Finite Group Databasebeta

← C113×#15214 #43283234

Subgroups — C113×#15214 #43283234

Order 28928.

1606 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C113C211yesmaximal, characteristic
2C2×#387×C113C213yesmaximal
3C113×#1446C211yesmaximal, characteristic
4C113×#1446C211yesmaximal, characteristic
5C113×#1444C213yesmaximal
6C113×#1442C213yesmaximal
7C113×#1434C213yesmaximal
8C23×Q8×C113C2211yescharacteristic
9C2×C4×Q8×C113—212no—
10C22×C4⋊C4×C113C2211yescharacteristic
11C22×C4⋊C4×C113C2213yes—
12C22×C4⋊C4×C113C2213yes—
13C22×C42×C113C2213yes—
14#387×C113—212no—
15C2×#95×C113C2213yes—
16C2×#95×C113C2213yes—
17C2×#95×C113C2213yes—
18C2×#95×C113C2213yes—
19C2×#95×C113C2216yes—
20C2×#95×C113C2213yes—
21C2×#95×C113C2213yes—
22C22×Q8×C113—26no—
23C22×Q8×C113—26no—
24C22×Q8×C113Q814yes—
25C23×C4×C113C2311yescharacteristic
26C23×C4×C113C2313yes—
27C23×C4×C113C2313yes—
28C23×C4×C113C2311yescharacteristic
29C23×C4×C113C2313yes—
30C23×C4×C113C2311yescharacteristic
31C23×C4×C113C2313yes—
32C4×Q8×C113—232no—
33C2×C4⋊C4×C113—212no—
34C2×C4⋊C4×C113—26no—
35C2×C4⋊C4×C113—26no—
36C2×C4⋊C4×C113—26no—
37C2×C4⋊C4×C113—26no—
38C2×C4⋊C4×C113—26no—
39C2×C42×C113—212no—
40C2×C42×C113D4112yes—
41#95×C113—26no—
42#95×C113—26no—
43#95×C113—26no—
44#95×C113—26no—
45#95×C113—26no—
46#95×C113—212no—
47#95×C113—26no—
48C24×C113C2411yescharacteristic
49C2×Q8×C113—28no—
50C2×Q8×C113—224no—
51C2×Q8×C113—224no—
52C22×C4×C113—26no—
53C22×C4×C113—26no—
54C22×C4×C113—23no—
55C22×C4×C113—21no—
56C22×C4×C113—23no—
57C22×C4×C113—23no—
58C22×C4×C113—26no—
59C22×C4×C113—26no—
60C22×C4×C113—26no—
61C22×C4×C113—23no—
62C22×C4×C113—23no—
63C22×C4×C113—23no—
64C22×C4×C113—23no—
65C22×C4×C113—26no—
66C22×C4×C113—23no—
67C22×C4×C113—23no—
68C22×C4×C113—26no—
69C22×C4×C113—26no—
70C22×C4×C113—23no—
71C22×C4×C113—21no—
72C22×C4×C113—23no—
73C22×C4×C113—23no—
74C22×C4×C113C2×D416yes—
75C22×C4×C113C2×D416yes—
76C22×C4×C113C2×D416yes—
77C22×C4×C113C2×Q816yes—
78C22×C4×C113#4116yes—
79C22×C4×C113#4112yes—
80C22×C4×C113#4116yes—
81C4⋊C4×C113—224no—
82C4⋊C4×C113—224no—
83C4⋊C4×C113—44no—
84C42×C113—224no—
85C23×C113C22×D413yes—
86C23×C113C22×Q811yescharacteristic
87C23×C113C2×#4113yes—
88C23×C113C2×#4111yescharacteristic
89C23×C113C2×#4113yes—
90C23×C1132−1+413yes—
91C23×C1132−1+411yescharacteristic
92Q8×C113—232no—
93C2×C4×C113—26no—
94C2×C4×C113—212no—
95C2×C4×C113—26no—
96C2×C4×C113—212no—
97C2×C4×C113—26no—
98C2×C4×C113—26no—
99C2×C4×C113—26no—
100C2×C4×C113—26no—
101C2×C4×C113—26no—
102C2×C4×C113—26no—
103C2×C4×C113—26no—
104C2×C4×C113—212no—
105C2×C4×C113—41no—
106C2×C4×C113—43no—
107C2×C4×C113—46no—
108C2×C4×C113—43no—
109C2×C4×C113—46no—
110C2×C4×C113—43no—
111C2×C4×C113—46no—
112C2×C4×C113—41no—
113C2×C4×C113—43no—
114C2×C4×C113—43no—
115C2×C4×C113—43no—
116C2×C4×C113—43no—
117C2×C4×C113—43no—
118C2×C4×C113—46no—
119C2×C4×C113—46no—
120C2×C4×C113#12014yes—
121C2×C4×C113C22⋊Q8112yes—
122C22×C113C2×#12011yescharacteristic
123C22×C113C2×C22⋊Q813yes—
124C22×C113#52513yes—
125C22×C113#52513yes—
126C22×C113#53213yes—
127C22×C113#53613yes—
128C22×C113#53613yes—
129C22×C113#55216yes—
130C22×C113#55613yes—
131C22×C113#55613yes—
132C22×C113#55713yes—
133C22×C113#55711yescharacteristic
134C4×C113—212no—
135C4×C113—24no—
136C4×C113—46no—
137C4×C113—46no—
138C4×C113—42no—
139C4×C113—83no—
140C4×C113—81no—
141#15214C11311yesmaximal, characteristic, direct product factor, Sylow
142C2×C113#238811yescharacteristic
143C2×C113#256513yes—
144C2×C113#258113yes—
145C2×C113#259913yes—
146C2×C113#260413yes—
147C2×C113#261411yescharacteristic
148C2×C113#284811yescharacteristic
149C22×C4×Q8C2×C11311yescharacteristic
150C2×#387C2×C11313yes—
151#1446C2×C11311yescharacteristic
152#1446C2×C11311yescharacteristic
153#1444C2×C11313yes—
154#1442C2×C11313yes—
155#1434C2×C11313yes—
156C113#1521411yescharacteristic, direct product factor, Sylow
157C23×Q8C22×C11311yescharacteristic
158C2×C4×Q8—212no—
159C22×C4⋊C4C22×C11313yes—
160C22×C4⋊C4C22×C11313yes—
161C22×C4⋊C4C22×C11311yescharacteristic
162C22×C42C22×C11313yes—
163#387—212no—
164C2×#95C22×C11313yes—
165C2×#95C22×C11316yes—
166C2×#95C22×C11313yes—
167C2×#95C22×C11313yes—
168C2×#95C22×C11313yes—
169C2×#95C22×C11313yes—
170C2×#95C22×C11313yes—
171C22×Q8—26no—
172C22×Q8—26no—
173C22×Q8Q8×C11314yes—
174C23×C4C23×C11311yescharacteristic
175C23×C4C23×C11313yes—
176C23×C4C23×C11313yes—
177C23×C4C23×C11311yescharacteristic
178C23×C4C23×C11313yes—
179C23×C4C23×C11311yescharacteristic
180C23×C4C23×C11313yes—
181C4×Q8—232no—
182C2×C4⋊C4—212no—
183C2×C4⋊C4—26no—
184C2×C4⋊C4—26no—
185C2×C4⋊C4—26no—
186C2×C4⋊C4—26no—
187C2×C4⋊C4—26no—
188C2×C42—212no—
189C2×C42D4×C113112yes—
190#95—26no—
191#95—26no—
192#95—26no—
193#95—26no—
194#95—26no—
195#95—212no—
196#95—26no—
197C24C24×C11311yescharacteristic
198C2×Q8—28no—
199C2×Q8—224no—
200C2×Q8—224no—
201C22×C4—26no—
202C22×C4—26no—
203C22×C4—23no—
204C22×C4—21no—
205C22×C4—23no—
206C22×C4—23no—
207C22×C4—26no—
208C22×C4—26no—
209C22×C4—26no—
210C22×C4—23no—
211C22×C4—23no—
212C22×C4—23no—
213C22×C4—23no—
214C22×C4—26no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—26no—
218C22×C4—26no—
219C22×C4—23no—
220C22×C4—21no—
221C22×C4—23no—
222C22×C4—23no—
223C22×C4C2×D4×C11316yes—
224C22×C4C2×D4×C11316yes—
225C22×C4C2×D4×C11316yes—
226C22×C4C2×Q8×C11316yes—
227C22×C4#41×C11316yes—
228C22×C4#41×C11312yes—
229C22×C4#41×C11316yes—
230C4⋊C4—224no—
231C4⋊C4—224no—
232C4⋊C4—44no—
233C42—224no—
234C23C22×D4×C11313yes—
235C23C22×Q8×C11311yescharacteristic
236C23C2×#41×C11313yes—
237C23C2×#41×C11311yescharacteristic
238C23C2×#41×C11313yes—
239C232−1+4×C11313yes—
240C232−1+4×C11311yescharacteristic
241Q8—232no—
242C2×C4—26no—
243C2×C4—212no—
244C2×C4—26no—
245C2×C4—212no—
246C2×C4—26no—
247C2×C4—26no—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—26no—
252C2×C4—26no—
253C2×C4—212no—
254C2×C4—41no—
255C2×C4—43no—
256C2×C4—46no—
257C2×C4—43no—
258C2×C4—46no—
259C2×C4—43no—
260C2×C4—46no—
261C2×C4—41no—
262C2×C4—43no—
263C2×C4—43no—
264C2×C4—43no—
265C2×C4—43no—
266C2×C4—43no—
267C2×C4—46no—
268C2×C4—46no—
269C2×C4#120×C11314yes—
270C2×C4C22⋊Q8×C113112yes—
271C22C2×#120×C11311yescharacteristic
272C22C2×C22⋊Q8×C11313yes—
273C22#525×C11313yes—
274C22#525×C11313yes—
275C22#532×C11313yes—
276C22#536×C11313yes—
277C22#536×C11313yes—
278C22#552×C11316yes—
279C22#556×C11313yes—
280C22#556×C11313yes—
281C22#557×C11313yes—
282C22#557×C11311yescharacteristic
283C4—212no—
284C4—24no—
285C4—46no—
286C4—46no—
287C4—42no—
288C4—83no—
289C4—81no—
290C2C113×#238811yescharacteristic
291C2C113×#256513yes—
292C2C113×#258113yes—
293C2C113×#259913yes—
294C2C113×#260413yes—
295C2C113×#261411yescharacteristic
296C2C113×#284811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C113C24
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
141. #15214C113direct (N × H)
156. C113#15214direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1132
C2×#387×C1132
C113×#14462
C113×#14442
C113×#14422
C113×#14342
#15214113