Finite Group Databasebeta

← C131×#29654 #45715538

Subgroups — C131×#29654 #45715538

Order 33536.

948 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3458×C131C211yesmaximal, characteristic, complemented
2#3094×C131C212yesmaximal
3#2500×C131C211yesmaximal, characteristic
4#2061×C131C212yesmaximal, complemented
5#2060×C131C212yesmaximal, complemented
6#2027×C131C212yesmaximal, complemented
7#2027×C131C212yesmaximal, complemented
8#1826×C131C212yesmaximal, complemented
9#1822×C131C211yesmaximal, characteristic, complemented
10#544×C131—22no—
11#544×C131—22no—
12#544×C131C2212yes—
13#544×C131C2212yes—
14#543×C131—22no—
15#533×C131—24no—
16#533×C131—22no—
17C2×#121×C131C2211yescharacteristic
18C2×#117×C131C2212yes—
19C2×#117×C131C2211yescharacteristic
20#482×C131—24no—
21#481×C131—22no—
22#480×C131—22no—
23#428×C131C2214yes—
24#418×C131C2214yes—
25#407×C131C2212yes—
26#394×C131—22no—
27#390×C131C2211yescharacteristic
28#390×C131C2211yescharacteristic
29#388×C131—22no—
30#384×C131C2211yescharacteristic
31#382×C131C2211yescharacteristic
32C4×C22⋊C4×C131C2211yescharacteristic
33#343×C131C2212yes—
34#343×C131C2212yes—
35#339×C131C2214yes—
36#339×C131C2214yes—
37C22×D4×C131—21no—
38C22×D4×C131C2311yescharacteristic
39C23×C4×C131C2311yescharacteristic
40C2×M16×C131C2314yes—
41C4⋊Q8×C131—22no—
42C4⋊Q8×C131—22no—
43C4⋊Q8×C131—24no—
44C4⋊Q8×C131—24no—
45#125×C131—24no—
46#125×C131—24no—
47#125×C131—24no—
48C22⋊Q8×C131—28no—
49C22⋊Q8×C131—28no—
50C22⋊Q8×C131—24no—
51C22⋊Q8×C131—24no—
52#121×C131—22no—
53#121×C131—22no—
54C4×Q8×C131—24no—
55C4×Q8×C131—24no—
56#117×C131—22no—
57#117×C131—22no—
58#117×C131—22no—
59#117×C131—22no—
60#117×C131D414yes—
61#117×C131C2314yes—
62C2×C4⋊C4×C131—22no—
63C2×C4⋊C4×C131D412yes—
64C2×C4⋊C4×C131D412yes—
65C2×C4⋊C4×C131C2311yescharacteristic
66C2×C4⋊C4×C131C2311yescharacteristic
67C2×C4⋊C4×C131C2311yescharacteristic
68C2×C22⋊C4×C131—22no—
69C2×C22⋊C4×C131—21no—
70C2×C22⋊C4×C131—21no—
71C2×C22⋊C4×C131—22no—
72C2×C22⋊C4×C131—22no—
73C2×C22⋊C4×C131D412yes—
74C2×C42×C131—22no—
75C2×C42×C131D412yes—
76C2×C42×C131C2311yescharacteristic
77C2×C42×C131C2311yescharacteristic
78#107×C131—24no—
79#106×C131—24no—
80#102×C131—24no—
81#102×C131—24no—
82C22⋊C8×C131—22no—
83C22⋊C8×C131—22no—
84#95×C131—21no—
85#95×C131—22no—
86C24×C131—21no—
87C24×C131C2×D411yescharacteristic
88C2×Q8×C131—24no—
89C2×Q8×C131—24no—
90C2×D4×C131—22no—
91C2×D4×C131—22no—
92C2×D4×C131—22no—
93C2×D4×C131—42no—
94C2×D4×C131—82no—
95C22×C4×C131—22no—
96C22×C4×C131—22no—
97C22×C4×C131—21no—
98C22×C4×C131—22no—
99C22×C4×C131—22no—
100C22×C4×C131—21no—
101C22×C4×C131—21no—
102C22×C4×C131C2×D411yescharacteristic
103C22×C4×C131C2×D412yes—
104C22×C4×C131C2×D412yes—
105C22×C4×C131C2×D412yes—
106C22×C4×C131C2×D412yes—
107C22×C4×C131C2411yescharacteristic
108M16×C131—24no—
109M16×C131—24no—
110C2×C8×C131—24no—
111C4⋊C4×C131—28no—
112C4⋊C4×C131—28no—
113C4⋊C4×C131—24no—
114C4⋊C4×C131—24no—
115C4⋊C4×C131—22no—
116C4⋊C4×C131—22no—
117C4⋊C4×C131—22no—
118C4⋊C4×C131—22no—
119C4⋊C4×C131—22no—
120C4⋊C4×C131—82no—
121C4⋊C4×C131C2×D414yes—
122C4⋊C4×C131C2×D414yes—
123C22⋊C4×C131—24no—
124C22⋊C4×C131—24no—
125C22⋊C4×C131—24no—
126C22⋊C4×C131—44no—
127C22⋊C4×C131—42no—
128C22⋊C4×C131—41no—
129C22⋊C4×C131—41no—
130C22⋊C4×C131—82no—
131C42×C131—24no—
132C42×C131—22no—
133C42×C131—22no—
134C42×C131—24no—
135C42×C131—22no—
136C42×C131—22no—
137C23×C131—21no—
138C23×C131—21no—
139C23×C131—41no—
140C23×C131—41no—
141C23×C131—42no—
142C23×C131—42no—
143C23×C131—41no—
144C23×C131—41no—
145C23×C131—41no—
146C23×C131#12012yes—
147C23×C131C22×D411yescharacteristic
148Q8×C131—84no—
149Q8×C131—84no—
150D4×C131—44no—
151D4×C131—84no—
152C2×C4×C131—21no—
153C2×C4×C131—21no—
154C2×C4×C131—24no—
155C2×C4×C131—24no—
156C2×C4×C131—22no—
157C2×C4×C131—22no—
158C2×C4×C131—22no—
159C2×C4×C131—24no—
160C2×C4×C131—24no—
161C2×C4×C131—41no—
162C2×C4×C131—41no—
163C2×C4×C131—42no—
164C2×C4×C131—42no—
165C2×C4×C131—41no—
166C2×C4×C131—41no—
167C2×C4×C131—42no—
168C2×C4×C131—41no—
169C2×C4×C131—41no—
170C2×C4×C131—82no—
171C2×C4×C131—82no—
172C2×C4×C131#12011yescharacteristic
173C2×C4×C131#12011yescharacteristic
174C2×C4×C131C22×D412yes—
175C2×C4×C1312−1+412yes—
176C2×C4×C1312−1+412yes—
177C8×C131—44no—
178C22×C131—21no—
179C22×C131—21no—
180C22×C131—22no—
181C22×C131—22no—
182C22×C131—22no—
183C22×C131—81no—
184C22×C131—81no—
185C22×C131—82no—
186C22×C131—82no—
187C22×C131—81no—
188C22×C131—81no—
189C22×C131—81no—
190C22×C131C2×#12011yescharacteristic
191C22×C131#53611yescharacteristic
192C22×C131#53611yescharacteristic
193C4×C131—21no—
194C4×C131—21no—
195C4×C131—42no—
196C4×C131—42no—
197C4×C131—44no—
198C4×C131—42no—
199C4×C131—44no—
200C4×C131—81no—
201C4×C131—81no—
202C4×C131#53614yes—
203C2×C131—21no—
204C2×C131—21no—
205C2×C131—42no—
206C2×C131—161no—
207C2×C131#261411yescharacteristic
208C2×C131#301811yescharacteristic
209C2×C131#302111yescharacteristic
210#29654C13111yesmaximal, characteristic, direct product factor, Sylow
211C131#2965411yescharacteristic, direct product factor, Sylow
212#3458C2×C13111yescharacteristic, complemented
213#3094C2×C13112yes—
214#2500C2×C13111yescharacteristic
215#2061C2×C13112yescomplemented
216#2060C2×C13112yescomplemented
217#2027C2×C13112yescomplemented
218#2027C2×C13112yescomplemented
219#1826C2×C13112yescomplemented
220#1822C2×C13111yescharacteristic, complemented
221#544—22no—
222#544—22no—
223#544C22×C13112yes—
224#544C22×C13112yes—
225#543—22no—
226#533—24no—
227#533—22no—
228C2×#121C22×C13111yescharacteristic
229C2×#117C22×C13112yes—
230C2×#117C22×C13111yescharacteristic
231#482—24no—
232#481—22no—
233#480—22no—
234#428C22×C13114yes—
235#418C22×C13114yes—
236#407C22×C13112yes—
237#394—22no—
238#390C22×C13111yescharacteristic
239#390C22×C13111yescharacteristic
240#388—22no—
241#384C22×C13111yescharacteristic
242#382C22×C13111yescharacteristic
243C4×C22⋊C4C22×C13111yescharacteristic
244#343C22×C13112yes—
245#343C22×C13112yes—
246#339C22×C13114yes—
247#339C22×C13114yes—
248C22×D4—21no—
249C22×D4C23×C13111yescharacteristic
250C23×C4C23×C13111yescharacteristic
251C2×M16C23×C13114yes—
252C4⋊Q8—22no—
253C4⋊Q8—22no—
254C4⋊Q8—24no—
255C4⋊Q8—24no—
256#125—24no—
257#125—24no—
258#125—24no—
259C22⋊Q8—28no—
260C22⋊Q8—28no—
261C22⋊Q8—24no—
262C22⋊Q8—24no—
263#121—22no—
264#121—22no—
265C4×Q8—24no—
266C4×Q8—24no—
267#117—22no—
268#117—22no—
269#117—22no—
270#117—22no—
271#117D4×C13114yes—
272#117C23×C13114yes—
273C2×C4⋊C4—22no—
274C2×C4⋊C4D4×C13112yes—
275C2×C4⋊C4D4×C13112yes—
276C2×C4⋊C4C23×C13111yescharacteristic
277C2×C4⋊C4C23×C13111yescharacteristic
278C2×C4⋊C4C23×C13111yescharacteristic
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4D4×C13112yes—
285C2×C42—22no—
286C2×C42D4×C13112yes—
287C2×C42C23×C13111yescharacteristic
288C2×C42C23×C13111yescharacteristic
289#107—24no—
290#106—24no—
291#102—24no—
292#102—24no—
293C22⋊C8—22no—
294C22⋊C8—22no—
295#95—21no—
296#95—22no—
297C24—21no—
298C24C2×D4×C13111yescharacteristic
299C2×Q8—24no—
300C2×Q8—24no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—42no—
305C2×D4—82no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4C2×D4×C13111yescharacteristic
314C22×C4C2×D4×C13112yes—
315C22×C4C2×D4×C13112yes—
316C22×C4C2×D4×C13112yes—
317C22×C4C2×D4×C13112yes—
318C22×C4C24×C13111yescharacteristic
319M16—24no—
320M16—24no—
321C2×C8—24no—
322C4⋊C4—28no—
323C4⋊C4—28no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—82no—
332C4⋊C4C2×D4×C13114yes—
333C4⋊C4C2×D4×C13114yes—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—44no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—82no—
342C42—24no—
343C42—22no—
344C42—22no—
345C42—24no—
346C42—22no—
347C42—22no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23#120×C13112yes—
358C23C22×D4×C13111yescharacteristic
359Q8—84no—
360Q8—84no—
361D4—44no—
362D4—84no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4#120×C13111yescharacteristic
384C2×C4#120×C13111yescharacteristic
385C2×C4C22×D4×C13112yes—
386C2×C42−1+4×C13112yes—
387C2×C42−1+4×C13112yes—
388C8—44no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—81no—
395C22—81no—
396C22—82no—
397C22—82no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22C2×#120×C13111yescharacteristic
402C22#536×C13111yescharacteristic
403C22#536×C13111yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—42no—
408C4—44no—
409C4—42no—
410C4—44no—
411C4—81no—
412C4—81no—
413C4#536×C13114yes—
414C2—21no—
415C2—21no—
416C2—42no—
417C2—161no—
418C2#2614×C13111yescharacteristic
419C2#3018×C13111yescharacteristic
420C2#3021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3458×C131C2semidirect
4. #2061×C131C2semidirect
5. #2060×C131C2semidirect
6. #2027×C131C2semidirect
7. #2027×C131C2semidirect
8. #1826×C131C2semidirect
9. #1822×C131C2semidirect
210. #29654C131direct (N × H)
211. C131#29654direct (N × H)
212. #3458C2×C131semidirect
215. #2061C2×C131semidirect
216. #2060C2×C131semidirect
217. #2027C2×C131semidirect
218. #2027C2×C131semidirect
219. #1826C2×C131semidirect
220. #1822C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3458×C1312
#3094×C1312
#2500×C1312
#2061×C1312
#2060×C1312
#2027×C1312
#1826×C1312
#1822×C1312
#29654131