Finite Group Databasebeta

← C31×#19177 #21475936

Subgroups — C31×#19177 #21475936

Order 7936.

650 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3141C211yesmaximal, characteristic
2C31×#3103C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4Q8×M16×C31C211yesmaximal, characteristic, complemented
5C31×#1702C212yesmaximal, complemented
6C31×#1700C212yesmaximal, complemented
7C31×#1682C212yesmaximal, complemented
8C31×#1680C212yesmaximal, complemented
9C31×#1565C211yesmaximal, characteristic, complemented
10C31×#1549C211yesmaximal, characteristic, complemented
11C31×#1547C211yesmaximal, characteristic
12C22×Q16×C31—21no—
13C31×#532C2211yescharacteristic
14C2×C31×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C31C2211yescharacteristic
16C31×#489—22no—
17C31×#487C2212yes—
18C31×#486C2212yes—
19C31×#481—21no—
20C31×#475C2211yescharacteristic
21C31×#475C2211yescharacteristic
22C31×#462—21no—
23C31×#462—21no—
24C31×#462C2212yes—
25C31×#462C2212yes—
26C31×#460C2211yescharacteristic
27C31×#460C2211yescharacteristic
28C31×#448—21no—
29C31×#446—22no—
30C31×#446C2212yes—
31C8×Q8×C31C2212yes—
32C4×SD16×C31—21no—
33C4×SD16×C31—21no—
34C31×#431C2211yescharacteristic
35C31×#423—21no—
36C31×#423C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C31×#417—21no—
39C31×#417—21no—
40C2×C31×#103—21no—
41C4×M16×C31—21no—
42C4×M16×C31C2211yescharacteristic
43C31×#335C2212yes—
44C31×#334C2212yes—
45C31×#332C2212yes—
46C31×#332C2212yes—
47C31×#332C2212yes—
48C31×#331C2212yes—
49C2×#41×C31—21no—
50C22×Q8×C31—21no—
51C22×Q8×C31D411yescharacteristic
52C2×Q16×C31—22no—
53C2×Q16×C31—22no—
54C2×Q16×C31—44no—
55C2×SD16×C31—21no—
56C2×SD16×C31—21no—
57C2×M16×C31—21no—
58C2×M16×C31D411yescharacteristic
59C2×M16×C31D411yescharacteristic
60C22×C8×C31—21no—
61C31×C4⋊Q8—21no—
62C31×C4⋊Q8—21no—
63C31×C4⋊Q8—21no—
64C31×C4⋊Q8C2312yes—
65C31×C4⋊Q8C2311yescharacteristic
66C31×#127C2311yescharacteristic
67C31×#124—21no—
68C31×#121—21no—
69C31×#121—21no—
70C4×Q8×C31—21no—
71C4×Q8×C31—21no—
72C4×Q8×C31D411yescharacteristic
73C4×Q8×C31D411yescharacteristic
74C4×Q8×C31C2311yescharacteristic
75C4×Q8×C31C2311yescharacteristic
76C4×D4×C31—21no—
77C4×D4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31D411yescharacteristic
82C2×C42×C31—21no—
83C2×C42×C31C2311yescharacteristic
84C31×#106—21no—
85C31×#106—21no—
86C31×C4⋊C8—22no—
87C31×C4⋊C8—22no—
88C31×C4⋊C8—21no—
89C31×C4⋊C8—21no—
90C31×C4⋊C8C2312yes—
91C31×C4⋊C8C2312yes—
92C31×C4⋊C8C2311yescharacteristic
93C31×C4⋊C8C2311yescharacteristic
94C31×#103—21no—
95C31×#103—21no—
96C31×#103—22no—
97C31×#103—22no—
98C31×#103—22no—
99C31×#103—22no—
100C31×#102—22no—
101C31×#102—22no—
102C31×#102—21no—
103C31×#102—21no—
104C31×C22⋊C8—21no—
105C31×#97—22no—
106C31×#97D412yes—
107C4×C8×C31—22no—
108C4×C8×C31—21no—
109C4×C8×C31C2312yes—
110#41×C31—42no—
111#41×C31—42no—
112C2×Q8×C31—21no—
113C2×Q8×C31—22no—
114C2×Q8×C31—21no—
115C2×Q8×C31—22no—
116C2×Q8×C31—41no—
117C2×Q8×C31—42no—
118C2×Q8×C31—42no—
119C2×Q8×C31—41no—
120C2×Q8×C31C2×D411yescharacteristic
121C2×Q8×C31C2×D411yescharacteristic
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—41no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—41no—
129C22×C4×C31—41no—
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31#4111yescharacteristic
133Q16×C31—44no—
134Q16×C31—44no—
135SD16×C31—42no—
136SD16×C31—42no—
137M16×C31—22no—
138M16×C31—22no—
139M16×C31—42no—
140C2×C8×C31—22no—
141C2×C8×C31—21no—
142C2×C8×C31—21no—
143C2×C8×C31—22no—
144C2×C8×C31—42no—
145C2×C8×C31C2×D412yes—
146C2×C8×C31C2×D412yes—
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—21no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—41no—
157C4⋊C4×C31—41no—
158C4⋊C4×C31C2×D411yescharacteristic
159C4⋊C4×C31C2×D411yescharacteristic
160C22⋊C4×C31—41no—
161C22⋊C4×C31—41no—
162C42×C31—21no—
163C42×C31—21no—
164C42×C31—21no—
165C42×C31—21no—
166C42×C31C2×D411yescharacteristic
167C42×C31C2×D411yescharacteristic
168C42×C31#4111yescharacteristic
169C42×C31C2411yescharacteristic
170#19177C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—41no—
172C23×C31#12111yescharacteristic
173Q8×C31—21no—
174Q8×C31—21no—
175Q8×C31—21no—
176Q8×C31—42no—
177Q8×C31—41no—
178Q8×C31—42no—
179Q8×C31—41no—
180Q8×C31—42no—
181Q8×C31—82no—
182Q8×C31AGL(1,ℤ/8)12yes—
183D4×C31—41no—
184D4×C31—41no—
185D4×C31—41no—
186D4×C31—41no—
187D4×C31—81no—
188D4×C31—82no—
189C2×C4×C31—21no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—41no—
196C2×C4×C31—42no—
197C2×C4×C31—41no—
198C2×C4×C31—42no—
199C2×C4×C31—81no—
200C2×C4×C31—82no—
201C2×C4×C31—82no—
202C2×C4×C31#12111yescharacteristic
203C2×C4×C31#12111yescharacteristic
204C2×C4×C31#12111yescharacteristic
205C2×C4×C31#13512yes—
206C2×C4×C31#13712yes—
207C2×C4×C31C22×D411yescharacteristic
208C2×C4×C31C22×D411yescharacteristic
209C2×C4×C31C2×#4111yescharacteristic
210C8×C31—22no—
211C8×C31—22no—
212C8×C31—42no—
213C8×C31—42no—
214C8×C31—41no—
215C8×C31—41no—
216#3141C2×C3111yescharacteristic
217#3103C2×C3111yescharacteristic
218C2×#462C2×C3111yescharacteristic, complemented
219Q8×M16C2×C3111yescharacteristic, complemented
220#1702C2×C3112yescomplemented
221#1700C2×C3112yescomplemented
222#1682C2×C3112yescomplemented
223#1680C2×C3112yescomplemented
224#1565C2×C3111yescharacteristic, complemented
225#1549C2×C3111yescharacteristic, complemented
226#1547C2×C3111yescharacteristic
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—81no—
230C22×C31—81no—
231C22×C31—81no—
232C22×C31#46412yes—
233C22×C31C2×#12111yescharacteristic
234C4×C31—21no—
235C4×C31—22no—
236C4×C31—21no—
237C4×C31—21no—
238C4×C31—41no—
239C4×C31—41no—
240C4×C31—41no—
241C4×C31—81no—
242C4×C31—82no—
243C4×C31#46412yes—
244C4×C31C2×#13511yescharacteristic
245C4×C31C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C31C2×#13711yescharacteristic
247C4×C31#57511yescharacteristic
248C22×Q16—21no—
249#532C22×C3111yescharacteristic
250C2×C4⋊Q8C22×C3111yescharacteristic
251C2×C4×Q8C22×C3111yescharacteristic
252#489—22no—
253#487C22×C3112yes—
254#486C22×C3112yes—
255#481—21no—
256#475C22×C3111yescharacteristic
257#475C22×C3111yescharacteristic
258#462—21no—
259#462—21no—
260#462C22×C3112yes—
261#462C22×C3112yes—
262#460C22×C3111yescharacteristic
263#460C22×C3111yescharacteristic
264#448—21no—
265#446—22no—
266#446C22×C3112yes—
267C8×Q8C22×C3112yes—
268C4×SD16—21no—
269C4×SD16—21no—
270#431C22×C3111yescharacteristic
271#423—21no—
272#423C22×C3111yescharacteristic
273C2×C4⋊C8C22×C3111yescharacteristic
274#417—21no—
275#417—21no—
276C2×#103—21no—
277C4×M16—21no—
278C4×M16C22×C3111yescharacteristic
279#335C22×C3112yes—
280#334C22×C3112yes—
281#332C22×C3112yes—
282#332C22×C3112yes—
283#332C22×C3112yes—
284#331C22×C3112yes—
285C2×C31—22no—
286C2×C31—161no—
287C2×C31C2×#46411yescharacteristic
288C2×C31#305511yescharacteristic
289C2×C31#306911yescharacteristic
290C2×#41—21no—
291C22×Q8—21no—
292C22×Q8D4×C3111yescharacteristic
293C2×Q16—22no—
294C2×Q16—22no—
295C2×Q16—44no—
296C2×SD16—21no—
297C2×SD16—21no—
298C2×M16—21no—
299C2×M16D4×C3111yescharacteristic
300C2×M16D4×C3111yescharacteristic
301C22×C8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C3112yes—
306C4⋊Q8C23×C3111yescharacteristic
307#127C23×C3111yescharacteristic
308#124—21no—
309#121—21no—
310#121—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8D4×C3111yescharacteristic
314C4×Q8D4×C3111yescharacteristic
315C4×Q8C23×C3111yescharacteristic
316C4×Q8C23×C3111yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C3111yescharacteristic
323C2×C42—21no—
324C2×C42C23×C3111yescharacteristic
325#106—21no—
326#106—21no—
327C4⋊C8—22no—
328C4⋊C8—22no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8C23×C3112yes—
332C4⋊C8C23×C3112yes—
333C4⋊C8C23×C3111yescharacteristic
334C4⋊C8C23×C3111yescharacteristic
335#103—21no—
336#103—21no—
337#103—22no—
338#103—22no—
339#103—22no—
340#103—22no—
341#102—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345C22⋊C8—21no—
346#97—22no—
347#97D4×C3112yes—
348C4×C8—22no—
349C4×C8—21no—
350C4×C8C23×C3112yes—
351C31#1917711yescharacteristic, direct product factor, Sylow
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8C2×D4×C3111yescharacteristic
363C2×Q8C2×D4×C3111yescharacteristic
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4C2×D4×C3111yescharacteristic
373C22×C4C2×D4×C3111yescharacteristic
374C22×C4#41×C3111yescharacteristic
375Q16—44no—
376Q16—44no—
377SD16—42no—
378SD16—42no—
379M16—22no—
380M16—22no—
381M16—42no—
382C2×C8—22no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8C2×D4×C3112yes—
388C2×C8C2×D4×C3112yes—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4C2×D4×C3111yescharacteristic
401C4⋊C4C2×D4×C3111yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42C2×D4×C3111yescharacteristic
409C42C2×D4×C3111yescharacteristic
410C42#41×C3111yescharacteristic
411C42C24×C3111yescharacteristic
412C23—41no—
413C23C31×#12111yescharacteristic
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—41no—
419Q8—42no—
420Q8—41no—
421Q8—42no—
422Q8—82no—
423Q8C31×AGL(1,ℤ/8)12yes—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—81no—
429D4—82no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4C31×#12111yescharacteristic
444C2×C4C31×#12111yescharacteristic
445C2×C4C31×#12111yescharacteristic
446C2×C4C31×#13512yes—
447C2×C4C31×#13712yes—
448C2×C4C22×D4×C3111yescharacteristic
449C2×C4C22×D4×C3111yescharacteristic
450C2×C4C2×#41×C3111yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22C31×#46412yes—
463C22C2×C31×#12111yescharacteristic
464C4—21no—
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—82no—
473C4C31×#46412yes—
474C4C2×C31×#13511yescharacteristic
475C4C2×C31×AGL(1,ℤ/8)11yescharacteristic
476C4C2×C31×#13711yescharacteristic
477C4C31×#57511yescharacteristic
478C2—22no—
479C2—161no—
480C2C2×C31×#46411yescharacteristic
481C2C31×#305511yescharacteristic
482C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
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
3. C2×C31×#462C2semidirect
4. Q8×M16×C31C2semidirect
5. C31×#1702C2semidirect
6. C31×#1700C2semidirect
7. C31×#1682C2semidirect
8. C31×#1680C2semidirect
9. C31×#1565C2semidirect
10. C31×#1549C2semidirect
170. #19177C31direct (N × H)
218. C2×#462C2×C31semidirect
219. Q8×M16C2×C31semidirect
220. #1702C2×C31semidirect
221. #1700C2×C31semidirect
222. #1682C2×C31semidirect
223. #1680C2×C31semidirect
224. #1565C2×C31semidirect
225. #1549C2×C31semidirect
351. C31#19177direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31412
C31×#31032
C2×C31×#4622
Q8×M16×C312
C31×#17022
C31×#17002
C31×#16822
C31×#16802
C31×#15652
C31×#15492
C31×#15472
#1917731