Finite Group Databasebeta

← C31×#11046 #21467805

Subgroups — C31×#11046 #21467805

Order 7936.

1178 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#99C212yesmaximal
2C31×#2315C211yesmaximal, characteristic, complemented
3C31×#2308C211yesmaximal, characteristic
4C2×C31×#342C212yesmaximal, complemented
5C2×C31×#342C211yesmaximal, characteristic, complemented
6C23×D4×C31C2211yescharacteristic
7C22×C22⋊C4×C31C2211yescharacteristic
8C22×C22⋊C4×C31C2212yes—
9C22×C22⋊C4×C31C2212yes—
10C22×C22⋊C4×C31C2211yescharacteristic
11C2×C31×#99—24no—
12C2×C31×#99—24no—
13C2×C31×#99—24no—
14C31×#386—22no—
15C31×#386—22no—
16C31×#385—24no—
17C31×#381C412yescomplemented
18C31×#380—22no—
19C31×#379C412yescomplemented
20C31×#342—24no—
21C31×#342—22no—
22C25×C31C2×C411yescharacteristic
23C25×C31C2311yescharacteristic
24C22×D4×C31—22no—
25C22×D4×C31—22no—
26C22×D4×C31—21no—
27C22×D4×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31D412yes—
33C22×D4×C31Q812yes—
34C23×C4×C31—22no—
35C23×C4×C31—21no—
36C23×C4×C31—22no—
37C23×C4×C31C2×C411yescharacteristic
38C23×C4×C31D412yes—
39C2×C4⋊C4×C31—24no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31—22no—
48C2×C22⋊C4×C31—22no—
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—22no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31C2×C412yes—
57C2×C22⋊C4×C31C2×C412yes—
58C2×C22⋊C4×C31D414yes—
59C2×C22⋊C4×C31D414yes—
60C2×C22⋊C4×C31D412yes—
61C31×#99—216no—
62C31×#95—24no—
63C31×#95—24no—
64C24×C31—21no—
65C24×C31—21no—
66C24×C31—22no—
67C24×C31—22no—
68C24×C31—82no—
69C24×C31—82no—
70C24×C31C4⋊C412yescomplemented
71C24×C31C22×C411yescharacteristic
72C24×C31C2×D411yescharacteristic
73C24×C31C2×D411yescharacteristic
74C24×C31C2×D412yes—
75C24×C31C2×D411yescharacteristic
76C24×C31C2×D412yes—
77C24×C31C2×Q811yescharacteristic
78C24×C31#4112yes—
79C24×C31#4111yescharacteristic
80C24×C31#4111yescharacteristic
81C24×C31#4112yes—
82C2×D4×C31—24no—
83C2×D4×C31—22no—
84C2×D4×C31—22no—
85C2×D4×C31—22no—
86C2×D4×C31—22no—
87C2×D4×C31—24no—
88C2×D4×C31—24no—
89C2×D4×C31—24no—
90C2×D4×C31—41no—
91C2×D4×C31—42no—
92C2×D4×C31—42no—
93C2×D4×C31—42no—
94C2×D4×C31—41no—
95C2×D4×C31—42no—
96C2×D4×C31—42no—
97C2×D4×C31—41no—
98C2×D4×C31—42no—
99C2×D4×C31—41no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—24no—
108C22×C4×C31—24no—
109C22×C4×C31—42no—
110C22×C4×C31—42no—
111C22×C4×C31—42no—
112C22×C4×C31—42no—
113C22×C4×C31—42no—
114C22×C4×C31—82no—
115C22×C4×C31—82no—
116C22×C4×C31—84no—
117C22×C4×C31—84no—
118C22×C4×C31C22⋊C414yes—
119C22×C4×C31C4⋊C412yescomplemented
120C4⋊C4×C31—84no—
121C22⋊C4×C31—24no—
122C22⋊C4×C31—24no—
123C22⋊C4×C31—24no—
124C22⋊C4×C31—24no—
125C22⋊C4×C31—24no—
126C22⋊C4×C31—24no—
127C22⋊C4×C31—24no—
128C22⋊C4×C31—42no—
129C22⋊C4×C31—42no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—42no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—42no—
134C22⋊C4×C31—84no—
135#11046C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—22no—
137C23×C31—24no—
138C23×C31—42no—
139C23×C31—44no—
140C23×C31—42no—
141C23×C31—44no—
142C23×C31—42no—
143C23×C31—44no—
144C23×C31—41no—
145C23×C31—42no—
146C23×C31—41no—
147C23×C31—84no—
148C23×C31—81no—
149C23×C31—82no—
150C23×C31—81no—
151C23×C31—81no—
152C23×C31—82no—
153C23×C31—81no—
154C23×C31—82no—
155C23×C31—82no—
156C23×C31—84no—
157C23×C31C2×C22⋊C411yescharacteristic
158C23×C31C2×C4⋊C411yescharacteristic
159C23×C31#11711yescharacteristic
160C23×C31C4×D412yes—
161C23×C31C4×D412yes—
162C23×C31#12011yescharacteristic
163C23×C31#12012yes—
164C23×C31#12112yes—
165C23×C31#12111yescharacteristic
166C23×C31#12111yescharacteristic
167C23×C31#12112yes—
168C23×C31#12112yes—
169C23×C31C22⋊Q811yescharacteristic
170C23×C31C22⋊Q811yescharacteristic
171C23×C31C22⋊Q812yes—
172C23×C31C22⋊Q812yes—
173C23×C31#12311yescharacteristic
174C23×C31#12312yes—
175C23×C31#12312yes—
176C23×C31#12412yes—
177C23×C31#12411yescharacteristic
178C23×C31#12612yes—
179C23×C31#12711yescharacteristic
180D4×C31—42no—
181D4×C31—42no—
182D4×C31—44no—
183D4×C31—44no—
184D4×C31—42no—
185D4×C31—42no—
186C2×C4×C31—22no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—44no—
190C2×C4×C31—41no—
191C2×C4×C31—42no—
192C2×C4×C31—41no—
193C2×C4×C31—44no—
194C2×C4×C31—44no—
195C2×C4×C31—48no—
196C2×C4×C31—42no—
197C2×C4×C31—44no—
198C2×C4×C31—44no—
199C2×C4×C31—82no—
200C2×C4×C31—84no—
201C2×C4×C31—84no—
202C2×C4×C31—84no—
203C2×C4×C31—84no—
204C2×C4×C31—84no—
205C2×C4×C31—84no—
206C22×#99C2×C3112yes—
207#2315C2×C3111yescharacteristic, complemented
208#2308C2×C3111yescharacteristic
209C2×#342C2×C3112yescomplemented
210C2×#342C2×C3111yescharacteristic, complemented
211C22×C31—22no—
212C22×C31—22no—
213C22×C31—24no—
214C22×C31—22no—
215C22×C31—24no—
216C22×C31—42no—
217C22×C31—42no—
218C22×C31—42no—
219C22×C31—42no—
220C22×C31—42no—
221C22×C31—41no—
222C22×C31—41no—
223C22×C31—42no—
224C22×C31—41no—
225C22×C31—41no—
226C22×C31—41no—
227C22×C31—41no—
228C22×C31—42no—
229C22×C31—42no—
230C22×C31—41no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—41no—
234C22×C31—44no—
235C22×C31—42no—
236C22×C31—84no—
237C22×C31—82no—
238C22×C31—84no—
239C22×C31—82no—
240C22×C31#38011yescharacteristic
241C22×C31#38512yes—
242C22×C31#38611yescharacteristic
243C22×C31#38812yes—
244C22×C31#39011yescharacteristic
245C22×C31#39211yescharacteristic
246C22×C31#39311yescharacteristic
247C22×C31#39412yes—
248C22×C31#39612yes—
249C22×C31#39711yescharacteristic
250C22×C31#39911yescharacteristic
251C4×C31—44no—
252C4×C31—42no—
253C4×C31—84no—
254C4×C31—82no—
255C4×C31—84no—
256C23×D4C22×C3111yescharacteristic
257C22×C22⋊C4C22×C3111yescharacteristic
258C22×C22⋊C4C22×C3112yes—
259C22×C22⋊C4C22×C3112yes—
260C22×C22⋊C4C22×C3111yescharacteristic
261C2×#99—24no—
262C2×#99—24no—
263C2×#99—24no—
264#386—22no—
265#386—22no—
266#385—24no—
267#381C4×C3112yescomplemented
268#380—22no—
269#379C4×C3112yescomplemented
270#342—24no—
271#342—22no—
272C2×C31—21no—
273C2×C31—21no—
274C2×C31—22no—
275C2×C31—21no—
276C2×C31—22no—
277C2×C31—22no—
278C2×C31—21no—
279C2×C31—22no—
280C2×C31—21no—
281C2×C31—21no—
282C2×C31—82no—
283C2×C31#143911yescharacteristic
284C2×C31#191312yes—
285C25C2×C4×C3111yescharacteristic
286C25C23×C3111yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4D4×C3112yes—
296C22×D4Q8×C3112yes—
297C23×C4—22no—
298C23×C4—21no—
299C23×C4—22no—
300C23×C4C2×C4×C3111yescharacteristic
301C23×C4D4×C3112yes—
302C2×C4⋊C4—24no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4C2×C4×C3112yes—
320C2×C22⋊C4C2×C4×C3112yes—
321C2×C22⋊C4D4×C3114yes—
322C2×C22⋊C4D4×C3114yes—
323C2×C22⋊C4D4×C3112yes—
324#99—216no—
325#95—24no—
326#95—24no—
327C31#1104611yescharacteristic, direct product factor, Sylow
328C24—21no—
329C24—21no—
330C24—22no—
331C24—22no—
332C24—82no—
333C24—82no—
334C24C4⋊C4×C3112yescomplemented
335C24C22×C4×C3111yescharacteristic
336C24C2×D4×C3111yescharacteristic
337C24C2×D4×C3111yescharacteristic
338C24C2×D4×C3112yes—
339C24C2×D4×C3111yescharacteristic
340C24C2×D4×C3112yes—
341C24C2×Q8×C3111yescharacteristic
342C24#41×C3112yes—
343C24#41×C3111yescharacteristic
344C24#41×C3111yescharacteristic
345C24#41×C3112yes—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—41no—
362C2×D4—42no—
363C2×D4—41no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—82no—
379C22×C4—82no—
380C22×C4—84no—
381C22×C4—84no—
382C22×C4C22⋊C4×C3114yes—
383C22×C4C4⋊C4×C3112yescomplemented
384C4⋊C4—84no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—41no—
395C22⋊C4—42no—
396C22⋊C4—41no—
397C22⋊C4—42no—
398C22⋊C4—84no—
399C23—22no—
400C23—24no—
401C23—42no—
402C23—44no—
403C23—42no—
404C23—44no—
405C23—42no—
406C23—44no—
407C23—41no—
408C23—42no—
409C23—41no—
410C23—84no—
411C23—81no—
412C23—82no—
413C23—81no—
414C23—81no—
415C23—82no—
416C23—81no—
417C23—82no—
418C23—82no—
419C23—84no—
420C23C2×C22⋊C4×C3111yescharacteristic
421C23C2×C4⋊C4×C3111yescharacteristic
422C23C31×#11711yescharacteristic
423C23C4×D4×C3112yes—
424C23C4×D4×C3112yes—
425C23C31×#12011yescharacteristic
426C23C31×#12012yes—
427C23C31×#12112yes—
428C23C31×#12112yes—
429C23C31×#12112yes—
430C23C31×#12111yescharacteristic
431C23C31×#12111yescharacteristic
432C23C31×C22⋊Q811yescharacteristic
433C23C31×C22⋊Q812yes—
434C23C31×C22⋊Q812yes—
435C23C31×C22⋊Q811yescharacteristic
436C23C31×#12311yescharacteristic
437C23C31×#12312yes—
438C23C31×#12312yes—
439C23C31×#12411yescharacteristic
440C23C31×#12412yes—
441C23C31×#12612yes—
442C23C31×#12711yescharacteristic
443D4—44no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—44no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—44no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—82no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4—84no—
469C22—22no—
470C22—22no—
471C22—24no—
472C22—22no—
473C22—24no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—41no—
480C22—41no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—42no—
487C22—42no—
488C22—41no—
489C22—42no—
490C22—42no—
491C22—41no—
492C22—44no—
493C22—42no—
494C22—84no—
495C22—82no—
496C22—84no—
497C22—82no—
498C22C31×#38011yescharacteristic
499C22C31×#38512yes—
500C22C31×#38611yescharacteristic
501C22C31×#38812yes—
502C22C31×#39011yescharacteristic
503C22C31×#39211yescharacteristic
504C22C31×#39311yescharacteristic
505C22C31×#39412yes—
506C22C31×#39612yes—
507C22C31×#39711yescharacteristic
508C22C31×#39911yescharacteristic
509C4—44no—
510C4—42no—
511C4—84no—
512C4—82no—
513C4—84no—
514C2—21no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2—82no—
525C2C31×#143911yescharacteristic
526C2C31×#191312yes—
subgroupG/H
center, socleC22×C31#386
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2315C2semidirect
4. C2×C31×#342C2semidirect
5. C2×C31×#342C2semidirect
17. C31×#381C4semidirect
19. C31×#379C4semidirect
70. C24×C31C4⋊C4semidirect
119. C22×C4×C31C4⋊C4semidirect
135. #11046C31direct (N × H)
207. #2315C2×C31semidirect
209. C2×#342C2×C31semidirect
210. C2×#342C2×C31semidirect
267. #381C4×C31semidirect
269. #379C4×C31semidirect
327. C31#11046direct (N × H)
334. C24C4⋊C4×C31semidirect
383. C22×C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#992
C31×#23152
C31×#23082
C2×C31×#3422
#1104631