Finite Group Databasebeta

← C31×#10247 #21467006

Subgroups — C31×#10247 #21467006

Order 7936.

556 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3229C211yesmaximal, characteristic, complemented
2C31×#3077C211yesmaximal, characteristic
3C31×#2547C211yesmaximal, characteristic
4C31×#1546C211yesmaximal, characteristic, complemented
5C31×#1503C211yesmaximal, characteristic, complemented
6C31×#1478C211yesmaximal, characteristic
7C31×#1303C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×#124—21no—
11C2×C4×D4×C31C2211yescharacteristic
12C31×#498—21no—
13C31×#487—21no—
14C31×#483—22no—
15C31×#478—22no—
16C31×#476—21no—
17C31×#475—22no—
18C31×#474—21no—
19C31×#431C2211yescharacteristic
20C31×#431C2211yescharacteristic
21C31×#428—21no—
22C31×#423C2211yescharacteristic
23C31×#418—21no—
24C31×#397—22no—
25C31×#391—21no—
26C31×#380—22no—
27C4×C4⋊C4×C31C2211yescharacteristic
28C31×#332—22no—
29C31×#328—22no—
30C31×D4⋊C8—22no—
31C22×Q8×C31—21no—
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C2×M16×C31—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8D411yescharacteristic
40C31×C4⋊Q8D411yescharacteristic
41C31×#125—21no—
42C31×#124—42no—
43C31×#124—42no—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C4×Q8×C31—21no—
47C4×Q8×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C31×#117—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D412yes—
57C2×C22⋊C4×C31—24no—
58C2×C22⋊C4×C31—21no—
59C2×C42×C31—21no—
60C2×C42×C31C2311yescharacteristic
61C31×#107—22no—
62C31×#106—22no—
63C31×#106—24no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8D412yes—
67C31×C4⋊C8D412yes—
68C31×#103—24no—
69C31×#102—22no—
70C31×#102—22no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C31×#95—24no—
76C31×#95D412yes—
77C24×C31—21no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—41no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×Q8×C31—41no—
86C2×D4×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31SD1612yes—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—44no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101M16×C31—41no—
102M16×C31—41no—
103C2×C8×C31—22no—
104C2×C8×C31—22no—
105C2×C8×C31—41no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—42no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C22⋊C4×C31—48no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C42×C31—41no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D411yescharacteristic
129C42×C31#4111yescharacteristic
130#10247C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—22no—
132C23×C31—42no—
133C23×C31—42no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31#12011yescharacteristic
137Q8×C31—42no—
138Q8×C31—81no—
139Q8×C31—81no—
140Q8×C31—81no—
141Q8×C31—81no—
142Q8×C31—81no—
143D4×C31—22no—
144D4×C31—22no—
145D4×C31—41no—
146D4×C31—41no—
147C2×C4×C31—22no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—82no—
160C2×C4×C31—82no—
161C2×C4×C31#12011yescharacteristic
162C2×C4×C31#12011yescharacteristic
163C2×C4×C31#12111yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12711yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31#13711yescharacteristic
171C8×C31—42no—
172C8×C31—42no—
173C8×C31—81no—
174#3229C2×C3111yescharacteristic, complemented
175#3077C2×C3111yescharacteristic
176#2547C2×C3111yescharacteristic
177#1546C2×C3111yescharacteristic, complemented
178#1503C2×C3111yescharacteristic, complemented
179#1478C2×C3111yescharacteristic
180#1303C2×C3111yescharacteristic, complemented
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—44no—
184C22×C31—42no—
185C22×C31—82no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31#39211yescharacteristic
189C22×C31#45011yescharacteristic
190C22×C31#45211yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—82no—
195C4×C31—82no—
196C4×C31—81no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31#44811yescharacteristic
200C4×C31#44911yescharacteristic
201C4×C31#45412yes—
202C4×C31#46511yescharacteristic
203C4×C31#46811yescharacteristic
204#533C22×C3111yescharacteristic
205C2×C4⋊Q8C22×C3111yescharacteristic
206C2×#124—21no—
207C2×C4×D4C22×C3111yescharacteristic
208#498—21no—
209#487—21no—
210#483—22no—
211#478—22no—
212#476—21no—
213#475—22no—
214#474—21no—
215#431C22×C3111yescharacteristic
216#431C22×C3111yescharacteristic
217#428—21no—
218#423C22×C3111yescharacteristic
219#418—21no—
220#397—22no—
221#391—21no—
222#380—22no—
223C4×C4⋊C4C22×C3111yescharacteristic
224#332—22no—
225#328—22no—
226D4⋊C8—22no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—82no—
230C2×C31#200011yescharacteristic
231C2×C31#200311yescharacteristic
232C2×C31#200911yescharacteristic
233C22×Q8—21no—
234C22×D4D4×C3111yescharacteristic
235C23×C4—21no—
236C2×M16—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C3111yescharacteristic
242C4⋊Q8D4×C3111yescharacteristic
243#125—21no—
244#124—42no—
245#124—42no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254#117—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C3111yescharacteristic
258C2×C4⋊C4D4×C3112yes—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—21no—
261C2×C42—21no—
262C2×C42C23×C3111yescharacteristic
263#107—22no—
264#106—22no—
265#106—24no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C3112yes—
269C4⋊C8D4×C3112yes—
270#103—24no—
271#102—22no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277#95—24no—
278#95D4×C3112yes—
279C31#1024711yescharacteristic, direct product factor, Sylow
280C24—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4SD16×C3112yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—44no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C3111yescharacteristic
302C22×C4C2×D4×C3111yescharacteristic
303C22×C4C2×D4×C3111yescharacteristic
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—48no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42C2×D4×C3111yescharacteristic
330C42C2×D4×C3111yescharacteristic
331C42C2×D4×C3111yescharacteristic
332C42#41×C3111yescharacteristic
333C23—22no—
334C23—42no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23C31×#12011yescharacteristic
339Q8—42no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4C31×#12011yescharacteristic
364C2×C4C31×#12011yescharacteristic
365C2×C4C31×#12111yescharacteristic
366C2×C4C31×#12111yescharacteristic
367C2×C4C31×#12111yescharacteristic
368C2×C4C31×#12711yescharacteristic
369C2×C4C2×SD16×C3111yescharacteristic
370C2×C4C31×#13511yescharacteristic
371C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C31×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22C31×#39211yescharacteristic
384C22C31×#45011yescharacteristic
385C22C31×#45211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C31×#44811yescharacteristic
395C4C31×#44911yescharacteristic
396C4C31×#45412yes—
397C4C31×#46511yescharacteristic
398C4C31×#46811yescharacteristic
399C2—21no—
400C2—21no—
401C2—82no—
402C2C31×#200011yescharacteristic
403C2C31×#200311yescharacteristic
404C2C31×#200911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×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×#3229C2semidirect
4. C31×#1546C2semidirect
5. C31×#1503C2semidirect
7. C31×#1303C2semidirect
130. #10247C31direct (N × H)
174. #3229C2×C31semidirect
177. #1546C2×C31semidirect
178. #1503C2×C31semidirect
180. #1303C2×C31semidirect
279. C31#10247direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32292
C31×#30772
C31×#25472
C31×#15462
C31×#15032
C31×#14782
C31×#13032
#1024731