Finite Group Databasebeta

← C31×#18365 #21475124

Subgroups — C31×#18365 #21475124

Order 7936.

862 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3507C211yesmaximal, characteristic
2C31×#3236C211yesmaximal, characteristic, complemented
3C31×#3234C211yesmaximal, characteristic
4C31×#2634C211yesmaximal, characteristic, complemented
5C31×#1615C214yesmaximal, complemented
6C31×#1609C214yesmaximal, complemented
7C31×#1515C211yesmaximal, characteristic, complemented
8C31×#1514C211yesmaximal, characteristic
9C31×#1467C211yesmaximal, characteristic, complemented
10C31×#559—21no—
11C31×#557—21no—
12C31×#556—21no—
13C31×#556—22no—
14C31×#554—21no—
15C31×#552—22no—
16C31×#539C2214yes—
17C31×#536—21no—
18C31×#533C2211yescharacteristic
19C31×#532C2211yescharacteristic
20C31×#529—22no—
21C2×C31×#125C2211yescharacteristic
22C31×#520—21no—
23C2×C4×Q8×C31C2211yescharacteristic
24C31×#501—21no—
25C31×#501—21no—
26C31×#491—21no—
27C31×#490—21no—
28C31×#484C2212yes—
29C31×#483C2212yes—
30C31×#481C2212yes—
31C31×#480C2212yes—
32C31×#479—22no—
33C31×#478—22no—
34C31×#432C2211yescharacteristic
35C31×#432C2211yescharacteristic
36C31×#400—21no—
37C31×#400C2212yes—
38C31×#398C2212yes—
39C31×#395—21no—
40C31×#387—22no—
41C31×#383C2211yescharacteristic
42C31×#328C2214yes—
43C31×#327C2214yes—
44C31×#324C2214yes—
45C2×#41×C31—21no—
46C22×Q8×C31D411yescharacteristic
47C31×C4⋊Q8—22no—
48C31×C4⋊Q8D411yescharacteristic
49C31×C4⋊Q8D411yescharacteristic
50C31×C4⋊Q8D411yescharacteristic
51C31×#127D411yescharacteristic
52C31×#126—24no—
53C31×#126—24no—
54C31×#125—22no—
55C31×#125—24no—
56C31×#125—21no—
57C31×#125—21no—
58C31×#125—21no—
59C31×#125—21no—
60C31×#125—21no—
61C31×#124—22no—
62C31×#124—22no—
63C31×#124—21no—
64C31×#123—24no—
65C31×#123—24no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8—22no—
68C31×C22⋊Q8—24no—
69C31×C22⋊Q8—21no—
70C31×C22⋊Q8C2312yes—
71C31×#121—21no—
72C31×#121C2312yes—
73C4×Q8×C31—22no—
74C4×Q8×C31—22no—
75C4×Q8×C31—21no—
76C4×Q8×C31—21no—
77C4×Q8×C31—21no—
78C4×Q8×C31—21no—
79C4×Q8×C31—21no—
80C4×Q8×C31D412yes—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—24no—
84C4×D4×C31—21no—
85C4×D4×C31D412yes—
86C31×#117—22no—
87C31×#117—24no—
88C31×#117—21no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2312yes—
97C2×C42×C31D412yes—
98C2×C42×C31C2311yescharacteristic
99C31×#107—22no—
100C31×#107—22no—
101C31×#106—22no—
102C31×#106—22no—
103C31×C4⋊C8—21no—
104C31×C4⋊C8—21no—
105C31×#103—22no—
106C31×#103—22no—
107C31×#102—22no—
108C31×#102—22no—
109C31×C22⋊C8C2312yes—
110C31×C22⋊C8C2312yes—
111C31×#97—21no—
112C31×#97—21no—
113C31×#95—21no—
114C31×#95—22no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—21no—
118C31×#95C2312yes—
119#41×C31—44no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—42no—
125C2×Q8×C31C2×D412yes—
126C2×D4×C31—22no—
127C2×D4×C31—21no—
128C2×D4×C31—21no—
129C2×D4×C31C2×D412yes—
130C22×C4×C31—24no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2411yescharacteristic
140C2×C8×C31—22no—
141C2×C8×C31—22no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—24no—
144C4⋊C4×C31—24no—
145C4⋊C4×C31—21no—
146C4⋊C4×C31—21no—
147C4⋊C4×C31—21no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—44no—
160C4⋊C4×C31—41no—
161C4⋊C4×C31—41no—
162C4⋊C4×C31—41no—
163C4⋊C4×C31—41no—
164C4⋊C4×C31C2×D412yes—
165C4⋊C4×C31C2×D412yes—
166C22⋊C4×C31—24no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—22no—
172C42×C31—24no—
173C42×C31—22no—
174C42×C31—22no—
175C42×C31—22no—
176C42×C31C2×D411yescharacteristic
177C42×C31C2×D411yescharacteristic
178C42×C31C2×D411yescharacteristic
179C42×C31C2×D411yescharacteristic
180#18365C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—22no—
182C23×C31C22×D411yescharacteristic
183Q8×C31—42no—
184Q8×C31—42no—
185Q8×C31—42no—
186Q8×C31—42no—
187Q8×C31—42no—
188D4×C31—42no—
189D4×C31—42no—
190D4×C31—42no—
191D4×C31—44no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—41no—
201C2×C4×C31—41no—
202C2×C4×C31—44no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—84no—
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#12011yescharacteristic
215C2×C4×C31#12011yescharacteristic
216C2×C4×C31C22×D411yescharacteristic
217C2×C4×C31C22×D411yescharacteristic
218C8×C31—42no—
219C8×C31—42no—
220#3507C2×C3111yescharacteristic
221#3236C2×C3111yescharacteristic, complemented
222#3234C2×C3111yescharacteristic
223#2634C2×C3111yescharacteristic, complemented
224#1615C2×C3114yescomplemented
225#1609C2×C3114yescomplemented
226#1515C2×C3111yescharacteristic, complemented
227#1514C2×C3111yescharacteristic
228#1467C2×C3111yescharacteristic, complemented
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31C2×#12011yescharacteristic
235C22×C31#57512yes—
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—42no—
243C4×C31—42no—
244C4×C31—42no—
245C4×C31—42no—
246C4×C31—42no—
247C4×C31—82no—
248C4×C31—81no—
249C4×C31—81no—
250#559—21no—
251#557—21no—
252#556—21no—
253#556—22no—
254#554—21no—
255#552—22no—
256#539C22×C3114yes—
257#536—21no—
258#533C22×C3111yescharacteristic
259#532C22×C3111yescharacteristic
260#529—22no—
261C2×#125C22×C3111yescharacteristic
262#520—21no—
263C2×C4×Q8C22×C3111yescharacteristic
264#501—21no—
265#501—21no—
266#491—21no—
267#490—21no—
268#484C22×C3112yes—
269#483C22×C3112yes—
270#481C22×C3112yes—
271#480C22×C3112yes—
272#479—22no—
273#478—22no—
274#432C22×C3111yescharacteristic
275#432C22×C3111yescharacteristic
276#400—21no—
277#400C22×C3112yes—
278#398C22×C3112yes—
279#395—21no—
280#387—22no—
281#383C22×C3111yescharacteristic
282#328C22×C3114yes—
283#327C22×C3114yes—
284#324C22×C3114yes—
285C2×C31—22no—
286C2×C31—82no—
287C2×C31#300511yescharacteristic
288C2×C31#302011yescharacteristic
289C2×C31#302811yescharacteristic
290C2×#41—21no—
291C22×Q8D4×C3111yescharacteristic
292C4⋊Q8—22no—
293C4⋊Q8D4×C3111yescharacteristic
294C4⋊Q8D4×C3111yescharacteristic
295C4⋊Q8D4×C3111yescharacteristic
296#127D4×C3111yescharacteristic
297#126—24no—
298#126—24no—
299#125—22no—
300#125—24no—
301#125—21no—
302#125—21no—
303#125—21no—
304#125—21no—
305#125—21no—
306#124—22no—
307#124—22no—
308#124—21no—
309#123—24no—
310#123—24no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314C22⋊Q8—21no—
315C22⋊Q8C23×C3112yes—
316#121—21no—
317#121C23×C3112yes—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8D4×C3112yes—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—24no—
329C4×D4—21no—
330C4×D4D4×C3112yes—
331#117—22no—
332#117—24no—
333#117—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4D4×C3111yescharacteristic
339C2×C4⋊C4C23×C3111yescharacteristic
340C2×C4⋊C4C23×C3111yescharacteristic
341C2×C4⋊C4C23×C3112yes—
342C2×C42D4×C3112yes—
343C2×C42C23×C3111yescharacteristic
344#107—22no—
345#107—22no—
346#106—22no—
347#106—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350#103—22no—
351#103—22no—
352#102—22no—
353#102—22no—
354C22⋊C8C23×C3112yes—
355C22⋊C8C23×C3112yes—
356#97—21no—
357#97—21no—
358#95—21no—
359#95—21no—
360#95—22no—
361#95—22no—
362#95—22no—
363#95C23×C3112yes—
364C31#1836511yescharacteristic, direct product factor, Sylow
365#41—44no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8C2×D4×C3112yes—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C2×D4×C3112yes—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4C2×D4×C3112yes—
382C22×C4C2×D4×C3111yescharacteristic
383C22×C4C2×D4×C3112yes—
384C22×C4C2×D4×C3111yescharacteristic
385C22×C4C24×C3111yescharacteristic
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—44no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4C2×D4×C3112yes—
411C4⋊C4C2×D4×C3112yes—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—22no—
422C42C2×D4×C3111yescharacteristic
423C42C2×D4×C3111yescharacteristic
424C42C2×D4×C3111yescharacteristic
425C42C2×D4×C3111yescharacteristic
426C23—22no—
427C23C22×D4×C3111yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—44no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—84no—
457C2×C4C31×#12011yescharacteristic
458C2×C4C31×#12011yescharacteristic
459C2×C4C31×#12011yescharacteristic
460C2×C4C31×#12011yescharacteristic
461C2×C4C22×D4×C3111yescharacteristic
462C2×C4C22×D4×C3111yescharacteristic
463C8—42no—
464C8—42no—
465C22—21no—
466C22—21no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C2×C31×#12011yescharacteristic
471C22C31×#57512yes—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—82no—
484C4—81no—
485C4—81no—
486C2—22no—
487C2—82no—
488C2C31×#300511yescharacteristic
489C2C31×#302011yescharacteristic
490C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#532C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3236C2semidirect
4. C31×#2634C2semidirect
5. C31×#1615C2semidirect
6. C31×#1609C2semidirect
7. C31×#1515C2semidirect
9. C31×#1467C2semidirect
180. #18365C31direct (N × H)
221. #3236C2×C31semidirect
223. #2634C2×C31semidirect
224. #1615C2×C31semidirect
225. #1609C2×C31semidirect
226. #1515C2×C31semidirect
228. #1467C2×C31semidirect
364. C31#18365direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35072
C31×#32362
C31×#32342
C31×#26342
C31×#16152
C31×#16092
C31×#15152
C31×#15142
C31×#14672
#1836531