Finite Group Databasebeta

← C31×#9781 #21466540

Subgroups — C31×#9781 #21466540

Order 7936.

564 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic
2C31×#1996C211yesmaximal, characteristic, complemented
3C31×#1964C211yesmaximal, characteristic
4C31×#1807C211yesmaximal, characteristic, complemented
5C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1520C211yesmaximal, characteristic, complemented
7C31×#1519C211yesmaximal, characteristic
8C22×SD16×C31C411yescharacteristic, complemented
9C23×C8×C31C2211yescharacteristic
10C2×C31×C22⋊Q8C2211yescharacteristic
11C2×C31×#121C2211yescharacteristic
12C31×#465—21no—
13C31×#465—21no—
14C31×#465—21no—
15C31×#465—21no—
16C2×C31×#106—21no—
17C2×C31×#106C411yescharacteristic, complemented
18C2×C31×#103C411yescharacteristic, complemented
19C2×C31×#102C411yescharacteristic, complemented
20C2×C31×#99—22no—
21C2×C31×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C31—21no—
23C31×#380C2211yescharacteristic
24C31×#380C2211yescharacteristic
25C4×C22⋊C4×C31C2211yescharacteristic
26C31×#342—22no—
27C31×#340—21no—
28C31×#336—21no—
29C31×#328—22no—
30C31×#327—22no—
31C22×Q8×C31C2×C411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31C2×C411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C2×SD16×C31—21no—
36C2×SD16×C31—21no—
37C2×SD16×C31—42no—
38C22×C8×C31—21no—
39C22×C8×C31—42no—
40C22×C8×C31C2×C411yescharacteristic
41C22×C8×C31C2×C411yescharacteristic
42C22×C8×C31D411yescharacteristic
43C22×C8×C31D411yescharacteristic
44C22×C8×C31D411yescharacteristic
45C22×C8×C31D411yescharacteristic
46C31×C22⋊Q8—21no—
47C31×C22⋊Q8—21no—
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C31×#121—21no—
51C31×#121—21no—
52C31×#121—21no—
53C31×#121—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31C2×C411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31D412yes—
64C2×C42×C31—21no—
65C31×#106—21no—
66C31×#106—21no—
67C31×#106—42no—
68C31×#103—21no—
69C31×#103—21no—
70C31×#102—21no—
71C31×#102—21no—
72C31×#99—44no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D412yes—
75C4×C8×C31—42no—
76C31×#95—21no—
77C31×#95—21no—
78C31×#95—21no—
79C24×C31—21no—
80C24×C31C2×D411yescharacteristic
81C2×Q8×C31—21no—
82C2×Q8×C31—21no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—42no—
92C2×D4×C31—42no—
93C22×C4×C31—22no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31C22×C411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31#4111yescharacteristic
106C22×C4×C31#4111yescharacteristic
107SD16×C31—42no—
108SD16×C31—42no—
109C2×C8×C31—22no—
110C2×C8×C31—22no—
111C2×C8×C31—22no—
112C2×C8×C31—22no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—41no—
118C2×C8×C31C22⋊C411yescharacteristic
119C2×C8×C31C22⋊C411yescharacteristic
120C2×C8×C31C22⋊C411yescharacteristic
121C2×C8×C31C22⋊C411yescharacteristic
122C4⋊C4×C31—21no—
123C4⋊C4×C31—21no—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—21no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31—41no—
132C22⋊C4×C31—22no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—42no—
138C22⋊C4×C31—42no—
139C22⋊C4×C31SD1614yescomplemented
140C42×C31—41no—
141C42×C31—41no—
142#9781C3111yesmaximal, characteristic, direct product factor, Sylow
143C23×C31—41no—
144C23×C31—41no—
145C23×C31—41no—
146C23×C31—42no—
147C23×C31—81no—
148C23×C31—81no—
149C23×C31C4×D411yescharacteristic
150C23×C31#12111yescharacteristic
151C23×C31#12711yescharacteristic
152C23×C31C2×SD1612yes—
153C23×C31#13512yes—
154Q8×C31—41no—
155Q8×C31—41no—
156Q8×C31—81no—
157D4×C31—41no—
158D4×C31—41no—
159D4×C31—81no—
160D4×C31—82no—
161D4×C31—81no—
162D4×C31—81no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—21no—
168C2×C4×C31—21no—
169C2×C4×C31—24no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—42no—
179C2×C4×C31—81no—
180C2×C4×C31—81no—
181C2×C4×C31—81no—
182C2×C4×C31—81no—
183C2×C4×C31—81no—
184C2×C4×C31—81no—
185C2×C4×C31—81no—
186C2×C4×C31—81no—
187C2×C4×C31C2×C22⋊C411yescharacteristic
188C2×C4×C31C4×D411yescharacteristic
189C2×C4×C31#12111yescharacteristic
190C2×C4×C31#12411yescharacteristic
191C8×C31—21no—
192C8×C31—21no—
193C8×C31—21no—
194C8×C31—42no—
195C8×C31#9912yescomplemented
196C2×#465C2×C3111yescharacteristic
197#1996C2×C3111yescharacteristic, complemented
198#1964C2×C3111yescharacteristic
199#1807C2×C3111yescharacteristic, complemented
200C8×C22⋊C4C2×C3111yescharacteristic, complemented
201#1520C2×C3111yescharacteristic, complemented
202#1519C2×C3111yescharacteristic
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—21no—
207C22×C31—21no—
208C22×C31—21no—
209C22×C31—42no—
210C22×C31—42no—
211C22×C31—81no—
212C22×C31—81no—
213C22×C31—81no—
214C22×C31—162no—
215C22×C31#39011yescharacteristic
216C22×C31C4×SD1612yes—
217C22×C31#46512yes—
218C22×C31#49211yescharacteristic
219C22×C31#49511yescharacteristic
220C4×C31—21no—
221C4×C31—21no—
222C4×C31—21no—
223C4×C31—44no—
224C4×C31—81no—
225C4×C31—81no—
226C4×C31—81no—
227C4×C31—161no—
228C4×C31—161no—
229C4×C31C2×#9911yescharacteristic
230C4×C31#41011yescharacteristic
231C22×SD16C4×C3111yescharacteristic, complemented
232C23×C8C22×C3111yescharacteristic
233C2×C22⋊Q8C22×C3111yescharacteristic
234C2×#121C22×C3111yescharacteristic
235#465—21no—
236#465—21no—
237#465—21no—
238#465—21no—
239C2×#106—21no—
240C2×#106C4×C3111yescharacteristic, complemented
241C2×#103C4×C3111yescharacteristic, complemented
242C2×#102C4×C3111yescharacteristic, complemented
243C2×#99—22no—
244C2×C22⋊C8C22×C3111yescharacteristic
245C2×C4×C8—21no—
246#380C22×C3111yescharacteristic
247#380C22×C3111yescharacteristic
248C4×C22⋊C4C22×C3111yescharacteristic
249#342—22no—
250#340—21no—
251#336—21no—
252#328—22no—
253#327—22no—
254C2×C31—22no—
255C2×C31—21no—
256C2×C31—21no—
257C2×C31—22no—
258C2×C31—161no—
259C2×C31#196411yescharacteristic
260C2×C31#196811yescharacteristic
261C2×C31#197611yescharacteristic
262C22×Q8C2×C4×C3111yescharacteristic
263C22×D4—21no—
264C22×D4C2×C4×C3111yescharacteristic
265C23×C4C23×C3111yescharacteristic
266C2×SD16—21no—
267C2×SD16—21no—
268C2×SD16—42no—
269C22×C8—21no—
270C22×C8—42no—
271C22×C8C2×C4×C3111yescharacteristic
272C22×C8C2×C4×C3111yescharacteristic
273C22×C8D4×C3111yescharacteristic
274C22×C8D4×C3111yescharacteristic
275C22×C8D4×C3111yescharacteristic
276C22×C8D4×C3111yescharacteristic
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4C2×C4×C3111yescharacteristic
289C2×C4⋊C4C2×C4×C3111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4D4×C3112yes—
295C2×C42—21no—
296#106—21no—
297#106—21no—
298#106—42no—
299#103—21no—
300#103—21no—
301#102—21no—
302#102—21no—
303#99—44no—
304C22⋊C8—21no—
305C22⋊C8D4×C3112yes—
306C4×C8—42no—
307#95—21no—
308#95—21no—
309#95—21no—
310C31#978111yescharacteristic, direct product factor, Sylow
311C24—21no—
312C24C2×D4×C3111yescharacteristic
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C22×C4×C3111yescharacteristic
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4C2×D4×C3111yescharacteristic
336C22×C4C2×D4×C3111yescharacteristic
337C22×C4#41×C3111yescharacteristic
338C22×C4#41×C3111yescharacteristic
339SD16—42no—
340SD16—42no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8C22⋊C4×C3111yescharacteristic
351C2×C8C22⋊C4×C3111yescharacteristic
352C2×C8C22⋊C4×C3111yescharacteristic
353C2×C8C22⋊C4×C3111yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C22⋊C4SD16×C3114yescomplemented
372C42—41no—
373C42—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23C4×D4×C3111yescharacteristic
381C23C31×#12111yescharacteristic
382C23C31×#12711yescharacteristic
383C23C2×SD16×C3112yes—
384C23C31×#13512yes—
385Q8—41no—
386Q8—41no—
387Q8—81no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—82no—
392D4—81no—
393D4—81no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—24no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4C2×C22⋊C4×C3111yescharacteristic
419C2×C4C4×D4×C3111yescharacteristic
420C2×C4C31×#12111yescharacteristic
421C2×C4C31×#12411yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—42no—
426C8C31×#9912yescomplemented
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—162no—
439C22C31×#39011yescharacteristic
440C22C4×SD16×C3112yes—
441C22C31×#46512yes—
442C22C31×#49211yescharacteristic
443C22C31×#49511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—44no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—161no—
452C4—161no—
453C4C2×C31×#9911yescharacteristic
454C4C31×#41011yescharacteristic
455C2—22no—
456C2—21no—
457C2—21no—
458C2—22no—
459C2—161no—
460C2C31×#196411yescharacteristic
461C2C31×#196811yescharacteristic
462C2C31×#197611yescharacteristic
subgroupG/H
center, socleC22×C31#390
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1996C2semidirect
4. C31×#1807C2semidirect
5. C8×C22⋊C4×C31C2semidirect
6. C31×#1520C2semidirect
8. C22×SD16×C31C4semidirect
17. C2×C31×#106C4semidirect
18. C2×C31×#103C4semidirect
19. C2×C31×#102C4semidirect
139. C22⋊C4×C31SD16semidirect
142. #9781C31direct (N × H)
195. C8×C31#99semidirect
197. #1996C2×C31semidirect
199. #1807C2×C31semidirect
200. C8×C22⋊C4C2×C31semidirect
201. #1520C2×C31semidirect
231. C22×SD16C4×C31semidirect
240. C2×#106C4×C31semidirect
241. C2×#103C4×C31semidirect
242. C2×#102C4×C31semidirect
310. C31#9781direct (N × H)
371. C22⋊C4SD16×C31semidirect
426. C8C31×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C31×#19962
C31×#19642
C31×#18072
C8×C22⋊C4×C312
C31×#15202
C31×#15192
#978131