Finite Group Databasebeta

← C31×#19082 #21475841

Subgroups — C31×#19082 #21475841

Order 7936.

864 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3553C211yesmaximal, characteristic, complemented
2C31×#3180C212yesmaximal, complemented
3C31×#3142C211yesmaximal, characteristic, complemented
4C31×#1664C212yesmaximal, complemented
5C31×#1663C211yesmaximal, characteristic, complemented
6C31×#1662C211yesmaximal, characteristic, complemented
7C31×#1658C211yesmaximal, characteristic, complemented
8C31×#1657C212yesmaximal, complemented
9C31×#1656C211yesmaximal, characteristic, complemented
10C31×#1524C212yesmaximal, complemented
11C2×C31×#330C211yesmaximal, characteristic, complemented
12C31×#564C2211yescharacteristic
13C31×#563C2212yes—
14C31×#562C2211yescharacteristic
15C31×#554—22no—
16C31×#553—22no—
17C31×#552—22no—
18C31×#541—22no—
19C31×#539—22no—
20C31×#539—22no—
21C31×#532C2211yescharacteristic
22C31×#529C2212yes—
23C2×C31×#125C2211yescharacteristic
24C31×#501C2212yes—
25C31×#496C2212yes—
26C31×#491C2211yescharacteristic
27C31×#491C2211yescharacteristic
28C31×#490C2211yescharacteristic
29C31×#490C2211yescharacteristic
30C31×#490C2212yes—
31C31×#489C2212yes—
32C31×#488—22no—
33C31×#466—22no—
34C31×#465—22no—
35C31×#442—22no—
36C31×#440—22no—
37C31×#417—22no—
38C4×M16×C31C2211yescharacteristic
39C2×C31×#97C2212yes—
40C31×#330C2211yescharacteristic
41C31×#330C2212yes—
42C31×#330C2212yes—
43C31×#330C2211yescharacteristic
44C31×#330C2212yes—
45C31×#329C2212yes—
46C31×#329C2212yes—
47C2×#41×C31—21no—
48C2×SD16×C31—22no—
49C2×D8×C31—22no—
50C2×M16×C31—21no—
51C22×C8×C31—22no—
52C31×C4⋊Q8—22no—
53C31×C4⋊Q8C2311yescharacteristic
54C31×#127C2311yescharacteristic
55C31×#126—22no—
56C31×#126—22no—
57C31×#126—22no—
58C31×#126—22no—
59C31×#126—22no—
60C31×#125—22no—
61C31×#125—22no—
62C31×#125—22no—
63C31×#125—22no—
64C31×#125—22no—
65C31×#125—22no—
66C31×#125D412yes—
67C31×#125C2311yescharacteristic
68C31×#125C2311yescharacteristic
69C31×#125C2312yes—
70C31×#124—21no—
71C31×#124C2312yes—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8D412yes—
84C31×#121—22no—
85C31×#121—22no—
86C31×#121—22no—
87C31×#121D412yes—
88C4×Q8×C31—22no—
89C4×Q8×C31D412yes—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31D412yes—
96C31×#117—22no—
97C31×#117—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31D412yes—
101C2×C42×C31C2311yescharacteristic
102C31×#107—22no—
103C31×#106—22no—
104C31×#103—22no—
105C31×#103—22no—
106C31×#103—22no—
107C31×#102—22no—
108C31×#102—22no—
109C31×#102—22no—
110C31×#102—22no—
111C31×#102—22no—
112C31×#97—22no—
113C31×#97C2312yes—
114C31×#97C2312yes—
115C31×#97C2311yescharacteristic
116C31×#97C2311yescharacteristic
117C4×C8×C31—21no—
118#41×C31—44no—
119C2×Q8×C31—22no—
120C2×Q8×C31—21no—
121C2×Q8×C31C2×D412yes—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—21no—
125C2×D4×C31—22no—
126C2×D4×C31—41no—
127C2×D4×C31C2×D412yes—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—41no—
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D412yes—
135SD16×C31—44no—
136D8×C31—44no—
137M16×C31—42no—
138C2×C8×C31—22no—
139C2×C8×C31—21no—
140C2×C8×C31—21no—
141C2×C8×C31—22no—
142C2×C8×C31—44no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31C2×D412yes—
160C4⋊C4×C31C2×D412yes—
161C4⋊C4×C31C2×D412yes—
162C4⋊C4×C31C2×D412yes—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—42no—
173C42×C31—22no—
174C42×C31—22no—
175C42×C31—22no—
176C42×C31C2×D411yescharacteristic
177C42×C31C2×D412yes—
178C42×C31C2411yescharacteristic
179#19082C3111yesmaximal, characteristic, direct product factor, Sylow
180C23×C31—22no—
181C23×C31—41no—
182C23×C31#12011yescharacteristic
183Q8×C31—42no—
184Q8×C31—42no—
185Q8×C31—82no—
186D4×C31—42no—
187D4×C31—42no—
188D4×C31—42no—
189D4×C31—42no—
190D4×C31—44no—
191D4×C31—82no—
192D4×C31—82no—
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—42no—
200C2×C4×C31—41no—
201C2×C4×C31—82no—
202C2×C4×C31—82no—
203C2×C4×C31—82no—
204C2×C4×C31—82no—
205C2×C4×C31—82no—
206C2×C4×C31#12012yes—
207C2×C4×C31#12011yescharacteristic
208C2×C4×C31C22×D411yescharacteristic
209C2×C4×C31C22×D412yes—
210C8×C31—24no—
211C8×C31—42no—
212C8×C31—41no—
213C8×C31—41no—
214#3553C2×C3111yescharacteristic, complemented
215#3180C2×C3112yescomplemented
216#3142C2×C3111yescharacteristic, complemented
217#1664C2×C3112yescomplemented
218#1663C2×C3111yescharacteristic, complemented
219#1662C2×C3111yescharacteristic, complemented
220#1658C2×C3111yescharacteristic, complemented
221#1657C2×C3112yescomplemented
222#1656C2×C3111yescharacteristic, complemented
223#1524C2×C3112yescomplemented
224C2×#330C2×C3111yescharacteristic, complemented
225C22×C31—22no—
226C22×C31—42no—
227C22×C31—42no—
228C22×C31—42no—
229C22×C31—81no—
230C22×C31—82no—
231C22×C31#45412yes—
232C22×C31C2×#12011yescharacteristic
233C4×C31—21no—
234C4×C31—21no—
235C4×C31—22no—
236C4×C31—22no—
237C4×C31—42no—
238C4×C31—42no—
239C4×C31—42no—
240C4×C31—42no—
241C4×C31—42no—
242C4×C31—81no—
243#564C22×C3111yescharacteristic
244#563C22×C3112yes—
245#562C22×C3111yescharacteristic
246#554—22no—
247#553—22no—
248#552—22no—
249#541—22no—
250#539—22no—
251#539—22no—
252#532C22×C3111yescharacteristic
253#529C22×C3112yes—
254C2×#125C22×C3111yescharacteristic
255#501C22×C3112yes—
256#496C22×C3112yes—
257#491C22×C3111yescharacteristic
258#491C22×C3111yescharacteristic
259#490C22×C3111yescharacteristic
260#490C22×C3111yescharacteristic
261#490C22×C3112yes—
262#489C22×C3112yes—
263#488—22no—
264#466—22no—
265#465—22no—
266#442—22no—
267#440—22no—
268#417—22no—
269C4×M16C22×C3111yescharacteristic
270C2×#97C22×C3112yes—
271#330C22×C3111yescharacteristic
272#330C22×C3112yes—
273#330C22×C3112yes—
274#330C22×C3111yescharacteristic
275#330C22×C3112yes—
276#329C22×C3112yes—
277#329C22×C3112yes—
278C2×C31—22no—
279C2×C31—82no—
280C2×C31—161no—
281C2×C31C2×#45411yescharacteristic
282C2×C31#301812yes—
283C2×#41—21no—
284C2×SD16—22no—
285C2×D8—22no—
286C2×M16—21no—
287C22×C8—22no—
288C4⋊Q8—22no—
289C4⋊Q8C23×C3111yescharacteristic
290#127C23×C3111yescharacteristic
291#126—22no—
292#126—22no—
293#126—22no—
294#126—22no—
295#126—22no—
296#125—22no—
297#125—22no—
298#125—22no—
299#125—22no—
300#125—22no—
301#125—22no—
302#125D4×C3112yes—
303#125C23×C3111yescharacteristic
304#125C23×C3111yescharacteristic
305#125C23×C3112yes—
306#124—21no—
307#124C23×C3112yes—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8D4×C3112yes—
320#121—22no—
321#121—22no—
322#121—22no—
323#121D4×C3112yes—
324C4×Q8—22no—
325C4×Q8D4×C3112yes—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4D4×C3112yes—
332#117—22no—
333#117—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4D4×C3112yes—
337C2×C42C23×C3111yescharacteristic
338#107—22no—
339#106—22no—
340#103—22no—
341#103—22no—
342#103—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#97—22no—
349#97C23×C3111yescharacteristic
350#97C23×C3111yescharacteristic
351#97C23×C3112yes—
352#97C23×C3112yes—
353C4×C8—21no—
354C31#1908211yescharacteristic, direct product factor, Sylow
355#41—44no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8C2×D4×C3112yes—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—41no—
364C2×D4C2×D4×C3112yes—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—41no—
370C22×C4C2×D4×C3111yescharacteristic
371C22×C4C2×D4×C3112yes—
372SD16—44no—
373D8—44no—
374M16—42no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—44no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4C2×D4×C3112yes—
397C4⋊C4C2×D4×C3112yes—
398C4⋊C4C2×D4×C3112yes—
399C4⋊C4C2×D4×C3112yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—42no—
410C42—22no—
411C42—22no—
412C42—22no—
413C42C2×D4×C3111yescharacteristic
414C42C2×D4×C3112yes—
415C42C24×C3111yescharacteristic
416C23—22no—
417C23—41no—
418C23C31×#12011yescharacteristic
419Q8—42no—
420Q8—42no—
421Q8—82no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—44no—
427D4—82no—
428D4—82no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4C31×#12012yes—
443C2×C4C31×#12011yescharacteristic
444C2×C4C22×D4×C3111yescharacteristic
445C2×C4C22×D4×C3112yes—
446C8—24no—
447C8—42no—
448C8—41no—
449C8—41no—
450C22—22no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—81no—
455C22—82no—
456C22C31×#45412yes—
457C22C2×C31×#12011yescharacteristic
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—81no—
468C2—22no—
469C2—82no—
470C2—161no—
471C2C2×C31×#45411yescharacteristic
472C2C31×#301812yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
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
1. C31×#3553C2semidirect
2. C31×#3180C2semidirect
3. C31×#3142C2semidirect
4. C31×#1664C2semidirect
5. C31×#1663C2semidirect
6. C31×#1662C2semidirect
7. C31×#1658C2semidirect
8. C31×#1657C2semidirect
9. C31×#1656C2semidirect
10. C31×#1524C2semidirect
11. C2×C31×#330C2semidirect
179. #19082C31direct (N × H)
214. #3553C2×C31semidirect
215. #3180C2×C31semidirect
216. #3142C2×C31semidirect
217. #1664C2×C31semidirect
218. #1663C2×C31semidirect
219. #1662C2×C31semidirect
220. #1658C2×C31semidirect
221. #1657C2×C31semidirect
222. #1656C2×C31semidirect
223. #1524C2×C31semidirect
224. C2×#330C2×C31semidirect
354. C31#19082direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35532
C31×#31802
C31×#31422
C31×#16642
C31×#16632
C31×#16622
C31×#16582
C31×#16572
C31×#16562
C31×#15242
C2×C31×#3302
#1908231