Finite Group Databasebeta

← C113×#22689 #43290709

Subgroups — C113×#22689 #43290709

Order 28928.

862 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#443×C113C211yesmaximal, characteristic
2C113×#2952C212yesmaximal
3C113×#2912C212yesmaximal, complemented
4C113×#1951C212yesmaximal, complemented
5C113×#1859C214yesmaximal, complemented
6C113×#1844C211yesmaximal, characteristic, complemented
7C113×#1815C212yesmaximal, complemented
8C113×#1772C211yesmaximal, characteristic, complemented
9C2×#135×C113C2211yescharacteristic
10C2×#131×C113C2212yes—
11#520×C113C2214yes—
12#443×C113C418yescomplemented
13#442×C113—22no—
14#441×C113—22no—
15C4×SD16×C113—24no—
16C2×#108×C113C2211yescharacteristic
17C2×#108×C113C2211yescharacteristic
18#428×C113—24no—
19#428×C113C2214yes—
20#427×C113—22no—
21#427×C113C2211yescharacteristic
22C2×#106×C113—22no—
23C2×#106×C113C2212yes—
24C2×#106×C113C2212yes—
25C2×#104×C113C2212yes—
26#417×C113C2214yes—
27#405×C113C2212yes—
28C2×C4×C8×C113C2211yescharacteristic
29#384×C113C2212yes—
30#343×C113C2214yes—
31#339×C113C2212yes—
32C2×#41×C113C2312yes—
33#135×C113C2×C414yes—
34#135×C113Q814yes—
35C2×Q16×C113D411yescharacteristic
36C2×SD16×C113D412yes—
37C2×D8×C113D411yescharacteristic
38#131×C113—24no—
39#131×C113C2×C418yescomplemented
40C2×M16×C113—22no—
41C2×M16×C113C2312yes—
42C2×M16×C113C2312yes—
43C22×C8×C113—22no—
44C22×C8×C113C2311yescharacteristic
45C22×C8×C113C2311yescharacteristic
46C4×Q8×C113—24no—
47C4×D4×C113—24no—
48C4×D4×C113—44no—
49#117×C113—24no—
50#117×C113C2312yes—
51C2×C4⋊C4×C113—24no—
52C2×C4⋊C4×C113—42no—
53C2×C4⋊C4×C113C2314yes—
54C2×C42×C113C2311yescharacteristic
55#108×C113—22no—
56#108×C113C2×C414yescomplemented
57#107×C113—24no—
58#107×C113D412yes—
59#106×C113—22no—
60#106×C113—22no—
61#106×C113—22no—
62#106×C113—22no—
63#106×C113—24no—
64#106×C113D412yes—
65#104×C113C2×C418yescomplemented
66#103×C113—24no—
67#102×C113—24no—
68#97×C113—22no—
69C4×C8×C113—22no—
70C4×C8×C113C2×C414yescomplemented
71#41×C113—22no—
72#41×C113—22no—
73#41×C113C22×C414yes—
74#41×C113C2×Q814yes—
75C2×Q8×C113C2×D412yes—
76C2×D4×C113—22no—
77C2×D4×C113C2×D412yes—
78C22×C4×C113—21no—
79C22×C4×C113—22no—
80C22×C4×C113—24no—
81C22×C4×C113—44no—
82C22×C4×C113C2411yescharacteristic
83Q16×C113C4⋊C414yescomplemented
84SD16×C113C4⋊C418yescomplemented
85D8×C113C4⋊C414yescomplemented
86M16×C113—22no—
87M16×C113—28no—
88M16×C113—22no—
89M16×C113—22no—
90M16×C113C22×C414yes—
91C2×C8×C113—22no—
92C2×C8×C113—28no—
93C2×C8×C113—22no—
94C2×C8×C113C22×C412yes—
95C2×C8×C113C22×C412yes—
96C2×C8×C113C2×D411yescharacteristic
97C2×C8×C113C2×D411yescharacteristic
98C2×C8×C113C2×D411yescharacteristic
99C2×C8×C113C2×D411yescharacteristic
100C2×C8×C113C2×Q812yes—
101C2×C8×C113#4112yes—
102C4⋊C4×C113—24no—
103C4⋊C4×C113—24no—
104C4⋊C4×C113—44no—
105C4⋊C4×C113—84no—
106C4⋊C4×C113C2×D414yes—
107C22⋊C4×C113—22no—
108C22⋊C4×C113—44no—
109C42×C113—22no—
110C42×C113—21no—
111C42×C113—44no—
112C42×C113C22×C412yes—
113C23×C113—22no—
114C23×C113H(5,𝔽2)11yescharacteristic
115Q8×C113—22no—
116Q8×C113C2×C4⋊C414yes—
117D4×C113—24no—
118D4×C113—24no—
119D4×C113—22no—
120D4×C113C2×C4⋊C414yes—
121C2×C4×C113—24no—
122C2×C4×C113—22no—
123C2×C4×C113—22no—
124C2×C4×C113—24no—
125C2×C4×C113—24no—
126C2×C4×C113—24no—
127C2×C4×C113—44no—
128C2×C4×C113—84no—
129C2×C4×C113—164no—
130C2×C4×C113C23×C411yescharacteristic
131C2×C4×C113C22×D411yescharacteristic
132C2×C4×C113C22×D411yescharacteristic
133C2×C4×C113C22×Q811yescharacteristic
134C2×C4×C113C2×#4111yescharacteristic
135C2×C4×C1132−1+411yescharacteristic
136C8×C113—24no—
137C8×C113—42no—
138C8×C113C2×C4⋊C412yes—
139C8×C113C2×C4⋊C412yes—
140C8×C113C4×D412yes—
141C8×C113C4×D412yes—
142C22×C113—22no—
143C22×C113—24no—
144C22×C113—44no—
145C22×C113#52011yescharacteristic
146C22×C113D4211yescharacteristic
147C22×C113#55411yescharacteristic
148C4×C113—24no—
149C4×C113—24no—
150C4×C113—44no—
151C4×C113—84no—
152C4×C113C22×C4⋊C411yescharacteristic
153C4×C113C2×C4×D411yescharacteristic
154C4×C113#54711yescharacteristic
155C4×C113D4×Q811yescharacteristic
156#22689C11311yesmaximal, characteristic, direct product factor, Sylow
157C2×C113—21no—
158C2×C113—21no—
159C2×C113—44no—
160C2×C113D4×C4⋊C411yescharacteristic
161C2×C113#329112yes—
162C2×#443C2×C11311yescharacteristic
163#2952C2×C11312yes—
164#2912C2×C11312yescomplemented
165#1951C2×C11312yescomplemented
166#1859C2×C11314yescomplemented
167#1844C2×C11311yescharacteristic, complemented
168#1815C2×C11312yescomplemented
169#1772C2×C11311yescharacteristic, complemented
170C113#2268911yescharacteristic, direct product factor, Sylow
171C2×#135C22×C11311yescharacteristic
172C2×#131C22×C11312yes—
173#520C22×C11314yes—
174#443C4×C11318yescomplemented
175#442—22no—
176#441—22no—
177C4×SD16—24no—
178C2×#108C22×C11311yescharacteristic
179C2×#108C22×C11311yescharacteristic
180#428—24no—
181#428C22×C11314yes—
182#427—22no—
183#427C22×C11311yescharacteristic
184C2×#106—22no—
185C2×#106C22×C11312yes—
186C2×#106C22×C11312yes—
187C2×#104C22×C11312yes—
188#417C22×C11314yes—
189#405C22×C11312yes—
190C2×C4×C8C22×C11311yescharacteristic
191#384C22×C11312yes—
192#343C22×C11314yes—
193#339C22×C11312yes—
194C2×#41C23×C11312yes—
195#135C2×C4×C11314yes—
196#135Q8×C11314yes—
197C2×Q16D4×C11311yescharacteristic
198C2×SD16D4×C11312yes—
199C2×D8D4×C11311yescharacteristic
200#131—24no—
201#131C2×C4×C11318yescomplemented
202C2×M16—22no—
203C2×M16C23×C11312yes—
204C2×M16C23×C11312yes—
205C22×C8—22no—
206C22×C8C23×C11311yescharacteristic
207C22×C8C23×C11311yescharacteristic
208C4×Q8—24no—
209C4×D4—24no—
210C4×D4—44no—
211#117—24no—
212#117C23×C11312yes—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4C23×C11314yes—
216C2×C42C23×C11311yescharacteristic
217#108—22no—
218#108C2×C4×C11314yescomplemented
219#107—24no—
220#107D4×C11312yes—
221#106—22no—
222#106—22no—
223#106—22no—
224#106—22no—
225#106—24no—
226#106D4×C11312yes—
227#104C2×C4×C11318yescomplemented
228#103—24no—
229#102—24no—
230#97—22no—
231C4×C8—22no—
232C4×C8C2×C4×C11314yescomplemented
233#41—22no—
234#41—22no—
235#41C22×C4×C11314yes—
236#41C2×Q8×C11314yes—
237C2×Q8C2×D4×C11312yes—
238C2×D4—22no—
239C2×D4C2×D4×C11312yes—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—44no—
244C22×C4C24×C11311yescharacteristic
245Q16C4⋊C4×C11314yescomplemented
246SD16C4⋊C4×C11318yescomplemented
247D8C4⋊C4×C11314yescomplemented
248M16—22no—
249M16—28no—
250M16—22no—
251M16—22no—
252M16C22×C4×C11314yes—
253C2×C8—22no—
254C2×C8—28no—
255C2×C8—22no—
256C2×C8C22×C4×C11312yes—
257C2×C8C22×C4×C11312yes—
258C2×C8C2×D4×C11311yescharacteristic
259C2×C8C2×D4×C11311yescharacteristic
260C2×C8C2×D4×C11311yescharacteristic
261C2×C8C2×D4×C11311yescharacteristic
262C2×C8C2×Q8×C11312yes—
263C2×C8#41×C11312yes—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—44no—
267C4⋊C4—84no—
268C4⋊C4C2×D4×C11314yes—
269C22⋊C4—22no—
270C22⋊C4—44no—
271C42—22no—
272C42—21no—
273C42—44no—
274C42C22×C4×C11312yes—
275C23—22no—
276C23H(5,𝔽2)×C11311yescharacteristic
277Q8—22no—
278Q8C2×C4⋊C4×C11314yes—
279D4—24no—
280D4—24no—
281D4—22no—
282D4C2×C4⋊C4×C11314yes—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—44no—
290C2×C4—84no—
291C2×C4—164no—
292C2×C4C23×C4×C11311yescharacteristic
293C2×C4C22×D4×C11311yescharacteristic
294C2×C4C22×D4×C11311yescharacteristic
295C2×C4C22×Q8×C11311yescharacteristic
296C2×C4C2×#41×C11311yescharacteristic
297C2×C42−1+4×C11311yescharacteristic
298C8—24no—
299C8—42no—
300C8C2×C4⋊C4×C11312yes—
301C8C2×C4⋊C4×C11312yes—
302C8C4×D4×C11312yes—
303C8C4×D4×C11312yes—
304C22—22no—
305C22—24no—
306C22—44no—
307C22#520×C11311yescharacteristic
308C22D42×C11311yescharacteristic
309C22#554×C11311yescharacteristic
310C4—24no—
311C4—24no—
312C4—44no—
313C4—84no—
314C4C22×C4⋊C4×C11311yescharacteristic
315C4C2×C4×D4×C11311yescharacteristic
316C4#547×C11311yescharacteristic
317C4D4×Q8×C11311yescharacteristic
318C2—21no—
319C2—21no—
320C2—44no—
321C2D4×C4⋊C4×C11311yescharacteristic
322C2C113×#329112yes—
subgroupG/H
center, socleC22×C113D42
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC2×#135×C113C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#2912C2semidirect
4. C113×#1951C2semidirect
5. C113×#1859C2semidirect
6. C113×#1844C2semidirect
7. C113×#1815C2semidirect
8. C113×#1772C2semidirect
12. #443×C113C4semidirect
39. #131×C113C2×C4semidirect
56. #108×C113C2×C4semidirect
65. #104×C113C2×C4semidirect
70. C4×C8×C113C2×C4semidirect
83. Q16×C113C4⋊C4semidirect
84. SD16×C113C4⋊C4semidirect
85. D8×C113C4⋊C4semidirect
156. #22689C113direct (N × H)
164. #2912C2×C113semidirect
165. #1951C2×C113semidirect
166. #1859C2×C113semidirect
167. #1844C2×C113semidirect
168. #1815C2×C113semidirect
169. #1772C2×C113semidirect
170. C113#22689direct (N × H)
174. #443C4×C113semidirect
201. #131C2×C4×C113semidirect
218. #108C2×C4×C113semidirect
227. #104C2×C4×C113semidirect
232. C4×C8C2×C4×C113semidirect
245. Q16C4⋊C4×C113semidirect
246. SD16C4⋊C4×C113semidirect
247. D8C4⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#443×C1132
C113×#29522
C113×#29122
C113×#19512
C113×#18592
C113×#18442
C113×#18152
C113×#17722
#22689113