Finite Group Databasebeta

← C31×#15102 #21471861

Subgroups — C31×#15102 #21471861

Order 7936.

1182 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#387C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
3C31×#1445C212yesmaximal
4C31×#1444C211yesmaximal, characteristic
5C31×#1443C212yesmaximal
6C31×#1442C211yesmaximal, characteristic
7C31×#1441C211yesmaximal, characteristic
8C31×#1441C211yesmaximal, characteristic
9C31×#1436C212yesmaximal
10C31×#1436C212yesmaximal
11C31×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C31×#387—24no—
20C4×C4⋊C4×C31—24no—
21C2×C31×#95C2212yes—
22C2×C31×#95C2211yescharacteristic
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2212yes—
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C23×C4×C31C2311yescharacteristic
38C23×C4×C31C2311yescharacteristic
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31Q814yes—
61C2×C42×C31—22no—
62C2×C42×C31—22no—
63C2×C42×C31—24no—
64C2×C42×C31—42no—
65C2×C42×C31—42no—
66C2×C42×C31D414yes—
67C31×#95—24no—
68C31×#95—22no—
69C31×#95—22no—
70C31×#95—22no—
71C31×#95—22no—
72C31×#95—24no—
73C31×#95—22no—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—22no—
80C31×#95—42no—
81C31×#95—42no—
82C31×#95—42no—
83C24×C31C2411yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×Q812yes—
143C22×C4×C31C2×Q812yes—
144C22×C4×C31C2×Q812yes—
145C22×C4×C31#4114yes—
146C22×C4×C31#4114yes—
147C22×C4×C31#4114yes—
148C22×C4×C31#4112yes—
149C22×C4×C31#4112yes—
150C22×C4×C31#4112yes—
151C4⋊C4×C31—28no—
152C4⋊C4×C31—28no—
153C4⋊C4×C31—28no—
154C4⋊C4×C31—48no—
155C4⋊C4×C31—44no—
156C42×C31—28no—
157C42×C31—48no—
158#15102C3111yesmaximal, characteristic, direct product factor, Sylow
159C23×C31C22×D411yescharacteristic
160C23×C31C22×Q811yescharacteristic
161C23×C31C2×#4111yescharacteristic
162C23×C31C2×#4111yescharacteristic
163C23×C31C2×#4111yescharacteristic
164C23×C31C2×#4112yes—
165C23×C31C2×#4112yes—
166C23×C31C2×#4112yes—
167C23×C31H(5,𝔽2)11yescharacteristic
168C23×C31H(5,𝔽2)11yescharacteristic
169C23×C312−1+412yes—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—24no—
174C2×C4×C31—24no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—22no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—41no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31C22⋊Q814yes—
236C2×C4×C31#12314yes—
237C2×#387C2×C3111yescharacteristic
238C2×C4×C4⋊C4C2×C3111yescharacteristic
239#1445C2×C3112yes—
240#1444C2×C3111yescharacteristic
241#1443C2×C3112yes—
242#1442C2×C3111yescharacteristic
243#1441C2×C3111yescharacteristic
244#1441C2×C3111yescharacteristic
245#1436C2×C3112yes—
246#1436C2×C3112yes—
247#1434C2×C3111yescharacteristic
248C22×C31C2×C22⋊Q811yescharacteristic
249C22×C31C2×#12311yescharacteristic
250C22×C31#52511yescharacteristic
251C22×C31#52511yescharacteristic
252C22×C31#52912yes—
253C22×C31#52912yes—
254C22×C31#52912yes—
255C22×C31#53211yescharacteristic
256C22×C31#53312yes—
257C22×C31#53511yescharacteristic
258C22×C31#53611yescharacteristic
259C22×C31#53912yes—
260C22×C31#53912yes—
261C22×C31#55112yes—
262C22×C31#55212yes—
263C22×C31#55311yescharacteristic
264C22×C31#55312yes—
265C22×C31#55311yescharacteristic
266C22×C31#55411yescharacteristic
267C22×C31#55411yescharacteristic
268C22×C31#55612yes—
269C22×C31#55612yes—
270C22×C31#55712yes—
271C4×C31—24no—
272C4×C31—24no—
273C4×C31—44no—
274C4×C31—44no—
275C4×C31—44no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—42no—
279C4×C31—82no—
280C4×C31—81no—
281C4×C31—81no—
282C22×C4⋊C4C22×C3111yescharacteristic
283C22×C4⋊C4C22×C3111yescharacteristic
284C22×C4⋊C4C22×C3111yescharacteristic
285C22×C4⋊C4C22×C3112yes—
286C22×C4⋊C4C22×C3111yescharacteristic
287C22×C42C22×C3111yescharacteristic
288C22×C42C22×C3112yes—
289#387—24no—
290C4×C4⋊C4—24no—
291C2×#95C22×C3112yes—
292C2×#95C22×C3111yescharacteristic
293C2×#95C22×C3111yescharacteristic
294C2×#95C22×C3112yes—
295C2×#95C22×C3111yescharacteristic
296C2×#95C22×C3112yes—
297C2×#95C22×C3112yes—
298C2×#95C22×C3112yes—
299C2×#95C22×C3112yes—
300C2×#95C22×C3111yescharacteristic
301C2×#95C22×C3111yescharacteristic
302C2×#95C22×C3112yes—
303C2×#95C22×C3111yescharacteristic
304C2×#95C22×C3112yes—
305C2×#95C22×C3112yes—
306C2×#95C22×C3112yes—
307C2×C31#239611yescharacteristic
308C2×C31#248711yescharacteristic
309C2×C31#249911yescharacteristic
310C2×C31#257312yes—
311C2×C31#258111yescharacteristic
312C2×C31#258512yes—
313C2×C31#258812yes—
314C2×C31#259412yes—
315C2×C31#260311yescharacteristic
316C2×C31#263311yescharacteristic
317C2×C31#285311yescharacteristic
318C23×C4C23×C3111yescharacteristic
319C23×C4C23×C3111yescharacteristic
320C23×C4C23×C3112yes—
321C23×C4C23×C3111yescharacteristic
322C23×C4C23×C3111yescharacteristic
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3112yes—
325C23×C4C23×C3112yes—
326C23×C4C23×C3112yes—
327C23×C4C23×C3111yescharacteristic
328C23×C4C23×C3111yescharacteristic
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4Q8×C3114yes—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—24no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42D4×C3114yes—
348#95—24no—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—22no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—22no—
361#95—42no—
362#95—42no—
363#95—42no—
364C31#1510211yescharacteristic, direct product factor, Sylow
365C24C24×C3111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4C2×D4×C3112yes—
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4C2×Q8×C3112yes—
425C22×C4C2×Q8×C3112yes—
426C22×C4C2×Q8×C3112yes—
427C22×C4#41×C3114yes—
428C22×C4#41×C3114yes—
429C22×C4#41×C3114yes—
430C22×C4#41×C3112yes—
431C22×C4#41×C3112yes—
432C22×C4#41×C3112yes—
433C4⋊C4—28no—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—48no—
437C4⋊C4—44no—
438C42—28no—
439C42—48no—
440C23C22×D4×C3111yescharacteristic
441C23C22×Q8×C3111yescharacteristic
442C23C2×#41×C3111yescharacteristic
443C23C2×#41×C3111yescharacteristic
444C23C2×#41×C3111yescharacteristic
445C23C2×#41×C3112yes—
446C23C2×#41×C3112yes—
447C23C2×#41×C3112yes—
448C23C31×H(5,𝔽2)11yescharacteristic
449C23C31×H(5,𝔽2)11yescharacteristic
450C23C31×2−1+412yes—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4C31×C22⋊Q814yes—
517C2×C4C31×#12314yes—
518C22C2×C31×C22⋊Q811yescharacteristic
519C22C2×C31×#12311yescharacteristic
520C22C31×#52511yescharacteristic
521C22C31×#52511yescharacteristic
522C22C31×#52912yes—
523C22C31×#52912yes—
524C22C31×#52912yes—
525C22C31×#53211yescharacteristic
526C22C31×#53312yes—
527C22C31×#53511yescharacteristic
528C22C31×#53611yescharacteristic
529C22C31×#53912yes—
530C22C31×#53912yes—
531C22C31×#55112yes—
532C22C31×#55212yes—
533C22C31×#55311yescharacteristic
534C22C31×#55312yes—
535C22C31×#55311yescharacteristic
536C22C31×#55411yescharacteristic
537C22C31×#55411yescharacteristic
538C22C31×#55612yes—
539C22C31×#55612yes—
540C22C31×#55712yes—
541C4—24no—
542C4—24no—
543C4—44no—
544C4—44no—
545C4—44no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—82no—
550C4—81no—
551C4—81no—
552C2C31×#239611yescharacteristic
553C2C31×#248711yescharacteristic
554C2C31×#249911yescharacteristic
555C2C31×#257312yes—
556C2C31×#258111yescharacteristic
557C2C31×#258512yes—
558C2C31×#258812yes—
559C2C31×#259412yes—
560C2C31×#260311yescharacteristic
561C2C31×#263311yescharacteristic
562C2C31×#285311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
158. #15102C31direct (N × H)
364. C31#15102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14442
C31×#14432
C31×#14422
C31×#14412
C31×#14362
C31×#14342
#1510231