Finite Group Databasebeta

← C31×#10433 #21467192

Subgroups — C31×#10433 #21467192

Order 7936.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2538C211yesmaximal, characteristic
2C31×#1834C211yesmaximal, characteristic, complemented
3C31×#1803C211yesmaximal, characteristic, complemented
4C31×#1802C211yesmaximal, characteristic
5C2×C31×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C31×D4⋊C8C211yesmaximal, characteristic
7C31×#1296C211yesmaximal, characteristic, complemented
8C2×C31×C22⋊Q8—21no—
9C2×C4×Q8×C31C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×C4⋊C8C2211yescharacteristic
13C2×C31×#103—21no—
14C2×C31×#102—21no—
15C2×C4×C8×C31C2211yescharacteristic
16C31×#396—22no—
17C31×#390—21no—
18C31×#389—21no—
19C31×#384C2211yescharacteristic
20C31×#384C2211yescharacteristic
21C31×#380—21no—
22C31×#340—21no—
23C31×#340—21no—
24C31×#340—22no—
25C31×Q8⋊C8—22no—
26C31×D4⋊C8—22no—
27C22×Q8×C31D411yescharacteristic
28C22×D4×C31D411yescharacteristic
29C23×C4×C31—21no—
30C22×C8×C31—21no—
31C22×C8×C31—21no—
32C22×C8×C31—21no—
33C31×C22⋊Q8—42no—
34C31×C22⋊Q8—42no—
35C4×Q8×C31—21no—
36C4×Q8×C31—21no—
37C4×Q8×C31—21no—
38C4×Q8×C31—21no—
39C4×D4×C31—21no—
40C4×D4×C31—21no—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C2×C4⋊C4×C31—22no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31D411yescharacteristic
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C4⋊C4×C31D412yes—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—22no—
56C2×C42×C31—21no—
57C2×C42×C31C2311yescharacteristic
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×#103—42no—
63C31×#102—42no—
64C4×C8×C31—21no—
65C4×C8×C31D412yes—
66C31×#95—22no—
67C24×C31—21no—
68C2×Q8×C31—21no—
69C2×Q8×C31—21no—
70C2×Q8×C31—21no—
71C2×Q8×C31—21no—
72C2×Q8×C31—21no—
73C2×Q8×C31D812yes—
74C2×D4×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31SD1612yes—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—22no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C2×C8×C31—22no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—44no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—42no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C22⋊C4×C31—44no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—82no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31C2×D411yescharacteristic
127C42×C31#4111yescharacteristic
128C42×C31#4111yescharacteristic
129C42×C31#4111yescharacteristic
130#10433C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—22no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31#12011yescharacteristic
139Q8×C31—22no—
140Q8×C31—22no—
141Q8×C31—41no—
142Q8×C31—41no—
143D4×C31—22no—
144D4×C31—22no—
145D4×C31—41no—
146D4×C31—41no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—22no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—42no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31—81no—
167C2×C4×C31—81no—
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12111yescharacteristic
170C2×C4×C31#12111yescharacteristic
171C2×C4×C31#12311yescharacteristic
172C2×C4×C31#12311yescharacteristic
173C2×C4×C31#12411yescharacteristic
174C2×C4×C31C2×D811yescharacteristic
175C2×C4×C31C2×SD1611yescharacteristic
176C2×C4×C31#13511yescharacteristic
177C2×C4×C31#13511yescharacteristic
178C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C31#13711yescharacteristic
180C2×C4×C31#13711yescharacteristic
181C2×C4×C31#13711yescharacteristic
182C8×C31—42no—
183C8×C31—81no—
184C8×C31—81no—
185#2538C2×C3111yescharacteristic
186#1834C2×C3111yescharacteristic, complemented
187#1803C2×C3111yescharacteristic, complemented
188#1802C2×C3111yescharacteristic
189C2×Q8⋊C8C2×C3111yescharacteristic, complemented
190C2×D4⋊C8C2×C3111yescharacteristic
191#1296C2×C3111yescharacteristic, complemented
192C22×C31—42no—
193C22×C31—42no—
194C22×C31—42no—
195C22×C31—81no—
196C22×C31—81no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31#39411yescharacteristic
200C22×C31#44711yescharacteristic
201C22×C31#44811yescharacteristic
202C22×C31#45211yescharacteristic
203C22×C31#45211yescharacteristic
204C22×C31#45411yescharacteristic
205C22×C31#45511yescharacteristic
206C4×C31—21no—
207C4×C31—21no—
208C4×C31—42no—
209C4×C31—82no—
210C4×C31—81no—
211C4×C31—81no—
212C4×C31—161no—
213C4×C31#46511yescharacteristic
214C4×C31#46611yescharacteristic
215C4×C31#46811yescharacteristic
216C4×C31#47011yescharacteristic
217C4×C31#48011yescharacteristic
218C4×C31#48211yescharacteristic
219C4×C31#48311yescharacteristic
220C4×C31#48511yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C4×Q8C22×C3111yescharacteristic
223C2×C4×D4C22×C3111yescharacteristic
224C2×C4⋊C8C22×C3111yescharacteristic
225C2×C4⋊C8C22×C3111yescharacteristic
226C2×#103—21no—
227C2×#102—21no—
228C2×C4×C8C22×C3111yescharacteristic
229#396—22no—
230#390—21no—
231#389—21no—
232#384C22×C3111yescharacteristic
233#384C22×C3111yescharacteristic
234#380—21no—
235#340—21no—
236#340—21no—
237#340—22no—
238Q8⋊C8—22no—
239D4⋊C8—22no—
240C2×C31—82no—
241C2×C31#162711yescharacteristic
242C2×C31#163811yescharacteristic
243C2×C31#164111yescharacteristic
244C2×C31#164311yescharacteristic
245C2×C31#203311yescharacteristic
246C2×C31#203511yescharacteristic
247C2×C31#204011yescharacteristic
248C22×Q8D4×C3111yescharacteristic
249C22×D4D4×C3111yescharacteristic
250C23×C4—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22⋊Q8—42no—
255C22⋊Q8—42no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C3111yescharacteristic
272C2×C4⋊C4D4×C3111yescharacteristic
273C2×C4⋊C4D4×C3112yes—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—22no—
277C2×C42—21no—
278C2×C42C23×C3111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283#103—42no—
284#102—42no—
285C4×C8—21no—
286C4×C8D4×C3112yes—
287#95—22no—
288C31#1043311yescharacteristic, direct product factor, Sylow
289C24—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8D8×C3112yes—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4SD16×C3112yes—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C2×D4×C3111yescharacteristic
314C22×C4C2×D4×C3111yescharacteristic
315C22×C4C2×D4×C3111yescharacteristic
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—44no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—82no—
346C42—41no—
347C42—41no—
348C42C2×D4×C3111yescharacteristic
349C42#41×C3111yescharacteristic
350C42#41×C3111yescharacteristic
351C42#41×C3111yescharacteristic
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23C31×#12011yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C31×#12111yescharacteristic
390C2×C4C31×#12111yescharacteristic
391C2×C4C31×#12111yescharacteristic
392C2×C4C31×#12311yescharacteristic
393C2×C4C31×#12311yescharacteristic
394C2×C4C31×#12411yescharacteristic
395C2×C4C2×D8×C3111yescharacteristic
396C2×C4C2×SD16×C3111yescharacteristic
397C2×C4C31×#13511yescharacteristic
398C2×C4C31×#13511yescharacteristic
399C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
400C2×C4C31×#13711yescharacteristic
401C2×C4C31×#13711yescharacteristic
402C2×C4C31×#13711yescharacteristic
403C8—42no—
404C8—81no—
405C8—81no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22C31×#39411yescharacteristic
414C22C31×#44711yescharacteristic
415C22C31×#44811yescharacteristic
416C22C31×#45211yescharacteristic
417C22C31×#45211yescharacteristic
418C22C31×#45411yescharacteristic
419C22C31×#45511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—82no—
424C4—81no—
425C4—81no—
426C4—161no—
427C4C31×#46511yescharacteristic
428C4C31×#46611yescharacteristic
429C4C31×#46811yescharacteristic
430C4C31×#47011yescharacteristic
431C4C31×#48011yescharacteristic
432C4C31×#48211yescharacteristic
433C4C31×#48311yescharacteristic
434C4C31×#48511yescharacteristic
435C2—82no—
436C2C31×#162711yescharacteristic
437C2C31×#163811yescharacteristic
438C2C31×#164111yescharacteristic
439C2C31×#164311yescharacteristic
440C2C31×#203311yescharacteristic
441C2C31×#203511yescharacteristic
442C2C31×#204011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1834C2semidirect
3. C31×#1803C2semidirect
5. C2×C31×Q8⋊C8C2semidirect
7. C31×#1296C2semidirect
130. #10433C31direct (N × H)
186. #1834C2×C31semidirect
187. #1803C2×C31semidirect
189. C2×Q8⋊C8C2×C31semidirect
191. #1296C2×C31semidirect
288. C31#10433direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25382
C31×#18342
C31×#18032
C31×#18022
C2×C31×Q8⋊C82
C2×C31×D4⋊C82
C31×#12962
#1043331