Finite Group Databasebeta

← C131×#13379 #45699263

Subgroups — C131×#13379 #45699263

Order 33536.

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

normal subgroups only

This group has 540 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#2809×C131C211yesmaximal, characteristic, complemented
2#1793×C131C212yesmaximal
3#1793×C131C211yesmaximal, characteristic
4#1394×C131C212yesmaximal, complemented
5#1394×C131C211yesmaximal, characteristic, complemented
6C2×2−1+4×C131C2211yescharacteristic
7C2×#104×C131—21no—
8C2×#104×C131—22no—
9#417×C131—22no—
10#417×C131—21no—
11C2×#101×C131C2211yescharacteristic
12C2×#101×C131C2212yes—
13#400×C131—21no—
14#398×C131—22no—
15#391×C131C2212yes—
16#391×C131C2211yescharacteristic
17#389×C131—21no—
18#387×C131—22no—
192−1+4×C131—21no—
202−1+4×C131—22no—
212−1+4×C131—42no—
222−1+4×C131Q812yes—
23C2×#41×C131—21no—
24C2×#41×C131—22no—
25C2×#41×C131—41no—
26C22×Q8×C131—41no—
27C22×Q8×C131C2311yescharacteristic
28C2×M16×C131—21no—
29C2×M16×C131—22no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131D412yes—
35C2×C4⋊C4×C131D411yescharacteristic
36C2×C42×C131D411yescharacteristic
37C2×C42×C131D412yes—
38#104×C131—42no—
39#104×C131—44no—
40#103×C131—42no—
41#103×C131—41no—
42#102×C131—42no—
43#102×C131—41no—
44#101×C131—22no—
45#101×C131—22no—
46#101×C131—22no—
47#95×C131—22no—
48#95×C131—21no—
49#95×C131—22no—
50#95×C131—22no—
51#95×C131—22no—
52#41×C131—22no—
53#41×C131—24no—
54#41×C131—22no—
55#41×C131—24no—
56#41×C131—41no—
57#41×C131—42no—
58#41×C131—42no—
59#41×C131—44no—
60#41×C131—42no—
61#41×C131—41no—
62#41×C131—42no—
63C2×Q8×C131—22no—
64C2×Q8×C131—21no—
65C2×Q8×C131—41no—
66C2×Q8×C131—41no—
67C2×Q8×C131—42no—
68C2×Q8×C131—44no—
69C2×Q8×C131—42no—
70C2×Q8×C131C2×Q811yescharacteristic
71C2×Q8×C131#4111yescharacteristic
72C2×Q8×C131#4112yes—
73C2×D4×C131—22no—
74C2×D4×C131—21no—
75C2×D4×C131—41no—
76C22×C4×C131—21no—
77C22×C4×C131—21no—
78C22×C4×C131—22no—
79C22×C4×C131—22no—
80C22×C4×C131—42no—
81C22×C4×C131—41no—
82C22×C4×C131C2×D411yescharacteristic
83C22×C4×C131C2×D412yes—
84M16×C131—41no—
85M16×C131—42no—
86M16×C131—41no—
87M16×C131—42no—
88C2×C8×C131—42no—
89C2×C8×C131—41no—
90C4⋊C4×C131—42no—
91C4⋊C4×C131—41no—
92C4⋊C4×C131—42no—
93C4⋊C4×C131—44no—
94C4⋊C4×C131—81no—
95C4⋊C4×C131—81no—
96C42×C131—41no—
97C42×C131—42no—
98C23×C131—41no—
99C23×C131#12011yescharacteristic
100Q8×C131—22no—
101Q8×C131—24no—
102Q8×C131—41no—
103Q8×C131—42no—
104Q8×C131—41no—
105Q8×C131—41no—
106Q8×C131—42no—
107D4×C131—22no—
108D4×C131—24no—
109D4×C131—41no—
110D4×C131—42no—
111D4×C131—42no—
112D4×C131—42no—
113C2×C4×C131—21no—
114C2×C4×C131—22no—
115C2×C4×C131—22no—
116C2×C4×C131—21no—
117C2×C4×C131—22no—
118C2×C4×C131—42no—
119C2×C4×C131—44no—
120C2×C4×C131—42no—
121C2×C4×C131—44no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131—42no—
126C2×C4×C131—42no—
127C2×C4×C131—42no—
128C2×C4×C131—42no—
129C2×C4×C131—42no—
130C2×C4×C131—42no—
131C2×C4×C131—41no—
132C2×C4×C131—42no—
133C2×C4×C131C22⋊Q811yescharacteristic
134C2×C4×C131C22⋊Q812yes—
135C2×C4×C131#12411yescharacteristic
136C2×C4×C131#12412yes—
137C8×C131—81no—
138C8×C131—82no—
139C22×C131—21no—
140C22×C131—21no—
141C22×C131—42no—
142C22×C131—81no—
143C22×C131—81no—
144C22×C131#39311yescharacteristic
145C22×C131B(4,𝔽2)11yescharacteristic
146C22×C131B(4,𝔽2)11yescharacteristic
147C4×C131—21no—
148C4×C131—22no—
149C4×C131—21no—
150C4×C131—22no—
151C4×C131—42no—
152C4×C131—42no—
153C4×C131—82no—
154C4×C131—81no—
155C4×C131—82no—
156C2×C131—21no—
157C2×C131—21no—
158C2×C131—82no—
159C2×C131#202911yescharacteristic
160C2×C131#220311yescharacteristic
161C2×C131#220411yescharacteristic
162#13379C13111yesmaximal, characteristic, direct product factor, Sylow
163C131#1337911yescharacteristic, direct product factor, Sylow
164#2809C2×C13111yescharacteristic, complemented
165#1793C2×C13111yescharacteristic
166#1793C2×C13112yes—
167#1394C2×C13111yescharacteristic, complemented
168#1394C2×C13112yescomplemented
169C2×2−1+4C22×C13111yescharacteristic
170C2×#104—22no—
171C2×#104—21no—
172#417—22no—
173#417—21no—
174C2×#101C22×C13112yes—
175C2×#101C22×C13111yescharacteristic
176#400—21no—
177#398—22no—
178#391C22×C13111yescharacteristic
179#391C22×C13112yes—
180#389—21no—
181#387—22no—
1822−1+4—22no—
1832−1+4—21no—
1842−1+4—42no—
1852−1+4Q8×C13112yes—
186C2×#41—22no—
187C2×#41—21no—
188C2×#41—41no—
189C22×Q8—41no—
190C22×Q8C23×C13111yescharacteristic
191C2×M16—22no—
192C2×M16—21no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4D4×C13112yes—
198C2×C4⋊C4D4×C13111yescharacteristic
199C2×C42D4×C13112yes—
200C2×C42D4×C13111yescharacteristic
201#104—42no—
202#104—44no—
203#103—42no—
204#103—41no—
205#102—42no—
206#102—41no—
207#101—22no—
208#101—22no—
209#101—22no—
210#95—21no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—22no—
215#41—22no—
216#41—24no—
217#41—24no—
218#41—22no—
219#41—41no—
220#41—42no—
221#41—42no—
222#41—44no—
223#41—42no—
224#41—42no—
225#41—41no—
226C2×Q8—22no—
227C2×Q8—21no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—44no—
232C2×Q8—42no—
233C2×Q8C2×Q8×C13111yescharacteristic
234C2×Q8#41×C13112yes—
235C2×Q8#41×C13111yescharacteristic
236C2×D4—22no—
237C2×D4—21no—
238C2×D4—41no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4C2×D4×C13112yes—
246C22×C4C2×D4×C13111yescharacteristic
247M16—41no—
248M16—42no—
249M16—42no—
250M16—41no—
251C2×C8—42no—
252C2×C8—41no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—44no—
256C4⋊C4—42no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C42—41no—
260C42—42no—
261C23—41no—
262C23#120×C13111yescharacteristic
263Q8—22no—
264Q8—24no—
265Q8—41no—
266Q8—42no—
267Q8—41no—
268Q8—41no—
269Q8—42no—
270D4—22no—
271D4—24no—
272D4—41no—
273D4—42no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4C22⋊Q8×C13112yes—
297C2×C4C22⋊Q8×C13111yescharacteristic
298C2×C4#124×C13112yes—
299C2×C4#124×C13111yescharacteristic
300C8—81no—
301C8—82no—
302C22—21no—
303C22—21no—
304C22—42no—
305C22—81no—
306C22—81no—
307C22#393×C13111yescharacteristic
308C22B(4,𝔽2)×C13111yescharacteristic
309C22B(4,𝔽2)×C13111yescharacteristic
310C4—21no—
311C4—22no—
312C4—21no—
313C4—22no—
314C4—42no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4—82no—
319C2—21no—
320C2—21no—
321C2—82no—
322C2#2029×C13111yescharacteristic
323C2#2203×C13111yescharacteristic
324C2#2204×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C131
prime radicalC2×2−1+4×C131C22
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
1. #2809×C131C2semidirect
4. #1394×C131C2semidirect
5. #1394×C131C2semidirect
162. #13379C131direct (N × H)
163. C131#13379direct (N × H)
164. #2809C2×C131semidirect
167. #1394C2×C131semidirect
168. #1394C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2809×C1312
#1793×C1312
#1394×C1312
#13379131