Finite Group Databasebeta

← C31×#18183 #21474942

Subgroups — C31×#18183 #21474942

Order 7936.

926 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3507C211yesmaximal, characteristic
2C31×#3113C211yesmaximal, characteristic, complemented
3C31×#3112C211yesmaximal, characteristic
4C31×#2399C211yesmaximal, characteristic, complemented
5C31×#1609C214yesmaximal, complemented
6C31×#1603C214yesmaximal, complemented
7C31×#1506C211yesmaximal, characteristic, complemented
8C31×#1505C211yesmaximal, 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—
21C31×#520—21no—
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C31×#483C2212yes—
25C31×#480C2212yes—
26C31×#477—21no—
27C31×#475—21no—
28C31×#462—21no—
29C31×#460—21no—
30C31×#451C2212yes—
31C31×#448C2212yes—
32C31×#441—22no—
33C31×#440—22no—
34C31×#432C2211yescharacteristic
35C31×#432C2211yescharacteristic
36C31×#398—21no—
37C31×#398C2212yes—
38C31×#395—21no—
39C31×#395C2212yes—
40C4×C4⋊C4×C31—22no—
41C31×#376C2211yescharacteristic
42C31×#328C2214yes—
43C31×#327C2214yes—
44C31×#324C2214yes—
45C2×#41×C31—21no—
46C22×Q8×C31D411yescharacteristic
47C22×Q8×C31C2311yescharacteristic
48C2×Q16×C31—22no—
49C2×SD16×C31—22no—
50C31×C4⋊Q8—22no—
51C31×C4⋊Q8D411yescharacteristic
52C31×C4⋊Q8D411yescharacteristic
53C31×C4⋊Q8D411yescharacteristic
54C31×#127D411yescharacteristic
55C31×#126—24no—
56C31×#126—24no—
57C31×#125—22no—
58C31×#125—24no—
59C31×#125—21no—
60C31×#124—22no—
61C31×#124—22no—
62C31×#124—21no—
63C31×#123—24no—
64C31×#123—24no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8—24no—
68C31×C22⋊Q8—21no—
69C31×C22⋊Q8C2312yes—
70C31×#121—21no—
71C31×#121C2312yes—
72C4×Q8×C31—22no—
73C4×Q8×C31—22no—
74C4×Q8×C31—21no—
75C4×Q8×C31—21no—
76C4×Q8×C31—21no—
77C4×Q8×C31—21no—
78C4×Q8×C31—21no—
79C4×Q8×C31—21no—
80C4×Q8×C31—21no—
81C4×Q8×C31—21no—
82C4×Q8×C31—21no—
83C4×Q8×C31D412yes—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—24no—
87C4×D4×C31—21no—
88C4×D4×C31D412yes—
89C31×#117—22no—
90C31×#117—24no—
91C31×#117—21no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2312yes—
99C2×C42×C31—21no—
100C2×C42×C31—21no—
101C2×C42×C31D412yes—
102C2×C42×C31C2311yescharacteristic
103C31×#107—22no—
104C31×#106—22no—
105C31×C4⋊C8—21no—
106C31×C4⋊C8—21no—
107C31×#103—22no—
108C31×#103—22no—
109C31×#103—22no—
110C31×#102—22no—
111C31×C22⋊C8C2312yes—
112C31×C22⋊C8C2312yes—
113C31×#97—21no—
114C31×#97—21no—
115C31×#95—22no—
116C31×#95—21no—
117C31×#95—22no—
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—21no—
125C2×Q8×C31—21no—
126C2×Q8×C31—42no—
127C2×Q8×C31—42no—
128C2×Q8×C31C2×D412yes—
129C2×D4×C31—22no—
130C2×D4×C31—21no—
131C2×D4×C31—21no—
132C2×D4×C31C2×D412yes—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—24no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2411yescharacteristic
143Q16×C31—44no—
144SD16×C31—44no—
145C2×C8×C31—22no—
146C2×C8×C31—22no—
147C4⋊C4×C31—24no—
148C4⋊C4×C31—24no—
149C4⋊C4×C31—24no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—44no—
163C4⋊C4×C31—44no—
164C4⋊C4×C31—41no—
165C4⋊C4×C31—41no—
166C4⋊C4×C31C2×D412yes—
167C4⋊C4×C31C2×D412yes—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—22no—
173C22⋊C4×C31—22no—
174C42×C31—24no—
175C42×C31—24no—
176C42×C31—22no—
177C42×C31—22no—
178C42×C31—22no—
179C42×C31—41no—
180C42×C31—41no—
181C42×C31C2×D411yescharacteristic
182C42×C31C2×D411yescharacteristic
183C42×C31C2×D411yescharacteristic
184C42×C31C2×D411yescharacteristic
185#18183C3111yesmaximal, characteristic, direct product factor, Sylow
186C23×C31—22no—
187C23×C31C22×D411yescharacteristic
188Q8×C31—22no—
189Q8×C31—22no—
190Q8×C31—42no—
191Q8×C31—42no—
192Q8×C31—42no—
193Q8×C31—41no—
194Q8×C31—41no—
195Q8×C31—42no—
196Q8×C31—42no—
197D4×C31—42no—
198D4×C31—42no—
199D4×C31—44no—
200D4×C31—42no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—24no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—41no—
213C2×C4×C31—44no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—84no—
222C2×C4×C31#12011yescharacteristic
223C2×C4×C31#12011yescharacteristic
224C2×C4×C31#12011yescharacteristic
225C2×C4×C31#12011yescharacteristic
226C2×C4×C31C22×D411yescharacteristic
227C2×C4×C31C22×D411yescharacteristic
228C8×C31—42no—
229C8×C31—42no—
230#3507C2×C3111yescharacteristic
231#3113C2×C3111yescharacteristic, complemented
232#3112C2×C3111yescharacteristic
233#2399C2×C3111yescharacteristic, complemented
234#1609C2×C3114yescomplemented
235#1603C2×C3114yescomplemented
236#1506C2×C3111yescharacteristic, complemented
237#1505C2×C3111yescharacteristic
238#1467C2×C3111yescharacteristic, complemented
239C22×C31—21no—
240C22×C31—21no—
241C22×C31—42no—
242C22×C31—42no—
243C22×C31—42no—
244C22×C31C2×#12011yescharacteristic
245C22×C31#57512yes—
246C4×C31—21no—
247C4×C31—21no—
248C4×C31—21no—
249C4×C31—21no—
250C4×C31—21no—
251C4×C31—44no—
252C4×C31—42no—
253C4×C31—42no—
254C4×C31—42no—
255C4×C31—42no—
256C4×C31—42no—
257C4×C31—42no—
258C4×C31—81no—
259C4×C31#45612yes—
260#559—21no—
261#557—21no—
262#556—21no—
263#556—22no—
264#554—21no—
265#552—22no—
266#539C22×C3114yes—
267#536—21no—
268#533C22×C3111yescharacteristic
269#532C22×C3111yescharacteristic
270#529—22no—
271#520—21no—
272C2×C4×Q8C22×C3111yescharacteristic
273C2×C4×Q8C22×C3111yescharacteristic
274#483C22×C3112yes—
275#480C22×C3112yes—
276#477—21no—
277#475—21no—
278#462—21no—
279#460—21no—
280#451C22×C3112yes—
281#448C22×C3112yes—
282#441—22no—
283#440—22no—
284#432C22×C3111yescharacteristic
285#432C22×C3111yescharacteristic
286#398—21no—
287#398C22×C3112yes—
288#395—21no—
289#395C22×C3112yes—
290C4×C4⋊C4—22no—
291#376C22×C3111yescharacteristic
292#328C22×C3114yes—
293#327C22×C3114yes—
294#324C22×C3114yes—
295C2×C31—22no—
296C2×C31—82no—
297C2×C31#300511yescharacteristic
298C2×C31C2×#45611yescharacteristic
299C2×C31#302511yescharacteristic
300C2×#41—21no—
301C22×Q8D4×C3111yescharacteristic
302C22×Q8C23×C3111yescharacteristic
303C2×Q16—22no—
304C2×SD16—22no—
305C4⋊Q8—22no—
306C4⋊Q8D4×C3111yescharacteristic
307C4⋊Q8D4×C3111yescharacteristic
308C4⋊Q8D4×C3111yescharacteristic
309#127D4×C3111yescharacteristic
310#126—24no—
311#126—24no—
312#125—22no—
313#125—24no—
314#125—21no—
315#124—22no—
316#124—22no—
317#124—21no—
318#123—24no—
319#123—24no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—21no—
324C22⋊Q8C23×C3112yes—
325#121—21no—
326#121C23×C3112yes—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8D4×C3112yes—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—21no—
343C4×D4D4×C3112yes—
344#117—22no—
345#117—24no—
346#117—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4D4×C3111yescharacteristic
352C2×C4⋊C4C23×C3111yescharacteristic
353C2×C4⋊C4C23×C3112yes—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42D4×C3112yes—
357C2×C42C23×C3111yescharacteristic
358#107—22no—
359#106—22no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362#103—22no—
363#103—22no—
364#103—22no—
365#102—22no—
366C22⋊C8C23×C3112yes—
367C22⋊C8C23×C3112yes—
368#97—21no—
369#97—21no—
370#95—21no—
371#95—22no—
372#95—22no—
373#95C23×C3112yes—
374C31#1818311yescharacteristic, direct product factor, Sylow
375#41—44no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8C2×D4×C3112yes—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4C2×D4×C3112yes—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4C2×D4×C3112yes—
395C22×C4C2×D4×C3111yescharacteristic
396C22×C4C2×D4×C3111yescharacteristic
397C22×C4C2×D4×C3112yes—
398C22×C4C24×C3111yescharacteristic
399Q16—44no—
400SD16—44no—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—44no—
419C4⋊C4—44no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4C2×D4×C3112yes—
423C4⋊C4C2×D4×C3112yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C42—24no—
431C42—24no—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—41no—
436C42—41no—
437C42C2×D4×C3111yescharacteristic
438C42C2×D4×C3111yescharacteristic
439C42C2×D4×C3111yescharacteristic
440C42C2×D4×C3111yescharacteristic
441C23—22no—
442C23C22×D4×C3111yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—41no—
449Q8—41no—
450Q8—42no—
451Q8—42no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—42no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—84no—
477C2×C4C31×#12011yescharacteristic
478C2×C4C31×#12011yescharacteristic
479C2×C4C31×#12011yescharacteristic
480C2×C4C31×#12011yescharacteristic
481C2×C4C22×D4×C3111yescharacteristic
482C2×C4C22×D4×C3111yescharacteristic
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×C31×#12011yescharacteristic
491C22C31×#57512yes—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—44no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4C31×#45612yes—
506C2—22no—
507C2—82no—
508C2C31×#300511yescharacteristic
509C2C2×C31×#45611yescharacteristic
510C2C31×#302511yescharacteristic
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×#3113C2semidirect
4. C31×#2399C2semidirect
5. C31×#1609C2semidirect
6. C31×#1603C2semidirect
7. C31×#1506C2semidirect
9. C31×#1467C2semidirect
185. #18183C31direct (N × H)
231. #3113C2×C31semidirect
233. #2399C2×C31semidirect
234. #1609C2×C31semidirect
235. #1603C2×C31semidirect
236. #1506C2×C31semidirect
238. #1467C2×C31semidirect
374. C31#18183direct (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×#31132
C31×#31122
C31×#23992
C31×#16092
C31×#16032
C31×#15062
C31×#15052
C31×#14672
#1818331