Finite Group Databasebeta

← C131×#29703 #45715587

Subgroups — C131×#29703 #45715587

Order 33536.

1074 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C131C211yesmaximal, characteristic
2#3079×C131C212yesmaximal, complemented
3#2542×C131C211yesmaximal, characteristic, complemented
4#2060×C131C212yesmaximal, complemented
5#2039×C131C212yesmaximal, complemented
6#2037×C131C214yesmaximal, complemented
7#1806×C131C212yesmaximal, complemented
8#1800×C131C211yesmaximal, characteristic, complemented
9#544×C131C2211yescharacteristic
10#542×C131—22no—
11#540×C131—22no—
12#538×C131—22no—
13#537×C131C2211yescharacteristic
14#535×C131C2212yes—
15#532×C131—22no—
16C2×C4⋊Q8×C131C2211yescharacteristic
17#529×C131—22no—
18#525×C131—22no—
19C2×C22⋊Q8×C131—22no—
20C4×#41×C131C2212yes—
21C2×C4×D4×C131C2211yescharacteristic
22#477×C131—22no—
23#476×C131—22no—
24#475×C131—22no—
25#474×C131—22no—
26#428×C131C2214yes—
27#423×C131C2212yes—
28C2×#104×C131C2214yes—
29#417×C131C2214yes—
30C2×#100×C131C2212yes—
31#399×C131—22no—
32#390×C131C2212yes—
33#384×C131C2212yes—
34C4×C4⋊C4×C131C2211yescharacteristic
35#343×C131C2212yes—
36#339×C131C2214yes—
37C2×#41×C131—22no—
38C2×#41×C131C2312yes—
39C22×Q8×C131—21no—
40C22×D4×C131C2311yescharacteristic
41C23×C4×C131D412yes—
42C2×M16×C131C2314yes—
43C4⋊Q8×C131—22no—
44C4⋊Q8×C131—22no—
45C4⋊Q8×C131—22no—
46#127×C131—22no—
47#126×C131—24no—
48#125×C131—22no—
49#124×C131—24no—
50#124×C131—22no—
51#123×C131—24no—
52#123×C131—24no—
53C22⋊Q8×C131—22no—
54C22⋊Q8×C131—22no—
55C22⋊Q8×C131—22no—
56C22⋊Q8×C131—48no—
57#121×C131—22no—
58#121×C131—24no—
59#121×C131—22no—
60#121×C131—22no—
61#121×C131—22no—
62#121×C131—22no—
63#120×C131—24no—
64C4×Q8×C131D412yes—
65C4×Q8×C131D412yes—
66C4×D4×C131—24no—
67C4×D4×C131—22no—
68C4×D4×C131—22no—
69C4×D4×C131—22no—
70C4×D4×C131—22no—
71C4×D4×C131D412yes—
72C4×D4×C131D412yes—
73#117×C131—22no—
74#117×C131—22no—
75#117×C131C2312yes—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131—21no—
78C2×C4⋊C4×C131—24no—
79C2×C4⋊C4×C131C2312yes—
80C2×C4⋊C4×C131C2311yescharacteristic
81C2×C22⋊C4×C131—24no—
82C2×C22⋊C4×C131D412yes—
83C2×C42×C131—22no—
84C2×C42×C131C2312yes—
85C2×C42×C131C2311yescharacteristic
86#107×C131—24no—
87#106×C131—24no—
88C4⋊C8×C131—22no—
89C4⋊C8×C131—22no—
90#104×C131—44no—
91#103×C131—24no—
92#102×C131—24no—
93#100×C131—42no—
94#95×C131—21no—
95C24×C131C2×D412yes—
96#41×C131—22no—
97#41×C131—22no—
98#41×C131—22no—
99#41×C131—22no—
100#41×C131—84no—
101C2×Q8×C131—22no—
102C2×Q8×C131—44no—
103C2×Q8×C131—41no—
104C2×Q8×C131—41no—
105C2×Q8×C131C2×D412yes—
106C2×D4×C131—22no—
107C2×D4×C131—24no—
108C2×D4×C131—24no—
109C2×D4×C131—22no—
110C2×D4×C131—22no—
111C2×D4×C131—21no—
112C2×D4×C131—21no—
113C2×D4×C131—22no—
114C2×D4×C131C2×D412yes—
115C22×C4×C131—22no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—22no—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—44no—
123C22×C4×C131C2×D411yescharacteristic
124C22×C4×C131C2×D412yes—
125C22×C4×C131C2×D411yescharacteristic
126C22×C4×C131C2411yescharacteristic
127M16×C131—24no—
128M16×C131—24no—
129C2×C8×C131—24no—
130C4⋊C4×C131—24no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—22no—
133C4⋊C4×C131—24no—
134C4⋊C4×C131—22no—
135C4⋊C4×C131—22no—
136C4⋊C4×C131—22no—
137C4⋊C4×C131—24no—
138C4⋊C4×C131—48no—
139C4⋊C4×C131—42no—
140C4⋊C4×C131C2×D412yes—
141C4⋊C4×C131C2×D412yes—
142C22⋊C4×C131—24no—
143C22⋊C4×C131—24no—
144C22⋊C4×C131—24no—
145C22⋊C4×C131—22no—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—22no—
148C22⋊C4×C131—22no—
149C22⋊C4×C131—48no—
150C42×C131—22no—
151C42×C131—22no—
152C42×C131—22no—
153C42×C131—22no—
154C42×C131—22no—
155C42×C131C2×D412yes—
156C42×C131C2×D412yes—
157C23×C131—22no—
158C23×C131—22no—
159C23×C131—22no—
160C23×C131—22no—
161C23×C131—42no—
162C23×C131—42no—
163C23×C131C22×D411yescharacteristic
164Q8×C131—22no—
165Q8×C131—22no—
166Q8×C131—82no—
167Q8×C131—82no—
168Q8×C131—82no—
169D4×C131—22no—
170D4×C131—22no—
171D4×C131—42no—
172D4×C131—42no—
173D4×C131—42no—
174D4×C131—42no—
175D4×C131—84no—
176D4×C131—82no—
177D4×C131—84no—
178C2×C4×C131—22no—
179C2×C4×C131—24no—
180C2×C4×C131—22no—
181C2×C4×C131—22no—
182C2×C4×C131—22no—
183C2×C4×C131—22no—
184C2×C4×C131—41no—
185C2×C4×C131—42no—
186C2×C4×C131—42no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—44no—
190C2×C4×C131—44no—
191C2×C4×C131—42no—
192C2×C4×C131—44no—
193C2×C4×C131—42no—
194C2×C4×C131—82no—
195C2×C4×C131—82no—
196C2×C4×C131#12012yes—
197C2×C4×C131#12011yescharacteristic
198C2×C4×C131#12011yescharacteristic
199C2×C4×C131C22×D412yes—
200C2×C4×C131H(5,𝔽2)11yescharacteristic
201C2×C4×C1312−1+411yescharacteristic
202C2×C4×C1312−1+412yes—
203C8×C131—44no—
204C22×C131—21no—
205C22×C131—21no—
206C22×C131—44no—
207C22×C131—42no—
208C22×C131—42no—
209C22×C131—42no—
210C22×C131—42no—
211C22×C131—42no—
212C22×C131—42no—
213C22×C131—82no—
214C22×C131C2×#12011yescharacteristic
215C22×C131#53611yescharacteristic
216C22×C131#53711yescharacteristic
217C4×C131—21no—
218C4×C131—22no—
219C4×C131—44no—
220C4×C131—42no—
221C4×C131—42no—
222C4×C131—42no—
223C4×C131—42no—
224C4×C131—82no—
225C4×C131#45312yes—
226C4×C131#53612yes—
227C4×C131#53712yes—
228C2×C131—21no—
229C2×C131—21no—
230C2×C131—82no—
231C2×C131—82no—
232C2×C131#261611yescharacteristic
233C2×C131C2×#45311yescharacteristic
234C2×C131#302211yescharacteristic
235#29703C13111yesmaximal, characteristic, direct product factor, Sylow
236C131#2970311yescharacteristic, direct product factor, Sylow
237#3460C2×C13111yescharacteristic
238#3079C2×C13112yescomplemented
239#2542C2×C13111yescharacteristic, complemented
240#2060C2×C13112yescomplemented
241#2039C2×C13112yescomplemented
242#2037C2×C13114yescomplemented
243#1806C2×C13112yescomplemented
244#1800C2×C13111yescharacteristic, complemented
245#544C22×C13111yescharacteristic
246#542—22no—
247#540—22no—
248#538—22no—
249#537C22×C13111yescharacteristic
250#535C22×C13112yes—
251#532—22no—
252C2×C4⋊Q8C22×C13111yescharacteristic
253#529—22no—
254#525—22no—
255C2×C22⋊Q8—22no—
256C4×#41C22×C13112yes—
257C2×C4×D4C22×C13111yescharacteristic
258#477—22no—
259#476—22no—
260#475—22no—
261#474—22no—
262#428C22×C13114yes—
263#423C22×C13112yes—
264C2×#104C22×C13114yes—
265#417C22×C13114yes—
266C2×#100C22×C13112yes—
267#399—22no—
268#390C22×C13112yes—
269#384C22×C13112yes—
270C4×C4⋊C4C22×C13111yescharacteristic
271#343C22×C13112yes—
272#339C22×C13114yes—
273C2×#41—22no—
274C2×#41C23×C13112yes—
275C22×Q8—21no—
276C22×D4C23×C13111yescharacteristic
277C23×C4D4×C13112yes—
278C2×M16C23×C13114yes—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—22no—
282#127—22no—
283#126—24no—
284#125—22no—
285#124—24no—
286#124—22no—
287#123—24no—
288#123—24no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—48no—
293#121—22no—
294#121—24no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121—22no—
299#120—24no—
300C4×Q8D4×C13112yes—
301C4×Q8D4×C13112yes—
302C4×D4—24no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4D4×C13112yes—
308C4×D4D4×C13112yes—
309#117—22no—
310#117—22no—
311#117C23×C13112yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C23×C13112yes—
316C2×C4⋊C4C23×C13111yescharacteristic
317C2×C22⋊C4—24no—
318C2×C22⋊C4D4×C13112yes—
319C2×C42—22no—
320C2×C42C23×C13112yes—
321C2×C42C23×C13111yescharacteristic
322#107—24no—
323#106—24no—
324C4⋊C8—22no—
325C4⋊C8—22no—
326#104—44no—
327#103—24no—
328#102—24no—
329#100—42no—
330#95—21no—
331C24C2×D4×C13112yes—
332#41—22no—
333#41—22no—
334#41—22no—
335#41—22no—
336#41—84no—
337C2×Q8—22no—
338C2×Q8—44no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8C2×D4×C13112yes—
342C2×D4—22no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—22no—
350C2×D4C2×D4×C13112yes—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—44no—
359C22×C4C2×D4×C13111yescharacteristic
360C22×C4C2×D4×C13112yes—
361C22×C4C2×D4×C13111yescharacteristic
362C22×C4C24×C13111yescharacteristic
363M16—24no—
364M16—24no—
365C2×C8—24no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—48no—
375C4⋊C4—42no—
376C4⋊C4C2×D4×C13112yes—
377C4⋊C4C2×D4×C13112yes—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—22no—
382C22⋊C4—24no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—48no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42—22no—
390C42—22no—
391C42C2×D4×C13112yes—
392C42C2×D4×C13112yes—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—42no—
398C23—42no—
399C23C22×D4×C13111yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—82no—
403Q8—82no—
404Q8—82no—
405D4—22no—
406D4—22no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—82no—
412D4—84no—
413D4—84no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4#120×C13112yes—
433C2×C4#120×C13111yescharacteristic
434C2×C4#120×C13111yescharacteristic
435C2×C4C22×D4×C13112yes—
436C2×C4H(5,𝔽2)×C13111yescharacteristic
437C2×C42−1+4×C13111yescharacteristic
438C2×C42−1+4×C13112yes—
439C8—44no—
440C22—21no—
441C22—21no—
442C22—44no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22C2×#120×C13111yescharacteristic
451C22#536×C13111yescharacteristic
452C22#537×C13111yescharacteristic
453C4—21no—
454C4—22no—
455C4—44no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4#453×C13112yes—
462C4#536×C13112yes—
463C4#537×C13112yes—
464C2—21no—
465C2—21no—
466C2—82no—
467C2—82no—
468C2#2616×C13111yescharacteristic
469C2C2×#453×C13111yescharacteristic
470C2#3022×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3460×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3079×C131C2semidirect
3. #2542×C131C2semidirect
4. #2060×C131C2semidirect
5. #2039×C131C2semidirect
6. #2037×C131C2semidirect
7. #1806×C131C2semidirect
8. #1800×C131C2semidirect
235. #29703C131direct (N × H)
236. C131#29703direct (N × H)
238. #3079C2×C131semidirect
239. #2542C2×C131semidirect
240. #2060C2×C131semidirect
241. #2039C2×C131semidirect
242. #2037C2×C131semidirect
243. #1806C2×C131semidirect
244. #1800C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3460×C1312
#3079×C1312
#2542×C1312
#2060×C1312
#2039×C1312
#2037×C1312
#1806×C1312
#1800×C1312
#29703131