Finite Group Databasebeta

← C131×#9497 #45695381

Subgroups — C131×#9497 #45695381

Order 33536.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 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#2403×C131C211yesmaximal, characteristic
2#2309×C131C211yesmaximal, characteristic, complemented
3#1781×C131C211yesmaximal, characteristic, complemented
4#1781×C131C212yesmaximal, complemented
5#1304×C131C212yesmaximal, complemented
6C23×D4×C131C2211yescharacteristic
7C23×D4×C131C2211yescharacteristic
8C2×#120×C131—21no—
9C2×#120×C131C412yescomplemented
10C2×#117×C131—21no—
11C2×#99×C131—22no—
12C2×#99×C131—24no—
13#392×C131—22no—
14#390×C131—24no—
15#386×C131—21no—
16#386×C131C412yescomplemented
17#379×C131—21no—
18#379×C131C2212yes—
19#379×C131C2211yescharacteristic
20#379×C131C2212yes—
21C25×C131C2×C411yescharacteristic
22C25×C131D411yescharacteristic
23C25×C131C2311yescharacteristic
24C22×D4×C131—22no—
25C22×D4×C131—22no—
26C22×D4×C131—21no—
27C22×D4×C131—22no—
28C22×D4×C131—21no—
29C22×D4×C131—22no—
30C22×D4×C131—22no—
31C22×D4×C131—44no—
32C22×D4×C131—44no—
33C22×D4×C131C2×C412yes—
34C22×D4×C131D412yes—
35C23×C4×C131C2×C411yescharacteristic
36C23×C4×C131D411yescharacteristic
37#120×C131—44no—
38#120×C131—44no—
39#117×C131—44no—
40C2×C4⋊C4×C131—22no—
41C2×C22⋊C4×C131—22no—
42C2×C22⋊C4×C131—22no—
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—22no—
45C2×C22⋊C4×C131—22no—
46C2×C22⋊C4×C131—22no—
47C2×C22⋊C4×C131—22no—
48C2×C22⋊C4×C131—22no—
49C2×C22⋊C4×C131—22no—
50C2×C22⋊C4×C131—21no—
51C2×C22⋊C4×C131—22no—
52C2×C22⋊C4×C131C2×C412yes—
53C2×C22⋊C4×C131D414yescomplemented
54C2×C42×C131—22no—
55#99×C131—48no—
56#99×C131—44no—
57#95×C131—22no—
58C24×C131—21no—
59C24×C131—21no—
60C24×C131—22no—
61C24×C131—21no—
62C24×C131—42no—
63C24×C131—42no—
64C24×C131—42no—
65C24×C131—42no—
66C24×C131—42no—
67C24×C131—42no—
68C24×C131—81no—
69C24×C131—81no—
70C24×C131—81no—
71C24×C131C22⋊C412yes—
72C24×C131C22×C411yescharacteristic
73C24×C131C2×D411yescharacteristic
74C24×C131C2×D411yescharacteristic
75C24×C131C2×D412yes—
76C24×C131#4112yes—
77C2×D4×C131—28no—
78C2×D4×C131—24no—
79C2×D4×C131—24no—
80C2×D4×C131—24no—
81C2×D4×C131—24no—
82C2×D4×C131—24no—
83C2×D4×C131—42no—
84C2×D4×C131—42no—
85C2×D4×C131—44no—
86C2×D4×C131—44no—
87C2×D4×C131—48no—
88C2×D4×C131—42no—
89C2×D4×C131—44no—
90C2×D4×C131—42no—
91C2×D4×C131—44no—
92C2×D4×C131—42no—
93C2×D4×C131—44no—
94C2×D4×C131—41no—
95C2×D4×C131—42no—
96C2×D4×C131—41no—
97C2×D4×C131—44no—
98C2×D4×C131—44no—
99C2×D4×C131—82no—
100C22×C4×C131—21no—
101C22×C4×C131—21no—
102C22×C4×C131—24no—
103C22×C4×C131—21no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—24no—
107C22×C4×C131—42no—
108C22×C4×C131—42no—
109C22×C4×C131C22⋊C412yes—
110C4⋊C4×C131—44no—
111C22⋊C4×C131—44no—
112C22⋊C4×C131—44no—
113C22⋊C4×C131—42no—
114C22⋊C4×C131—44no—
115C22⋊C4×C131—44no—
116C22⋊C4×C131—42no—
117C22⋊C4×C131—44no—
118C22⋊C4×C131—44no—
119C22⋊C4×C131—82no—
120C22⋊C4×C131—82no—
121C22⋊C4×C131—81no—
122C22⋊C4×C131—82no—
123C22⋊C4×C131—82no—
124C42×C131—44no—
125C23×C131—22no—
126C23×C131—22no—
127C23×C131—22no—
128C23×C131—22no—
129C23×C131—24no—
130C23×C131—22no—
131C23×C131—24no—
132C23×C131—22no—
133C23×C131—22no—
134C23×C131—22no—
135C23×C131—41no—
136C23×C131—41no—
137C23×C131—41no—
138C23×C131—42no—
139C23×C131—41no—
140C23×C131—42no—
141C23×C131—41no—
142C23×C131—42no—
143C23×C131—42no—
144C23×C131—42no—
145C23×C131—42no—
146C23×C131—42no—
147C23×C131—42no—
148C23×C131—41no—
149C23×C131—42no—
150C23×C131—42no—
151C23×C131—42no—
152C23×C131—42no—
153C23×C131—41no—
154C23×C131—42no—
155C23×C131—42no—
156C23×C131—81no—
157C23×C131—81no—
158C23×C131—82no—
159C23×C131—82no—
160C23×C131—88no—
161C23×C131—88no—
162C23×C131—88no—
163C23×C131C2×C22⋊C411yescharacteristic
164C23×C131C4×D412yes—
165C23×C131#12011yescharacteristic
166C23×C131#12112yes—
167C23×C131#12311yescharacteristic
168D4×C131—48no—
169D4×C131—48no—
170D4×C131—48no—
171D4×C131—44no—
172D4×C131—44no—
173D4×C131—88no—
174C2×C4×C131—22no—
175C2×C4×C131—22no—
176C2×C4×C131—24no—
177C2×C4×C131—22no—
178C2×C4×C131—22no—
179C2×C4×C131—22no—
180C2×C4×C131—24no—
181C2×C4×C131—41no—
182C2×C4×C131—42no—
183C2×C4×C131—41no—
184C2×C4×C131—44no—
185C2×C4×C131—42no—
186C2×C4×C131—44no—
187C2×C4×C131—42no—
188C2×C4×C131—42no—
189C2×C4×C131—44no—
190C2×C4×C131—82no—
191C2×C4×C131—82no—
192C2×C4×C131—82no—
193C2×C4×C131#9914yescomplemented
194C22×C131—21no—
195C22×C131—21no—
196C22×C131—21no—
197C22×C131—21no—
198C22×C131—22no—
199C22×C131—22no—
200C22×C131—21no—
201C22×C131—21no—
202C22×C131—22no—
203C22×C131—22no—
204C22×C131—22no—
205C22×C131—22no—
206C22×C131—21no—
207C22×C131—44no—
208C22×C131—44no—
209C22×C131—44no—
210C22×C131—44no—
211C22×C131—42no—
212C22×C131—42no—
213C22×C131—42no—
214C22×C131—42no—
215C22×C131—84no—
216C22×C131—82no—
217C22×C131—82no—
218C22×C131—84no—
219C22×C131—82no—
220C22×C131—84no—
221C22×C131—84no—
222C22×C131—84no—
223C22×C131—84no—
224C22×C131—81no—
225C22×C131—81no—
226C22×C131#38611yescharacteristic
227C22×C131C2×#9912yes—
228C22×C131B(4,𝔽2)12yes—
229C4×C131—24no—
230C4×C131—42no—
231C4×C131—84no—
232C4×C131—82no—
233C4×C131—162no—
234C2×C131—22no—
235C2×C131—22no—
236C2×C131—42no—
237C2×C131—42no—
238C2×C131—41no—
239C2×C131—82no—
240C2×C131—82no—
241C2×C131#188911yescharacteristic
242C2×C131#189811yescharacteristic
243C2×C131#191311yescharacteristic
244#9497C13111yesmaximal, characteristic, direct product factor, Sylow
245C131#949711yescharacteristic, direct product factor, Sylow
246#2403C2×C13111yescharacteristic
247#2309C2×C13111yescharacteristic, complemented
248#1781C2×C13112yescomplemented
249#1781C2×C13111yescharacteristic, complemented
250#1304C2×C13112yescomplemented
251C23×D4C22×C13111yescharacteristic
252C23×D4C22×C13111yescharacteristic
253C2×#120—21no—
254C2×#120C4×C13112yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C13112yescomplemented
262#379—21no—
263#379C22×C13112yes—
264#379C22×C13111yescharacteristic
265#379C22×C13112yes—
266C25C2×C4×C13111yescharacteristic
267C25D4×C13111yescharacteristic
268C25C23×C13111yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C13112yes—
279C22×D4D4×C13112yes—
280C23×C4C2×C4×C13111yescharacteristic
281C23×C4D4×C13111yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C13112yes—
298C2×C22⋊C4D4×C13114yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C13112yes—
317C24C22×C4×C13111yescharacteristic
318C24C2×D4×C13111yescharacteristic
319C24C2×D4×C13111yescharacteristic
320C24C2×D4×C13112yes—
321C24#41×C13112yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C13112yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C13111yescharacteristic
409C23C4×D4×C13112yes—
410C23#120×C13111yescharacteristic
411C23#121×C13112yes—
412C23#123×C13111yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C13114yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C13111yescharacteristic
472C22C2×#99×C13112yes—
473C22B(4,𝔽2)×C13112yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2#1889×C13111yescharacteristic
487C2#1898×C13111yescharacteristic
488C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC24C22×C4×C131
Frattini, cosocleC25C23×C131
prime radical#2403×C131C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2309×C131C2semidirect
3. #1781×C131C2semidirect
4. #1781×C131C2semidirect
5. #1304×C131C2semidirect
9. C2×#120×C131C4semidirect
16. #386×C131C4semidirect
53. C2×C22⋊C4×C131D4semidirect
193. C2×C4×C131#99semidirect
244. #9497C131direct (N × H)
245. C131#9497direct (N × H)
247. #2309C2×C131semidirect
248. #1781C2×C131semidirect
249. #1781C2×C131semidirect
250. #1304C2×C131semidirect
254. C2×#120C4×C131semidirect
261. #386C4×C131semidirect
298. C2×C22⋊C4D4×C131semidirect
438. C2×C4#99×C131semidirect

Maximal subgroups

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

subgroupindex
#2403×C1312
#2309×C1312
#1781×C1312
#1304×C1312
#9497131