Finite Group Databasebeta

← C31×#10245 #21467004

Subgroups — C31×#10245 #21467004

Order 7936.

558 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3227C211yesmaximal, characteristic
2C31×#3037C211yesmaximal, characteristic
3C31×#2567C211yesmaximal, characteristic, complemented
4C31×#1549C211yesmaximal, characteristic, complemented
5C31×#1502C211yesmaximal, characteristic
6C31×#1479C211yesmaximal, characteristic, complemented
7C31×#1303C211yesmaximal, characteristic, complemented
8C2×C31×#137—21no—
9C31×#532C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C31C2211yescharacteristic
12C31×#498—21no—
13C31×#486—21no—
14C31×#481—22no—
15C31×#476—22no—
16C31×#464—22no—
17C31×#462—21no—
18C31×#460—21no—
19C31×#431C2211yescharacteristic
20C31×#431C2211yescharacteristic
21C31×#423C2211yescharacteristic
22C31×#417—21no—
23C31×#395—22no—
24C31×#391—21no—
25C31×#389—22no—
26C31×#384—21no—
27C4×C4⋊C4×C31C2211yescharacteristic
28C31×#332—22no—
29C31×#327—22no—
30C31×Q8⋊C8—22no—
31C2×#41×C31—21no—
32C22×Q8×C31—21no—
33C22×Q8×C31D411yescharacteristic
34C31×#137—42no—
35C31×#137—42no—
36C2×Q16×C31—22no—
37C2×SD16×C31—22no—
38C2×M16×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8D411yescharacteristic
44C31×#127D411yescharacteristic
45C31×#124—21no—
46C31×#121—21no—
47C31×#121—21no—
48C4×Q8×C31—21no—
49C4×Q8×C31—21no—
50C4×Q8×C31—21no—
51C4×Q8×C31—21no—
52C4×D4×C31—21no—
53C4×D4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C4⋊C4×C31D412yes—
60C2×C42×C31—21no—
61C2×C42×C31—21no—
62C2×C42×C31C2311yescharacteristic
63C31×#106—24no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8D412yes—
67C31×C4⋊C8D412yes—
68C31×#103—22no—
69C31×#102—22no—
70C31×#102—24no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C31×#95—24no—
76C31×#95D412yes—
77#41×C31—41no—
78#41×C31—41no—
79#41×C31—41no—
80#41×C31—41no—
81C2×Q8×C31—21no—
82C2×Q8×C31—21no—
83C2×Q8×C31—21no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—41no—
88C2×Q8×C31—41no—
89C2×Q8×C31—82no—
90C2×Q8×C31SD1612yes—
91C2×D4×C31—21no—
92C2×D4×C31—21no—
93C2×D4×C31—21no—
94C2×D4×C31—41no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—21no—
99C22×C4×C31—41no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103Q16×C31—44no—
104SD16×C31—44no—
105M16×C31—41no—
106M16×C31—41no—
107C2×C8×C31—22no—
108C2×C8×C31—22no—
109C2×C8×C31—41no—
110C4⋊C4×C31—24no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—22no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—84no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31—41no—
127C42×C31—41no—
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C42×C31#4111yescharacteristic
132#10245C3111yesmaximal, characteristic, direct product factor, Sylow
133C23×C31—41no—
134C23×C31#12011yescharacteristic
135Q8×C31—22no—
136Q8×C31—22no—
137Q8×C31—41no—
138Q8×C31—41no—
139Q8×C31—41no—
140Q8×C31—41no—
141Q8×C31—82no—
142Q8×C31—82no—
143D4×C31—41no—
144D4×C31—41no—
145D4×C31—42no—
146D4×C31—81no—
147D4×C31—81no—
148D4×C31—81no—
149C2×C4×C31—22no—
150C2×C4×C31—24no—
151C2×C4×C31—22no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—41no—
157C2×C4×C31—42no—
158C2×C4×C31—44no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—42no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31#12011yescharacteristic
165C2×C4×C31#12011yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12711yescharacteristic
170C2×C4×C31C2×SD1611yescharacteristic
171C2×C4×C31#13511yescharacteristic
172C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C31#13711yescharacteristic
174C8×C31—42no—
175C8×C31—42no—
176C8×C31—81no—
177#3227C2×C3111yescharacteristic
178#3037C2×C3111yescharacteristic
179#2567C2×C3111yescharacteristic, complemented
180#1549C2×C3111yescharacteristic, complemented
181#1502C2×C3111yescharacteristic
182#1479C2×C3111yescharacteristic, complemented
183#1303C2×C3111yescharacteristic, complemented
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31#39211yescharacteristic
190C22×C31#44811yescharacteristic
191C22×C31#44911yescharacteristic
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—44no—
196C4×C31—42no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31—82no—
200C4×C31#45011yescharacteristic
201C4×C31#45211yescharacteristic
202C4×C31#45612yes—
203C4×C31#46511yescharacteristic
204C4×C31#46811yescharacteristic
205C2×#137—21no—
206#532C22×C3111yescharacteristic
207C2×C4⋊Q8C22×C3111yescharacteristic
208C2×C4×Q8C22×C3111yescharacteristic
209#498—21no—
210#486—21no—
211#481—22no—
212#476—22no—
213#464—22no—
214#462—21no—
215#460—21no—
216#431C22×C3111yescharacteristic
217#431C22×C3111yescharacteristic
218#423C22×C3111yescharacteristic
219#417—21no—
220#395—22no—
221#391—21no—
222#389—22no—
223#384—21no—
224C4×C4⋊C4C22×C3111yescharacteristic
225#332—22no—
226#327—22no—
227Q8⋊C8—22no—
228C2×C31—21no—
229C2×C31—21no—
230C2×C31—161no—
231C2×C31#200011yescharacteristic
232C2×C31#200511yescharacteristic
233C2×C31#200811yescharacteristic
234C2×#41—21no—
235C22×Q8—21no—
236C22×Q8D4×C3111yescharacteristic
237#137—42no—
238#137—42no—
239C2×Q16—22no—
240C2×SD16—22no—
241C2×M16—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8D4×C3111yescharacteristic
247#127D4×C3111yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×D4—21no—
256C4×D4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4D4×C3111yescharacteristic
262C2×C4⋊C4D4×C3112yes—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42C23×C3111yescharacteristic
266#106—24no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C3112yes—
270C4⋊C8D4×C3112yes—
271#103—22no—
272#102—22no—
273#102—24no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C4×C8—21no—
277C4×C8—21no—
278#95—24no—
279#95D4×C3112yes—
280C31#1024511yescharacteristic, direct product factor, Sylow
281#41—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×Q8SD16×C3112yes—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×D4×C3111yescharacteristic
306C22×C4C2×D4×C3111yescharacteristic
307Q16—44no—
308SD16—44no—
309M16—41no—
310M16—41no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C4⋊C4—24no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—84no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42C2×D4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C42#41×C3111yescharacteristic
336C23—41no—
337C23C31×#12011yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—82no—
345Q8—82no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4C31×#12011yescharacteristic
368C2×C4C31×#12011yescharacteristic
369C2×C4C31×#12111yescharacteristic
370C2×C4C31×#12111yescharacteristic
371C2×C4C31×#12111yescharacteristic
372C2×C4C31×#12711yescharacteristic
373C2×C4C2×SD16×C3111yescharacteristic
374C2×C4C31×#13511yescharacteristic
375C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C31×#13711yescharacteristic
377C8—42no—
378C8—42no—
379C8—81no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C31×#39211yescharacteristic
386C22C31×#44811yescharacteristic
387C22C31×#44911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—81no—
394C4—82no—
395C4—81no—
396C4C31×#45011yescharacteristic
397C4C31×#45211yescharacteristic
398C4C31×#45612yes—
399C4C31×#46511yescharacteristic
400C4C31×#46811yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2C31×#200011yescharacteristic
405C2C31×#200511yescharacteristic
406C2C31×#200811yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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
3. C31×#2567C2semidirect
4. C31×#1549C2semidirect
6. C31×#1479C2semidirect
7. C31×#1303C2semidirect
132. #10245C31direct (N × H)
179. #2567C2×C31semidirect
180. #1549C2×C31semidirect
182. #1479C2×C31semidirect
183. #1303C2×C31semidirect
280. C31#10245direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32272
C31×#30372
C31×#25672
C31×#15492
C31×#15022
C31×#14792
C31×#13032
#1024531