Finite Group Databasebeta

← C2×C113×#1808 #43288677

Subgroups — C2×C113×#1808 #43288677

Order 28928.

1790 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C8×C113C211yesmaximal, characteristic
2C22×#107×C113C212yesmaximal, complemented
3C2×#380×C113C212yesmaximal
4C113×#1808C218yesmaximal, direct product factor
5C2×#340×C113C212yesmaximal, complemented
6C24×C4×C113C2211yescharacteristic
7C23×C8×C113—28no—
8C23×C8×C113C418yescomplemented
9C23×C8×C113C2211yescharacteristic
10C23×C8×C113C2214yes—
11C23×C8×C113C2211yescharacteristic
12C22×C4⋊C4×C113C2214yes—
13C22×C22⋊C4×C113—22no—
14C2×#107×C113—28no—
15C2×#107×C113C2218yescomplemented
16#380×C113—24no—
17#380×C113C2218yes—
18C2×#95×C113—22no—
19#340×C113C2218yescomplemented
20C25×C113D411yescharacteristic
21C23×C4×C113—24no—
22C23×C4×C113—24no—
23C23×C4×C113—24no—
24C23×C4×C113C2×C414yes—
25C23×C4×C113D412yes—
26C23×C4×C113D411yescharacteristic
27C23×C4×C113Q814yes—
28C23×C4×C113C2312yes—
29C23×C4×C113C2311yescharacteristic
30C22×C8×C113—24no—
31C22×C8×C113—232no—
32C22×C8×C113—216no—
33C22×C8×C113C2×C414yes—
34C22×C8×C113C2×C414yes—
35C22×C8×C113C2×C4116yescomplemented
36C22×C8×C113D418yes—
37C22×C8×C113C2312yes—
38C22×C8×C113C2312yes—
39C2×C4⋊C4×C113—28no—
40C2×C4⋊C4×C113—28no—
41C2×C4⋊C4×C113—24no—
42C2×C4⋊C4×C113C2318yes—
43C2×C22⋊C4×C113—28no—
44C2×C22⋊C4×C113—48no—
45#107×C113—216no—
46#95×C113—28no—
47C24×C113—24no—
48C24×C113—24no—
49C24×C113C4⋊C414yes—
50C24×C113D814yes—
51C24×C113Q1614yes—
52C24×C113C2×D412yes—
53C24×C113C2×D411yescharacteristic
54C22×C4×C113—24no—
55C22×C4×C113—28no—
56C22×C4×C113—28no—
57C22×C4×C113—28no—
58C22×C4×C113—216no—
59C22×C4×C113—24no—
60C22×C4×C113—24no—
61C22×C4×C113—28no—
62C22×C4×C113—48no—
63C22×C4×C113—48no—
64C22×C4×C113—48no—
65C22×C4×C113C4⋊C414yes—
66C22×C4×C113C4⋊C418yes—
67C22×C4×C113C22×C414yes—
68C22×C4×C113C22×C412yes—
69C22×C4×C113C2×D412yes—
70C22×C4×C113C2×D414yes—
71C22×C4×C113C2×D411yescharacteristic
72C22×C4×C113C2×Q814yes—
73C22×C4×C113C2×Q812yes—
74C22×C4×C113#4114yes—
75C22×C4×C113C2411yescharacteristic
76C2×C8×C113—28no—
77C2×C8×C113—24no—
78C2×C8×C113—232no—
79C2×C8×C113C22⋊C4116yescomplemented
80C2×C8×C113C22×C414yes—
81C2×C8×C113C22×C414yes—
82C2×C8×C113C2×D418yes—
83C4⋊C4×C113—28no—
84C4⋊C4×C113—28no—
85C4⋊C4×C113—48no—
86C22⋊C4×C113—416no—
87C23×C113—24no—
88C23×C113—24no—
89C23×C113—28no—
90C23×C113—28no—
91C23×C113—216no—
92C23×C113—216no—
93C23×C113#107116yescomplemented
94C23×C113C2×C4⋊C414yes—
95C23×C113C2×C4⋊C412yes—
96C23×C113#12114yes—
97C23×C113C2×D814yes—
98C23×C113C2×D812yes—
99C23×C113C2×Q1614yes—
100C23×C113C2×Q1612yes—
101C23×C113#13514yes—
102C23×C113C22×D411yescharacteristic
103C2×C4×C113—24no—
104C2×C4×C113—28no—
105C2×C4×C113—24no—
106C2×C4×C113—24no—
107C2×C4×C113—28no—
108C2×C4×C113—216no—
109C2×C4×C113—48no—
110C2×C4×C113—48no—
111C2×C4×C113—48no—
112C2×C4×C113—816no—
113C2×C4×C113C2×C22⋊C414yes—
114C2×C4×C113C2×C4⋊C414yes—
115C2×C4×C113C2×C4⋊C412yes—
116C2×C4×C113#11714yes—
117C2×C4×C113#12114yes—
118C2×C4×C113C22⋊Q818yes—
119C2×C4×C113C23×C411yescharacteristic
120C2×C4×C113C22×D412yes—
121C2×C4×C113C22×Q811yescharacteristic
122C2×C4×C113C2×#4112yes—
123C8×C113—24no—
124C8×C113C2×C22⋊C418yescomplemented
125C22×C113—232no—
126C22×C113—24no—
127C22×C113—24no—
128C22×C113—28no—
129C22×C113—28no—
130C22×C113#38014yes—
131C22×C113C2×#10714yes—
132C22×C113C2×#10718yescomplemented
133C22×C113#42714yes—
134C22×C113#46618yes—
135C22×C113#46718yes—
136C22×C113C22×C4⋊C411yescharacteristic
137C22×C113C2×#12112yes—
138C22×C113C22×D811yescharacteristic
139C22×C113C22×Q1611yescharacteristic
140C22×C113C2×#13512yes—
141C4×C113—24no—
142C4×C113—88no—
143C4×C113#38014yes—
144C4×C113C22×C22⋊C411yescharacteristic
145C4×C113C2×#11711yescharacteristic
146C4×C113C2×C22⋊Q812yes—
147C2×#1808C11311yesmaximal, characteristic, direct product factor, Sylow
148C2×C113—28no—
149C2×C113#180818yesdirect product factor
150C2×C113C2×#38011yescharacteristic
151C2×C113C22×#10711yescharacteristic
152C2×C113C2×#42711yescharacteristic
153C2×C113C2×#46612yes—
154C2×C113C2×#46712yes—
155C24×C8C2×C11311yescharacteristic
156C22×#107C2×C11312yescomplemented
157C2×#380C2×C11312yes—
158#1808C2×C11318yesdirect product factor
159C2×#340C2×C11312yescomplemented
160C113C2×#180811yescharacteristic, direct product factor, Sylow
161C24×C4C22×C11311yescharacteristic
162C23×C8—28no—
163C23×C8C4×C11318yescomplemented
164C23×C8C22×C11311yescharacteristic
165C23×C8C22×C11314yes—
166C23×C8C22×C11311yescharacteristic
167C22×C4⋊C4C22×C11314yes—
168C22×C22⋊C4—22no—
169C2×#107—28no—
170C2×#107C22×C11318yescomplemented
171#380—24no—
172#380C22×C11318yes—
173C2×#95—22no—
174#340C22×C11318yescomplemented
175C25D4×C11311yescharacteristic
176C23×C4—24no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4C2×C4×C11314yes—
180C23×C4D4×C11311yescharacteristic
181C23×C4D4×C11312yes—
182C23×C4Q8×C11314yes—
183C23×C4C23×C11312yes—
184C23×C4C23×C11311yescharacteristic
185C22×C8—24no—
186C22×C8—232no—
187C22×C8—216no—
188C22×C8C2×C4×C11314yes—
189C22×C8C2×C4×C11314yes—
190C22×C8C2×C4×C113116yescomplemented
191C22×C8D4×C11318yes—
192C22×C8C23×C11312yes—
193C22×C8C23×C11312yes—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—28no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4C23×C11318yes—
198C2×C22⋊C4—28no—
199C2×C22⋊C4—48no—
200#107—216no—
201#95—28no—
202C24—24no—
203C24—24no—
204C24C4⋊C4×C11314yes—
205C24D8×C11314yes—
206C24Q16×C11314yes—
207C24C2×D4×C11312yes—
208C24C2×D4×C11311yescharacteristic
209C22×C4—24no—
210C22×C4—28no—
211C22×C4—28no—
212C22×C4—28no—
213C22×C4—216no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—28no—
217C22×C4—48no—
218C22×C4—48no—
219C22×C4—48no—
220C22×C4C4⋊C4×C11314yes—
221C22×C4C4⋊C4×C11318yes—
222C22×C4C22×C4×C11314yes—
223C22×C4C22×C4×C11312yes—
224C22×C4C2×D4×C11312yes—
225C22×C4C2×D4×C11314yes—
226C22×C4C2×D4×C11311yescharacteristic
227C22×C4C2×Q8×C11314yes—
228C22×C4C2×Q8×C11312yes—
229C22×C4#41×C11314yes—
230C22×C4C24×C11311yescharacteristic
231C2×C8—28no—
232C2×C8—24no—
233C2×C8—232no—
234C2×C8C22⋊C4×C113116yescomplemented
235C2×C8C22×C4×C11314yes—
236C2×C8C22×C4×C11314yes—
237C2×C8C2×D4×C11318yes—
238C4⋊C4—28no—
239C4⋊C4—28no—
240C4⋊C4—48no—
241C22⋊C4—416no—
242C23—24no—
243C23—24no—
244C23—28no—
245C23—28no—
246C23—216no—
247C23—216no—
248C23#107×C113116yescomplemented
249C23C2×C4⋊C4×C11314yes—
250C23C2×C4⋊C4×C11312yes—
251C23#121×C11314yes—
252C23C2×D8×C11314yes—
253C23C2×D8×C11312yes—
254C23C2×Q16×C11314yes—
255C23C2×Q16×C11312yes—
256C23#135×C11314yes—
257C23C22×D4×C11311yescharacteristic
258C2×C4—24no—
259C2×C4—28no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—28no—
263C2×C4—216no—
264C2×C4—48no—
265C2×C4—48no—
266C2×C4—48no—
267C2×C4—816no—
268C2×C4C2×C22⋊C4×C11314yes—
269C2×C4C2×C4⋊C4×C11314yes—
270C2×C4C2×C4⋊C4×C11312yes—
271C2×C4#117×C11314yes—
272C2×C4#121×C11314yes—
273C2×C4C22⋊Q8×C11318yes—
274C2×C4C23×C4×C11311yescharacteristic
275C2×C4C22×D4×C11312yes—
276C2×C4C22×Q8×C11311yescharacteristic
277C2×C4C2×#41×C11312yes—
278C8—24no—
279C8C2×C22⋊C4×C11318yescomplemented
280C22—24no—
281C22—28no—
282C22—28no—
283C22—232no—
284C22—24no—
285C22#380×C11314yes—
286C22C2×#107×C11314yes—
287C22C2×#107×C11318yescomplemented
288C22#427×C11314yes—
289C22#466×C11318yes—
290C22#467×C11318yes—
291C22C22×C4⋊C4×C11311yescharacteristic
292C22C2×#121×C11312yes—
293C22C22×D8×C11311yescharacteristic
294C22C22×Q16×C11311yescharacteristic
295C22C2×#135×C11312yes—
296C4—24no—
297C4—88no—
298C4#380×C11314yes—
299C4C22×C22⋊C4×C11311yescharacteristic
300C4C2×#117×C11311yescharacteristic
301C4C2×C22⋊Q8×C11312yes—
302C2—28no—
303C2C113×#180818yesdirect product factor
304C2C2×#380×C11311yescharacteristic
305C2C22×#107×C11311yescharacteristic
306C2C2×#427×C11311yescharacteristic
307C2C2×#466×C11312yes—
308C2C2×#467×C11312yes—
subgroupG/H
center, socleC24×C113C2×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC25×C113D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C113 ◁ C24×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#107×C113C2semidirect
4. C113×#1808C2direct (N × H)
5. C2×#340×C113C2semidirect
8. C23×C8×C113C4semidirect
15. C2×#107×C113C22semidirect
19. #340×C113C22semidirect
35. C22×C8×C113C2×C4semidirect
79. C2×C8×C113C22⋊C4semidirect
93. C23×C113#107semidirect
124. C8×C113C2×C22⋊C4semidirect
132. C22×C113C2×#107semidirect
147. C2×#1808C113direct (N × H)
149. C2×C113#1808direct (N × H)
156. C22×#107C2×C113semidirect
158. #1808C2×C113direct (N × H)
159. C2×#340C2×C113semidirect
160. C113C2×#1808direct (N × H)
163. C23×C8C4×C113semidirect
170. C2×#107C22×C113semidirect
174. #340C22×C113semidirect
190. C22×C8C2×C4×C113semidirect
234. C2×C8C22⋊C4×C113semidirect
248. C23#107×C113semidirect
279. C8C2×C22⋊C4×C113semidirect
287. C22C2×#107×C113semidirect
303. C2C113×#1808direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C8×C1132
C22×#107×C1132
C2×#380×C1132
C113×#18082
C2×#340×C1132
C2×#1808113