Finite Group Databasebeta

← C131×#13426 #45699310

Subgroups — C131×#13426 #45699310

Order 33536.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2733×C131C211yesmaximal, characteristic
2C2×#355×C131C212yesmaximal, complemented
3#1888×C131C212yesmaximal, complemented
4#1857×C131C211yesmaximal, characteristic, complemented
5#1394×C131C211yesmaximal, characteristic, complemented
6C2×#124×C131C2212yes—
7#519×C131C2211yescharacteristic
8#428×C131—21no—
9#418×C131—22no—
10C2×#101×C131C2212yes—
11C2×#101×C131C2211yescharacteristic
12#394×C131—21no—
13#392×C131—22no—
14#391×C131C2211yescharacteristic
15#390×C131—21no—
16#388×C131—22no—
17#355×C131—24no—
18#339×C131—21no—
19#339×C131—22no—
20C22×Q8×C131C2311yescharacteristic
21C22×D4×C131—21no—
22C22×D4×C131—21no—
23C22×D4×C131D412yes—
24C2×M16×C131—21no—
25C2×M16×C131—22no—
26#124×C131—22no—
27#124×C131—22no—
28#124×C131—22no—
29#124×C131—22no—
30C4×Q8×C131—41no—
31C4×Q8×C131—41no—
32#117×C131—22no—
33#117×C131—21no—
34C2×C4⋊C4×C131—21no—
35C2×C4⋊C4×C131D411yescharacteristic
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131—22no—
38C2×C22⋊C4×C131—22no—
39C2×C22⋊C4×C131—22no—
40C2×C42×C131D412yes—
41C2×C42×C131D411yescharacteristic
42#107×C131—41no—
43#106×C131—41no—
44#102×C131—42no—
45#102×C131—42no—
46#101×C131—21no—
47#101×C131—22no—
48#101×C131—22no—
49#101×C131D412yescomplemented
50#95×C131—21no—
51#95×C131—22no—
52C24×C131—22no—
53C2×Q8×C131—41no—
54C2×Q8×C131—41no—
55C2×Q8×C131C2×D411yescharacteristic
56C2×Q8×C131#4111yescharacteristic
57C2×Q8×C131#4112yes—
58C2×D4×C131—22no—
59C2×D4×C131—22no—
60C2×D4×C131—42no—
61C2×D4×C131—42no—
62C2×D4×C131—42no—
63C2×D4×C131—81no—
64C2×D4×C131—81no—
65C2×D4×C131—82no—
66C2×D4×C131—81no—
67C22×C4×C131—21no—
68C22×C4×C131—21no—
69C22×C4×C131—22no—
70C22×C4×C131C2×D412yes—
71C22×C4×C131C2×D411yescharacteristic
72M16×C131—22no—
73M16×C131—41no—
74M16×C131—42no—
75M16×C131—42no—
76C2×C8×C131—41no—
77C2×C8×C131—42no—
78C4⋊C4×C131—22no—
79C4⋊C4×C131—22no—
80C4⋊C4×C131—21no—
81C4⋊C4×C131—21no—
82C4⋊C4×C131—41no—
83C4⋊C4×C131—81no—
84C22⋊C4×C131—44no—
85C22⋊C4×C131—41no—
86C22⋊C4×C131—42no—
87C22⋊C4×C131—42no—
88C22⋊C4×C131—42no—
89C22⋊C4×C131—42no—
90C22⋊C4×C131—82no—
91C42×C131—22no—
92C42×C131—22no—
93C42×C131—41no—
94C42×C131—41no—
95C42×C131—42no—
96C23×C131—42no—
97C23×C131—42no—
98C23×C131—42no—
99C23×C131—42no—
100C23×C131—42no—
101C23×C131—42no—
102C23×C131—42no—
103C23×C131#12011yescharacteristic
104Q8×C131—41no—
105Q8×C131—41no—
106Q8×C131—42no—
107D4×C131—44no—
108D4×C131—82no—
109D4×C131—84no—
110D4×C131—84no—
111C2×C4×C131—21no—
112C2×C4×C131—22no—
113C2×C4×C131—21no—
114C2×C4×C131—22no—
115C2×C4×C131—22no—
116C2×C4×C131—41no—
117C2×C4×C131—41no—
118C2×C4×C131—42no—
119C2×C4×C131—42no—
120C2×C4×C131—42no—
121C2×C4×C131—42no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131#12112yes—
126C2×C4×C131#12111yescharacteristic
127C2×C4×C131#12312yes—
128C2×C4×C131#12411yescharacteristic
129C8×C131—42no—
130C8×C131—82no—
131C22×C131—21no—
132C22×C131—21no—
133C22×C131—82no—
134C22×C131—82no—
135C22×C131—82no—
136C22×C131—82no—
137C22×C131—82no—
138C22×C131—82no—
139C22×C131—82no—
140C22×C131#39411yescharacteristic
141C22×C131B(4,𝔽2)11yescharacteristic
142C22×C131#45811yescharacteristic
143C4×C131—21no—
144C4×C131—22no—
145C4×C131—22no—
146C4×C131—21no—
147C4×C131—42no—
148C4×C131—82no—
149C4×C131—81no—
150C4×C131—81no—
151C4×C131—81no—
152C2×C131—21no—
153C2×C131—21no—
154C2×C131—162no—
155C2×C131#204411yescharacteristic
156C2×C131#220211yescharacteristic
157C2×C131#220411yescharacteristic
158#13426C13111yesmaximal, characteristic, direct product factor, Sylow
159C131#1342611yescharacteristic, direct product factor, Sylow
160#2733C2×C13111yescharacteristic
161C2×#355C2×C13112yescomplemented
162#1888C2×C13112yescomplemented
163#1857C2×C13111yescharacteristic, complemented
164#1394C2×C13111yescharacteristic, complemented
165C2×#124C22×C13112yes—
166#519C22×C13111yescharacteristic
167#428—21no—
168#418—22no—
169C2×#101C22×C13112yes—
170C2×#101C22×C13111yescharacteristic
171#394—21no—
172#392—22no—
173#391C22×C13111yescharacteristic
174#390—21no—
175#388—22no—
176#355—24no—
177#339—21no—
178#339—22no—
179C22×Q8C23×C13111yescharacteristic
180C22×D4—21no—
181C22×D4—21no—
182C22×D4D4×C13112yes—
183C2×M16—21no—
184C2×M16—22no—
185#124—22no—
186#124—22no—
187#124—22no—
188#124—22no—
189C4×Q8—41no—
190C4×Q8—41no—
191#117—22no—
192#117—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4D4×C13111yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C42D4×C13112yes—
200C2×C42D4×C13111yescharacteristic
201#107—41no—
202#106—41no—
203#102—42no—
204#102—42no—
205#101—21no—
206#101—22no—
207#101—22no—
208#101D4×C13112yescomplemented
209#95—21no—
210#95—22no—
211C24—22no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C2×D4×C13111yescharacteristic
215C2×Q8#41×C13111yescharacteristic
216C2×Q8#41×C13112yes—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—42no—
222C2×D4—81no—
223C2×D4—81no—
224C2×D4—82no—
225C2×D4—81no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4C2×D4×C13112yes—
230C22×C4C2×D4×C13111yescharacteristic
231M16—22no—
232M16—41no—
233M16—42no—
234M16—42no—
235C2×C8—41no—
236C2×C8—42no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—81no—
243C22⋊C4—44no—
244C22⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—82no—
250C42—22no—
251C42—22no—
252C42—41no—
253C42—41no—
254C42—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23#120×C13111yescharacteristic
263Q8—41no—
264Q8—41no—
265Q8—42no—
266D4—44no—
267D4—82no—
268D4—84no—
269D4—84no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4#121×C13112yes—
285C2×C4#121×C13111yescharacteristic
286C2×C4#123×C13112yes—
287C2×C4#124×C13111yescharacteristic
288C8—42no—
289C8—82no—
290C22—21no—
291C22—21no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22#394×C13111yescharacteristic
300C22B(4,𝔽2)×C13111yescharacteristic
301C22#458×C13111yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—42no—
307C4—82no—
308C4—81no—
309C4—81no—
310C4—81no—
311C2—21no—
312C2—21no—
313C2—162no—
314C2#2044×C13111yescharacteristic
315C2#2202×C13111yescharacteristic
316C2#2204×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C131
prime radical#2733×C131C2
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#355×C131C2semidirect
3. #1888×C131C2semidirect
4. #1857×C131C2semidirect
5. #1394×C131C2semidirect
49. #101×C131D4semidirect
158. #13426C131direct (N × H)
159. C131#13426direct (N × H)
161. C2×#355C2×C131semidirect
162. #1888C2×C131semidirect
163. #1857C2×C131semidirect
164. #1394C2×C131semidirect
208. #101D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2733×C1312
C2×#355×C1312
#1888×C1312
#1857×C1312
#1394×C1312
#13426131