Finite Group Databasebeta

← C31×#11392 #21468151

Subgroups — C31×#11392 #21468151

Order 7936.

974 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C2×C31×#343C211yesmaximal, characteristic
3C31×#1736C212yesmaximal
4C2×C31×#339C212yesmaximal
5C31×C4⋊#95C211yesmaximal, characteristic
6C22×M16×C31C2212yes—
7C31×#544—24no—
8C31×#544—22no—
9C31×#544C414yescomplemented
10C2×C31×C4⋊Q8—22no—
11C2×C31×#125—22no—
12C2×C31×C22⋊Q8—22no—
13C2×C31×#117C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C42×C31C2211yescharacteristic
17C2×C31×#95—22no—
18C31×#343—22no—
19C31×#340—22no—
20C31×#340—22no—
21C31×#339—24no—
22C22×Q8×C31—22no—
23C23×C4×C31—21no—
24C23×C4×C31—21no—
25C23×C4×C31D412yes—
26C23×C4×C31C2311yescharacteristic
27C2×M16×C31—22no—
28C2×M16×C31—22no—
29C2×M16×C31—22no—
30C2×M16×C31—22no—
31C2×M16×C31—22no—
32C2×M16×C31Q814yescomplemented
33C22×C8×C31—22no—
34C31×C4⋊Q8—28no—
35C31×C4⋊Q8—28no—
36C31×#125—28no—
37C31×#125—28no—
38C31×C22⋊Q8—28no—
39C31×C22⋊Q8—28no—
40C31×#117—22no—
41C31×#117—22no—
42C31×#117C2×C414yes—
43C31×#117D414yes—
44C2×C4⋊C4×C31—22no—
45C2×C4⋊C4×C31—24no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31C2×C412yes—
52C2×C4⋊C4×C31D412yes—
53C2×C4⋊C4×C31D412yes—
54C2×C4⋊C4×C31D412yes—
55C2×C4⋊C4×C31Q812yescomplemented
56C2×C22⋊C4×C31—22no—
57C2×C42×C31—22no—
58C2×C42×C31—22no—
59C2×C42×C31—22no—
60C2×C42×C31—21no—
61C2×C42×C31Q812yescomplemented
62C31×#95—44no—
63C24×C31C2×D411yescharacteristic
64C2×Q8×C31—28no—
65C2×Q8×C31—82no—
66C2×Q8×C31—82no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31C22⋊C414yes—
86C22×C4×C31C22×C411yescharacteristic
87C22×C4×C31C2×D412yes—
88C22×C4×C31C2×D412yes—
89C22×C4×C31C2×D411yescharacteristic
90C22×C4×C31C2×Q812yes—
91C22×C4×C31C2×Q811yescharacteristic
92C22×C4×C31C2×Q811yescharacteristic
93C22×C4×C31#4112yes—
94C22×C4×C31#4111yescharacteristic
95C22×C4×C31#4111yescharacteristic
96M16×C31—24no—
97M16×C31—24no—
98M16×C31—42no—
99M16×C31—42no—
100C2×C8×C31—24no—
101C2×C8×C31—42no—
102C2×C8×C31—42no—
103C4⋊C4×C31—28no—
104C4⋊C4×C31—216no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—24no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31C22⋊C414yes—
112C4⋊C4×C31C22⋊C414yes—
113C22⋊C4×C31—24no—
114C22⋊C4×C31—24no—
115C42×C31—24no—
116C42×C31—24no—
117C42×C31—24no—
118C42×C31—42no—
119#11392C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31C2×C22⋊C411yescharacteristic
125C23×C31#12011yescharacteristic
126C23×C31#12011yescharacteristic
127C23×C31C22⋊Q811yescharacteristic
128C23×C31C22⋊Q811yescharacteristic
129C23×C31#12411yescharacteristic
130C23×C31C4⋊Q811yescharacteristic
131Q8×C31—88no—
132C2×C4×C31—24no—
133C2×C4×C31—24no—
134C2×C4×C31—24no—
135C2×C4×C31—24no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—42no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—44no—
149C2×C4×C31—44no—
150C2×C4×C31—42no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31—81no—
154C2×C4×C31—81no—
155C2×C4×C31C2×C22⋊C412yes—
156C2×C4×C31C4×Q812yes—
157C2×C4×C31C4×Q811yescharacteristic
158C2×C4×C31C4×Q811yescharacteristic
159C2×C4×C31#12012yes—
160C2×C4×C31C22⋊Q812yes—
161C2×C4×C31C22⋊Q812yes—
162C2×C4×C31C22⋊Q812yes—
163C2×C4×C31C22⋊Q812yes—
164C2×C4×C31C22⋊Q812yes—
165C2×C4×C31#12412yes—
166C2×C4×C31#12412yes—
167C2×C4×C31#12411yescharacteristic
168C2×C4×C31C4⋊Q812yes—
169C2×C4×C31C4⋊Q812yes—
170C2×C4×C31C4⋊Q811yescharacteristic
171C8×C31—44no—
172C2×#544C2×C3111yescharacteristic
173C2×#343C2×C3111yescharacteristic
174#1736C2×C3112yes—
175C2×#339C2×C3112yes—
176C4⋊#95C2×C3111yescharacteristic
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31#37911yescharacteristic
190C22×C31#39111yescharacteristic
191C22×C31#39111yescharacteristic
192C22×C31#39311yescharacteristic
193C22×C31#39311yescharacteristic
194C22×C31#39511yescharacteristic
195C22×C31#39511yescharacteristic
196C22×C31#45311yescharacteristic
197C22×C31#45411yescharacteristic
198C22×C31#45511yescharacteristic
199C22×C31#45611yescharacteristic
200C4×C31—44no—
201C4×C31—44no—
202C4×C31—44no—
203C4×C31—44no—
204C4×C31—82no—
205C4×C31#39112yes—
206C4×C31#39112yes—
207C4×C31#39312yes—
208C4×C31#39512yes—
209C22×M16C22×C3112yes—
210#544—24no—
211#544—22no—
212#544C4×C3114yescomplemented
213C2×C4⋊Q8—22no—
214C2×#125—22no—
215C2×C22⋊Q8—22no—
216C2×#117C22×C3112yes—
217C22×C4⋊C4C22×C3111yescharacteristic
218C22×C4⋊C4C22×C3111yescharacteristic
219C22×C42C22×C3111yescharacteristic
220C2×#95—22no—
221#343—22no—
222#340—22no—
223#340—22no—
224#339—24no—
225C2×C31—21no—
226C2×C31—21no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31#144611yescharacteristic
230C2×C31#179211yescharacteristic
231C2×C31#179311yescharacteristic
232C2×C31#202711yescharacteristic
233C2×C31#202811yescharacteristic
234C2×C31#206011yescharacteristic
235C2×C31#206111yescharacteristic
236C22×Q8—22no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4D4×C3112yes—
240C23×C4C23×C3111yescharacteristic
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16Q8×C3114yescomplemented
247C22×C8—22no—
248C4⋊Q8—28no—
249C4⋊Q8—28no—
250#125—28no—
251#125—28no—
252C22⋊Q8—28no—
253C22⋊Q8—28no—
254#117—22no—
255#117—22no—
256#117C2×C4×C3114yes—
257#117D4×C3114yes—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C3112yes—
266C2×C4⋊C4D4×C3112yes—
267C2×C4⋊C4D4×C3112yes—
268C2×C4⋊C4D4×C3112yes—
269C2×C4⋊C4Q8×C3112yescomplemented
270C2×C22⋊C4—22no—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42Q8×C3112yescomplemented
276#95—44no—
277C31#1139211yescharacteristic, direct product factor, Sylow
278C24C2×D4×C3111yescharacteristic
279C2×Q8—28no—
280C2×Q8—82no—
281C2×Q8—82no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C22⋊C4×C3114yes—
301C22×C4C22×C4×C3111yescharacteristic
302C22×C4C2×D4×C3112yes—
303C22×C4C2×D4×C3112yes—
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×Q8×C3112yes—
306C22×C4C2×Q8×C3111yescharacteristic
307C22×C4C2×Q8×C3111yescharacteristic
308C22×C4#41×C3112yes—
309C22×C4#41×C3111yescharacteristic
310C22×C4#41×C3111yescharacteristic
311M16—24no—
312M16—24no—
313M16—42no—
314M16—42no—
315C2×C8—24no—
316C2×C8—42no—
317C2×C8—42no—
318C4⋊C4—28no—
319C4⋊C4—216no—
320C4⋊C4—24no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—42no—
326C4⋊C4C22⋊C4×C3114yes—
327C4⋊C4C22⋊C4×C3114yes—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C42—24no—
331C42—24no—
332C42—24no—
333C42—42no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23C2×C22⋊C4×C3111yescharacteristic
339C23C31×#12011yescharacteristic
340C23C31×#12011yescharacteristic
341C23C31×C22⋊Q811yescharacteristic
342C23C31×C22⋊Q811yescharacteristic
343C23C31×#12411yescharacteristic
344C23C31×C4⋊Q811yescharacteristic
345Q8—88no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C2×C22⋊C4×C3112yes—
370C2×C4C4×Q8×C3112yes—
371C2×C4C4×Q8×C3111yescharacteristic
372C2×C4C4×Q8×C3111yescharacteristic
373C2×C4C31×#12012yes—
374C2×C4C31×C22⋊Q812yes—
375C2×C4C31×C22⋊Q812yes—
376C2×C4C31×C22⋊Q812yes—
377C2×C4C31×C22⋊Q812yes—
378C2×C4C31×C22⋊Q812yes—
379C2×C4C31×#12412yes—
380C2×C4C31×#12412yes—
381C2×C4C31×#12411yescharacteristic
382C2×C4C31×C4⋊Q811yescharacteristic
383C2×C4C31×C4⋊Q812yes—
384C2×C4C31×C4⋊Q812yes—
385C8—44no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22C31×#37911yescharacteristic
399C22C31×#39111yescharacteristic
400C22C31×#39111yescharacteristic
401C22C31×#39311yescharacteristic
402C22C31×#39311yescharacteristic
403C22C31×#39511yescharacteristic
404C22C31×#39511yescharacteristic
405C22C31×#45311yescharacteristic
406C22C31×#45411yescharacteristic
407C22C31×#45511yescharacteristic
408C22C31×#45611yescharacteristic
409C4—44no—
410C4—44no—
411C4—44no—
412C4—44no—
413C4—82no—
414C4C31×#39112yes—
415C4C31×#39112yes—
416C4C31×#39312yes—
417C4C31×#39512yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2C31×#144611yescharacteristic
423C2C31×#179211yescharacteristic
424C2C31×#179311yescharacteristic
425C2C31×#202711yescharacteristic
426C2C31×#202811yescharacteristic
427C2C31×#206011yescharacteristic
428C2C31×#206111yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
9. C31×#544C4semidirect
32. C2×M16×C31Q8semidirect
55. C2×C4⋊C4×C31Q8semidirect
61. C2×C42×C31Q8semidirect
119. #11392C31direct (N × H)
212. #544C4×C31semidirect
246. C2×M16Q8×C31semidirect
269. C2×C4⋊C4Q8×C31semidirect
275. C2×C42Q8×C31semidirect
277. C31#11392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C2×C31×#3432
C31×#17362
C2×C31×#3392
C31×C4⋊#952
#1139231