Finite Group Databasebeta

← C131×#8427 #45694311

Subgroups — C131×#8427 #45694311

Order 33536.

700 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3509×C131C211yesmaximal, characteristic
2#1988×C131C211yesmaximal, characteristic, complemented
3#1806×C131C211yesmaximal, characteristic
4#1550×C131C211yesmaximal, characteristic, complemented
5#1546×C131C211yesmaximal, characteristic, complemented
6#1503×C131C211yesmaximal, characteristic, complemented
7#1477×C131C211yesmaximal, characteristic
8#557×C131—21no—
9#557×C131C412yescomplemented
10#556×C131—21no—
11#556×C131C412yescomplemented
12#552×C131—22no—
13#552×C131—22no—
14#541×C131—22no—
15#536×C131—21no—
16#533×C131—21no—
17#533×C131—21no—
18#533×C131C2211yescharacteristic
19C2×C4⋊Q8×C131C2211yescharacteristic
20#519×C131—21no—
21C4×#41×C131C2211yescharacteristic
22#431×C131C2211yescharacteristic
23#423×C131C2211yescharacteristic
24C2×C4⋊C8×C131C2211yescharacteristic
25C2×#104×C131—21no—
26C4×C4⋊C4×C131C2211yescharacteristic
27#340×C131—22no—
28#339×C131—21no—
29#333×C131—21no—
30#332×C131—22no—
31#332×C131—21no—
32#328×C131—22no—
33Q8⋊C8×C131—21no—
34D4⋊C8×C131—21no—
35C2×#41×C131D411yescharacteristic
36C22×Q8×C131—21no—
37C2×M16×C131—21no—
38C22×C8×C131—21no—
39C4⋊Q8×C131—22no—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131—21no—
42C4⋊Q8×C131C2×C412yes—
43C4⋊Q8×C131D411yescharacteristic
44C4⋊Q8×C131D412yes—
45C4⋊Q8×C131D411yescharacteristic
46#126×C131—24no—
47#126×C131—24no—
48#125×C131—22no—
49#125×C131—24no—
50#125×C131—22no—
51#125×C131—24no—
52#125×C131—21no—
53#124×C131—22no—
54#123×C131—24no—
55C22⋊Q8×C131—22no—
56C22⋊Q8×C131—22no—
57C22⋊Q8×C131—22no—
58C22⋊Q8×C131—22no—
59C22⋊Q8×C131—21no—
60C22⋊Q8×C131D412yes—
61C4×Q8×C131—22no—
62C4×Q8×C131—22no—
63C4×Q8×C131—22no—
64C4×Q8×C131—22no—
65C4×Q8×C131—22no—
66C4×Q8×C131—22no—
67C4×Q8×C131—21no—
68C4×Q8×C131C2×C411yescharacteristic
69C4×Q8×C131C2×C412yes—
70C4×Q8×C131D411yescharacteristic
71C4×D4×C131—21no—
72C4×D4×C131—21no—
73C4×D4×C131C2×C411yescharacteristic
74C4×D4×C131D411yescharacteristic
75#117×C131—24no—
76#117×C131—22no—
77#117×C131—21no—
78#117×C131—22no—
79#117×C131—21no—
80#117×C131D411yescharacteristic
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131—21no—
83C2×C4⋊C4×C131D412yes—
84C2×C42×C131—21no—
85C2×C42×C131—21no—
86C2×C42×C131C2311yescharacteristic
87C4⋊C8×C131—21no—
88C4⋊C8×C131—21no—
89C4⋊C8×C131—21no—
90C4⋊C8×C131—21no—
91C4⋊C8×C131—21no—
92#104×C131—42no—
93C22⋊C8×C131—21no—
94C4×C8×C131—21no—
95#95×C131—21no—
96#41×C131—21no—
97#41×C131—21no—
98#41×C131—21no—
99#41×C131—21no—
100C2×Q8×C131—22no—
101C2×Q8×C131—21no—
102C2×Q8×C131—22no—
103C2×Q8×C131—41no—
104C2×Q8×C131—41no—
105C2×Q8×C131—41no—
106C2×Q8×C131—41no—
107C2×Q8×C131C22⋊C411yescharacteristic
108C2×Q8×C131C22⋊C412yes—
109C2×D4×C131—21no—
110C2×D4×C131C22⋊C411yescharacteristic
111C22×C4×C131—22no—
112C22×C4×C131—21no—
113C22×C4×C131—21no—
114C22×C4×C131—21no—
115C22×C4×C131—41no—
116C22×C4×C131C2×D411yescharacteristic
117C22×C4×C131C2×D411yescharacteristic
118C22×C4×C131C2×D411yescharacteristic
119M16×C131—41no—
120M16×C131—41no—
121C2×C8×C131—42no—
122C2×C8×C131—41no—
123C2×C8×C131—41no—
124C2×C8×C131—41no—
125C4⋊C4×C131—24no—
126C4⋊C4×C131—24no—
127C4⋊C4×C131—24no—
128C4⋊C4×C131—24no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—21no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—22no—
134C4⋊C4×C131—21no—
135C4⋊C4×C131—21no—
136C4⋊C4×C131—21no—
137C4⋊C4×C131—21no—
138C4⋊C4×C131—22no—
139C4⋊C4×C131—22no—
140C4⋊C4×C131—41no—
141C4⋊C4×C131C22⋊C414yes—
142C4⋊C4×C131C22⋊C412yes—
143C4⋊C4×C131C22⋊C411yescharacteristic
144C4⋊C4×C131C22⋊C411yescharacteristic
145C22⋊C4×C131—24no—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—21no—
148C22⋊C4×C131—22no—
149C22⋊C4×C131—21no—
150C22⋊C4×C131—21no—
151C42×C131—24no—
152C42×C131—24no—
153C42×C131—21no—
154C42×C131—22no—
155C42×C131—21no—
156C42×C131—21no—
157C42×C131—41no—
158C42×C131—41no—
159C42×C131C22×C411yescharacteristic
160C42×C131C2×D411yescharacteristic
161C42×C131C2×D411yescharacteristic
162C42×C131C2×D411yescharacteristic
163C23×C131—21no—
164C23×C131#12011yescharacteristic
165Q8×C131—21no—
166Q8×C131—21no—
167Q8×C131—42no—
168Q8×C131—42no—
169Q8×C131—42no—
170Q8×C131—42no—
171Q8×C131—42no—
172Q8×C131—41no—
173Q8×C131—41no—
174D4×C131—21no—
175D4×C131—21no—
176D4×C131—41no—
177D4×C131—41no—
178C2×C4×C131—21no—
179C2×C4×C131—21no—
180C2×C4×C131—21no—
181C2×C4×C131—21no—
182C2×C4×C131—22no—
183C2×C4×C131—22no—
184C2×C4×C131—24no—
185C2×C4×C131—21no—
186C2×C4×C131—41no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—42no—
190C2×C4×C131—41no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—41no—
194C2×C4×C131—42no—
195C2×C4×C131—81no—
196C2×C4×C131—81no—
197C2×C4×C131C2×C22⋊C411yescharacteristic
198C2×C4×C131C2×C22⋊C411yescharacteristic
199C2×C4×C131C2×C22⋊C411yescharacteristic
200C2×C4×C131#12011yescharacteristic
201C2×C4×C131#12011yescharacteristic
202C2×C4×C131#12011yescharacteristic
203C2×C4×C131#13511yescharacteristic
204C2×C4×C131#13511yescharacteristic
205C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C131#13711yescharacteristic
207C8×C131—81no—
208C8×C131—81no—
209C8×C131—81no—
210C22×C131—21no—
211C22×C131—21no—
212C22×C131—41no—
213C22×C131—41no—
214C22×C131—41no—
215C22×C131#37911yescharacteristic
216C22×C131#44911yescharacteristic
217C22×C131#45211yescharacteristic
218C4×C131—21no—
219C4×C131—21no—
220C4×C131—21no—
221C4×C131—41no—
222C4×C131—42no—
223C4×C131—41no—
224C4×C131—42no—
225C4×C131—41no—
226C4×C131—44no—
227C4×C131—82no—
228C4×C131#41611yescharacteristic
229C4×C131#41711yescharacteristic
230C4×C131#44911yescharacteristic
231C4×C131#45211yescharacteristic
232C4×C131#45411yescharacteristic
233C4×C131#45611yescharacteristic
234C2×C131—21no—
235C2×C131—21no—
236C2×C131—81no—
237C2×C131#178811yescharacteristic
238C2×C131#179311yescharacteristic
239C2×C131#179611yescharacteristic
240#8427C13111yesmaximal, characteristic, direct product factor, Sylow
241C131#842711yescharacteristic, direct product factor, Sylow
242#3509C2×C13111yescharacteristic
243#1988C2×C13111yescharacteristic, complemented
244#1806C2×C13111yescharacteristic
245#1550C2×C13111yescharacteristic, complemented
246#1546C2×C13111yescharacteristic, complemented
247#1503C2×C13111yescharacteristic, complemented
248#1477C2×C13111yescharacteristic
249#557—21no—
250#557C4×C13112yescomplemented
251#556—21no—
252#556C4×C13112yescomplemented
253#552—22no—
254#552—22no—
255#541—22no—
256#536—21no—
257#533—21no—
258#533—21no—
259#533C22×C13111yescharacteristic
260C2×C4⋊Q8C22×C13111yescharacteristic
261#519—21no—
262C4×#41C22×C13111yescharacteristic
263#431C22×C13111yescharacteristic
264#423C22×C13111yescharacteristic
265C2×C4⋊C8C22×C13111yescharacteristic
266C2×#104—21no—
267C4×C4⋊C4C22×C13111yescharacteristic
268#340—22no—
269#339—21no—
270#333—21no—
271#332—22no—
272#332—21no—
273#328—22no—
274Q8⋊C8—21no—
275D4⋊C8—21no—
276C2×#41D4×C13111yescharacteristic
277C22×Q8—21no—
278C2×M16—21no—
279C22×C8—21no—
280C4⋊Q8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8C2×C4×C13112yes—
284C4⋊Q8D4×C13111yescharacteristic
285C4⋊Q8D4×C13112yes—
286C4⋊Q8D4×C13111yescharacteristic
287#126—24no—
288#126—24no—
289#125—22no—
290#125—24no—
291#125—22no—
292#125—24no—
293#125—21no—
294#124—22no—
295#123—24no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—21no—
301C22⋊Q8D4×C13112yes—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—21no—
309C4×Q8C2×C4×C13111yescharacteristic
310C4×Q8C2×C4×C13112yes—
311C4×Q8D4×C13111yescharacteristic
312C4×D4—21no—
313C4×D4—21no—
314C4×D4C2×C4×C13111yescharacteristic
315C4×D4D4×C13111yescharacteristic
316#117—24no—
317#117—22no—
318#117—21no—
319#117—22no—
320#117—21no—
321#117D4×C13111yescharacteristic
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C13112yes—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C23×C13111yescharacteristic
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333#104—42no—
334C22⋊C8—21no—
335C4×C8—21no—
336#95—21no—
337#41—21no—
338#41—21no—
339#41—21no—
340#41—21no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8C22⋊C4×C13111yescharacteristic
349C2×Q8C22⋊C4×C13112yes—
350C2×D4—21no—
351C2×D4C22⋊C4×C13111yescharacteristic
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C13111yescharacteristic
358C22×C4C2×D4×C13111yescharacteristic
359C22×C4C2×D4×C13111yescharacteristic
360M16—41no—
361M16—41no—
362C2×C8—42no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4C22⋊C4×C13114yes—
383C4⋊C4C22⋊C4×C13112yes—
384C4⋊C4C22⋊C4×C13111yescharacteristic
385C4⋊C4C22⋊C4×C13111yescharacteristic
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—21no—
389C22⋊C4—22no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C42—24no—
393C42—24no—
394C42—21no—
395C42—22no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42—41no—
400C42C22×C4×C13111yescharacteristic
401C42C2×D4×C13111yescharacteristic
402C42C2×D4×C13111yescharacteristic
403C42C2×D4×C13111yescharacteristic
404C23—21no—
405C23#120×C13111yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—42no—
413Q8—41no—
414Q8—41no—
415D4—21no—
416D4—21no—
417D4—41no—
418D4—41no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4C2×C22⋊C4×C13111yescharacteristic
439C2×C4C2×C22⋊C4×C13111yescharacteristic
440C2×C4C2×C22⋊C4×C13111yescharacteristic
441C2×C4#120×C13111yescharacteristic
442C2×C4#120×C13111yescharacteristic
443C2×C4#120×C13111yescharacteristic
444C2×C4#135×C13111yescharacteristic
445C2×C4#135×C13111yescharacteristic
446C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
447C2×C4#137×C13111yescharacteristic
448C8—81no—
449C8—81no—
450C8—81no—
451C22—21no—
452C22—21no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22#379×C13111yescharacteristic
457C22#449×C13111yescharacteristic
458C22#452×C13111yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—44no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—42no—
468C4—82no—
469C4#416×C13111yescharacteristic
470C4#417×C13111yescharacteristic
471C4#449×C13111yescharacteristic
472C4#452×C13111yescharacteristic
473C4#454×C13111yescharacteristic
474C4#456×C13111yescharacteristic
475C2—21no—
476C2—21no—
477C2—81no—
478C2#1788×C13111yescharacteristic
479C2#1793×C13111yescharacteristic
480C2#1796×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#379
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#41×C131D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1988×C131C2semidirect
4. #1550×C131C2semidirect
5. #1546×C131C2semidirect
6. #1503×C131C2semidirect
9. #557×C131C4semidirect
11. #556×C131C4semidirect
240. #8427C131direct (N × H)
241. C131#8427direct (N × H)
243. #1988C2×C131semidirect
245. #1550C2×C131semidirect
246. #1546C2×C131semidirect
247. #1503C2×C131semidirect
250. #557C4×C131semidirect
252. #556C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3509×C1312
#1988×C1312
#1806×C1312
#1550×C1312
#1546×C1312
#1503×C1312
#1477×C1312
#8427131