Finite Group Databasebeta

← C31×#13978 #21470737

Subgroups — C31×#13978 #21470737

Order 7936.

1750 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic
5C2×C31×#382C211yesmaximal, characteristic
6C31×#1442C214yesmaximal
7C31×#1436C214yesmaximal
8C31×C4⋊#95C211yesmaximal, characteristic
9C4×C31×#95C211yesmaximal, characteristic
10C23×Q8×C31C2211yescharacteristic
11C2×C4×Q8×C31—24no—
12C2×C4×Q8×C31—24no—
13C2×C4×Q8×C31—24no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C31×#391—24no—
24C31×#391C418yescomplemented
25C31×#389—24no—
26C31×#382—24no—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2214yes—
30C2×C31×#95C2214yes—
31C2×C31×#95C2214yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2214yes—
34C22×Q8×C31—22no—
35C22×Q8×C31—22no—
36C22×Q8×C31—22no—
37C22×Q8×C31—22no—
38C22×Q8×C31C2×C414yes—
39C22×Q8×C31D414yes—
40C22×Q8×C31Q814yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C4×Q8×C31—232no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—28no—
63C2×C4⋊C4×C31C2×C414yes—
64C2×C4⋊C4×C31D414yes—
65C2×C42×C31—24no—
66C2×C42×C31—24no—
67C2×C42×C31—24no—
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—22no—
71C2×C42×C31—22no—
72C2×C42×C31—22no—
73C2×C42×C31—22no—
74C2×C42×C31—22no—
75C2×C42×C31C2×C414yes—
76C2×C42×C31D414yes—
77C31×#95—28no—
78C31×#95—24no—
79C31×#95—28no—
80C31×#95—24no—
81C31×#95—28no—
82C31×#95—24no—
83C31×#95C2×C4116yes—
84C24×C31C2411yescharacteristic
85C2×Q8×C31—28no—
86C2×Q8×C31—28no—
87C2×Q8×C31—28no—
88C2×Q8×C31—28no—
89C2×Q8×C31—28no—
90C2×Q8×C31—28no—
91C2×Q8×C31C4⋊C4116yescomplemented
92C22×C4×C31—21no—
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—22no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—24no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—24no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—24no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—24no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—24no—
127C22×C4×C31—24no—
128C22×C4×C31C22×C414yes—
129C22×C4×C31C22×C414yes—
130C22×C4×C31C22×C414yes—
131C22×C4×C31C22×C412yes—
132C22×C4×C31C2×D414yes—
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2×D414yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×Q814yes—
140C22×C4×C31C2×Q812yes—
141C22×C4×C31#4114yes—
142C22×C4×C31#4114yes—
143C22×C4×C31#4112yes—
144C22×C4×C31#4112yes—
145C4⋊C4×C31—216no—
146C4⋊C4×C31—28no—
147C4⋊C4×C31—28no—
148C4⋊C4×C31—44no—
149C4⋊C4×C31—48no—
150C42×C31—216no—
151C42×C31—28no—
152C42×C31—28no—
153C42×C31—44no—
154#13978C3111yesmaximal, characteristic, direct product factor, Sylow
155C23×C31C23×C411yescharacteristic
156C23×C31C22×D411yescharacteristic
157C23×C31C22×D411yescharacteristic
158C23×C31C22×D411yescharacteristic
159C23×C31C22×Q811yescharacteristic
160C23×C31C2×#4111yescharacteristic
161C23×C31C2×#4111yescharacteristic
162C23×C31C2×#4112yes—
163C23×C31C2×#4112yes—
164C23×C312−1+412yes—
165C23×C312−1+412yes—
166Q8×C31—232no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—22no—
170C2×C4×C31—24no—
171C2×C4×C31—24no—
172C2×C4×C31—24no—
173C2×C4×C31—24no—
174C2×C4×C31—22no—
175C2×C4×C31—24no—
176C2×C4×C31—24no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—24no—
180C2×C4×C31—28no—
181C2×C4×C31—24no—
182C2×C4×C31—24no—
183C2×C4×C31—22no—
184C2×C4×C31—24no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—28no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—42no—
191C2×C4×C31—42no—
192C2×C4×C31—44no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—44no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—44no—
210C2×C4×C31—44no—
211C2×C4×C31C2×C4⋊C418yes—
212C2×C4×C31C2×C4⋊C414yes—
213C2×C4×C31C4×D414yes—
214C2×C4×C31C4×D414yes—
215C2×C4×C31#12014yes—
216C2×C4×C31C22⋊Q814yes—
217C2×C4×C31C22⋊Q814yes—
218C2×C4×C31#12314yes—
219C2×C4×C31#12414yes—
220C22×C4×Q8C2×C3111yescharacteristic
221C2×#391C2×C3111yescharacteristic
222C2×#391C2×C3111yescharacteristic
223C2×#389C2×C3111yescharacteristic
224C2×#382C2×C3111yescharacteristic
225#1442C2×C3114yes—
226#1436C2×C3114yes—
227C4⋊#95C2×C3111yescharacteristic
228C4×#95C2×C3111yescharacteristic
229C22×C31C22×C4⋊C411yescharacteristic
230C22×C31C2×C4×D411yescharacteristic
231C22×C31C2×C4×D411yescharacteristic
232C22×C31C4×#4112yes—
233C22×C31#51912yes—
234C22×C31C2×#12011yescharacteristic
235C22×C31C2×C22⋊Q811yescharacteristic
236C22×C31C2×C22⋊Q811yescharacteristic
237C22×C31C2×#12311yescharacteristic
238C22×C31C2×#12411yescharacteristic
239C22×C31#52912yes—
240C22×C31#53211yescharacteristic
241C22×C31#53611yescharacteristic
242C22×C31#53611yescharacteristic
243C22×C31#54112yes—
244C22×C31#54712yes—
245C22×C31#54812yes—
246C22×C31#54812yes—
247C22×C31#54812yes—
248C22×C31#55212yes—
249C22×C31#55612yes—
250C22×C31#55712yes—
251C22×C31#55712yes—
252C4×C31—24no—
253C4×C31—28no—
254C4×C31—44no—
255C4×C31—44no—
256C4×C31—42no—
257C4×C31—44no—
258C4×C31—44no—
259C4×C31—82no—
260C4×C31#38518yes—
261C23×Q8C22×C3111yescharacteristic
262C2×C4×Q8—24no—
263C2×C4×Q8—24no—
264C2×C4×Q8—24no—
265C22×C4⋊C4C22×C3112yes—
266C22×C4⋊C4C22×C3112yes—
267C22×C4⋊C4C22×C3111yescharacteristic
268C22×C4⋊C4C22×C3111yescharacteristic
269C22×C4⋊C4C22×C3111yescharacteristic
270C22×C42C22×C3112yes—
271C22×C42C22×C3111yescharacteristic
272C22×C42C22×C3111yescharacteristic
273C22×C42C22×C3111yescharacteristic
274#391—24no—
275#391C4×C3118yescomplemented
276#389—24no—
277#382—24no—
278C2×#95C22×C3112yes—
279C2×#95C22×C3112yes—
280C2×#95C22×C3114yes—
281C2×#95C22×C3114yes—
282C2×#95C22×C3114yes—
283C2×#95C22×C3112yes—
284C2×#95C22×C3114yes—
285C2×C31C2×#38511yescharacteristic
286C2×C31C4×#12411yescharacteristic
287C2×C31#232711yescharacteristic
288C2×C31#235112yes—
289C2×C31#236212yes—
290C2×C31#242112yes—
291C2×C31#243211yescharacteristic
292C2×C31#243611yescharacteristic
293C2×C31#245312yes—
294C2×C31#256511yescharacteristic
295C2×C31#256811yescharacteristic
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8C2×C4×C3114yes—
301C22×Q8D4×C3114yes—
302C22×Q8Q8×C3114yes—
303C23×C4C23×C3112yes—
304C23×C4C23×C3112yes—
305C23×C4C23×C3112yes—
306C23×C4C23×C3112yes—
307C23×C4C23×C3111yescharacteristic
308C23×C4C23×C3112yes—
309C23×C4C23×C3112yes—
310C23×C4C23×C3111yescharacteristic
311C23×C4C23×C3111yescharacteristic
312C4×Q8—232no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4C2×C4×C3114yes—
326C2×C4⋊C4D4×C3114yes—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42C2×C4×C3114yes—
338C2×C42D4×C3114yes—
339#95—28no—
340#95—24no—
341#95—28no—
342#95—24no—
343#95—28no—
344#95—24no—
345#95C2×C4×C31116yes—
346C31#1397811yescharacteristic, direct product factor, Sylow
347C24C24×C3111yescharacteristic
348C2×Q8—28no—
349C2×Q8—28no—
350C2×Q8—28no—
351C2×Q8—28no—
352C2×Q8—28no—
353C2×Q8—28no—
354C2×Q8C4⋊C4×C31116yescomplemented
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4C22×C4×C3114yes—
392C22×C4C22×C4×C3114yes—
393C22×C4C22×C4×C3114yes—
394C22×C4C22×C4×C3112yes—
395C22×C4C2×D4×C3114yes—
396C22×C4C2×D4×C3112yes—
397C22×C4C2×D4×C3114yes—
398C22×C4C2×D4×C3112yes—
399C22×C4C2×D4×C3112yes—
400C22×C4C2×D4×C3112yes—
401C22×C4C2×D4×C3112yes—
402C22×C4C2×Q8×C3114yes—
403C22×C4C2×Q8×C3112yes—
404C22×C4#41×C3114yes—
405C22×C4#41×C3114yes—
406C22×C4#41×C3112yes—
407C22×C4#41×C3112yes—
408C4⋊C4—216no—
409C4⋊C4—28no—
410C4⋊C4—28no—
411C4⋊C4—44no—
412C4⋊C4—48no—
413C42—216no—
414C42—28no—
415C42—28no—
416C42—44no—
417C23C23×C4×C3111yescharacteristic
418C23C22×D4×C3111yescharacteristic
419C23C22×D4×C3111yescharacteristic
420C23C22×D4×C3111yescharacteristic
421C23C22×Q8×C3111yescharacteristic
422C23C2×#41×C3111yescharacteristic
423C23C2×#41×C3111yescharacteristic
424C23C2×#41×C3112yes—
425C23C2×#41×C3112yes—
426C23C31×2−1+412yes—
427C23C31×2−1+412yes—
428Q8—232no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—28no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4C2×C4⋊C4×C3118yes—
474C2×C4C2×C4⋊C4×C3114yes—
475C2×C4C4×D4×C3114yes—
476C2×C4C4×D4×C3114yes—
477C2×C4C31×#12014yes—
478C2×C4C31×C22⋊Q814yes—
479C2×C4C31×C22⋊Q814yes—
480C2×C4C31×#12314yes—
481C2×C4C31×#12414yes—
482C22C22×C4⋊C4×C3111yescharacteristic
483C22C2×C4×D4×C3111yescharacteristic
484C22C2×C4×D4×C3111yescharacteristic
485C22C4×#41×C3112yes—
486C22C31×#51912yes—
487C22C2×C31×#12011yescharacteristic
488C22C2×C31×C22⋊Q811yescharacteristic
489C22C2×C31×C22⋊Q811yescharacteristic
490C22C2×C31×#12311yescharacteristic
491C22C2×C31×#12411yescharacteristic
492C22C31×#52912yes—
493C22C31×#53211yescharacteristic
494C22C31×#53611yescharacteristic
495C22C31×#53611yescharacteristic
496C22C31×#54112yes—
497C22C31×#54712yes—
498C22C31×#54812yes—
499C22C31×#54812yes—
500C22C31×#54812yes—
501C22C31×#55212yes—
502C22C31×#55612yes—
503C22C31×#55712yes—
504C22C31×#55712yes—
505C4—24no—
506C4—28no—
507C4—44no—
508C4—44no—
509C4—42no—
510C4—44no—
511C4—44no—
512C4—82no—
513C4C31×#38518yes—
514C2C2×C31×#38511yescharacteristic
515C2C4×C31×#12411yescharacteristic
516C2C31×#232711yescharacteristic
517C2C31×#235112yes—
518C2C31×#236212yes—
519C2C31×#242112yes—
520C2C31×#243211yescharacteristic
521C2C31×#243611yescharacteristic
522C2C31×#245312yes—
523C2C31×#256511yescharacteristic
524C2C31×#256811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
24. C31×#391C4semidirect
91. C2×Q8×C31C4⋊C4semidirect
154. #13978C31direct (N × H)
275. #391C4×C31semidirect
346. C31#13978direct (N × H)
354. C2×Q8C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#3912
C2×C31×#3892
C2×C31×#3822
C31×#14422
C31×#14362
C31×C4⋊#952
C4×C31×#952
#1397831