Finite Group Databasebeta

← C31×#19066 #21475825

Subgroups — C31×#19066 #21475825

Order 7936.

852 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3550C211yesmaximal, characteristic
2C31×#3237C211yesmaximal, characteristic, complemented
3C31×#3216C211yesmaximal, characteristic
4C31×#3162C211yesmaximal, characteristic, complemented
5C31×#1664C214yesmaximal, complemented
6C31×#1660C214yesmaximal, complemented
7C31×#1537C211yesmaximal, characteristic, complemented
8C31×#1531C211yesmaximal, characteristic, complemented
9C31×#1530C211yesmaximal, characteristic
10C31×#563C2214yes—
11C31×#559—21no—
12Q82×C31—21no—
13C31×#556—21no—
14C31×#556—21no—
15D4×Q8×C31—21no—
16D4×Q8×C31—21no—
17C31×#542—22no—
18C31×#542—22no—
19C31×#536—22no—
20C31×#533C2211yescharacteristic
21C31×#533C2211yescharacteristic
22C31×#533C2211yescharacteristic
23C31×#532C2211yescharacteristic
24C31×#501—21no—
25C31×#501—21no—
26C31×#501C2212yes—
27C31×#501C2212yes—
28C31×#501C2212yes—
29C31×#497C2212yes—
30C31×#491C2212yes—
31C31×#489C2212yes—
32C31×#485—22no—
33C31×#477—21no—
34C31×#475—21no—
35C31×#462—21no—
36C31×#460—21no—
37C31×#452—22no—
38C31×#432C2211yescharacteristic
39C31×#432C2211yescharacteristic
40C31×#427—22no—
41C2×C31×#97C2211yescharacteristic
42C31×#330C2214yes—
43C31×#330C2214yes—
44C31×#329C2214yes—
45C2×#41×C31D412yes—
46C22×Q8×C31—22no—
47C2×Q16×C31—22no—
48C2×SD16×C31—22no—
49C22×C8×C31—21no—
50C31×C4⋊Q8—22no—
51C31×C4⋊Q8—22no—
52C31×C4⋊Q8—24no—
53C31×C4⋊Q8D411yescharacteristic
54C31×C4⋊Q8D411yescharacteristic
55C31×C4⋊Q8D411yescharacteristic
56C31×C4⋊Q8D411yescharacteristic
57C31×C4⋊Q8D411yescharacteristic
58C31×C4⋊Q8C2311yescharacteristic
59C31×C4⋊Q8C2311yescharacteristic
60C31×#127D411yescharacteristic
61C31×#126—24no—
62C31×#126—24no—
63C31×#125—21no—
64C31×#125C2312yes—
65C31×#125C2312yes—
66C31×#124—24no—
67C31×#124—22no—
68C31×#124—22no—
69C31×#124C2312yes—
70C31×#123—24no—
71C31×#123—24no—
72C31×C22⋊Q8—22no—
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—21no—
75C31×C22⋊Q8—21no—
76C31×C22⋊Q8—21no—
77C31×C22⋊Q8—21no—
78C31×C22⋊Q8—24no—
79C31×C22⋊Q8—24no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×#121—21no—
83C31×#121—21no—
84C4×Q8×C31—22no—
85C4×Q8×C31—22no—
86C4×Q8×C31—21no—
87C4×Q8×C31—21no—
88C4×Q8×C31—21no—
89C4×Q8×C31—21no—
90C4×Q8×C31—21no—
91C4×Q8×C31—21no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—21no—
95C4×D4×C31—21no—
96C31×#117—22no—
97C31×#117—21no—
98C31×#117D412yes—
99C31×#117D412yes—
100C2×C42×C31C2311yescharacteristic
101C31×#107—22no—
102C31×#107—22no—
103C31×#107—22no—
104C31×#106—22no—
105C31×#106—22no—
106C31×#106—22no—
107C31×C4⋊C8—21no—
108C31×C4⋊C8—21no—
109C31×#103—22no—
110C31×#103—22no—
111C31×#103—22no—
112C31×#102—22no—
113C31×C22⋊C8—21no—
114C31×C22⋊C8—21no—
115C31×#97—21no—
116C31×#97C2312yes—
117C31×#97C2312yes—
118C31×#97C2312yes—
119#41×C31—82no—
120C2×Q8×C31—24no—
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31—21no—
125C2×Q8×C31—21no—
126C2×Q8×C31—21no—
127C2×Q8×C31—84no—
128C2×Q8×C31C2×D412yes—
129C2×D4×C31—22no—
130C2×D4×C31—21no—
131C2×D4×C31—21no—
132C2×D4×C31C2×D412yes—
133C22×C4×C31—24no—
134C22×C4×C31—22no—
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138Q16×C31—82no—
139SD16×C31—82no—
140C2×C8×C31—24no—
141C2×C8×C31—22no—
142C2×C8×C31—22no—
143C2×C8×C31—22no—
144C4⋊C4×C31—24no—
145C4⋊C4×C31—24no—
146C4⋊C4×C31—21no—
147C4⋊C4×C31—21no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—41no—
161C4⋊C4×C31—41no—
162C4⋊C4×C31C2×D412yes—
163C4⋊C4×C31C2×D412yes—
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—
172C22⋊C4×C31—22no—
173C22⋊C4×C31—41no—
174C42×C31—24no—
175C42×C31—22no—
176C42×C31—22no—
177C42×C31—41no—
178C42×C31C2×D411yescharacteristic
179C42×C31C2×D411yescharacteristic
180C42×C31C2×D411yescharacteristic
181C42×C31C2411yescharacteristic
182#19066C3111yesmaximal, characteristic, direct product factor, Sylow
183C23×C31—22no—
184C23×C31#12011yescharacteristic
185Q8×C31—42no—
186Q8×C31—42no—
187Q8×C31—42no—
188Q8×C31—42no—
189Q8×C31—41no—
190Q8×C31—41no—
191Q8×C31—42no—
192Q8×C31—42no—
193Q8×C31—84no—
194D4×C31—42no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—82no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—44no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—84no—
210C2×C4×C31#12011yescharacteristic
211C2×C4×C31#12011yescharacteristic
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31C22×D411yescharacteristic
214C2×C4×C31C22×D411yescharacteristic
215C2×C4×C31C22×D411yescharacteristic
216C8×C31—24no—
217C8×C31—42no—
218C8×C31—42no—
219#3550C2×C3111yescharacteristic
220#3237C2×C3111yescharacteristic, complemented
221#3216C2×C3111yescharacteristic
222#3162C2×C3111yescharacteristic, complemented
223#1664C2×C3114yescomplemented
224#1660C2×C3114yescomplemented
225#1537C2×C3111yescharacteristic, complemented
226#1531C2×C3111yescharacteristic, complemented
227#1530C2×C3111yescharacteristic
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31C2×#12011yescharacteristic
235C4×C31—21no—
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—42no—
241C4×C31—42no—
242C4×C31—42no—
243C4×C31—42no—
244C4×C31—42no—
245C4×C31—81no—
246C4×C31—81no—
247C4×C31#45612yes—
248#563C22×C3114yes—
249#559—21no—
250Q82—21no—
251#556—21no—
252#556—21no—
253D4×Q8—21no—
254D4×Q8—21no—
255#542—22no—
256#542—22no—
257#536—22no—
258#533C22×C3111yescharacteristic
259#533C22×C3111yescharacteristic
260#533C22×C3111yescharacteristic
261#532C22×C3111yescharacteristic
262#501—21no—
263#501—21no—
264#501C22×C3112yes—
265#501C22×C3112yes—
266#501C22×C3112yes—
267#497C22×C3112yes—
268#491C22×C3112yes—
269#489C22×C3112yes—
270#485—22no—
271#477—21no—
272#475—21no—
273#462—21no—
274#460—21no—
275#452—22no—
276#432C22×C3111yescharacteristic
277#432C22×C3111yescharacteristic
278#427—22no—
279C2×#97C22×C3111yescharacteristic
280#330C22×C3114yes—
281#330C22×C3114yes—
282#329C22×C3114yes—
283C2×C31—41no—
284C2×C31—82no—
285C2×C31C2×#45611yescharacteristic
286C2×C31#301911yescharacteristic
287C2×C31#302011yescharacteristic
288C2×#41D4×C3112yes—
289C22×Q8—22no—
290C2×Q16—22no—
291C2×SD16—22no—
292C22×C8—21no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8—24no—
296C4⋊Q8D4×C3111yescharacteristic
297C4⋊Q8D4×C3111yescharacteristic
298C4⋊Q8D4×C3111yescharacteristic
299C4⋊Q8D4×C3111yescharacteristic
300C4⋊Q8D4×C3111yescharacteristic
301C4⋊Q8C23×C3111yescharacteristic
302C4⋊Q8C23×C3111yescharacteristic
303#127D4×C3111yescharacteristic
304#126—24no—
305#126—24no—
306#125—21no—
307#125C23×C3112yes—
308#125C23×C3112yes—
309#124—24no—
310#124—22no—
311#124—22no—
312#124C23×C3112yes—
313#123—24no—
314#123—24no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325#121—21no—
326#121—21no—
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×D4—22no—
336C4×D4—22no—
337C4×D4—21no—
338C4×D4—21no—
339#117—22no—
340#117—21no—
341#117D4×C3112yes—
342#117D4×C3112yes—
343C2×C42C23×C3111yescharacteristic
344#107—22no—
345#107—22no—
346#107—22no—
347#106—22no—
348#106—22no—
349#106—22no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352#103—22no—
353#103—22no—
354#103—22no—
355#102—22no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358#97—21no—
359#97C23×C3112yes—
360#97C23×C3112yes—
361#97C23×C3112yes—
362C31#1906611yescharacteristic, direct product factor, Sylow
363#41—82no—
364C2×Q8—24no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—84no—
372C2×Q8C2×D4×C3112yes—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4C2×D4×C3112yes—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4C2×D4×C3111yescharacteristic
380C22×C4C2×D4×C3111yescharacteristic
381C22×C4C2×D4×C3111yescharacteristic
382Q16—82no—
383SD16—82no—
384C2×C8—24no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C3112yes—
407C4⋊C4C2×D4×C3112yes—
408C4⋊C4C2×D4×C3112yes—
409C4⋊C4C2×D4×C3112yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—41no—
418C42—24no—
419C42—22no—
420C42—22no—
421C42—41no—
422C42C2×D4×C3111yescharacteristic
423C42C2×D4×C3111yescharacteristic
424C42C2×D4×C3111yescharacteristic
425C42C24×C3111yescharacteristic
426C23—22no—
427C23C31×#12011yescharacteristic
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—42no—
435Q8—42no—
436Q8—84no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—82no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—84no—
453C2×C4C31×#12011yescharacteristic
454C2×C4C31×#12011yescharacteristic
455C2×C4C31×#12011yescharacteristic
456C2×C4C22×D4×C3111yescharacteristic
457C2×C4C22×D4×C3111yescharacteristic
458C2×C4C22×D4×C3111yescharacteristic
459C8—24no—
460C8—42no—
461C8—42no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22C2×C31×#12011yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—81no—
481C4C31×#45612yes—
482C2—41no—
483C2—82no—
484C2C2×C31×#45611yescharacteristic
485C2C31×#301911yescharacteristic
486C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ 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×#3237C2semidirect
4. C31×#3162C2semidirect
5. C31×#1664C2semidirect
6. C31×#1660C2semidirect
7. C31×#1537C2semidirect
8. C31×#1531C2semidirect
182. #19066C31direct (N × H)
220. #3237C2×C31semidirect
222. #3162C2×C31semidirect
223. #1664C2×C31semidirect
224. #1660C2×C31semidirect
225. #1537C2×C31semidirect
226. #1531C2×C31semidirect
362. C31#19066direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35502
C31×#32372
C31×#32162
C31×#31622
C31×#16642
C31×#16602
C31×#15372
C31×#15312
C31×#15302
#1906631