Finite Group Databasebeta

← C113×#14454 #43282474

Subgroups — C113×#14454 #43282474

Order 28928.

1190 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#384×C113C211yesmaximal, characteristic
2C113×#1441C214yesmaximal
3C113×#1441C212yesmaximal
4C113×#1436C212yesmaximal
5C113×#1436C214yesmaximal
6C113×#1434C212yesmaximal
7C22×C4⋊C4×C113C2212yes—
8C22×C4⋊C4×C113C2211yescharacteristic
9C22×C4⋊C4×C113C2214yes—
10C22×C4⋊C4×C113C2211yescharacteristic
11C22×C42×C113C2211yescharacteristic
12C22×C42×C113C2212yes—
13#384×C113C418yescomplemented
14C2×#95×C113C2214yes—
15C2×#95×C113C2214yes—
16C2×#95×C113C2212yes—
17C2×#95×C113C2214yes—
18C2×#95×C113C2212yes—
19C2×#95×C113C2212yes—
20C2×#95×C113C2214yes—
21C2×#95×C113C2212yes—
22C23×C4×C113C2314yes—
23C23×C4×C113C2312yes—
24C23×C4×C113C2312yes—
25C23×C4×C113C2314yes—
26C23×C4×C113C2312yes—
27C23×C4×C113C2311yescharacteristic
28C2×C4⋊C4×C113—41no—
29C2×C4⋊C4×C113—44no—
30C2×C4⋊C4×C113—41no—
31C2×C4⋊C4×C113—41no—
32C2×C4⋊C4×C113—44no—
33C2×C4⋊C4×C113—41no—
34C2×C4⋊C4×C113—42no—
35C2×C4⋊C4×C113—44no—
36C2×C4⋊C4×C113C2×C414yes—
37C2×C4⋊C4×C113C2×C414yes—
38C2×C4⋊C4×C113C2×C4116yes—
39C2×C42×C113—24no—
40C2×C42×C113—44no—
41C2×C42×C113—42no—
42C2×C42×C113C2×C414yes—
43#95×C113—28no—
44#95×C113—28no—
45#95×C113—24no—
46#95×C113—42no—
47#95×C113—44no—
48#95×C113—44no—
49#95×C113—42no—
50#95×C113Q818yes—
51C24×C113C2411yescharacteristic
52C22×C4×C113—24no—
53C22×C4×C113—21no—
54C22×C4×C113—21no—
55C22×C4×C113—24no—
56C22×C4×C113—22no—
57C22×C4×C113—24no—
58C22×C4×C113—24no—
59C22×C4×C113—24no—
60C22×C4×C113—24no—
61C22×C4×C113—24no—
62C22×C4×C113—22no—
63C22×C4×C113—22no—
64C22×C4×C113—24no—
65C22×C4×C113—24no—
66C22×C4×C113—22no—
67C22×C4×C113—24no—
68C22×C4×C113—22no—
69C22×C4×C113—24no—
70C22×C4×C113—24no—
71C22×C4×C113—24no—
72C22×C4×C113—24no—
73C22×C4×C113—24no—
74C22×C4×C113—24no—
75C22×C4×C113—24no—
76C22×C4×C113—24no—
77C22×C4×C113—24no—
78C22×C4×C113C22×C414yes—
79C22×C4×C113C22×C414yes—
80C22×C4×C113C22×C412yes—
81C22×C4×C113C22×C414yes—
82C22×C4×C113C2×Q818yes—
83C22×C4×C113C2×Q814yes—
84C22×C4×C113#4114yes—
85C22×C4×C113#4114yes—
86C4⋊C4×C113—44no—
87C4⋊C4×C113—44no—
88C4⋊C4×C113—416no—
89C4⋊C4×C113—48no—
90C42×C113—28no—
91C42×C113—48no—
92C23×C113C23×C411yescharacteristic
93C23×C113C22×Q812yes—
94C23×C113C2×#4112yes—
95C23×C113C2×#4112yes—
96C23×C113H(5,𝔽2)11yescharacteristic
97C23×C113H(5,𝔽2)11yescharacteristic
98C23×C113H(5,𝔽2)14yes—
99C23×C1132−1+412yes—
100C2×C4×C113—24no—
101C2×C4×C113—22no—
102C2×C4×C113—24no—
103C2×C4×C113—22no—
104C2×C4×C113—24no—
105C2×C4×C113—24no—
106C2×C4×C113—28no—
107C2×C4×C113—28no—
108C2×C4×C113—24no—
109C2×C4×C113—24no—
110C2×C4×C113—28no—
111C2×C4×C113—28no—
112C2×C4×C113—28no—
113C2×C4×C113—28no—
114C2×C4×C113—28no—
115C2×C4×C113—44no—
116C2×C4×C113—44no—
117C2×C4×C113—44no—
118C2×C4×C113—42no—
119C2×C4×C113—44no—
120C2×C4×C113—42no—
121C2×C4×C113—42no—
122C2×C4×C113—44no—
123C2×C4×C113—44no—
124C2×C4×C113—42no—
125C2×C4×C113—44no—
126C2×C4×C113—44no—
127C2×C4×C113—44no—
128C2×C4×C113—44no—
129C2×C4×C113—44no—
130C2×C4×C113—44no—
131C2×C4×C113—44no—
132C2×C4×C113#11714yes—
133C2×C4×C113C4×Q818yes—
134C22×C113C2×#11711yescharacteristic
135C22×C113C2×C4×Q812yes—
136C22×C113#51811yescharacteristic
137C22×C113#51812yes—
138C22×C113#51911yescharacteristic
139C22×C113#53912yes—
140C22×C113#53912yes—
141C22×C113#54214yes—
142C22×C113#54414yes—
143C22×C113#55314yes—
144C22×C113#55414yes—
145C22×C113#55412yes—
146C22×C113#55511yescharacteristic
147C22×C113Q8211yescharacteristic
148C22×C113#56012yes—
149C22×C113#56012yes—
150C4×C113—24no—
151C4×C113—28no—
152C4×C113—44no—
153C4×C113—44no—
154C4×C113—48no—
155C4×C113—84no—
156#14454C11311yesmaximal, characteristic, direct product factor, Sylow
157C2×C113#231311yescharacteristic
158C2×C113#233112yes—
159C2×C113#234512yes—
160C2×C113#236911yescharacteristic
161C2×C113#238011yescharacteristic
162C2×C113#279014yes—
163C2×C113#279212yes—
164C2×C113#279512yes—
165C2×#384C2×C11311yescharacteristic
166#1441C2×C11314yes—
167#1441C2×C11312yes—
168#1436C2×C11312yes—
169#1436C2×C11314yes—
170#1434C2×C11312yes—
171C113#1445411yescharacteristic, direct product factor, Sylow
172C22×C4⋊C4C22×C11312yes—
173C22×C4⋊C4C22×C11311yescharacteristic
174C22×C4⋊C4C22×C11314yes—
175C22×C4⋊C4C22×C11311yescharacteristic
176C22×C42C22×C11311yescharacteristic
177C22×C42C22×C11312yes—
178#384C4×C11318yescomplemented
179C2×#95C22×C11314yes—
180C2×#95C22×C11314yes—
181C2×#95C22×C11312yes—
182C2×#95C22×C11314yes—
183C2×#95C22×C11312yes—
184C2×#95C22×C11312yes—
185C2×#95C22×C11314yes—
186C2×#95C22×C11312yes—
187C23×C4C23×C11314yes—
188C23×C4C23×C11312yes—
189C23×C4C23×C11312yes—
190C23×C4C23×C11314yes—
191C23×C4C23×C11312yes—
192C23×C4C23×C11311yescharacteristic
193C2×C4⋊C4—41no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4C2×C4×C11314yes—
202C2×C4⋊C4C2×C4×C11314yes—
203C2×C4⋊C4C2×C4×C113116yes—
204C2×C42—24no—
205C2×C42—44no—
206C2×C42—42no—
207C2×C42C2×C4×C11314yes—
208#95—28no—
209#95—28no—
210#95—24no—
211#95—42no—
212#95—44no—
213#95—44no—
214#95—42no—
215#95Q8×C11318yes—
216C24C24×C11311yescharacteristic
217C22×C4—24no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4C22×C4×C11314yes—
244C22×C4C22×C4×C11314yes—
245C22×C4C22×C4×C11312yes—
246C22×C4C22×C4×C11314yes—
247C22×C4C2×Q8×C11318yes—
248C22×C4C2×Q8×C11314yes—
249C22×C4#41×C11314yes—
250C22×C4#41×C11314yes—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4—416no—
254C4⋊C4—48no—
255C42—28no—
256C42—48no—
257C23C23×C4×C11311yescharacteristic
258C23C22×Q8×C11312yes—
259C23C2×#41×C11312yes—
260C23C2×#41×C11312yes—
261C23H(5,𝔽2)×C11311yescharacteristic
262C23H(5,𝔽2)×C11311yescharacteristic
263C23H(5,𝔽2)×C11314yes—
264C232−1+4×C11312yes—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—28no—
272C2×C4—28no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—28no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4#117×C11314yes—
298C2×C4C4×Q8×C11318yes—
299C22C2×#117×C11311yescharacteristic
300C22C2×C4×Q8×C11312yes—
301C22#518×C11311yescharacteristic
302C22#518×C11312yes—
303C22#519×C11311yescharacteristic
304C22#539×C11312yes—
305C22#539×C11312yes—
306C22#542×C11314yes—
307C22#544×C11314yes—
308C22#553×C11314yes—
309C22#554×C11312yes—
310C22#554×C11314yes—
311C22#555×C11311yescharacteristic
312C22Q82×C11311yescharacteristic
313C22#560×C11312yes—
314C22#560×C11312yes—
315C4—24no—
316C4—28no—
317C4—48no—
318C4—44no—
319C4—44no—
320C4—84no—
321C2C113×#231311yescharacteristic
322C2C113×#233112yes—
323C2C113×#234512yes—
324C2C113×#236911yescharacteristic
325C2C113×#238011yescharacteristic
326C2C113×#279014yes—
327C2C113×#279212yes—
328C2C113×#279512yes—
subgroupG/H
center, socle, prime radicalC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
13. #384×C113C4semidirect
156. #14454C113direct (N × H)
171. C113#14454direct (N × H)
178. #384C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#384×C1132
C113×#14412
C113×#14362
C113×#14342
#14454113