Finite Group Databasebeta

← C113×#8717 #43276737

Subgroups — C113×#8717 #43276737

Order 28928.

588 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2285C211yesmaximal, characteristic
2C113×#1817C211yesmaximal, characteristic
3C113×#1434C211yesmaximal, characteristic
4C113×#1294C214yesmaximal
5C2×#117×C113—21no—
6C22×C42×C113C2211yescharacteristic
7C2×C22⋊C8×C113C2212yes—
8#384×C113C411yescharacteristic, complemented
9#384×C113C411yescharacteristic, complemented
10#382×C113—21no—
11#380×C113—21no—
12#380×C113C2212yes—
13C4×C4⋊C4×C113—21no—
14C4×C4⋊C4×C113C412yescomplemented
15C2×#95×C113—21no—
16C2×#95×C113—21no—
17C2×#95×C113C2212yes—
18#336×C113—21no—
19#336×C113—21no—
20C23×C4×C113—22no—
21C23×C4×C113D411yescharacteristic
22C23×C4×C113D411yescharacteristic
23C23×C4×C113C2311yescharacteristic
24C22×C8×C113—22no—
25#117×C113—44no—
26C2×C4⋊C4×C113—21no—
27C2×C4⋊C4×C113—21no—
28C2×C4⋊C4×C113—21no—
29C2×C4⋊C4×C113—21no—
30C2×C4⋊C4×C113C2×C412yes—
31C2×C4⋊C4×C113C2×C412yes—
32C2×C22⋊C4×C113—22no—
33C2×C42×C113—24no—
34C2×C42×C113—22no—
35C2×C42×C113C2×C411yescharacteristic
36C2×C42×C113C2×C411yescharacteristic
37C2×C42×C113D411yescharacteristic
38C2×C42×C113D411yescharacteristic
39C22⋊C8×C113—24no—
40#95×C113—24no—
41#95×C113—22no—
42#95×C113—22no—
43#95×C113—24no—
44#95×C113—42no—
45C24×C113C2×D411yescharacteristic
46C22×C4×C113—22no—
47C22×C4×C113—22no—
48C22×C4×C113—22no—
49C22×C4×C113—22no—
50C22×C4×C113—24no—
51C22×C4×C113—22no—
52C22×C4×C113—22no—
53C22×C4×C113—41no—
54C22×C4×C113—41no—
55C22×C4×C113—41no—
56C22×C4×C113—42no—
57C22×C4×C113—42no—
58C22×C4×C113—42no—
59C22×C4×C113—42no—
60C22×C4×C113—42no—
61C22×C4×C113—42no—
62C22×C4×C113C22⋊C411yescharacteristic
63C22×C4×C113C22⋊C411yescharacteristic
64C22×C4×C113C22⋊C411yescharacteristic
65C22×C4×C113C22⋊C411yescharacteristic
66C22×C4×C113SD1612yes—
67C22×C4×C113Q1612yes—
68C22×C4×C113C22×C411yescharacteristic
69C22×C4×C113C2×D411yescharacteristic
70C22×C4×C113#4114yes—
71C2×C8×C113—42no—
72C2×C8×C113—42no—
73C2×C8×C113—42no—
74C4⋊C4×C113—42no—
75C4⋊C4×C113—42no—
76C4⋊C4×C113—42no—
77C4⋊C4×C113—42no—
78C4⋊C4×C113—42no—
79C4⋊C4×C113—42no—
80C22⋊C4×C113—44no—
81C42×C113—22no—
82C42×C113—22no—
83C42×C113—22no—
84C42×C113—22no—
85C42×C113—44no—
86C23×C113—21no—
87C23×C113—21no—
88C23×C113—21no—
89C23×C113—21no—
90C23×C113C2×C22⋊C411yescharacteristic
91C23×C113#12312yes—
92C23×C113C2×SD1611yescharacteristic
93C23×C113C2×Q1611yescharacteristic
94C23×C113AGL(1,ℤ/8)12yes—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113—21no—
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—24no—
106C2×C4×C113—24no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—44no—
111C2×C4×C113—44no—
112C2×C4×C113—44no—
113C2×C4×C113—44no—
114C2×C4×C113—44no—
115C2×C4×C113—42no—
116C2×C4×C113—42no—
117C2×C4×C113—42no—
118C2×C4×C113—42no—
119C2×C4×C113—42no—
120C2×C4×C113—42no—
121C2×C4×C113—82no—
122C2×C4×C113—82no—
123C2×C4×C113—82no—
124C2×C4×C113—82no—
125C2×C4×C113#10312yes—
126C2×C4×C113#10312yes—
127C2×C4×C113#10412yes—
128C2×C4×C113#11712yes—
129C2×C4×C113#12312yes—
130C8×C113—82no—
131C22×C113—22no—
132C22×C113—22no—
133C22×C113—21no—
134C22×C113—21no—
135C22×C113—22no—
136C22×C113—22no—
137C22×C113—21no—
138C22×C113—21no—
139C22×C113#38111yescharacteristic
140C22×C113#41011yescharacteristic
141C22×C113#41011yescharacteristic
142C22×C113C2×#10311yescharacteristic
143C22×C113#41811yescharacteristic
144C22×C113C2×#10411yescharacteristic
145C22×C113#42111yescharacteristic
146C22×C113#48112yes—
147C22×C113#48412yes—
148C4×C113—22no—
149C4×C113—22no—
150C4×C113—22no—
151C4×C113—22no—
152C4×C113—22no—
153C4×C113—41no—
154C4×C113—84no—
155C4×C113—82no—
156C4×C113—82no—
157#8717C11311yesmaximal, characteristic, direct product factor, Sylow
158C2×C113—22no—
159C2×C113—22no—
160C2×C113#150311yescharacteristic
161C2×C113#150511yescharacteristic
162C2×C113#151411yescharacteristic
163C2×C113#151811yescharacteristic
164C2×C113#182011yescharacteristic
165C2×C113#182411yescharacteristic
166C2×C113#182611yescharacteristic
167#2285C2×C11311yescharacteristic
168#1817C2×C11311yescharacteristic
169#1434C2×C11311yescharacteristic
170#1294C2×C11314yes—
171C113#871711yescharacteristic, direct product factor, Sylow
172C2×#117—21no—
173C22×C42C22×C11311yescharacteristic
174C2×C22⋊C8C22×C11312yes—
175#384C4×C11311yescharacteristic, complemented
176#384C4×C11311yescharacteristic, complemented
177#382—21no—
178#380—21no—
179#380C22×C11312yes—
180C4×C4⋊C4—21no—
181C4×C4⋊C4C4×C11312yescomplemented
182C2×#95—21no—
183C2×#95—21no—
184C2×#95C22×C11312yes—
185#336—21no—
186#336—21no—
187C23×C4—22no—
188C23×C4D4×C11311yescharacteristic
189C23×C4D4×C11311yescharacteristic
190C23×C4C23×C11311yescharacteristic
191C22×C8—22no—
192#117—44no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C11312yes—
198C2×C4⋊C4C2×C4×C11312yes—
199C2×C22⋊C4—22no—
200C2×C42—24no—
201C2×C42—22no—
202C2×C42C2×C4×C11311yescharacteristic
203C2×C42C2×C4×C11311yescharacteristic
204C2×C42D4×C11311yescharacteristic
205C2×C42D4×C11311yescharacteristic
206C22⋊C8—24no—
207#95—24no—
208#95—22no—
209#95—22no—
210#95—24no—
211#95—42no—
212C24C2×D4×C11311yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C22⋊C4×C11311yescharacteristic
230C22×C4C22⋊C4×C11311yescharacteristic
231C22×C4C22⋊C4×C11311yescharacteristic
232C22×C4C22⋊C4×C11311yescharacteristic
233C22×C4SD16×C11312yes—
234C22×C4Q16×C11312yes—
235C22×C4C22×C4×C11311yescharacteristic
236C22×C4C2×D4×C11311yescharacteristic
237C22×C4#41×C11314yes—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—44no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—22no—
252C42—44no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C2×C22⋊C4×C11311yescharacteristic
258C23#123×C11312yes—
259C23C2×SD16×C11311yescharacteristic
260C23C2×Q16×C11311yescharacteristic
261C23AGL(1,ℤ/8)×C11312yes—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4#103×C11312yes—
293C2×C4#103×C11312yes—
294C2×C4#104×C11312yes—
295C2×C4#117×C11312yes—
296C2×C4#123×C11312yes—
297C8—82no—
298C22—22no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—22no—
303C22—21no—
304C22—21no—
305C22—22no—
306C22#381×C11311yescharacteristic
307C22#410×C11311yescharacteristic
308C22#410×C11311yescharacteristic
309C22C2×#103×C11311yescharacteristic
310C22#418×C11311yescharacteristic
311C22C2×#104×C11311yescharacteristic
312C22#421×C11311yescharacteristic
313C22#481×C11312yes—
314C22#484×C11312yes—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—84no—
322C4—82no—
323C4—82no—
324C2—22no—
325C2—22no—
326C2C113×#150311yescharacteristic
327C2C113×#150511yescharacteristic
328C2C113×#151411yescharacteristic
329C2C113×#151811yescharacteristic
330C2C113×#182011yescharacteristic
331C2C113×#182411yescharacteristic
332C2C113×#182611yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC24×C113C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
8. #384×C113C4semidirect
9. #384×C113C4semidirect
14. C4×C4⋊C4×C113C4semidirect
157. #8717C113direct (N × H)
171. C113#8717direct (N × H)
175. #384C4×C113semidirect
176. #384C4×C113semidirect
181. C4×C4⋊C4C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#22852
C113×#18172
C113×#14342
C113×#12942
#8717113