Finite Group Databasebeta

← C31×#8315 #21465074

Subgroups — C31×#8315 #21465074

Order 7936.

868 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic, complemented
3C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C31×Q8⋊C8C212yesmaximal, complemented
5C2×C31×D4⋊C8C212yesmaximal, complemented
6C31×#529—24no—
7C31×#529—24no—
8C2×C31×#126—21no—
9C2×C31×#125C411yescharacteristic
10C2×C31×#124C411yescharacteristic
11C2×C31×#123—21no—
12C2×C31×C22⋊Q8C411yescharacteristic
13C2×C31×#121C411yescharacteristic
14C2×C4×Q8×C31C2211yescharacteristic
15C2×C4×D4×C31—21no—
16C2×C4×D4×C31C2211yescharacteristic
17C2×C31×#117—21no—
18C22×C42×C31C2211yescharacteristic
19C2×C31×C4⋊C8C2212yes—
20C2×C31×C22⋊C8—21no—
21C2×C31×C22⋊C8—21no—
22C2×C4×C8×C31C2212yes—
23C31×#336—21no—
24C31×#336—21no—
25C31×Q8⋊C8—24no—
26C31×D4⋊C8—24no—
27C22×Q8×C31C2×C411yescharacteristic
28C22×D4×C31—21no—
29C22×D4×C31C2×C411yescharacteristic
30C23×C4×C31—21no—
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31D411yescharacteristic
33C23×C4×C31D411yescharacteristic
34C22×C8×C31—22no—
35C22×C8×C31—22no—
36C31×#126—28no—
37C31×#125—22no—
38C31×#125—22no—
39C31×#124—22no—
40C31×#124—22no—
41C31×#123—28no—
42C31×C22⋊Q8—22no—
43C31×C22⋊Q8—22no—
44C31×#121—22no—
45C31×#121—22no—
46C4×Q8×C31—22no—
47C4×Q8×C31D414yes—
48C4×D4×C31—28no—
49C4×D4×C31—22no—
50C4×D4×C31D414yes—
51C31×#117—28no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31C2×C411yescharacteristic
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C42×C31—21no—
64C2×C42×C31—22no—
65C2×C42×C31—22no—
66C2×C42×C31C2×C411yescharacteristic
67C2×C42×C31D411yescharacteristic
68C2×C42×C31D411yescharacteristic
69C2×C42×C31C2311yescharacteristic
70C31×C4⋊C8—22no—
71C31×C4⋊C8—22no—
72C31×C22⋊C8—24no—
73C31×C22⋊C8—42no—
74C4×C8×C31—22no—
75C4×C8×C31—22no—
76C24×C31—21no—
77C24×C31C22⋊C411yescharacteristic
78C2×Q8×C31—21no—
79C2×Q8×C31—22no—
80C2×Q8×C31—22no—
81C2×Q8×C31C22⋊C412yes—
82C2×D4×C31—24no—
83C2×D4×C31—21no—
84C2×D4×C31—22no—
85C2×D4×C31—22no—
86C2×D4×C31—42no—
87C2×D4×C31—42no—
88C2×D4×C31C22⋊C412yes—
89C22×C4×C31—22no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—24no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—41no—
104C22×C4×C31—42no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31C22⋊C411yescharacteristic
108C22×C4×C31C22⋊C411yescharacteristic
109C22×C4×C31C22⋊C411yescharacteristic
110C22×C4×C31C22×C411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C2×C8×C31—24no—
114C2×C8×C31—42no—
115C2×C8×C31—42no—
116C2×C8×C31—42no—
117C2×C8×C31—42no—
118C2×C8×C31—42no—
119C4⋊C4×C31—24no—
120C4⋊C4×C31—24no—
121C4⋊C4×C31—24no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—21no—
124C4⋊C4×C31—24no—
125C4⋊C4×C31C22⋊C412yes—
126C4⋊C4×C31C22⋊C412yes—
127C22⋊C4×C31—24no—
128C22⋊C4×C31—24no—
129C22⋊C4×C31—24no—
130C22⋊C4×C31—24no—
131C22⋊C4×C31—24no—
132C42×C31—21no—
133C42×C31—21no—
134C42×C31—22no—
135C42×C31—22no—
136C42×C31—24no—
137C42×C31C2×D412yes—
138C42×C31C2×D412yes—
139#8315C3111yesmaximal, characteristic, direct product factor, Sylow
140C23×C31—21no—
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—21no—
144C23×C31—21no—
145C23×C31—21no—
146C23×C31—22no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31#10412yes—
154C23×C31C2×C22⋊C411yescharacteristic
155Q8×C31—24no—
156Q8×C31—42no—
157D4×C31—24no—
158D4×C31—48no—
159D4×C31—42no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—22no—
166C2×C4×C31—22no—
167C2×C4×C31—22no—
168C2×C4×C31—21no—
169C2×C4×C31—21no—
170C2×C4×C31—21no—
171C2×C4×C31—21no—
172C2×C4×C31—21no—
173C2×C4×C31—21no—
174C2×C4×C31—44no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—42no—
182C2×C4×C31—42no—
183C2×C4×C31—42no—
184C2×C4×C31—44no—
185C2×C4×C31—42no—
186C2×C4×C31—44no—
187C2×C4×C31C2×C22⋊C411yescharacteristic
188C2×C4×C31C2×C22⋊C411yescharacteristic
189C2×C4×C31#12012yes—
190C2×C4×C31#12012yes—
191C2×C4×C31#13112yes—
192C2×C4×C31#13112yes—
193C2×C4×C31#13512yes—
194C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C31#13711yescharacteristic
196C8×C31—44no—
197C8×C31—82no—
198C2×#529C2×C3111yescharacteristic
199#1797C2×C3111yescharacteristic, complemented
200C4×C22⋊C8C2×C3111yescharacteristic, complemented
201C2×Q8⋊C8C2×C3112yescomplemented
202C2×D4⋊C8C2×C3112yescomplemented
203C22×C31—22no—
204C22×C31—22no—
205C22×C31—22no—
206C22×C31—41no—
207C22×C31—41no—
208C22×C31—41no—
209C22×C31—41no—
210C22×C31—42no—
211C22×C31—42no—
212C22×C31—42no—
213C22×C31—81no—
214C22×C31—81no—
215C22×C31—81no—
216C22×C31—81no—
217C22×C31#37911yescharacteristic
218C22×C31#40811yescharacteristic
219C22×C31#40811yescharacteristic
220C22×C31#41611yescharacteristic
221C22×C31#41711yescharacteristic
222C22×C31C2×#10411yescharacteristic
223C22×C31#42111yescharacteristic
224C4×C31—22no—
225C4×C31—41no—
226C4×C31—42no—
227C4×C31—41no—
228C4×C31—42no—
229C4×C31—41no—
230C4×C31—42no—
231C4×C31#40812yes—
232C4×C31#40812yes—
233C4×C31#44912yes—
234C4×C31#45212yes—
235#529—24no—
236#529—24no—
237C2×#126—21no—
238C2×#125C4×C3111yescharacteristic
239C2×#124C4×C3111yescharacteristic
240C2×#123—21no—
241C2×C22⋊Q8C4×C3111yescharacteristic
242C2×#121C4×C3111yescharacteristic
243C2×C4×Q8C22×C3111yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C22×C3111yescharacteristic
246C2×#117—21no—
247C22×C42C22×C3111yescharacteristic
248C2×C4⋊C8C22×C3112yes—
249C2×C22⋊C8—21no—
250C2×C22⋊C8—21no—
251C2×C4×C8C22×C3112yes—
252#336—21no—
253#336—21no—
254Q8⋊C8—24no—
255D4⋊C8—24no—
256C2×C31—42no—
257C2×C31—82no—
258C2×C31#148211yescharacteristic
259C2×C31#148311yescharacteristic
260C2×C31#149411yescharacteristic
261C2×C31#149511yescharacteristic
262C2×C31#178011yescharacteristic
263C2×C31#178811yescharacteristic
264C2×C31#178911yescharacteristic
265C22×Q8C2×C4×C3111yescharacteristic
266C22×D4—21no—
267C22×D4C2×C4×C3111yescharacteristic
268C23×C4—21no—
269C23×C4C2×C4×C3111yescharacteristic
270C23×C4D4×C3111yescharacteristic
271C23×C4D4×C3111yescharacteristic
272C22×C8—22no—
273C22×C8—22no—
274#126—28no—
275#125—22no—
276#125—22no—
277#124—22no—
278#124—22no—
279#123—28no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282#121—22no—
283#121—22no—
284C4×Q8—22no—
285C4×Q8D4×C3114yes—
286C4×D4—28no—
287C4×D4—22no—
288C4×D4D4×C3114yes—
289#117—28no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4C2×C4×C3111yescharacteristic
295C2×C4⋊C4C2×C4×C3111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C42—21no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42C2×C4×C3111yescharacteristic
305C2×C42D4×C3111yescharacteristic
306C2×C42D4×C3111yescharacteristic
307C2×C42C23×C3111yescharacteristic
308C4⋊C8—22no—
309C4⋊C8—22no—
310C22⋊C8—24no—
311C22⋊C8—42no—
312C4×C8—22no—
313C4×C8—22no—
314C31#831511yescharacteristic, direct product factor, Sylow
315C24—21no—
316C24C22⋊C4×C3111yescharacteristic
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8C22⋊C4×C3112yes—
321C2×D4—24no—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4C22⋊C4×C3112yes—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—41no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4C22⋊C4×C3111yescharacteristic
347C22×C4C22⋊C4×C3111yescharacteristic
348C22×C4C22⋊C4×C3111yescharacteristic
349C22×C4C22×C4×C3111yescharacteristic
350C22×C4C2×D4×C3111yescharacteristic
351C22×C4C2×D4×C3111yescharacteristic
352C2×C8—24no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—42no—
357C2×C8—42no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—24no—
364C4⋊C4C22⋊C4×C3112yes—
365C4⋊C4C22⋊C4×C3112yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C42—21no—
372C42—21no—
373C42—22no—
374C42—22no—
375C42—24no—
376C42C2×D4×C3112yes—
377C42C2×D4×C3112yes—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23C31×#10412yes—
392C23C2×C22⋊C4×C3111yescharacteristic
393Q8—24no—
394Q8—42no—
395D4—24no—
396D4—48no—
397D4—42no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—44no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4C2×C22⋊C4×C3111yescharacteristic
426C2×C4C2×C22⋊C4×C3111yescharacteristic
427C2×C4C31×#12012yes—
428C2×C4C31×#12012yes—
429C2×C4C31×#13112yes—
430C2×C4C31×#13112yes—
431C2×C4C31×#13512yes—
432C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
433C2×C4C31×#13711yescharacteristic
434C8—44no—
435C8—82no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C31×#37911yescharacteristic
451C22C31×#40811yescharacteristic
452C22C31×#40811yescharacteristic
453C22C31×#41611yescharacteristic
454C22C31×#41711yescharacteristic
455C22C2×C31×#10411yescharacteristic
456C22C31×#42111yescharacteristic
457C4—22no—
458C4—41no—
459C4—42no—
460C4—41no—
461C4—42no—
462C4—41no—
463C4—42no—
464C4C31×#40812yes—
465C4C31×#40812yes—
466C4C31×#44912yes—
467C4C31×#45212yes—
468C2—42no—
469C2—82no—
470C2C31×#148211yescharacteristic
471C2C31×#148311yescharacteristic
472C2C31×#149411yescharacteristic
473C2C31×#149511yescharacteristic
474C2C31×#178011yescharacteristic
475C2C31×#178811yescharacteristic
476C2C31×#178911yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC23×C31C2×C22⋊C4
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1797C2semidirect
3. C4×C31×C22⋊C8C2semidirect
4. C2×C31×Q8⋊C8C2semidirect
5. C2×C31×D4⋊C8C2semidirect
139. #8315C31direct (N × H)
199. #1797C2×C31semidirect
200. C4×C22⋊C8C2×C31semidirect
201. C2×Q8⋊C8C2×C31semidirect
202. C2×D4⋊C8C2×C31semidirect
314. C31#8315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C31×#17972
C4×C31×C22⋊C82
C2×C31×Q8⋊C82
C2×C31×D4⋊C82
#831531