Finite Group Databasebeta

← C131×#8458 #45694342

Subgroups — C131×#8458 #45694342

Order 33536.

766 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C131C211yesmaximal, characteristic
2#1955×C131C211yesmaximal, characteristic, complemented
3#1552×C131C211yesmaximal, characteristic, complemented
4#1551×C131C211yesmaximal, characteristic, complemented
5#1531×C131C211yesmaximal, characteristic, complemented
6#1530×C131C211yesmaximal, characteristic, complemented
7#1466×C131C211yesmaximal, characteristic, complemented
8#559×C131—22no—
9#556×C131—21no—
10#555×C131—21no—
11#553×C131—22no—
12#550×C131—21no—
13#547×C131—21no—
14#538×C131—22no—
15#535×C131C412yes—
16#533×C131C2211yescharacteristic
17#532×C131C2211yescharacteristic
18#525×C131—22no—
19#520×C131C412yes—
20C2×C4×D4×C131C2211yescharacteristic
21#432×C131C2211yescharacteristic
22#432×C131C2211yescharacteristic
23C2×C4⋊C8×C131C2211yescharacteristic
24C2×C22⋊C8×C131—22no—
25C2×#97×C131C2211yescharacteristic
26#333×C131—21no—
27#332×C131—21no—
28#332×C131—21no—
29#331×C131—21no—
30#330×C131—22no—
31#329×C131—22no—
32#323×C131—22no—
33C2×#41×C131—22no—
34C2×#41×C131C2×C412yes—
35C22×D4×C131C2×C411yescharacteristic
36C23×C4×C131D412yes—
37C22×C8×C131—21no—
38C22×C8×C131—21no—
39C4⋊Q8×C131D411yescharacteristic
40C4⋊Q8×C131D411yescharacteristic
41C4⋊Q8×C131D411yescharacteristic
42#127×C131—22no—
43#127×C131D411yescharacteristic
44#126×C131—24no—
45#125×C131D412yes—
46#124×C131—24no—
47#124×C131—22no—
48#124×C131D412yes—
49#123×C131—24no—
50#123×C131—24no—
51C22⋊Q8×C131—22no—
52C22⋊Q8×C131—21no—
53C22⋊Q8×C131—21no—
54#121×C131—22no—
55#121×C131—24no—
56#121×C131—21no—
57#121×C131—21no—
58#121×C131—22no—
59#121×C131—22no—
60#120×C131—24no—
61C4×Q8×C131—22no—
62C4×Q8×C131—21no—
63C4×Q8×C131—21no—
64C4×D4×C131—24no—
65C4×D4×C131—22no—
66C4×D4×C131—24no—
67C4×D4×C131—21no—
68C4×D4×C131—21no—
69C4×D4×C131—21no—
70C4×D4×C131—21no—
71C4×D4×C131—21no—
72C4×D4×C131—21no—
73#117×C131—22no—
74#117×C131—22no—
75#117×C131C2×C412yes—
76C2×C4⋊C4×C131—22no—
77C2×C4⋊C4×C131C2×C411yescharacteristic
78C2×C22⋊C4×C131D412yes—
79C2×C42×C131C2311yescharacteristic
80C4⋊C8×C131—21no—
81C4⋊C8×C131—21no—
82C4⋊C8×C131—21no—
83C4⋊C8×C131—21no—
84C22⋊C8×C131—21no—
85C22⋊C8×C131—21no—
86C22⋊C8×C131—44no—
87#97×C131—21no—
88#97×C131—21no—
89#97×C131—21no—
90#97×C131—21no—
91C24×C131C22⋊C412yes—
92#41×C131—44no—
93#41×C131—82no—
94#41×C131—82no—
95C2×Q8×C131—21no—
96C2×Q8×C131—21no—
97C2×Q8×C131C22⋊C412yes—
98C2×D4×C131—22no—
99C2×D4×C131—24no—
100C2×D4×C131—24no—
101C2×D4×C131—21no—
102C2×D4×C131—21no—
103C2×D4×C131—21no—
104C2×D4×C131—21no—
105C2×D4×C131—42no—
106C2×D4×C131C22⋊C412yes—
107C22×C4×C131—24no—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—42no—
112C22×C4×C131—42no—
113C22×C4×C131C22⋊C412yes—
114C22×C4×C131C22×C411yescharacteristic
115C22×C4×C131C2×D411yescharacteristic
116C22×C4×C131C2×D411yescharacteristic
117C2×C8×C131—22no—
118C2×C8×C131—41no—
119C2×C8×C131—41no—
120C2×C8×C131—42no—
121C2×C8×C131—41no—
122C2×C8×C131—41no—
123C2×C8×C131—41no—
124C4⋊C4×C131—24no—
125C4⋊C4×C131—21no—
126C4⋊C4×C131—21no—
127C4⋊C4×C131—21no—
128C4⋊C4×C131—21no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—21no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—21no—
133C4⋊C4×C131C22⋊C412yes—
134C4⋊C4×C131C22⋊C412yes—
135C22⋊C4×C131—24no—
136C22⋊C4×C131—24no—
137C22⋊C4×C131—24no—
138C22⋊C4×C131—22no—
139C22⋊C4×C131—22no—
140C22⋊C4×C131—22no—
141C22⋊C4×C131—22no—
142C22⋊C4×C131—22no—
143C42×C131—24no—
144C42×C131—22no—
145C42×C131C2×D411yescharacteristic
146C42×C131C2×D411yescharacteristic
147C42×C131C2×D411yescharacteristic
148C42×C131C2×D411yescharacteristic
149C23×C131—22no—
150C23×C131—22no—
151C23×C131—22no—
152C23×C131—22no—
153C23×C131—42no—
154C23×C131—42no—
155C23×C131C2×C22⋊C411yescharacteristic
156Q8×C131—42no—
157Q8×C131—41no—
158Q8×C131—41no—
159Q8×C131—81no—
160D4×C131—42no—
161D4×C131—42no—
162D4×C131—42no—
163D4×C131—44no—
164D4×C131—41no—
165D4×C131—41no—
166D4×C131—81no—
167D4×C131—84no—
168D4×C131—84no—
169C2×C4×C131—22no—
170C2×C4×C131—21no—
171C2×C4×C131—21no—
172C2×C4×C131—22no—
173C2×C4×C131—22no—
174C2×C4×C131—22no—
175C2×C4×C131—22no—
176C2×C4×C131—41no—
177C2×C4×C131—44no—
178C2×C4×C131—42no—
179C2×C4×C131—42no—
180C2×C4×C131—42no—
181C2×C4×C131—82no—
182C2×C4×C131—84no—
183C2×C4×C131C2×C22⋊C411yescharacteristic
184C2×C4×C131C2×C22⋊C411yescharacteristic
185C2×C4×C131#12011yescharacteristic
186C2×C4×C131#12011yescharacteristic
187C2×C4×C131#12011yescharacteristic
188C2×C4×C131#12011yescharacteristic
189C8×C131—42no—
190C8×C131—81no—
191C8×C131—81no—
192C8×C131—81no—
193C22×C131—21no—
194C22×C131—21no—
195C22×C131—44no—
196C22×C131—42no—
197C22×C131—42no—
198C22×C131—42no—
199C22×C131—42no—
200C22×C131—42no—
201C22×C131—42no—
202C22×C131—82no—
203C22×C131#37911yescharacteristic
204C22×C131#41312yes—
205C4×C131—21no—
206C4×C131—21no—
207C4×C131—21no—
208C4×C131—21no—
209C4×C131—21no—
210C4×C131—42no—
211C4×C131—42no—
212C4×C131—42no—
213C4×C131—42no—
214C4×C131#45311yescharacteristic
215C4×C131#45511yescharacteristic
216C2×C131—22no—
217C2×C131—82no—
218C2×C131—82no—
219C2×C131#178511yescharacteristic
220C2×C131#179211yescharacteristic
221C2×C131#179411yescharacteristic
222#8458C13111yesmaximal, characteristic, direct product factor, Sylow
223C131#845811yescharacteristic, direct product factor, Sylow
224#3506C2×C13111yescharacteristic
225#1955C2×C13111yescharacteristic, complemented
226#1552C2×C13111yescharacteristic, complemented
227#1551C2×C13111yescharacteristic, complemented
228#1531C2×C13111yescharacteristic, complemented
229#1530C2×C13111yescharacteristic, complemented
230#1466C2×C13111yescharacteristic, complemented
231#559—22no—
232#556—21no—
233#555—21no—
234#553—22no—
235#550—21no—
236#547—21no—
237#538—22no—
238#535C4×C13112yes—
239#533C22×C13111yescharacteristic
240#532C22×C13111yescharacteristic
241#525—22no—
242#520C4×C13112yes—
243C2×C4×D4C22×C13111yescharacteristic
244#432C22×C13111yescharacteristic
245#432C22×C13111yescharacteristic
246C2×C4⋊C8C22×C13111yescharacteristic
247C2×C22⋊C8—22no—
248C2×#97C22×C13111yescharacteristic
249#333—21no—
250#332—21no—
251#332—21no—
252#331—21no—
253#330—22no—
254#329—22no—
255#323—22no—
256C2×#41—22no—
257C2×#41C2×C4×C13112yes—
258C22×D4C2×C4×C13111yescharacteristic
259C23×C4D4×C13112yes—
260C22×C8—21no—
261C22×C8—21no—
262C4⋊Q8D4×C13111yescharacteristic
263C4⋊Q8D4×C13111yescharacteristic
264C4⋊Q8D4×C13111yescharacteristic
265#127—22no—
266#127D4×C13111yescharacteristic
267#126—24no—
268#125D4×C13112yes—
269#124—24no—
270#124—22no—
271#124D4×C13112yes—
272#123—24no—
273#123—24no—
274C22⋊Q8—22no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277#121—22no—
278#121—24no—
279#121—21no—
280#121—21no—
281#121—22no—
282#121—22no—
283#120—24no—
284C4×Q8—22no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—24no—
288C4×D4—22no—
289C4×D4—24no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296#117—22no—
297#117—22no—
298#117C2×C4×C13112yes—
299C2×C4⋊C4—22no—
300C2×C4⋊C4C2×C4×C13111yescharacteristic
301C2×C22⋊C4D4×C13112yes—
302C2×C42C23×C13111yescharacteristic
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—44no—
310#97—21no—
311#97—21no—
312#97—21no—
313#97—21no—
314C24C22⋊C4×C13112yes—
315#41—44no—
316#41—82no—
317#41—82no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8C22⋊C4×C13112yes—
321C2×D4—22no—
322C2×D4—24no—
323C2×D4—24no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—42no—
329C2×D4C22⋊C4×C13112yes—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4C22⋊C4×C13112yes—
337C22×C4C22×C4×C13111yescharacteristic
338C22×C4C2×D4×C13111yescharacteristic
339C22×C4C2×D4×C13111yescharacteristic
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—42no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—24no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4C22⋊C4×C13112yes—
357C4⋊C4C22⋊C4×C13112yes—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C42—24no—
367C42—22no—
368C42C2×D4×C13111yescharacteristic
369C42C2×D4×C13111yescharacteristic
370C42C2×D4×C13111yescharacteristic
371C42C2×D4×C13111yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—42no—
377C23—42no—
378C23C2×C22⋊C4×C13111yescharacteristic
379Q8—42no—
380Q8—41no—
381Q8—41no—
382Q8—81no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—44no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—84no—
391D4—84no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—84no—
406C2×C4C2×C22⋊C4×C13111yescharacteristic
407C2×C4C2×C22⋊C4×C13111yescharacteristic
408C2×C4#120×C13111yescharacteristic
409C2×C4#120×C13111yescharacteristic
410C2×C4#120×C13111yescharacteristic
411C2×C4#120×C13111yescharacteristic
412C8—42no—
413C8—81no—
414C8—81no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—82no—
426C22#379×C13111yescharacteristic
427C22#413×C13112yes—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4#453×C13111yescharacteristic
438C4#455×C13111yescharacteristic
439C2—22no—
440C2—82no—
441C2—82no—
442C2#1785×C13111yescharacteristic
443C2#1792×C13111yescharacteristic
444C2#1794×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#379
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3506×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1955×C131C2semidirect
3. #1552×C131C2semidirect
4. #1551×C131C2semidirect
5. #1531×C131C2semidirect
6. #1530×C131C2semidirect
7. #1466×C131C2semidirect
222. #8458C131direct (N × H)
223. C131#8458direct (N × H)
225. #1955C2×C131semidirect
226. #1552C2×C131semidirect
227. #1551C2×C131semidirect
228. #1531C2×C131semidirect
229. #1530C2×C131semidirect
230. #1466C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3506×C1312
#1955×C1312
#1552×C1312
#1551×C1312
#1531×C1312
#1530×C1312
#1466×C1312
#8458131