Finite Group Databasebeta

← C113×#9158 #43277178

Subgroups — C113×#9158 #43277178

Order 28928.

980 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2847C211yesmaximal, characteristic
2C2×#381×C113C211yesmaximal, characteristic, complemented
3C113×#1779C211yesmaximal, characteristic, complemented
4C2×#327×C113C212yesmaximal, complemented
5C113×#1294C212yesmaximal, complemented
6C24×C4×C113C2211yescharacteristic
7C2×#121×C113C412yescomplemented
8C2×#121×C113C2211yescharacteristic
9C2×#120×C113—21no—
10C22×C22⋊C4×C113—21no—
11C2×C22⋊C8×C113—22no—
12C2×C22⋊C8×C113C2212yes—
13#386×C113—21no—
14#386×C113—22no—
15#381×C113—24no—
16#380×C113C412yescomplemented
17#380×C113C2211yescharacteristic
18C2×#95×C113—21no—
19C2×#95×C113C2212yes—
20#327×C113—24no—
21C25×C113D411yescharacteristic
22C22×D4×C113—22no—
23C22×D4×C113—21no—
24C22×D4×C113C2×C411yescharacteristic
25C23×C4×C113—22no—
26C23×C4×C113—22no—
27C23×C4×C113—22no—
28C23×C4×C113—44no—
29C23×C4×C113C2×C412yes—
30C23×C4×C113D412yes—
31C23×C4×C113D411yescharacteristic
32C23×C4×C113C2311yescharacteristic
33C22×C8×C113—22no—
34#121×C113—22no—
35#121×C113—22no—
36#121×C113—44no—
37#120×C113—44no—
38C2×C4⋊C4×C113C2×C411yescharacteristic
39C2×C4⋊C4×C113C2×C412yes—
40C2×C22⋊C4×C113—24no—
41C2×C22⋊C4×C113—22no—
42C2×C22⋊C4×C113—21no—
43C2×C22⋊C4×C113—22no—
44C2×C22⋊C4×C113—21no—
45C2×C22⋊C4×C113—44no—
46C22⋊C8×C113—22no—
47C22⋊C8×C113—22no—
48C22⋊C8×C113—44no—
49#95×C113—24no—
50#95×C113—22no—
51#95×C113—22no—
52#95×C113—21no—
53#95×C113D414yescomplemented
54C24×C113—24no—
55C24×C113—21no—
56C24×C113—21no—
57C24×C113—22no—
58C24×C113—22no—
59C24×C113—21no—
60C24×C113—42no—
61C24×C113C22⋊C412yes—
62C24×C113C2×D411yescharacteristic
63C2×D4×C113—22no—
64C2×D4×C113—42no—
65C2×D4×C113—44no—
66C2×D4×C113—44no—
67C2×D4×C113—44no—
68C2×D4×C113—41no—
69C2×D4×C113—41no—
70C2×D4×C113—42no—
71C2×D4×C113—42no—
72C22×C4×C113—24no—
73C22×C4×C113—24no—
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113—24no—
77C22×C4×C113—24no—
78C22×C4×C113—21no—
79C22×C4×C113—22no—
80C22×C4×C113—24no—
81C22×C4×C113—42no—
82C22×C4×C113—42no—
83C22×C4×C113—42no—
84C22×C4×C113—42no—
85C22×C4×C113—48no—
86C22×C4×C113—48no—
87C22×C4×C113—44no—
88C22×C4×C113—44no—
89C22×C4×C113—42no—
90C22×C4×C113—42no—
91C22×C4×C113C22⋊C412yes—
92C22×C4×C113C22×C411yescharacteristic
93C22×C4×C113C2×D411yescharacteristic
94C22×C4×C113C2×D412yes—
95C22×C4×C113#4112yes—
96C2×C8×C113—44no—
97C2×C8×C113—42no—
98C4⋊C4×C113—22no—
99C4⋊C4×C113—42no—
100C22⋊C4×C113—44no—
101C22⋊C4×C113—48no—
102C22⋊C4×C113—44no—
103C22⋊C4×C113—42no—
104C22⋊C4×C113—42no—
105C23×C113—22no—
106C23×C113—22no—
107C23×C113—24no—
108C23×C113—24no—
109C23×C113—22no—
110C23×C113—22no—
111C23×C113—22no—
112C23×C113—22no—
113C23×C113—22no—
114C23×C113—22no—
115C23×C113—48no—
116C23×C113—48no—
117C23×C113—42no—
118C23×C113—42no—
119C23×C113—42no—
120C23×C113—42no—
121C23×C113—41no—
122C23×C113—42no—
123C23×C113—41no—
124C23×C113—41no—
125C23×C113—42no—
126C23×C113#9914yes—
127C23×C113C2×C22⋊C411yescharacteristic
128C23×C113#12011yescharacteristic
129C23×C113#12311yescharacteristic
130C23×C113#13512yes—
131C23×C113AGL(1,ℤ/8)12yes—
132D4×C113—82no—
133D4×C113—88no—
134D4×C113—82no—
135D4×C113—82no—
136C2×C4×C113—22no—
137C2×C4×C113—22no—
138C2×C4×C113—22no—
139C2×C4×C113—22no—
140C2×C4×C113—22no—
141C2×C4×C113—42no—
142C2×C4×C113—42no—
143C2×C4×C113—48no—
144C2×C4×C113—48no—
145C2×C4×C113—42no—
146C2×C4×C113—42no—
147C2×C4×C113—44no—
148C2×C4×C113—44no—
149C2×C4×C113—41no—
150C2×C4×C113—42no—
151C2×C4×C113—41no—
152C2×C4×C113—41no—
153C2×C4×C113—42no—
154C2×C4×C113—42no—
155C2×C4×C113—44no—
156C2×C4×C113—84no—
157C2×C4×C113—84no—
158C2×C4×C113C4×D412yes—
159C2×C4×C113#12112yes—
160C8×C113—82no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—24no—
166C22×C113—24no—
167C22×C113—24no—
168C22×C113—24no—
169C22×C113—24no—
170C22×C113—48no—
171C22×C113—48no—
172C22×C113—42no—
173C22×C113—42no—
174C22×C113—42no—
175C22×C113—42no—
176C22×C113—81no—
177C22×C113—81no—
178C22×C113—81no—
179C22×C113—82no—
180C22×C113—82no—
181C22×C113#38611yescharacteristic
182C22×C113C2×#9912yes—
183C22×C113#41611yescharacteristic
184C22×C113#41811yescharacteristic
185C22×C113#42112yes—
186C22×C113#44912yes—
187C22×C113#48212yes—
188C4×C113—22no—
189C4×C113—22no—
190C4×C113—42no—
191C4×C113—84no—
192C4×C113—81no—
193C4×C113—82no—
194#9158C11311yesmaximal, characteristic, direct product factor, Sylow
195C2×C113—22no—
196C2×C113—22no—
197C2×C113—44no—
198C2×C113—161no—
199C2×C113#151012yes—
200C2×C113#151612yes—
201C2×C113#187511yescharacteristic
202C2×C113#189711yescharacteristic
203C2×C113#189811yescharacteristic
204#2847C2×C11311yescharacteristic
205C2×#381C2×C11311yescharacteristic, complemented
206#1779C2×C11311yescharacteristic, complemented
207C2×#327C2×C11312yescomplemented
208#1294C2×C11312yescomplemented
209C113#915811yescharacteristic, direct product factor, Sylow
210C24×C4C22×C11311yescharacteristic
211C2×#121C4×C11312yescomplemented
212C2×#121C22×C11311yescharacteristic
213C2×#120—21no—
214C22×C22⋊C4—21no—
215C2×C22⋊C8—22no—
216C2×C22⋊C8C22×C11312yes—
217#386—21no—
218#386—22no—
219#381—24no—
220#380C4×C11312yescomplemented
221#380C22×C11311yescharacteristic
222C2×#95—21no—
223C2×#95C22×C11312yes—
224#327—24no—
225C25D4×C11311yescharacteristic
226C22×D4—22no—
227C22×D4—21no—
228C22×D4C2×C4×C11311yescharacteristic
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—44no—
233C23×C4C2×C4×C11312yes—
234C23×C4D4×C11312yes—
235C23×C4D4×C11311yescharacteristic
236C23×C4C23×C11311yescharacteristic
237C22×C8—22no—
238#121—22no—
239#121—22no—
240#121—44no—
241#120—44no—
242C2×C4⋊C4C2×C4×C11311yescharacteristic
243C2×C4⋊C4C2×C4×C11312yes—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—44no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8—44no—
253#95—24no—
254#95—22no—
255#95—22no—
256#95—21no—
257#95D4×C11314yescomplemented
258C24—24no—
259C24—21no—
260C24—21no—
261C24—22no—
262C24—22no—
263C24—21no—
264C24—42no—
265C24C22⋊C4×C11312yes—
266C24C2×D4×C11311yescharacteristic
267C2×D4—22no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—48no—
290C22×C4—48no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C22⋊C4×C11312yes—
296C22×C4C22×C4×C11311yescharacteristic
297C22×C4C2×D4×C11311yescharacteristic
298C22×C4C2×D4×C11312yes—
299C22×C4#41×C11312yes—
300C2×C8—44no—
301C2×C8—42no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—48no—
306C22⋊C4—44no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—24no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—48no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—42no—
330C23#99×C11314yes—
331C23C2×C22⋊C4×C11311yescharacteristic
332C23#120×C11311yescharacteristic
333C23#123×C11311yescharacteristic
334C23#135×C11312yes—
335C23AGL(1,ℤ/8)×C11312yes—
336D4—82no—
337D4—88no—
338D4—82no—
339D4—82no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—44no—
360C2×C4—84no—
361C2×C4—84no—
362C2×C4C4×D4×C11312yes—
363C2×C4#121×C11312yes—
364C8—82no—
365C22—24no—
366C22—24no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—82no—
381C22—82no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#386×C11311yescharacteristic
386C22C2×#99×C11312yes—
387C22#416×C11311yescharacteristic
388C22#418×C11311yescharacteristic
389C22#421×C11312yes—
390C22#449×C11312yes—
391C22#482×C11312yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—84no—
396C4—82no—
397C4—81no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—161no—
402C2C113×#151012yes—
403C2C113×#151612yes—
404C2C113×#187511yescharacteristic
405C2C113×#189711yescharacteristic
406C2C113×#189811yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC113×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C24×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#381×C113C2semidirect
3. C113×#1779C2semidirect
4. C2×#327×C113C2semidirect
5. C113×#1294C2semidirect
7. C2×#121×C113C4semidirect
16. #380×C113C4semidirect
53. #95×C113D4semidirect
194. #9158C113direct (N × H)
205. C2×#381C2×C113semidirect
206. #1779C2×C113semidirect
207. C2×#327C2×C113semidirect
208. #1294C2×C113semidirect
209. C113#9158direct (N × H)
211. C2×#121C4×C113semidirect
220. #380C4×C113semidirect
257. #95D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#28472
C2×#381×C1132
C113×#17792
C2×#327×C1132
C113×#12942
#9158113