Finite Group Databasebeta

← C113×#20348 #43288368

Subgroups — C113×#20348 #43288368

Order 28928.

2158 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#131×C113C211yesmaximal, characteristic
2C2×#520×C113C212yesmaximal
3C113×#1736C216yesmaximal, complemented
4C113×#1735C213yesmaximal, complemented
5C2×#340×C113C213yesmaximal, complemented
6C22×#41×C113C2211yescharacteristic
7C2×#131×C113—28no—
8C2×#131×C113C418yescomplemented
9C22×M16×C113C2213yes—
10C23×C8×C113C2213yes—
11#520×C113—28no—
12#520×C113C4116yescomplemented
13C2×C4×Q8×C113—22no—
14C2×C4×D4×C113—26no—
15C2×#117×C113C2216yes—
16C22×C4⋊C4×C113C2216yes—
17#340×C113C2213yes—
18#340×C113C2216yes—
19#340×C113C2211yescharacteristic
20#340×C113C2216yes—
21C2×#41×C113C2×C418yes—
22C2×#41×C113C2×C414yes—
23C2×#41×C113D418yes—
24C2×#41×C113Q814yes—
25C22×Q8×C113D411yescharacteristic
26C22×D4×C113D413yes—
27C23×C4×C113—26no—
28C23×C4×C113C2313yes—
29#131×C113—232no—
30C2×M16×C113—212no—
31C2×M16×C113C2×C4112yescomplemented
32C22×C8×C113—212no—
33C22×C8×C113C2×C4112yescomplemented
34C22×C8×C113C2311yescharacteristic
35C22×C8×C113C2313yes—
36C4×Q8×C113—216no—
37C4×D4×C113—248no—
38#117×C113—212no—
39#117×C113C2×C4124yescomplemented
40C2×C4⋊C4×C113—26no—
41C2×C4⋊C4×C113—212no—
42C2×C4⋊C4×C113C2×C4124yescomplemented
43C2×C4⋊C4×C113C2316yes—
44C2×C4⋊C4×C113C2312yes—
45C2×C22⋊C4×C113—26no—
46C2×C42×C113—26no—
47C24×C113C2×D413yes—
48#41×C113C42116yes—
49#41×C113C22⋊C4116yes—
50#41×C113C4⋊C4132yes—
51C2×Q8×C113C22⋊C418yes—
52C2×Q8×C113C4⋊C414yes—
53C2×D4×C113C22⋊C4124yes—
54C2×D4×C113C4⋊C4112yes—
55C22×C4×C113—22no—
56C22×C4×C113—26no—
57C22×C4×C113—224no—
58C22×C4×C113—86no—
59C22×C4×C113—86no—
60C22×C4×C113C22×C416yes—
61C22×C4×C113C22×C4112yes—
62C22×C4×C113C2×D413yes—
63C22×C4×C113C2×D4112yes—
64C22×C4×C113C2×Q816yes—
65C22×C4×C113C2411yescharacteristic
66M16×C113—224no—
67C2×C8×C113—224no—
68C2×C8×C113—22no—
69C2×C8×C113—26no—
70C2×C8×C113C22×C412yes—
71C2×C8×C113C22×C416yes—
72C4⋊C4×C113—224no—
73C4⋊C4×C113—26no—
74C4⋊C4×C113—22no—
75C4⋊C4×C113C22×C4112yes—
76C4⋊C4×C113C22×C414yes—
77C22⋊C4×C113—224no—
78C42×C113—224no—
79C23×C113—23no—
80C23×C113—26no—
81C23×C113—23no—
82C23×C113C2×C22⋊C4112yes—
83C23×C113C2×C4⋊C416yes—
84C23×C113C22×D411yescharacteristic
85Q8×C113#95116yes—
86D4×C113#95148yes—
87C2×C4×C113—24no—
88C2×C4×C113—212no—
89C2×C4×C113—46no—
90C2×C4×C113—42no—
91C2×C4×C113—46no—
92C2×C4×C113—42no—
93C2×C4×C113—824no—
94C2×C4×C113C2×C42112yes—
95C2×C4×C113C2×C22⋊C4112yes—
96C2×C4×C113C2×C22⋊C4112yes—
97C2×C4×C113C2×C4⋊C4124yes—
98C2×C4×C113C2×C4⋊C416yes—
99C2×C4×C113C23×C411yescharacteristic
100C2×C4×C113C23×C412yes—
101C2×C4×C113C22×D412yes—
102C2×C4×C113C22×Q811yescharacteristic
103C8×C113—22no—
104C8×C113—26no—
105C22×C113—212no—
106C22×C113—212no—
107C22×C113—26no—
108C22×C113—26no—
109C22×C113C2×#95112yes—
110C22×C113C22×C22⋊C412yes—
111C22×C113C22×C4⋊C411yescharacteristic
112C22×C113#57611yescharacteristic
113C22×C113#57712yes—
114C22×C113#57811yescharacteristic
115C4×C113—412no—
116C4×C113—44no—
117C4×C113C2×#95112yes—
118C4×C113C22×C4211yescharacteristic
119C4×C113C22×C22⋊C411yescharacteristic
120C4×C113C22×C4⋊C412yes—
121#20348C11311yesmaximal, characteristic, direct product factor, Sylow
122C2×C113—212no—
123C2×C113C22×#9511yescharacteristic
124C2×C113#289712yes—
125C2×C113#289812yes—
126C2×C113#291211yescharacteristic
127C2×C113#291311yescharacteristic
128C22×#131C2×C11311yescharacteristic
129C2×#520C2×C11312yes—
130#1736C2×C11316yescomplemented
131#1735C2×C11313yescomplemented
132C2×#340C2×C11313yescomplemented
133C113#2034811yescharacteristic, direct product factor, Sylow
134C22×#41C22×C11311yescharacteristic
135C2×#131—28no—
136C2×#131C4×C11318yescomplemented
137C22×M16C22×C11313yes—
138C23×C8C22×C11313yes—
139#520—28no—
140#520C4×C113116yescomplemented
141C2×C4×Q8—22no—
142C2×C4×D4—26no—
143C2×#117C22×C11316yes—
144C22×C4⋊C4C22×C11316yes—
145#340C22×C11313yes—
146#340C22×C11316yes—
147#340C22×C11311yescharacteristic
148#340C22×C11316yes—
149C2×#41C2×C4×C11318yes—
150C2×#41C2×C4×C11314yes—
151C2×#41D4×C11318yes—
152C2×#41Q8×C11314yes—
153C22×Q8D4×C11311yescharacteristic
154C22×D4D4×C11313yes—
155C23×C4—26no—
156C23×C4C23×C11313yes—
157#131—232no—
158C2×M16—212no—
159C2×M16C2×C4×C113112yescomplemented
160C22×C8—212no—
161C22×C8C2×C4×C113112yescomplemented
162C22×C8C23×C11311yescharacteristic
163C22×C8C23×C11313yes—
164C4×Q8—216no—
165C4×D4—248no—
166#117—212no—
167#117C2×C4×C113124yescomplemented
168C2×C4⋊C4—26no—
169C2×C4⋊C4—212no—
170C2×C4⋊C4C2×C4×C113124yescomplemented
171C2×C4⋊C4C23×C11316yes—
172C2×C4⋊C4C23×C11312yes—
173C2×C22⋊C4—26no—
174C2×C42—26no—
175C24C2×D4×C11313yes—
176#41C42×C113116yes—
177#41C22⋊C4×C113116yes—
178#41C4⋊C4×C113132yes—
179C2×Q8C22⋊C4×C11318yes—
180C2×Q8C4⋊C4×C11314yes—
181C2×D4C22⋊C4×C113124yes—
182C2×D4C4⋊C4×C113112yes—
183C22×C4—22no—
184C22×C4—26no—
185C22×C4—224no—
186C22×C4—86no—
187C22×C4—86no—
188C22×C4C22×C4×C11316yes—
189C22×C4C22×C4×C113112yes—
190C22×C4C2×D4×C11313yes—
191C22×C4C2×D4×C113112yes—
192C22×C4C2×Q8×C11316yes—
193C22×C4C24×C11311yescharacteristic
194M16—224no—
195C2×C8—224no—
196C2×C8—22no—
197C2×C8—26no—
198C2×C8C22×C4×C11312yes—
199C2×C8C22×C4×C11316yes—
200C4⋊C4—224no—
201C4⋊C4—26no—
202C4⋊C4—22no—
203C4⋊C4C22×C4×C113112yes—
204C4⋊C4C22×C4×C11314yes—
205C22⋊C4—224no—
206C42—224no—
207C23—23no—
208C23—26no—
209C23—23no—
210C23C2×C22⋊C4×C113112yes—
211C23C2×C4⋊C4×C11316yes—
212C23C22×D4×C11311yescharacteristic
213Q8#95×C113116yes—
214D4#95×C113148yes—
215C2×C4—24no—
216C2×C4—212no—
217C2×C4—46no—
218C2×C4—46no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—824no—
222C2×C4C2×C42×C113112yes—
223C2×C4C2×C22⋊C4×C113112yes—
224C2×C4C2×C22⋊C4×C113112yes—
225C2×C4C2×C4⋊C4×C113124yes—
226C2×C4C2×C4⋊C4×C11316yes—
227C2×C4C23×C4×C11311yescharacteristic
228C2×C4C23×C4×C11312yes—
229C2×C4C22×D4×C11312yes—
230C2×C4C22×Q8×C11311yescharacteristic
231C8—22no—
232C8—26no—
233C22—212no—
234C22—212no—
235C22—26no—
236C22—26no—
237C22C2×#95×C113112yes—
238C22C22×C22⋊C4×C11312yes—
239C22C22×C4⋊C4×C11311yescharacteristic
240C22#576×C11311yescharacteristic
241C22#577×C11312yes—
242C22#578×C11311yescharacteristic
243C4—412no—
244C4—44no—
245C4C2×#95×C113112yes—
246C4C22×C42×C11311yescharacteristic
247C4C22×C22⋊C4×C11311yescharacteristic
248C4C22×C4⋊C4×C11312yes—
249C2—212no—
250C2C22×#95×C11311yescharacteristic
251C2C113×#289712yes—
252C2C113×#289812yes—
253C2C113×#291211yescharacteristic
254C2C113×#291311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutatorC4C22×C42×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC22×#41×C113C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×#41×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1736C2semidirect
4. C113×#1735C2semidirect
5. C2×#340×C113C2semidirect
8. C2×#131×C113C4semidirect
12. #520×C113C4semidirect
31. C2×M16×C113C2×C4semidirect
33. C22×C8×C113C2×C4semidirect
39. #117×C113C2×C4semidirect
42. C2×C4⋊C4×C113C2×C4semidirect
121. #20348C113direct (N × H)
130. #1736C2×C113semidirect
131. #1735C2×C113semidirect
132. C2×#340C2×C113semidirect
133. C113#20348direct (N × H)
136. C2×#131C4×C113semidirect
140. #520C4×C113semidirect
159. C2×M16C2×C4×C113semidirect
161. C22×C8C2×C4×C113semidirect
167. #117C2×C4×C113semidirect
170. C2×C4⋊C4C2×C4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#131×C1132
C2×#520×C1132
C113×#17362
C113×#17352
C2×#340×C1132
#20348113