Finite Group Databasebeta

← C31×#10474 #21467233

Subgroups — C31×#10474 #21467233

Order 7936.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic
2C31×#1984C211yesmaximal, characteristic, complemented
3C31×#1957C211yesmaximal, characteristic
4C31×#1803C211yesmaximal, characteristic, complemented
5C2×C31×#335C211yesmaximal, characteristic, complemented
6C2×C31×#331C211yesmaximal, characteristic
7C31×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×#127C2211yescharacteristic
10C2×C4×Q8×C31C2211yescharacteristic
11C31×#460—22no—
12C31×#460—22no—
13C2×C31×C4⋊C8C2211yescharacteristic
14C2×C31×C4⋊C8C2211yescharacteristic
15C2×C31×C4⋊C8C2211yescharacteristic
16C2×C31×#103—21no—
17C2×C31×#102—21no—
18C2×C31×#102—21no—
19C2×C31×#102—21no—
20C2×C4×C8×C31C2211yescharacteristic
21C31×#384C2211yescharacteristic
22C31×#340—21no—
23C31×#336—21no—
24C31×#336—21no—
25C31×#335—22no—
26C31×#331—22no—
27C22×Q8×C31D411yescharacteristic
28C22×D4×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C2×SD16×C31—24no—
32C2×SD16×C31—42no—
33C2×SD16×C31—42no—
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C22×C8×C31D411yescharacteristic
38C22×C8×C31D411yescharacteristic
39C31×#127—21no—
40C31×#127—21no—
41C31×#127—21no—
42C31×#127D412yes—
43C4×Q8×C31—21no—
44C4×Q8×C31—21no—
45C4×Q8×C31—21no—
46C4×Q8×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C42×C31—21no—
53C2×C42×C31C2311yescharacteristic
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8D412yes—
60C31×#103—42no—
61C31×#102—24no—
62C31×#102—42no—
63C31×#102—42no—
64C4×C8×C31—21no—
65C4×C8×C31—21no—
66C24×C31—41no—
67C2×Q8×C31—21no—
68C2×Q8×C31—21no—
69C2×Q8×C31—21no—
70C2×Q8×C31—21no—
71C2×Q8×C31—21no—
72C2×Q8×C31D812yes—
73C2×D4×C31—22no—
74C2×D4×C31—22no—
75C2×D4×C31—22no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—41no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—81no—
88C2×D4×C31—81no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—41no—
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31#4111yescharacteristic
95SD16×C31—48no—
96C2×C8×C31—21no—
97C2×C8×C31—21no—
98C2×C8×C31—22no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—21no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C2×C8×C31—41no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C2×C8×C31—41no—
110C2×C8×C31SD1612yescomplemented
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
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—81no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31C2×D411yescharacteristic
123C42×C31C2×D411yescharacteristic
124C42×C31#4111yescharacteristic
125C42×C31#4111yescharacteristic
126#10474C3111yesmaximal, characteristic, direct product factor, Sylow
127C23×C31—42no—
128C23×C31—81no—
129C23×C31—81no—
130C23×C31—81no—
131C23×C31—81no—
132C23×C31—81no—
133C23×C31—81no—
134C23×C31#12111yescharacteristic
135Q8×C31—22no—
136Q8×C31—22no—
137Q8×C31—41no—
138Q8×C31—41no—
139D4×C31—42no—
140D4×C31—42no—
141D4×C31—42no—
142D4×C31—42no—
143D4×C31—82no—
144D4×C31—82no—
145D4×C31—81no—
146D4×C31—81no—
147D4×C31—81no—
148D4×C31—81no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—22no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31#12011yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12111yescharacteristic
163C2×C4×C31#12311yescharacteristic
164C2×C4×C31#12311yescharacteristic
165C2×C4×C31#12411yescharacteristic
166C2×C4×C31C2×D811yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31#13511yescharacteristic
170C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C31#13711yescharacteristic
173C2×C4×C31#13711yescharacteristic
174C8×C31—22no—
175C8×C31—42no—
176C8×C31—41no—
177C8×C31—81no—
178C8×C31—81no—
179C2×#460C2×C3111yescharacteristic
180#1984C2×C3111yescharacteristic, complemented
181#1957C2×C3111yescharacteristic
182#1803C2×C3111yescharacteristic, complemented
183C2×#335C2×C3111yescharacteristic, complemented
184C2×#331C2×C3111yescharacteristic
185#1296C2×C3111yescharacteristic, complemented
186C22×C31—82no—
187C22×C31—82no—
188C22×C31—82no—
189C22×C31—161no—
190C22×C31—161no—
191C22×C31—161no—
192C22×C31—161no—
193C22×C31#39411yescharacteristic
194C22×C31#46011yescharacteristic
195C22×C31#46411yescharacteristic
196C22×C31#46611yescharacteristic
197C22×C31#46811yescharacteristic
198C22×C31#47111yescharacteristic
199C22×C31#47211yescharacteristic
200C4×C31—21no—
201C4×C31—21no—
202C4×C31—42no—
203C4×C31—81no—
204C4×C31—161no—
205C4×C31#44711yescharacteristic
206C4×C31#45211yescharacteristic
207C4×C31#46111yescharacteristic
208C4×C31#46311yescharacteristic
209C4×C31#46511yescharacteristic
210C4×C31#46811yescharacteristic
211C4×C31#48011yescharacteristic
212C4×C31#48211yescharacteristic
213C22×SD16—21no—
214C2×#127C22×C3111yescharacteristic
215C2×C4×Q8C22×C3111yescharacteristic
216#460—22no—
217#460—22no—
218C2×C4⋊C8C22×C3111yescharacteristic
219C2×C4⋊C8C22×C3111yescharacteristic
220C2×C4⋊C8C22×C3111yescharacteristic
221C2×#103—21no—
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×C4×C8C22×C3111yescharacteristic
226#384C22×C3111yescharacteristic
227#340—21no—
228#336—21no—
229#336—21no—
230#335—22no—
231#331—22no—
232C2×C31—162no—
233C2×C31#166811yescharacteristic
234C2×C31#168211yescharacteristic
235C2×C31#168611yescharacteristic
236C2×C31#169811yescharacteristic
237C2×C31#203311yescharacteristic
238C2×C31#205111yescharacteristic
239C2×C31#205511yescharacteristic
240C22×Q8D4×C3111yescharacteristic
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244C2×SD16—24no—
245C2×SD16—42no—
246C2×SD16—42no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8D4×C3111yescharacteristic
251C22×C8D4×C3111yescharacteristic
252#127—21no—
253#127—21no—
254#127—21no—
255#127D4×C3112yes—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C3111yescharacteristic
265C2×C42—21no—
266C2×C42C23×C3111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8D4×C3112yes—
273#103—42no—
274#102—24no—
275#102—42no—
276#102—42no—
277C4×C8—21no—
278C4×C8—21no—
279C31#1047411yescharacteristic, direct product factor, Sylow
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8D8×C3112yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×D4×C3111yescharacteristic
307C22×C4C2×D4×C3111yescharacteristic
308C22×C4#41×C3111yescharacteristic
309SD16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C3112yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42C2×D4×C3111yescharacteristic
337C42C2×D4×C3111yescharacteristic
338C42#41×C3111yescharacteristic
339C42#41×C3111yescharacteristic
340C23—42no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23C31×#12111yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C31×#12011yescharacteristic
374C2×C4C31×#12111yescharacteristic
375C2×C4C31×#12111yescharacteristic
376C2×C4C31×#12311yescharacteristic
377C2×C4C31×#12311yescharacteristic
378C2×C4C31×#12411yescharacteristic
379C2×C4C2×D8×C3111yescharacteristic
380C2×C4C2×SD16×C3111yescharacteristic
381C2×C4C31×#13511yescharacteristic
382C2×C4C31×#13511yescharacteristic
383C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
385C2×C4C31×#13711yescharacteristic
386C2×C4C31×#13711yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—81no—
391C8—81no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—161no—
396C22—161no—
397C22—161no—
398C22—161no—
399C22C31×#39411yescharacteristic
400C22C31×#46011yescharacteristic
401C22C31×#46411yescharacteristic
402C22C31×#46611yescharacteristic
403C22C31×#46811yescharacteristic
404C22C31×#47111yescharacteristic
405C22C31×#47211yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4C31×#44711yescharacteristic
412C4C31×#45211yescharacteristic
413C4C31×#46111yescharacteristic
414C4C31×#46311yescharacteristic
415C4C31×#46511yescharacteristic
416C4C31×#46811yescharacteristic
417C4C31×#48011yescharacteristic
418C4C31×#48211yescharacteristic
419C2—162no—
420C2C31×#166811yescharacteristic
421C2C31×#168211yescharacteristic
422C2C31×#168611yescharacteristic
423C2C31×#169811yescharacteristic
424C2C31×#203311yescharacteristic
425C2C31×#205111yescharacteristic
426C2C31×#205511yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
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×#1984C2semidirect
4. C31×#1803C2semidirect
5. C2×C31×#335C2semidirect
7. C31×#1296C2semidirect
110. C2×C8×C31SD16semidirect
126. #10474C31direct (N × H)
180. #1984C2×C31semidirect
182. #1803C2×C31semidirect
183. C2×#335C2×C31semidirect
185. #1296C2×C31semidirect
279. C31#10474direct (N × H)
324. C2×C8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C31×#19842
C31×#19572
C31×#18032
C2×C31×#3352
C2×C31×#3312
C31×#12962
#1047431