Finite Group Databasebeta

← C31×#18287 #21475046

Subgroups — C31×#18287 #21475046

Order 7936.

1064 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#543C211yesmaximal, characteristic
2C31×#3189C212yesmaximal, complemented
3C31×#2626C211yesmaximal, characteristic
4C31×#1614C214yesmaximal, complemented
5C31×#1602C214yesmaximal, complemented
6C31×#1520C212yesmaximal, complemented
7C2×C31×#323C211yesmaximal, characteristic
8C31×#543—24no—
9C31×#543—22no—
10C31×#543C2214yes—
11C2×C31×C22⋊Q8—22no—
12C2×C31×C22⋊Q8—21no—
13C2×C31×C22⋊Q8—22no—
14C2×C31×C22⋊Q8C2212yes—
15C2×C31×C22⋊Q8C2211yescharacteristic
16C22×C22⋊C4×C31—21no—
17C22×C22⋊C4×C31C2211yescharacteristic
18C31×#484—22no—
19C31×#484C2214yescomplemented
20C31×#467—24no—
21C31×#451—22no—
22C31×#451C2214yescomplemented
23C2×C31×C22⋊C8C2212yes—
24C31×#399C2212yes—
25C31×#396—22no—
26C31×#393C2212yes—
27C31×#385—21no—
28C31×#380C2211yescharacteristic
29C31×#379—21no—
30C31×#328C2218yescomplemented
31C31×#323C2214yes—
32C25×C31D411yescharacteristic
33C22×Q8×C31—21no—
34C22×Q8×C31D412yes—
35C22×Q8×C31C2311yescharacteristic
36C23×C4×C31—21no—
37C23×C4×C31—21no—
38C23×C4×C31D411yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C2×Q16×C31—24no—
41C22×C8×C31—22no—
42C31×C22⋊Q8—28no—
43C31×C22⋊Q8—28no—
44C31×C22⋊Q8—24no—
45C31×C22⋊Q8—28no—
46C31×C22⋊Q8—24no—
47C31×C22⋊Q8—22no—
48C31×C22⋊Q8—22no—
49C31×C22⋊Q8—28no—
50C31×C22⋊Q8—22no—
51C31×C22⋊Q8—22no—
52C31×C22⋊Q8D414yes—
53C31×C22⋊Q8C2314yes—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31D412yes—
61C2×C4⋊C4×C31C2311yescharacteristic
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—21no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31D412yes—
73C2×C22⋊C4×C31C2312yes—
74C31×#107—24no—
75C31×#103—24no—
76C31×#103—24no—
77C31×C22⋊C8—22no—
78C31×C22⋊C8C2314yes—
79C31×#95—22no—
80C31×#95C2312yes—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—22no—
84C24×C31—81no—
85C24×C31—81no—
86C24×C31Q1614yescomplemented
87C24×C31C2×D412yes—
88C24×C31C2×D411yescharacteristic
89C2×Q8×C31—24no—
90C2×Q8×C31—22no—
91C2×Q8×C31—22no—
92C2×Q8×C31—81no—
93C2×Q8×C31—82no—
94C2×Q8×C31—82no—
95C2×Q8×C31C2×D414yes—
96C22×C4×C31—22no—
97C22×C4×C31—21no—
98C22×C4×C31—22no—
99C22×C4×C31—24no—
100C22×C4×C31—24no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—81no—
106C22×C4×C31—81no—
107C22×C4×C31—82no—
108C22×C4×C31—82no—
109C22×C4×C31C2×D412yes—
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D412yes—
112C22×C4×C31C2×D412yes—
113C22×C4×C31C2411yescharacteristic
114Q16×C31—84no—
115C2×C8×C31—24no—
116C2×C8×C31—82no—
117C4⋊C4×C31—24no—
118C4⋊C4×C31—28no—
119C4⋊C4×C31—24no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—24no—
122C4⋊C4×C31—22no—
123C4⋊C4×C31—42no—
124C4⋊C4×C31—81no—
125C4⋊C4×C31—82no—
126C4⋊C4×C31C2×D414yes—
127C22⋊C4×C31—28no—
128C22⋊C4×C31—24no—
129C22⋊C4×C31—24no—
130C22⋊C4×C31—24no—
131C22⋊C4×C31—24no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—42no—
135C22⋊C4×C31—82no—
136C22⋊C4×C31—82no—
137#18287C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—24no—
140C23×C31—22no—
141C23×C31—24no—
142C23×C31—41no—
143C23×C31—41no—
144C23×C31—42no—
145C23×C31—42no—
146C23×C31—42no—
147C23×C31—42no—
148C23×C31—81no—
149C23×C31—81no—
150C23×C31—84no—
151C23×C31—84no—
152C23×C31#12011yescharacteristic
153C23×C31#12011yescharacteristic
154C23×C31C2×Q1614yes—
155C23×C31C2×Q1612yes—
156C23×C31#13712yes—
157C23×C31C22×D411yescharacteristic
158Q8×C31—44no—
159Q8×C31—44no—
160Q8×C31—82no—
161Q8×C31—84no—
162C2×C4×C31—24no—
163C2×C4×C31—22no—
164C2×C4×C31—24no—
165C2×C4×C31—41no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—41no—
169C2×C4×C31—42no—
170C2×C4×C31—44no—
171C2×C4×C31—44no—
172C2×C4×C31—42no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—42no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—42no—
180C2×C4×C31—81no—
181C2×C4×C31—84no—
182C2×C4×C31—84no—
183C2×C4×C31#12012yes—
184C2×C4×C31C22×D412yes—
185C8×C31—44no—
186C2×#543C2×C3111yescharacteristic
187#3189C2×C3112yescomplemented
188#2626C2×C3111yescharacteristic
189#1614C2×C3114yescomplemented
190#1602C2×C3114yescomplemented
191#1520C2×C3112yescomplemented
192C2×#323C2×C3111yescharacteristic
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—24no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—44no—
203C22×C31—48no—
204C22×C31—42no—
205C22×C31—42no—
206C22×C31—82no—
207C22×C31—84no—
208C22×C31#45112yes—
209C22×C31#45112yes—
210C22×C31C2×#12011yescharacteristic
211C22×C31C22×Q1611yescharacteristic
212C22×C31C2×#13711yescharacteristic
213C4×C31—22no—
214C4×C31—22no—
215C4×C31—42no—
216C4×C31—44no—
217C4×C31—44no—
218C4×C31—82no—
219C4×C31—81no—
220C4×C31—81no—
221#543—24no—
222#543—22no—
223#543C22×C3114yes—
224C2×C22⋊Q8—22no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—22no—
227C2×C22⋊Q8C22×C3112yes—
228C2×C22⋊Q8C22×C3111yescharacteristic
229C22×C22⋊C4—21no—
230C22×C22⋊C4C22×C3111yescharacteristic
231#484—22no—
232#484C22×C3114yescomplemented
233#467—24no—
234#451—22no—
235#451C22×C3114yescomplemented
236C2×C22⋊C8C22×C3112yes—
237#399C22×C3112yes—
238#396—22no—
239#393C22×C3112yes—
240#385—21no—
241#380C22×C3111yescharacteristic
242#379—21no—
243#328C22×C3118yescomplemented
244#323C22×C3114yes—
245C2×C31—21no—
246C2×C31—21no—
247C2×C31—22no—
248C2×C31—22no—
249C2×C31—44no—
250C2×C31C2×#45111yescharacteristic
251C2×C31#301911yescharacteristic
252C2×C31#302611yescharacteristic
253C25D4×C3111yescharacteristic
254C22×Q8—21no—
255C22×Q8D4×C3112yes—
256C22×Q8C23×C3111yescharacteristic
257C23×C4—21no—
258C23×C4—21no—
259C23×C4D4×C3111yescharacteristic
260C23×C4C23×C3111yescharacteristic
261C2×Q16—24no—
262C22×C8—22no—
263C22⋊Q8—28no—
264C22⋊Q8—28no—
265C22⋊Q8—24no—
266C22⋊Q8—28no—
267C22⋊Q8—24no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270C22⋊Q8—28no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8D4×C3114yes—
274C22⋊Q8C23×C3114yes—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4D4×C3112yes—
282C2×C4⋊C4C23×C3111yescharacteristic
283C2×C22⋊C4—22no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4D4×C3112yes—
294C2×C22⋊C4C23×C3112yes—
295#107—24no—
296#103—24no—
297#103—24no—
298C22⋊C8—22no—
299C22⋊C8C23×C3114yes—
300#95—22no—
301#95C23×C3112yes—
302C31#1828711yescharacteristic, direct product factor, Sylow
303C24—21no—
304C24—21no—
305C24—22no—
306C24—81no—
307C24—81no—
308C24Q16×C3114yescomplemented
309C24C2×D4×C3112yes—
310C24C2×D4×C3111yescharacteristic
311C2×Q8—24no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—81no—
315C2×Q8—82no—
316C2×Q8—82no—
317C2×Q8C2×D4×C3114yes—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—81no—
328C22×C4—81no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4C2×D4×C3112yes—
332C22×C4C2×D4×C3111yescharacteristic
333C22×C4C2×D4×C3112yes—
334C22×C4C2×D4×C3112yes—
335C22×C4C24×C3111yescharacteristic
336Q16—84no—
337C2×C8—24no—
338C2×C8—82no—
339C4⋊C4—24no—
340C4⋊C4—28no—
341C4⋊C4—24no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—42no—
346C4⋊C4—81no—
347C4⋊C4—82no—
348C4⋊C4C2×D4×C3114yes—
349C22⋊C4—28no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—42no—
357C22⋊C4—82no—
358C22⋊C4—82no—
359C23—24no—
360C23—22no—
361C23—24no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23C31×#12011yescharacteristic
374C23C31×#12011yescharacteristic
375C23C2×Q16×C3114yes—
376C23C2×Q16×C3112yes—
377C23C31×#13712yes—
378C23C22×D4×C3111yescharacteristic
379Q8—44no—
380Q8—44no—
381Q8—82no—
382Q8—84no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4C31×#12012yes—
405C2×C4C22×D4×C3112yes—
406C8—44no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—24no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—48no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—84no—
422C22C31×#45112yes—
423C22C31×#45112yes—
424C22C2×C31×#12011yescharacteristic
425C22C22×Q16×C3111yescharacteristic
426C22C2×C31×#13711yescharacteristic
427C4—22no—
428C4—22no—
429C4—42no—
430C4—44no—
431C4—44no—
432C4—82no—
433C4—81no—
434C4—81no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—22no—
439C2—44no—
440C2C2×C31×#45111yescharacteristic
441C2C31×#301911yescharacteristic
442C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC25×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×#3189C2semidirect
4. C31×#1614C2semidirect
5. C31×#1602C2semidirect
6. C31×#1520C2semidirect
19. C31×#484C22semidirect
22. C31×#451C22semidirect
30. C31×#328C22semidirect
86. C24×C31Q16semidirect
137. #18287C31direct (N × H)
187. #3189C2×C31semidirect
189. #1614C2×C31semidirect
190. #1602C2×C31semidirect
191. #1520C2×C31semidirect
232. #484C22×C31semidirect
235. #451C22×C31semidirect
243. #328C22×C31semidirect
302. C31#18287direct (N × H)
308. C24Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C31×#31892
C31×#26262
C31×#16142
C31×#16022
C31×#15202
C2×C31×#3232
#1828731