Finite Group Databasebeta

← C131×#17398 #45703282

Subgroups — C131×#17398 #45703282

Order 33536.

1034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C131C211yesmaximal, characteristic
2#2920×C131C212yesmaximal, complemented
3#1473×C131C218yesmaximal, complemented
4#1463×C131C212yesmaximal, complemented
5#1462×C131C212yesmaximal
6C2×#126×C131—22no—
7C2×#126×C131—22no—
8C2×#126×C131—22no—
9C2×#126×C131—22no—
10C2×#126×C131C414yes—
11C2×#126×C131C2214yes—
12C22×C4⋊C4×C131C411yescharacteristic
13C22×C4⋊C4×C131C411yescharacteristic
14C22×C4⋊C4×C131C2211yescharacteristic
15C22×C22⋊C4×C131C411yescharacteristic
16C22×C22⋊C4×C131C411yescharacteristic
17C22×C22⋊C4×C131C2211yescharacteristic
18C22×C42×C131C2211yescharacteristic
19#432×C131—22no—
20#432×C131C2214yescomplemented
21#431×C131—22no—
22#431×C131C2214yescomplemented
23#423×C131—22no—
24#407×C131C2214yes—
25C4×M16×C131—22no—
26#324×C131C2218yescomplemented
27#323×C131C2218yes—
28C25×C131C2×C411yescharacteristic
29C23×C4×C131C2×C411yescharacteristic
30C23×C4×C131C2×C411yescharacteristic
31C23×C4×C131C2×C411yescharacteristic
32C23×C4×C131C2×C411yescharacteristic
33C23×C4×C131C2×C411yescharacteristic
34C23×C4×C131C2311yescharacteristic
35C2×M16×C131—24no—
36#126×C131—24no—
37#126×C131—24no—
38#126×C131—24no—
39#126×C131—24no—
40#126×C131—24no—
41#126×C131—24no—
42#126×C131—24no—
43#126×C131—24no—
44C2×C4⋊C4×C131—22no—
45C2×C4⋊C4×C131—22no—
46C2×C4⋊C4×C131—21no—
47C2×C4⋊C4×C131—21no—
48C2×C4⋊C4×C131—21no—
49C2×C4⋊C4×C131—21no—
50C2×C4⋊C4×C131—22no—
51C2×C4⋊C4×C131—22no—
52C2×C4⋊C4×C131C2×C414yes—
53C2×C4⋊C4×C131C2×C414yes—
54C2×C4⋊C4×C131C2×C412yes—
55C2×C4⋊C4×C131C2312yes—
56C2×C22⋊C4×C131—22no—
57C2×C22⋊C4×C131—21no—
58C2×C22⋊C4×C131—21no—
59C2×C22⋊C4×C131—21no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131—22no—
62C2×C22⋊C4×C131—22no—
63C2×C22⋊C4×C131—22no—
64C2×C22⋊C4×C131C2×C414yes—
65C2×C22⋊C4×C131C2×C414yes—
66C2×C22⋊C4×C131C2×C412yes—
67C2×C22⋊C4×C131C2312yes—
68C2×C42×C131C2×C412yes—
69C2×C42×C131D412yes—
70C2×C42×C131D412yes—
71C2×C42×C131D412yes—
72C2×C42×C131D412yes—
73C2×C42×C131C2312yes—
74C4⋊C8×C131—24no—
75C4⋊C8×C131—24no—
76C22⋊C8×C131—24no—
77C22⋊C8×C131C2318yes—
78#97×C131—24no—
79C4×C8×C131—24no—
80C24×C131—21no—
81C24×C131—21no—
82C24×C131—42no—
83C24×C131—42no—
84C24×C131—42no—
85C24×C131C22×C411yescharacteristic
86C24×C131C22×C412yes—
87C22×C4×C131—21no—
88C22×C4×C131—21no—
89C22×C4×C131—21no—
90C22×C4×C131—21no—
91C22×C4×C131—21no—
92C22×C4×C131—21no—
93C22×C4×C131—42no—
94C22×C4×C131—42no—
95C22×C4×C131—42no—
96C22×C4×C131—42no—
97C22×C4×C131—42no—
98C22×C4×C131—42no—
99C22×C4×C131C22⋊C412yes—
100C22×C4×C131C22⋊C411yescharacteristic
101C22×C4×C131C22⋊C412yes—
102C22×C4×C131C22⋊C411yescharacteristic
103C22×C4×C131C22⋊C411yescharacteristic
104C22×C4×C131C22⋊C411yescharacteristic
105C22×C4×C131C22×C412yes—
106C22×C4×C131C22×C412yes—
107C22×C4×C131C22×C412yes—
108C22×C4×C131C22×C412yes—
109C22×C4×C131C22×C411yescharacteristic
110C22×C4×C131C22×C412yes—
111C22×C4×C131C2×D412yes—
112C22×C4×C131C2×D412yes—
113C22×C4×C131C2411yescharacteristic
114M16×C131—48no—
115C2×C8×C131—28no—
116C4⋊C4×C131—24no—
117C4⋊C4×C131—24no—
118C4⋊C4×C131—24no—
119C4⋊C4×C131—24no—
120C4⋊C4×C131—24no—
121C4⋊C4×C131—24no—
122C22⋊C4×C131—24no—
123C22⋊C4×C131—24no—
124C22⋊C4×C131—24no—
125C22⋊C4×C131—24no—
126C22⋊C4×C131—24no—
127C22⋊C4×C131—24no—
128C42×C131C22⋊C412yes—
129C42×C131C22⋊C412yes—
130C42×C131C22⋊C412yes—
131C42×C131C22⋊C412yes—
132C42×C131C2×D412yes—
133C42×C131C2×D412yes—
134C42×C131C2×D412yes—
135C42×C131C2×D412yes—
136C23×C131—22no—
137C23×C131—22no—
138C23×C131—22no—
139C23×C131—22no—
140C23×C131—24no—
141C23×C131—42no—
142C23×C131—42no—
143C23×C131—42no—
144C23×C131—42no—
145C23×C131—42no—
146C23×C131—42no—
147C23×C131—42no—
148C23×C131—42no—
149C23×C131—88no—
150C23×C131C2×C22⋊C411yescharacteristic
151C23×C131C2×C22⋊C411yescharacteristic
152C23×C131C23×C411yescharacteristic
153C2×C4×C131—24no—
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—42no—
161C2×C4×C131—41no—
162C2×C4×C131—41no—
163C2×C4×C131—41no—
164C2×C4×C131—41no—
165C2×C4×C131—41no—
166C2×C4×C131—42no—
167C2×C4×C131—42no—
168C2×C4×C131—41no—
169C2×C4×C131—42no—
170C2×C4×C131—42no—
171C2×C4×C131—42no—
172C2×C4×C131—42no—
173C2×C4×C131—42no—
174C2×C4×C131—42no—
175C2×C4×C131—42no—
176C2×C4×C131—42no—
177C2×C4×C131C2×C22⋊C412yes—
178C2×C4×C131C2×C22⋊C412yes—
179C2×C4×C131C2×C22⋊C412yes—
180C2×C4×C131C2×C22⋊C412yes—
181C2×C4×C131C2×C22⋊C412yes—
182C2×C4×C131C22×D412yes—
183C8×C131—48no—
184C22×C131—28no—
185C22×C131—21no—
186C22×C131—21no—
187C22×C131—21no—
188C22×C131—21no—
189C22×C131—21no—
190C22×C131—21no—
191C22×C131—42no—
192C22×C131—42no—
193C22×C131—42no—
194C22×C131—84no—
195C22×C131—84no—
196C22×C131—84no—
197C22×C131#41012yes—
198C22×C131#41312yes—
199C22×C131C22×C22⋊C411yescharacteristic
200C22×C131#56812yes—
201C4×C131—22no—
202C4×C131—22no—
203C4×C131—22no—
204C4×C131—22no—
205C4×C131—22no—
206C4×C131—22no—
207C4×C131—42no—
208C4×C131—42no—
209C4×C131—42no—
210C2×C131—22no—
211C2×C131—22no—
212C2×C131—22no—
213C2×C131—82no—
214C2×C131#287911yescharacteristic
215C2×C131C2×#41011yescharacteristic
216C2×C131C2×#41311yescharacteristic
217#17398C13111yesmaximal, characteristic, direct product factor, Sylow
218C131#1739811yescharacteristic, direct product factor, Sylow
219C22×#126C2×C13111yescharacteristic
220#2920C2×C13112yescomplemented
221#1473C2×C13118yescomplemented
222#1463C2×C13112yescomplemented
223#1462C2×C13112yes—
224C2×#126—22no—
225C2×#126—22no—
226C2×#126—22no—
227C2×#126—22no—
228C2×#126C4×C13114yes—
229C2×#126C22×C13114yes—
230C22×C4⋊C4C4×C13111yescharacteristic
231C22×C4⋊C4C4×C13111yescharacteristic
232C22×C4⋊C4C22×C13111yescharacteristic
233C22×C22⋊C4C4×C13111yescharacteristic
234C22×C22⋊C4C4×C13111yescharacteristic
235C22×C22⋊C4C22×C13111yescharacteristic
236C22×C42C22×C13111yescharacteristic
237#432—22no—
238#432C22×C13114yescomplemented
239#431—22no—
240#431C22×C13114yescomplemented
241#423—22no—
242#407C22×C13114yes—
243C4×M16—22no—
244#324C22×C13118yescomplemented
245#323C22×C13118yes—
246C25C2×C4×C13111yescharacteristic
247C23×C4C2×C4×C13111yescharacteristic
248C23×C4C2×C4×C13111yescharacteristic
249C23×C4C2×C4×C13111yescharacteristic
250C23×C4C2×C4×C13111yescharacteristic
251C23×C4C2×C4×C13111yescharacteristic
252C23×C4C23×C13111yescharacteristic
253C2×M16—24no—
254#126—24no—
255#126—24no—
256#126—24no—
257#126—24no—
258#126—24no—
259#126—24no—
260#126—24no—
261#126—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4C2×C4×C13114yes—
271C2×C4⋊C4C2×C4×C13114yes—
272C2×C4⋊C4C2×C4×C13112yes—
273C2×C4⋊C4C23×C13112yes—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4C2×C4×C13114yes—
283C2×C22⋊C4C2×C4×C13114yes—
284C2×C22⋊C4C2×C4×C13112yes—
285C2×C22⋊C4C23×C13112yes—
286C2×C42C2×C4×C13112yes—
287C2×C42D4×C13112yes—
288C2×C42D4×C13112yes—
289C2×C42D4×C13112yes—
290C2×C42D4×C13112yes—
291C2×C42C23×C13112yes—
292C4⋊C8—24no—
293C4⋊C8—24no—
294C22⋊C8—24no—
295C22⋊C8C23×C13118yes—
296#97—24no—
297C4×C8—24no—
298C24—21no—
299C24—21no—
300C24—42no—
301C24—42no—
302C24—42no—
303C24C22×C4×C13111yescharacteristic
304C24C22×C4×C13112yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4C22⋊C4×C13112yes—
318C22×C4C22⋊C4×C13111yescharacteristic
319C22×C4C22⋊C4×C13112yes—
320C22×C4C22⋊C4×C13111yescharacteristic
321C22×C4C22⋊C4×C13111yescharacteristic
322C22×C4C22⋊C4×C13111yescharacteristic
323C22×C4C22×C4×C13112yes—
324C22×C4C22×C4×C13112yes—
325C22×C4C22×C4×C13112yes—
326C22×C4C22×C4×C13112yes—
327C22×C4C22×C4×C13111yescharacteristic
328C22×C4C22×C4×C13112yes—
329C22×C4C2×D4×C13112yes—
330C22×C4C2×D4×C13112yes—
331C22×C4C24×C13111yescharacteristic
332M16—48no—
333C2×C8—28no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—24no—
346C42C22⋊C4×C13112yes—
347C42C22⋊C4×C13112yes—
348C42C22⋊C4×C13112yes—
349C42C22⋊C4×C13112yes—
350C42C2×D4×C13112yes—
351C42C2×D4×C13112yes—
352C42C2×D4×C13112yes—
353C42C2×D4×C13112yes—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—24no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—88no—
368C23C2×C22⋊C4×C13111yescharacteristic
369C23C2×C22⋊C4×C13111yescharacteristic
370C23C23×C4×C13111yescharacteristic
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4C2×C22⋊C4×C13112yes—
396C2×C4C2×C22⋊C4×C13112yes—
397C2×C4C2×C22⋊C4×C13112yes—
398C2×C4C2×C22⋊C4×C13112yes—
399C2×C4C2×C22⋊C4×C13112yes—
400C2×C4C22×D4×C13112yes—
401C8—48no—
402C22—28no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—84no—
414C22—84no—
415C22#410×C13112yes—
416C22#413×C13112yes—
417C22C22×C22⋊C4×C13111yescharacteristic
418C22#568×C13112yes—
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—42no—
427C4—42no—
428C2—22no—
429C2—22no—
430C2—22no—
431C2—82no—
432C2#2879×C13111yescharacteristic
433C2C2×#410×C13111yescharacteristic
434C2C2×#413×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C22×C22⋊C4
commutatorC23C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC25×C131C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2920×C131C2semidirect
3. #1473×C131C2semidirect
4. #1463×C131C2semidirect
20. #432×C131C22semidirect
22. #431×C131C22semidirect
26. #324×C131C22semidirect
217. #17398C131direct (N × H)
218. C131#17398direct (N × H)
220. #2920C2×C131semidirect
221. #1473C2×C131semidirect
222. #1463C2×C131semidirect
238. #432C22×C131semidirect
240. #431C22×C131semidirect
244. #324C22×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1312
#2920×C1312
#1473×C1312
#1463×C1312
#1462×C1312
#17398131