Finite Group Databasebeta

← C31×#8351 #21465110

Subgroups — C31×#8351 #21465110

Order 7936.

834 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#1892C212yesmaximal, complemented
3C31×#1869C211yesmaximal, characteristic
4C31×#1799C211yesmaximal, characteristic
5C31×#1520C212yesmaximal, complemented
6C23×C8×C31C2211yescharacteristic
7C31×#554—24no—
8C31×#554—22no—
9D4×Q8×C31—22no—
10C31×#544C412yescomplemented
11C31×#543—21no—
12C31×#543C412yescomplemented
13C31×#533—21no—
14C2×C31×C22⋊Q8—21no—
15C2×C31×C22⋊Q8C2212yes—
16C31×#518—21no—
17C2×C4×D4×C31C2211yescharacteristic
18C2×C31×#103—22no—
19C2×C31×#99—21no—
20C2×C31×C22⋊C8—21no—
21C2×C31×C22⋊C8C2211yescharacteristic
22C31×#380C2212yes—
23C31×#342—21no—
24C31×#340—22no—
25C31×#336—21no—
26C31×#328—24no—
27C22×Q8×C31—21no—
28C22×Q8×C31D412yes—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31C2311yescharacteristic
32C22×C8×C31—21no—
33C22×C8×C31—22no—
34C22×C8×C31—21no—
35C22×C8×C31—42no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—24no—
39C31×#125—22no—
40C31×#125—24no—
41C31×C22⋊Q8—22no—
42C31×C22⋊Q8—22no—
43C31×C22⋊Q8—24no—
44C31×C22⋊Q8—24no—
45C31×C22⋊Q8—24no—
46C31×C22⋊Q8—22no—
47C31×C22⋊Q8—22no—
48C31×C22⋊Q8—22no—
49C31×C22⋊Q8—22no—
50C31×C22⋊Q8—24no—
51C31×C22⋊Q8C2×C414yes—
52C31×C22⋊Q8D414yes—
53C4×Q8×C31—22no—
54C4×Q8×C31—22no—
55C4×D4×C31—24no—
56C4×D4×C31—24no—
57C4×D4×C31—22no—
58C4×D4×C31—22no—
59C31×#117—22no—
60C2×C4⋊C4×C31—21no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31C2×C411yescharacteristic
65C2×C4⋊C4×C31D412yes—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31C2×C411yescharacteristic
70C2×C22⋊C4×C31D411yescharacteristic
71C2×C42×C31D411yescharacteristic
72C31×#103—44no—
73C31×#99—42no—
74C31×C22⋊C8—22no—
75C31×C22⋊C8—42no—
76C31×#95—22no—
77C24×C31C22⋊C411yescharacteristic
78C24×C31C2×D411yescharacteristic
79C2×Q8×C31—22no—
80C2×Q8×C31—22no—
81C2×Q8×C31—22no—
82C2×Q8×C31—42no—
83C2×Q8×C31—42no—
84C2×Q8×C31—81no—
85C2×Q8×C31—81no—
86C2×Q8×C31C22⋊C414yes—
87C2×D4×C31—22no—
88C2×D4×C31—22no—
89C2×D4×C31SD1612yes—
90C2×D4×C31Q1612yes—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
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×C31—42no—
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22⋊C411yescharacteristic
105C22×C4×C31C22×C411yescharacteristic
106C22×C4×C31C2×D412yes—
107C22×C4×C31C2×D411yescharacteristic
108C22×C4×C31C2×D412yes—
109C2×C8×C31—22no—
110C2×C8×C31—24no—
111C2×C8×C31—42no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—24no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—24no—
122C4⋊C4×C31—22no—
123C4⋊C4×C31—24no—
124C4⋊C4×C31—22no—
125C4⋊C4×C31—24no—
126C4⋊C4×C31—22no—
127C4⋊C4×C31—42no—
128C4⋊C4×C31—42no—
129C4⋊C4×C31C22⋊C414yes—
130C22⋊C4×C31—24no—
131C22⋊C4×C31—24no—
132C22⋊C4×C31—24no—
133C22⋊C4×C31—22no—
134C22⋊C4×C31—22no—
135C22⋊C4×C31—42no—
136C22⋊C4×C31—42no—
137C42×C31—24no—
138C42×C31—21no—
139C42×C31—21no—
140#8351C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—41no—
144C23×C31—41no—
145C23×C31—41no—
146C23×C31—41no—
147C23×C31#10312yescomplemented
148C23×C31C2×C22⋊C411yescharacteristic
149C23×C31#12012yes—
150C23×C31C2×SD1611yescharacteristic
151C23×C31C2×Q1611yescharacteristic
152C23×C31#13712yes—
153Q8×C31—44no—
154Q8×C31—42no—
155Q8×C31—42no—
156Q8×C31—82no—
157Q8×C31—82no—
158D4×C31—24no—
159D4×C31—24no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—22no—
163C2×C4×C31—21no—
164C2×C4×C31—22no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—21no—
170C2×C4×C31—41no—
171C2×C4×C31—42no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—81no—
177C2×C4×C31—82no—
178C2×C4×C31—82no—
179C2×C4×C31—82no—
180C2×C4×C31—82no—
181C2×C4×C31—82no—
182C2×C4×C31—82no—
183C2×C4×C31—82no—
184C2×C4×C31#10312yescomplemented
185C2×C4×C31C2×C22⋊C412yes—
186C2×C4×C31#12011yescharacteristic
187C2×C4×C31#12011yescharacteristic
188C8×C31—42no—
189C8×C31—81no—
190#3501C2×C3111yescharacteristic
191#1892C2×C3112yescomplemented
192#1869C2×C3111yescharacteristic
193#1799C2×C3111yescharacteristic
194#1520C2×C3112yescomplemented
195C22×C31—21no—
196C22×C31—22no—
197C22×C31—21no—
198C22×C31—22no—
199C22×C31—22no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—42no—
203C22×C31—42no—
204C22×C31—41no—
205C22×C31—41no—
206C22×C31—81no—
207C22×C31#37911yescharacteristic
208C22×C31C2×#10311yescharacteristic
209C22×C31#41911yescharacteristic
210C22×C31#44812yes—
211C22×C31#45112yes—
212C4×C31—22no—
213C4×C31—21no—
214C4×C31—22no—
215C4×C31—41no—
216C4×C31—44no—
217C4×C31—41no—
218C4×C31—44no—
219C4×C31—162no—
220C4×C31B(4,𝔽2)11yescharacteristic
221C4×C31#45811yescharacteristic
222C23×C8C22×C3111yescharacteristic
223#554—24no—
224#554—22no—
225D4×Q8—22no—
226#544C4×C3112yescomplemented
227#543—21no—
228#543C4×C3112yescomplemented
229#533—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C22×C3112yes—
232#518—21no—
233C2×C4×D4C22×C3111yescharacteristic
234C2×#103—22no—
235C2×#99—21no—
236C2×C22⋊C8—21no—
237C2×C22⋊C8C22×C3111yescharacteristic
238#380C22×C3112yes—
239#342—21no—
240#340—22no—
241#336—21no—
242#328—24no—
243C2×C31—22no—
244C2×C31—21no—
245C2×C31—21no—
246C2×C31—22no—
247C2×C31—42no—
248C2×C31#178711yescharacteristic
249C2×C31#179011yescharacteristic
250C2×C31#179411yescharacteristic
251C22×Q8—21no—
252C22×Q8D4×C3112yes—
253C22×D4D4×C3111yescharacteristic
254C23×C4D4×C3111yescharacteristic
255C23×C4C23×C3111yescharacteristic
256C22×C8—21no—
257C22×C8—22no—
258C22×C8—21no—
259C22×C8—42no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—24no—
263#125—22no—
264#125—24no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8—24no—
268C22⋊Q8—24no—
269C22⋊Q8—24no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8C2×C4×C3114yes—
276C22⋊Q8D4×C3114yes—
277C4×Q8—22no—
278C4×Q8—22no—
279C4×D4—24no—
280C4×D4—24no—
281C4×D4—22no—
282C4×D4—22no—
283#117—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4C2×C4×C3111yescharacteristic
289C2×C4⋊C4D4×C3112yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4C2×C4×C3111yescharacteristic
294C2×C22⋊C4D4×C3111yescharacteristic
295C2×C42D4×C3111yescharacteristic
296#103—44no—
297#99—42no—
298C22⋊C8—22no—
299C22⋊C8—42no—
300#95—22no—
301C31#835111yescharacteristic, direct product factor, Sylow
302C24C22⋊C4×C3111yescharacteristic
303C24C2×D4×C3111yescharacteristic
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—42no—
308C2×Q8—42no—
309C2×Q8—81no—
310C2×Q8—81no—
311C2×Q8C22⋊C4×C3114yes—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4SD16×C3112yes—
315C2×D4Q16×C3112yes—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4C22⋊C4×C3111yescharacteristic
328C22×C4C22⋊C4×C3111yescharacteristic
329C22×C4C22⋊C4×C3111yescharacteristic
330C22×C4C22×C4×C3111yescharacteristic
331C22×C4C2×D4×C3112yes—
332C22×C4C2×D4×C3111yescharacteristic
333C22×C4C2×D4×C3112yes—
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4C22⋊C4×C3114yes—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C42—24no—
363C42—21no—
364C42—21no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23C31×#10312yescomplemented
372C23C2×C22⋊C4×C3111yescharacteristic
373C23C31×#12012yes—
374C23C2×SD16×C3111yescharacteristic
375C23C2×Q16×C3111yescharacteristic
376C23C31×#13712yes—
377Q8—44no—
378Q8—42no—
379Q8—42no—
380Q8—82no—
381Q8—82no—
382D4—24no—
383D4—24no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4C31×#10312yescomplemented
409C2×C4C2×C22⋊C4×C3112yes—
410C2×C4C31×#12011yescharacteristic
411C2×C4C31×#12011yescharacteristic
412C8—42no—
413C8—81no—
414C22—21no—
415C22—22no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—41no—
420C22—41no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22C31×#37911yescharacteristic
427C22C2×C31×#10311yescharacteristic
428C22C31×#41911yescharacteristic
429C22C31×#44812yes—
430C22C31×#45112yes—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—44no—
436C4—41no—
437C4—44no—
438C4—162no—
439C4C31×B(4,𝔽2)11yescharacteristic
440C4C31×#45811yescharacteristic
441C2—22no—
442C2—21no—
443C2—21no—
444C2—22no—
445C2—42no—
446C2C31×#178711yescharacteristic
447C2C31×#179011yescharacteristic
448C2C31×#179411yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31D4
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×#1892C2semidirect
5. C31×#1520C2semidirect
10. C31×#544C4semidirect
12. C31×#543C4semidirect
140. #8351C31direct (N × H)
147. C23×C31#103semidirect
184. C2×C4×C31#103semidirect
191. #1892C2×C31semidirect
194. #1520C2×C31semidirect
226. #544C4×C31semidirect
228. #543C4×C31semidirect
301. C31#8351direct (N × H)
371. C23C31×#103semidirect
408. C2×C4C31×#103semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#18922
C31×#18692
C31×#17992
C31×#15202
#835131