
103C22×C101—42no—
104C22×C101—42no—
105C22×C101—41no—
106C22×C101—41no—
107C22×C101—41no—
108C22×C101—42no—
109C22×C101—81no—
110C22×C101—81no—
111C22×C101—81no—
112C22×C101—81no—
113C22×C101#12011yescharacteristic
114C22×C101C2×D811yescharacteristic
115C22×C101AGL(1,ℤ/8)11yescharacteristic
116C2×D101—41no—
117C2×D101—41no—
118C2×D101—41no—
119C4×C101—21no—
120C4×C101—21no—
121C4×C101—41no—
122Dic101—22no—
123Dic101—41no—
124Dic101—41no—
125Dic101—81no—
126C2×C101—21no—
127C2×C101—21no—
128C2×C101—81no—
129C2×C101—82no—
130C2×C101#44711yescharacteristic
131C2×C101#45411yescharacteristic
132C2×C101B(4,𝔽2)11yescharacteristic
133D101—81no—
134#1598—1011nomaximal, Sylow
135C101#159811yescharacteristic, complemented, Sylow
136#537—1011no—
137#447—1011no—
138#447D10111yescharacteristic, complemented
139#394—1011no—
140#327—1011no—
141#327—1011no—
142#324—1011no—
143C2×#41—2021no—
144C22×D4C2×D10111yescharacteristic
145C2×D8—21no—
146C2×D8—2021no—
147C22⋊Q8—2021no—
148C22⋊Q8—2021no—
149#121—1011no—
150#121—2021no—
151#121—2021no—
152#121—2021no—
153#121C2×D10111yescharacteristic
154C2×C4⋊C4—1011no—
155C2×C22⋊C4—2021no—
156C2×C22⋊C4—2021no—
157#102—21no—
158#102—2021no—
159C22⋊C8—1011no—
160C22⋊C8C2×D10111yescharacteristic
161#95—1011no—
162C24—21no—
163#41—4042no—
164#41—4042no—
165C2×Q8—2021no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—42no—
170C2×D4—1011no—
171C2×D4—2021no—
172C2×D4—2021no—
173C2×D4—2021no—
174C2×D4C22⋊D10111yescharacteristic
175C22×C4—1011no—
176C22×C4—1011no—
177C22×C4—2021no—
178C22×C4—2021no—
179C22×C4—2021no—
180C22×C4C22×D10111yescharacteristic
181D8—42no—
182D8—4042no—
183C2×C8—21no—
184C2×C8—2021no—
185C4⋊C4—1011no—
186C4⋊C4—2021no—
187C4⋊C4—2021no—
188C4⋊C4—2021no—
189C4⋊C4C22⋊D10111yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—4042no—
192C22⋊C4—4042no—
193C22⋊C4—2021no—
194C22⋊C4—2021no—
195C22⋊C4—2021no—
196C23—22no—
197C23—21no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—2021no—
205C23D4×D10111yescharacteristic
206Q8—4042no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—41no—
213D4—41no—
214D4—8081no—
215D4—4041no—
216D4—4041no—
217D4—4041no—
218D4—4042no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—1012no—
222C2×C4—4042no—
223C2×C4—4041no—
224C2×C4—4041no—
225C2×C4—4041no—
226C2×C4—4042no—
227C2×C4—4041no—
228C2×C4—2021no—
229C2×C4—2021no—
230C2×C4—2021no—
231C2×C4—2021no—
232C2×C4D4×D10111yescharacteristic
233C2×C4C2×C22⋊D10111yescharacteristic
234C8—41no—
235C8—4041no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—42no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—4041no—
249C22—4041no—
250C22—4041no—
251C22#1569222311yescharacteristic
252C22D8×D10111yescharacteristic
253C22#1569227911yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—8081no—
258C4—4041no—
259C4—4041no—
260C4—2022no—
261C2—21no—
262C2—21no—
263C2—82no—
264C2—81no—
265C2—8081no—
266C2#2026530911yescharacteristic
267C2#2026534811yescharacteristic
268C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#447×C101C2
socleC22×C101#120
hypercenter#447D101
hypocenterC101#1598
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20265754C2semidirect
2. #20265311C2semidirect
3. #20265091C2semidirect
4. #20264912C2semidirect
5. #20264911C2semidirect
6. #20264902C2semidirect
7. #447×C101C2semidirect
95. C2×Dic101D8semidirect
135. C101#1598semidirect
138. #447D101semidirect

Maximal subgroups

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

subgroupindex
#202657542
#202653112
#202650912
#202649122
#202649112
#202649022
#447×C1012
#1598101