Finite Group Databasebeta

← C31×#8712 #21465471

Subgroups — C31×#8712 #21465471

Order 7936.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#380C211yesmaximal, characteristic
2C31×#1779C211yesmaximal, characteristic
3C31×C22⋊#95C211yesmaximal, characteristic
4C31×#1294C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×C4⋊C4×C31C411yescharacteristic, complemented
7C22×C4⋊C4×C31C411yescharacteristic, complemented
8C22×C22⋊C4×C31—21no—
9C22×C22⋊C4×C31—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8C2212yes—
13C31×#380—21no—
14C31×#380—21no—
15C31×#380C412yescomplemented
16C31×#380C2212yes—
17C2×C31×#95—21no—
18C2×C31×#95—21no—
19C2×C31×#95C2212yes—
20C25×C31D411yescharacteristic
21C23×C4×C31—24no—
22C23×C4×C31—21no—
23C23×C4×C31—21no—
24C23×C4×C31—22no—
25C23×C4×C31—42no—
26C23×C4×C31—42no—
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C23×C4×C31C2311yescharacteristic
33C22×C8×C31—22no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—42no—
37C2×C4⋊C4×C31—42no—
38C2×C4⋊C4×C31C2×C412yes—
39C2×C4⋊C4×C31C2×C412yes—
40C2×C22⋊C4×C31—24no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—42no—
44C2×C22⋊C4×C31—42no—
45C2×C22⋊C4×C31—42no—
46C2×C22⋊C4×C31—42no—
47C31×C22⋊C8—24no—
48C31×C22⋊C8—42no—
49C31×C22⋊C8—42no—
50C31×#95—22no—
51C31×#95—22no—
52C31×#95—24no—
53C31×#95—42no—
54C24×C31—22no—
55C24×C31—22no—
56C24×C31—22no—
57C24×C31—22no—
58C24×C31—41no—
59C24×C31—41no—
60C24×C31C22⋊C411yescharacteristic
61C24×C31C22⋊C411yescharacteristic
62C24×C31D812yes—
63C24×C31SD1612yes—
64C24×C31C2×D411yescharacteristic
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—24no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—416no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31C22⋊C411yescharacteristic
99C22×C4×C31C22⋊C411yescharacteristic
100C22×C4×C31C22×C411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4114yes—
103C2×C8×C31—42no—
104C2×C8×C31—42no—
105C2×C8×C31—42no—
106C4⋊C4×C31—42no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—42no—
110C22⋊C4×C31—48no—
111C22⋊C4×C31—44no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114#8712C3111yesmaximal, characteristic, direct product factor, Sylow
115C23×C31—21no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—24no—
124C23×C31—24no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—21no—
129C23×C31—21no—
130C23×C31—21no—
131C23×C31—24no—
132C23×C31—24no—
133C23×C31—42no—
134C23×C31—42no—
135C23×C31—44no—
136C23×C31—44no—
137C23×C31—44no—
138C23×C31—44no—
139C23×C31#9912yes—
140C23×C31#10212yes—
141C23×C31#10212yes—
142C23×C31#10412yes—
143C23×C31C2×C22⋊C411yescharacteristic
144C23×C31#12312yes—
145C23×C31C2×D811yescharacteristic
146C23×C31C2×SD1611yescharacteristic
147C23×C31#13712yes—
148C2×C4×C31—28no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—44no—
159C2×C4×C31—44no—
160C2×C4×C31—44no—
161C2×C4×C31—44no—
162C2×C4×C31—44no—
163C2×C4×C31—44no—
164C2×C4×C31—44no—
165C2×C4×C31—44no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—82no—
173C2×C4×C31—82no—
174C2×C4×C31—82no—
175C2×C4×C31—84no—
176C2×C4×C31—84no—
177C2×C4×C31—82no—
178C2×C4×C31#9912yes—
179C2×C4×C31#11712yes—
180C2×C4×C31#12312yes—
181C8×C31—82no—
182C2×#380C2×C3111yescharacteristic
183#1779C2×C3111yescharacteristic
184C22⋊#95C2×C3111yescharacteristic
185#1294C2×C3114yescomplemented
186C22×C31—22no—
187C22×C31—22no—
188C22×C31—22no—
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—22no—
194C22×C31—22no—
195C22×C31—22no—
196C22×C31—22no—
197C22×C31—22no—
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—22no—
201C22×C31—22no—
202C22×C31—22no—
203C22×C31—48no—
204C22×C31—48no—
205C22×C31—41no—
206C22×C31—41no—
207C22×C31—41no—
208C22×C31—41no—
209C22×C31#32714yes—
210C22×C31#38111yescharacteristic
211C22×C31C2×#9911yescharacteristic
212C22×C31C2×#9911yescharacteristic
213C22×C31C2×#10211yescharacteristic
214C22×C31#41911yescharacteristic
215C22×C31C2×#10411yescharacteristic
216C22×C31#42111yescharacteristic
217C22×C31#48012yes—
218C22×C31#48312yes—
219C4×C31—22no—
220C4×C31—22no—
221C4×C31—22no—
222C4×C31—41no—
223C4×C31—84no—
224C4×C31—82no—
225C4×C31—82no—
226C24×C4C22×C3111yescharacteristic
227C22×C4⋊C4C4×C3111yescharacteristic, complemented
228C22×C4⋊C4C4×C3111yescharacteristic, complemented
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8—21no—
233C2×C22⋊C8C22×C3112yes—
234#380—21no—
235#380—21no—
236#380C4×C3112yescomplemented
237#380C22×C3112yes—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95C22×C3112yes—
241C2×C31—22no—
242C2×C31—24no—
243C2×C31—22no—
244C2×C31—42no—
245C2×C31C2×#32711yescharacteristic
246C2×C31#150811yescharacteristic
247C2×C31#151111yescharacteristic
248C2×C31#151911yescharacteristic
249C2×C31#181911yescharacteristic
250C2×C31#182311yescharacteristic
251C2×C31#182611yescharacteristic
252C25D4×C3111yescharacteristic
253C23×C4—24no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—22no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4C2×C4×C3111yescharacteristic
260C23×C4C2×C4×C3111yescharacteristic
261C23×C4D4×C3111yescharacteristic
262C23×C4D4×C3111yescharacteristic
263C23×C4D4×C3111yescharacteristic
264C23×C4C23×C3111yescharacteristic
265C22×C8—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4C2×C4×C3112yes—
271C2×C4⋊C4C2×C4×C3112yes—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—42no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C22⋊C8—24no—
280C22⋊C8—42no—
281C22⋊C8—42no—
282#95—22no—
283#95—22no—
284#95—24no—
285#95—42no—
286C31#871211yescharacteristic, direct product factor, Sylow
287C24—22no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—41no—
292C24—41no—
293C24C22⋊C4×C3111yescharacteristic
294C24C22⋊C4×C3111yescharacteristic
295C24D8×C3112yes—
296C24SD16×C3112yes—
297C24C2×D4×C3111yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—416no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4C22⋊C4×C3111yescharacteristic
332C22×C4C22⋊C4×C3111yescharacteristic
333C22×C4C22×C4×C3111yescharacteristic
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4#41×C3114yes—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C22⋊C4—48no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—24no—
361C23—24no—
362C23—24no—
363C23—24no—
364C23—21no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23C31×#9912yes—
372C23C31×#10212yes—
373C23C31×#10212yes—
374C23C31×#10412yes—
375C23C2×C22⋊C4×C3111yescharacteristic
376C23C31×#12312yes—
377C23C2×D8×C3111yescharacteristic
378C23C2×SD16×C3111yescharacteristic
379C23C31×#13712yes—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4—82no—
409C2×C4—84no—
410C2×C4C31×#9912yes—
411C2×C4C31×#11712yes—
412C2×C4C31×#12312yes—
413C8—82no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22C31×#32714yes—
438C22C31×#38111yescharacteristic
439C22C2×C31×#9911yescharacteristic
440C22C2×C31×#9911yescharacteristic
441C22C2×C31×#10211yescharacteristic
442C22C31×#41911yescharacteristic
443C22C2×C31×#10411yescharacteristic
444C22C31×#42111yescharacteristic
445C22C31×#48012yes—
446C22C31×#48312yes—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—84no—
452C4—82no—
453C4—82no—
454C2—22no—
455C2—22no—
456C2—24no—
457C2—42no—
458C2C2×C31×#32711yescharacteristic
459C2C31×#150811yescharacteristic
460C2C31×#151111yescharacteristic
461C2C31×#151911yescharacteristic
462C2C31×#181911yescharacteristic
463C2C31×#182311yescharacteristic
464C2C31×#182611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1294C2semidirect
6. C22×C4⋊C4×C31C4semidirect
7. C22×C4⋊C4×C31C4semidirect
15. C31×#380C4semidirect
114. #8712C31direct (N × H)
185. #1294C2×C31semidirect
227. C22×C4⋊C4C4×C31semidirect
228. C22×C4⋊C4C4×C31semidirect
236. #380C4×C31semidirect
286. C31#8712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3802
C31×#17792
C31×C22⋊#952
C31×#12942
#871231