Finite Group Databasebeta

← C31×#10249 #21467008

Subgroups — C31×#10249 #21467008

Order 7936.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3230C211yesmaximal, characteristic, complemented
2C31×#3077C211yesmaximal, characteristic
3C31×#2563C211yesmaximal, characteristic
4C31×#1549C211yesmaximal, characteristic, complemented
5C31×#1503C211yesmaximal, characteristic, complemented
6C31×#1478C211yesmaximal, characteristic
7C31×#1303C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C31×#500—21no—
12C31×#487—21no—
13C31×#484—22no—
14C31×#478—22no—
15C31×#477—22no—
16C31×#476—21no—
17C31×#474—21no—
18C31×#431C2211yescharacteristic
19C31×#431C2211yescharacteristic
20C31×#428—21no—
21C31×#423C2211yescharacteristic
22C31×#418—21no—
23C31×#393—22no—
24C31×#390—21no—
25C31×#382—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×C22⋊Q8—21no—
43C31×C22⋊Q8—21no—
44C4×Q8×C31—21no—
45C4×Q8×C31—21no—
46C4×D4×C31—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C31×#117—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C4⋊C4×C31D412yes—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—24no—
57C2×C42×C31—21no—
58C2×C42×C31C2311yescharacteristic
59C31×#107—22no—
60C31×#107—24no—
61C31×#106—22no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8D412yes—
65C31×C4⋊C8D412yes—
66C31×#103—24no—
67C31×#102—22no—
68C31×#102—22no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C4×C8×C31—21no—
72C4×C8×C31—21no—
73C31×#95—24no—
74C31×#95D412yes—
75C24×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—41no—
79C2×Q8×C31—41no—
80C2×Q8×C31—82no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31Q1612yes—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—44no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96M16×C31—41no—
97M16×C31—41no—
98C2×C8×C31—22no—
99C2×C8×C31—22no—
100C2×C8×C31—41no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—42no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—84no—
118C42×C31—41no—
119C42×C31—41no—
120C42×C31—41no—
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123C42×C31C2×D411yescharacteristic
124C42×C31#4111yescharacteristic
125#10249C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31—22no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31#12011yescharacteristic
132Q8×C31—42no—
133Q8×C31—81no—
134Q8×C31—82no—
135Q8×C31—82no—
136D4×C31—22no—
137D4×C31—22no—
138D4×C31—41no—
139D4×C31—41no—
140C2×C4×C31—22no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—44no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31#12011yescharacteristic
154C2×C4×C31#12011yescharacteristic
155C2×C4×C31#12111yescharacteristic
156C2×C4×C31#12111yescharacteristic
157C2×C4×C31#12111yescharacteristic
158C2×C4×C31#12711yescharacteristic
159C2×C4×C31C2×Q1611yescharacteristic
160C2×C4×C31#13511yescharacteristic
161C2×C4×C31#13711yescharacteristic
162C2×C4×C31#13711yescharacteristic
163C8×C31—42no—
164C8×C31—42no—
165C8×C31—81no—
166#3230C2×C3111yescharacteristic, complemented
167#3077C2×C3111yescharacteristic
168#2563C2×C3111yescharacteristic
169#1549C2×C3111yescharacteristic, complemented
170#1503C2×C3111yescharacteristic, complemented
171#1478C2×C3111yescharacteristic
172#1303C2×C3111yescharacteristic, complemented
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—44no—
176C22×C31—42no—
177C22×C31—82no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31#39211yescharacteristic
181C22×C31#45111yescharacteristic
182C22×C31#45211yescharacteristic
183C4×C31—21no—
184C4×C31—21no—
185C4×C31—21no—
186C4×C31—82no—
187C4×C31—81no—
188C4×C31—81no—
189C4×C31—82no—
190C4×C31—81no—
191C4×C31#45111yescharacteristic
192C4×C31#45211yescharacteristic
193C4×C31#45412yes—
194C4×C31#46711yescharacteristic
195C4×C31#47011yescharacteristic
196#533C22×C3111yescharacteristic
197C2×C4⋊Q8C22×C3111yescharacteristic
198C2×C4×D4C22×C3111yescharacteristic
199#500—21no—
200#487—21no—
201#484—22no—
202#478—22no—
203#477—22no—
204#476—21no—
205#474—21no—
206#431C22×C3111yescharacteristic
207#431C22×C3111yescharacteristic
208#428—21no—
209#423C22×C3111yescharacteristic
210#418—21no—
211#393—22no—
212#390—21no—
213#382—21no—
214#380—22no—
215C4×C4⋊C4C22×C3111yescharacteristic
216#332—22no—
217#328—22no—
218D4⋊C8—22no—
219C2×C31—21no—
220C2×C31—21no—
221C2×C31—82no—
222C2×C31#200111yescharacteristic
223C2×C31#200311yescharacteristic
224C2×C31#200811yescharacteristic
225C22×Q8—21no—
226C22×D4D4×C3111yescharacteristic
227C23×C4—21no—
228C2×M16—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8D4×C3111yescharacteristic
234C4⋊Q8D4×C3111yescharacteristic
235#125—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C3111yescharacteristic
248C2×C4⋊C4D4×C3112yes—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—24no—
251C2×C42—21no—
252C2×C42C23×C3111yescharacteristic
253#107—22no—
254#107—24no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8D4×C3112yes—
259C4⋊C8D4×C3112yes—
260#103—24no—
261#102—22no—
262#102—22no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C4×C8—21no—
266C4×C8—21no—
267#95—24no—
268#95D4×C3112yes—
269C31#1024911yescharacteristic, direct product factor, Sylow
270C24—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4Q16×C3112yes—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—44no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291M16—41no—
292M16—41no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—84no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42C2×D4×C3111yescharacteristic
317C42C2×D4×C3111yescharacteristic
318C42C2×D4×C3111yescharacteristic
319C42#41×C3111yescharacteristic
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23C31×#12011yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—82no—
329Q8—82no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4C31×#12011yescharacteristic
348C2×C4C31×#12011yescharacteristic
349C2×C4C31×#12111yescharacteristic
350C2×C4C31×#12111yescharacteristic
351C2×C4C31×#12111yescharacteristic
352C2×C4C31×#12711yescharacteristic
353C2×C4C2×Q16×C3111yescharacteristic
354C2×C4C31×#13511yescharacteristic
355C2×C4C31×#13711yescharacteristic
356C2×C4C31×#13711yescharacteristic
357C8—42no—
358C8—42no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22C31×#39211yescharacteristic
368C22C31×#45111yescharacteristic
369C22C31×#45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—82no—
377C4—81no—
378C4C31×#45111yescharacteristic
379C4C31×#45211yescharacteristic
380C4C31×#45412yes—
381C4C31×#46711yescharacteristic
382C4C31×#47011yescharacteristic
383C2—21no—
384C2—21no—
385C2—82no—
386C2C31×#200111yescharacteristic
387C2C31×#200311yescharacteristic
388C2C31×#200811yescharacteristic
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×#3230C2semidirect
4. C31×#1549C2semidirect
5. C31×#1503C2semidirect
7. C31×#1303C2semidirect
125. #10249C31direct (N × H)
166. #3230C2×C31semidirect
169. #1549C2×C31semidirect
170. #1503C2×C31semidirect
172. #1303C2×C31semidirect
269. C31#10249direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32302
C31×#30772
C31×#25632
C31×#15492
C31×#15032
C31×#14782
C31×#13032
#1024931