Finite Group Databasebeta

← C31×#9928 #21466687

Subgroups — C31×#9928 #21466687

Order 7936.

778 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic, complemented
2C31×#2626C211yesmaximal, characteristic
3C2×C31×#399C211yesmaximal, characteristic
4C31×#1824C211yesmaximal, characteristic, complemented
5C2×C31×#328C211yesmaximal, characteristic, complemented
6C2×C31×#323C211yesmaximal, characteristic
7C31×#1294C211yesmaximal, characteristic, complemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31—21no—
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C22⋊C4×C31—21no—
12C22×C22⋊C4×C31C2211yescharacteristic
13C31×#484—22no—
14C31×#484—22no—
15C2×C31×#107—21no—
16C2×C31×#103—21no—
17C2×C31×C22⋊C8C2211yescharacteristic
18C2×C31×C22⋊C8C2211yescharacteristic
19C31×#399—21no—
20C31×#399—22no—
21C31×#399—22no—
22C31×#396—22no—
23C31×#393—21no—
24C31×#385—21no—
25C31×#380C2211yescharacteristic
26C31×#379—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#328—22no—
30C31×#323—22no—
31C25×C31D411yescharacteristic
32C22×Q8×C31D411yescharacteristic
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31D411yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—44no—
52C2×C4⋊C4×C31D411yescharacteristic
53C2×C4⋊C4×C31D412yes—
54C2×C4⋊C4×C31D412yes—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—44no—
67C31×#107—24no—
68C31×#103—24no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8D412yes—
73C31×#95—22no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95D412yes—
77C24×C31—21no—
78C24×C31—21no—
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—42no—
84C24×C31—42no—
85C24×C31Q1612yes—
86C24×C31C2×D411yescharacteristic
87C2×Q8×C31—21no—
88C2×Q8×C31—21no—
89C2×Q8×C31—42no—
90C22×C4×C31—24no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31—41no—
102C22×C4×C31—41no—
103C22×C4×C31—42no—
104C22×C4×C31—42no—
105C22×C4×C31—42no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31C2×D411yescharacteristic
109C22×C4×C31C2×D411yescharacteristic
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31#4111yescharacteristic
114C2×C8×C31—22no—
115C2×C8×C31—42no—
116C2×C8×C31—42no—
117C2×C8×C31—41no—
118C4⋊C4×C31—22no—
119C4⋊C4×C31—21no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—21no—
122C4⋊C4×C31—48no—
123C4⋊C4×C31—42no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—82no—
129C22⋊C4×C31—48no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—82no—
139C22⋊C4×C31—82no—
140#9928C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—22no—
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—44no—
147C23×C31—42no—
148C23×C31—44no—
149C23×C31—42no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—42no—
154C23×C31—42no—
155C23×C31—41no—
156C23×C31—82no—
157C23×C31—82no—
158C23×C31—81no—
159C23×C31—81no—
160C23×C31#12011yescharacteristic
161C23×C31#12011yescharacteristic
162C23×C31#12111yescharacteristic
163C23×C31C2×Q1611yescharacteristic
164C23×C31#13511yescharacteristic
165C23×C31#13711yescharacteristic
166C23×C31#13711yescharacteristic
167Q8×C31—42no—
168Q8×C31—81no—
169C2×C4×C31—22no—
170C2×C4×C31—22no—
171C2×C4×C31—24no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—44no—
177C2×C4×C31—44no—
178C2×C4×C31—42no—
179C2×C4×C31—42no—
180C2×C4×C31—42no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—42no—
193C2×C4×C31—82no—
194C2×C4×C31—82no—
195C2×C4×C31—81no—
196C2×C4×C31#12011yescharacteristic
197C2×C4×C31#12111yescharacteristic
198C2×C4×C31#12111yescharacteristic
199C2×C4×C31#12711yescharacteristic
200C8×C31—42no—
201C8×C31—81no—
202C2×#484C2×C3111yescharacteristic, complemented
203#2626C2×C3111yescharacteristic
204C2×#399C2×C3111yescharacteristic
205#1824C2×C3111yescharacteristic, complemented
206C2×#328C2×C3111yescharacteristic, complemented
207C2×#323C2×C3111yescharacteristic
208#1294C2×C3111yescharacteristic, complemented
209C22×C31—22no—
210C22×C31—22no—
211C22×C31—22no—
212C22×C31—22no—
213C22×C31—21no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—21no—
217C22×C31—44no—
218C22×C31—44no—
219C22×C31—42no—
220C22×C31—82no—
221C22×C31—82no—
222C22×C31—82no—
223C22×C31—82no—
224C22×C31—81no—
225C22×C31—81no—
226C22×C31#39211yescharacteristic
227C22×C31#45111yescharacteristic
228C22×C31#45111yescharacteristic
229C22×C31#45211yescharacteristic
230C22×C31#45211yescharacteristic
231C22×C31#45312yes—
232C22×C31#45812yes—
233C22×C31#46711yescharacteristic
234C22×C31#47011yescharacteristic
235C4×C31—21no—
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—44no—
240C4×C31—82no—
241C4×C31—81no—
242C4×C31—81no—
243C4×C31—82no—
244C4×C31—81no—
245C2×C22⋊Q8C22×C3111yescharacteristic
246C22×C4⋊C4—21no—
247C22×C4⋊C4C22×C3111yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4C22×C3111yescharacteristic
250#484—22no—
251#484—22no—
252C2×#107—21no—
253C2×#103—21no—
254C2×C22⋊C8C22×C3111yescharacteristic
255C2×C22⋊C8C22×C3111yescharacteristic
256#399—21no—
257#399—22no—
258#399—22no—
259#396—22no—
260#393—21no—
261#385—21no—
262#380C22×C3111yescharacteristic
263#379—21no—
264C2×#95C22×C3111yescharacteristic
265#340—22no—
266#328—22no—
267#323—22no—
268C2×C31—21no—
269C2×C31—21no—
270C2×C31—21no—
271C2×C31—21no—
272C2×C31—82no—
273C2×C31#161412yes—
274C2×C31#161812yes—
275C2×C31#200111yescharacteristic
276C2×C31#200211yescharacteristic
277C2×C31#202211yescharacteristic
278C25D4×C3111yescharacteristic
279C22×Q8D4×C3111yescharacteristic
280C23×C4—21no—
281C23×C4—21no—
282C23×C4D4×C3111yescharacteristic
283C23×C4C23×C3111yescharacteristic
284C22×C8—21no—
285C22×C8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4D4×C3112yes—
300C2×C4⋊C4D4×C3111yescharacteristic
301C2×C4⋊C4D4×C3112yes—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—44no—
314#107—24no—
315#103—24no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8D4×C3112yes—
320#95—22no—
321#95—21no—
322#95—21no—
323#95D4×C3112yes—
324C31#992811yescharacteristic, direct product factor, Sylow
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—42no—
332C24—42no—
333C24Q16×C3112yes—
334C24C2×D4×C3111yescharacteristic
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C3111yescharacteristic
357C22×C4C2×D4×C3111yescharacteristic
358C22×C4C2×D4×C3111yescharacteristic
359C22×C4C2×D4×C3111yescharacteristic
360C22×C4C2×D4×C3111yescharacteristic
361C22×C4#41×C3111yescharacteristic
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—41no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—48no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—82no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—82no—
387C22⋊C4—82no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—44no—
394C23—42no—
395C23—44no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—82no—
404C23—82no—
405C23—81no—
406C23—81no—
407C23C31×#12011yescharacteristic
408C23C31×#12011yescharacteristic
409C23C31×#12111yescharacteristic
410C23C2×Q16×C3111yescharacteristic
411C23C31×#13511yescharacteristic
412C23C31×#13711yescharacteristic
413C23C31×#13711yescharacteristic
414Q8—42no—
415Q8—81no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4C31×#12011yescharacteristic
444C2×C4C31×#12111yescharacteristic
445C2×C4C31×#12111yescharacteristic
446C2×C4C31×#12711yescharacteristic
447C8—42no—
448C8—81no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—44no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22C31×#39211yescharacteristic
467C22C31×#45111yescharacteristic
468C22C31×#45111yescharacteristic
469C22C31×#45211yescharacteristic
470C22C31×#45211yescharacteristic
471C22C31×#45312yes—
472C22C31×#45812yes—
473C22C31×#46711yescharacteristic
474C22C31×#47011yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—44no—
480C4—82no—
481C4—81no—
482C4—82no—
483C4—81no—
484C4—81no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—82no—
490C2C31×#161412yes—
491C2C31×#161812yes—
492C2C31×#200111yescharacteristic
493C2C31×#200211yescharacteristic
494C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#484C2semidirect
4. C31×#1824C2semidirect
5. C2×C31×#328C2semidirect
7. C31×#1294C2semidirect
140. #9928C31direct (N × H)
202. C2×#484C2×C31semidirect
205. #1824C2×C31semidirect
206. C2×#328C2×C31semidirect
208. #1294C2×C31semidirect
324. C31#9928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C31×#26262
C2×C31×#3992
C31×#18242
C2×C31×#3282
C2×C31×#3232
C31×#12942
#992831