Finite Group Databasebeta

← C113×#2505 #28387301

Subgroups — C113×#2505 #28387301

Order 14464.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#400×C113C211yesmaximal, characteristic, complemented
2#400×C113C211yesmaximal, characteristic, complemented
3#400×C113C211yesmaximal, characteristic, complemented
4#398×C113C211yesmaximal, characteristic, complemented
5#389×C113C211yesmaximal, characteristic, complemented
6#387×C113C211yesmaximal, characteristic, complemented
7#387×C113C211yesmaximal, characteristic, complemented
8#385×C113C211yesmaximal, characteristic
9#385×C113C211yesmaximal, characteristic
10#385×C113C211yesmaximal, characteristic
11#385×C113C211yesmaximal, characteristic
12#382×C113C211yesmaximal, characteristic, complemented
13#380×C113C211yesmaximal, characteristic
14C4×C22⋊C4×C113C211yesmaximal, characteristic
15C2×#95×C113C211yesmaximal, characteristic
16C23×C4×C113C2211yescharacteristic
17C23×C4×C113C2211yescharacteristic
18C23×C4×C113C2211yescharacteristic
19C2×C4⋊C4×C113C2211yescharacteristic
20C2×C4⋊C4×C113C2211yescharacteristic
21C2×C4⋊C4×C113C2211yescharacteristic
22C2×C4⋊C4×C113C2211yescharacteristic
23C2×C4⋊C4×C113C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25C2×C4⋊C4×C113C2211yescharacteristic
26C2×C4⋊C4×C113C2211yescharacteristic
27C2×C4⋊C4×C113C2211yescharacteristic
28C2×C4⋊C4×C113C2211yescharacteristic
29C2×C22⋊C4×C113C2211yescharacteristic
30C2×C22⋊C4×C113C2211yescharacteristic
31C2×C22⋊C4×C113C2211yescharacteristic
32C2×C22⋊C4×C113C2211yescharacteristic
33C2×C42×C113C2211yescharacteristic
34C2×C42×C113C2211yescharacteristic
35#95×C113C2211yescharacteristic
36#95×C113C2211yescharacteristic
37#95×C113C2211yescharacteristic
38#95×C113C2211yescharacteristic
39#95×C113C2211yescharacteristic
40#95×C113C2211yescharacteristic
41#95×C113C2211yescharacteristic
42#95×C113C2211yescharacteristic
43#95×C113C2211yescharacteristic
44#95×C113C2211yescharacteristic
45#95×C113C2211yescharacteristic
46#95×C113C2211yescharacteristic
47#95×C113C2211yescharacteristic
48#95×C113C2211yescharacteristic
49#95×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51C24×C113C2311yescharacteristic
52C22×C4×C113—22no—
53C22×C4×C113—22no—
54C22×C4×C113—22no—
55C22×C4×C113—22no—
56C22×C4×C113—22no—
57C22×C4×C113—41no—
58C22×C4×C113—41no—
59C22×C4×C113—41no—
60C22×C4×C113—41no—
61C22×C4×C113C2311yescharacteristic
62C22×C4×C113C2311yescharacteristic
63C22×C4×C113C2311yescharacteristic
64C22×C4×C113C2311yescharacteristic
65C22×C4×C113C2311yescharacteristic
66C22×C4×C113C2311yescharacteristic
67C22×C4×C113C2311yescharacteristic
68C22×C4×C113C2311yescharacteristic
69C22×C4×C113C2311yescharacteristic
70C22×C4×C113C2311yescharacteristic
71C22×C4×C113C2311yescharacteristic
72C22×C4×C113C2311yescharacteristic
73C22×C4×C113C2311yescharacteristic
74C22×C4×C113C2311yescharacteristic
75C4⋊C4×C113—22no—
76C4⋊C4×C113—22no—
77C4⋊C4×C113—22no—
78C4⋊C4×C113—41no—
79C4⋊C4×C113—41no—
80C4⋊C4×C113—41no—
81C4⋊C4×C113—41no—
82C4⋊C4×C113—41no—
83C4⋊C4×C113—41no—
84C4⋊C4×C113—41no—
85C22⋊C4×C113—22no—
86C22⋊C4×C113—22no—
87C22⋊C4×C113—22no—
88C22⋊C4×C113Q814yes—
89C42×C113—22no—
90C42×C113—41no—
91C23×C113—21no—
92C23×C113—21no—
93C23×C113—21no—
94C23×C113—21no—
95C23×C113C2×Q812yes—
96C23×C113#4112yes—
97C23×C113#4112yes—
98C23×C113C2411yescharacteristic
99C2×C4×C113—21no—
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—44no—
138C2×C4×C113—44no—
139C2×C4×C113—44no—
140C2×C4×C113C2×Q812yes—
141C2×C4×C113C2×Q812yes—
142C2×C4×C113#4112yes—
143C2×C4×C113#4112yes—
144C22×C113—22no—
145C22×C113—22no—
146C22×C113—22no—
147C22×C113—22no—
148C22×C113—22no—
149C22×C113—22no—
150C22×C113#12514yes—
151C22×C113C22×Q811yescharacteristic
152C22×C113C2×#4111yescharacteristic
153C22×C113C2×#4111yescharacteristic
154C22×C113C2×#4111yescharacteristic
155C22×C113C2×#4111yescharacteristic
156C22×C113H(5,𝔽2)11yescharacteristic
157C22×C113H(5,𝔽2)11yescharacteristic
158C4×C113—22no—
159C4×C113—22no—
160C4×C113—22no—
161C4×C113—22no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C2×C113—24no—
173C2×C113C2×#12511yescharacteristic
174C2×C113#52911yescharacteristic
175C2×C113#53811yescharacteristic
176C2×C113#55111yescharacteristic
177C2×C113#55111yescharacteristic
178C2×C113#55411yescharacteristic
179C2×C113#55411yescharacteristic
180#2505C11311yesmaximal, characteristic, direct product factor, Sylow
181C113#250511yescharacteristic, direct product factor, Sylow
182#400C2×C11311yescharacteristic, complemented
183#400C2×C11311yescharacteristic, complemented
184#400C2×C11311yescharacteristic, complemented
185#398C2×C11311yescharacteristic, complemented
186#389C2×C11311yescharacteristic, complemented
187#387C2×C11311yescharacteristic, complemented
188#387C2×C11311yescharacteristic, complemented
189#385C2×C11311yescharacteristic
190#385C2×C11311yescharacteristic
191#385C2×C11311yescharacteristic
192#385C2×C11311yescharacteristic
193#382C2×C11311yescharacteristic, complemented
194#380C2×C11311yescharacteristic
195C4×C22⋊C4C2×C11311yescharacteristic
196C2×#95C2×C11311yescharacteristic
197C23×C4C22×C11311yescharacteristic
198C23×C4C22×C11311yescharacteristic
199C23×C4C22×C11311yescharacteristic
200C2×C4⋊C4C22×C11311yescharacteristic
201C2×C4⋊C4C22×C11311yescharacteristic
202C2×C4⋊C4C22×C11311yescharacteristic
203C2×C4⋊C4C22×C11311yescharacteristic
204C2×C4⋊C4C22×C11311yescharacteristic
205C2×C4⋊C4C22×C11311yescharacteristic
206C2×C4⋊C4C22×C11311yescharacteristic
207C2×C4⋊C4C22×C11311yescharacteristic
208C2×C4⋊C4C22×C11311yescharacteristic
209C2×C4⋊C4C22×C11311yescharacteristic
210C2×C22⋊C4C22×C11311yescharacteristic
211C2×C22⋊C4C22×C11311yescharacteristic
212C2×C22⋊C4C22×C11311yescharacteristic
213C2×C22⋊C4C22×C11311yescharacteristic
214C2×C42C22×C11311yescharacteristic
215C2×C42C22×C11311yescharacteristic
216#95C22×C11311yescharacteristic
217#95C22×C11311yescharacteristic
218#95C22×C11311yescharacteristic
219#95C22×C11311yescharacteristic
220#95C22×C11311yescharacteristic
221#95C22×C11311yescharacteristic
222#95C22×C11311yescharacteristic
223#95C22×C11311yescharacteristic
224#95C22×C11311yescharacteristic
225#95C22×C11311yescharacteristic
226#95C22×C11311yescharacteristic
227#95C22×C11311yescharacteristic
228#95C22×C11311yescharacteristic
229#95C22×C11311yescharacteristic
230#95C22×C11311yescharacteristic
231#95C22×C11311yescharacteristic
232C24C23×C11311yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C23×C11311yescharacteristic
243C22×C4C23×C11311yescharacteristic
244C22×C4C23×C11311yescharacteristic
245C22×C4C23×C11311yescharacteristic
246C22×C4C23×C11311yescharacteristic
247C22×C4C23×C11311yescharacteristic
248C22×C4C23×C11311yescharacteristic
249C22×C4C23×C11311yescharacteristic
250C22×C4C23×C11311yescharacteristic
251C22×C4C23×C11311yescharacteristic
252C22×C4C23×C11311yescharacteristic
253C22×C4C23×C11311yescharacteristic
254C22×C4C23×C11311yescharacteristic
255C22×C4C23×C11311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4Q8×C11314yes—
270C42—22no—
271C42—41no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×Q8×C11312yes—
277C23#41×C11312yes—
278C23#41×C11312yes—
279C23C24×C11311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4C2×Q8×C11312yes—
322C2×C4C2×Q8×C11312yes—
323C2×C4#41×C11312yes—
324C2×C4#41×C11312yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22#125×C11314yes—
332C22C22×Q8×C11311yescharacteristic
333C22C2×#41×C11311yescharacteristic
334C22C2×#41×C11311yescharacteristic
335C22C2×#41×C11311yescharacteristic
336C22C2×#41×C11311yescharacteristic
337C22H(5,𝔽2)×C11311yescharacteristic
338C22H(5,𝔽2)×C11311yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C2—24no—
354C2C2×#125×C11311yescharacteristic
355C2#529×C11311yescharacteristic
356C2#538×C11311yescharacteristic
357C2#551×C11311yescharacteristic
358C2#551×C11311yescharacteristic
359C2#554×C11311yescharacteristic
360C2#554×C11311yescharacteristic
subgroupG/H
center, socleC23×C113C24
commutator, Frattini, cosocleC23C24×C113
prime radicalC24×C113C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. #400×C113C2semidirect
2. #400×C113C2semidirect
3. #400×C113C2semidirect
4. #398×C113C2semidirect
5. #389×C113C2semidirect
6. #387×C113C2semidirect
7. #387×C113C2semidirect
12. #382×C113C2semidirect
180. #2505C113direct (N × H)
181. C113#2505direct (N × H)
182. #400C2×C113semidirect
183. #400C2×C113semidirect
184. #400C2×C113semidirect
185. #398C2×C113semidirect
186. #389C2×C113semidirect
187. #387C2×C113semidirect
188. #387C2×C113semidirect
193. #382C2×C113semidirect

Maximal subgroups

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

subgroupindex
#400×C1132
#398×C1132
#389×C1132
#387×C1132
#385×C1132
#382×C1132
#380×C1132
C4×C22⋊C4×C1132
C2×#95×C1132
#2505113