Finite Group Databasebeta

← C31×#9813 #21466572

Subgroups — C31×#9813 #21466572

Order 7936.

522 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic
2C31×#1810C211yesmaximal, characteristic, complemented
3C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
4C31×#1508C211yesmaximal, characteristic, complemented
5C31×#1507C211yesmaximal, characteristic
6C31×#1472C211yesmaximal, characteristic, complemented
7C31×#1471C211yesmaximal, characteristic
8C22×SD16×C31C411yescharacteristic, complemented
9C23×C8×C31C2211yescharacteristic
10C2×C31×C22⋊Q8C2211yescharacteristic
11C2×C31×#121C2211yescharacteristic
12C31×#465—21no—
13C31×#465—21no—
14C31×#465—21no—
15C31×#465—21no—
16C2×C31×#108—21no—
17C2×C31×#106C411yescharacteristic, complemented
18C2×C31×#103C411yescharacteristic, complemented
19C2×C31×#102C411yescharacteristic, complemented
20C31×#407C2211yescharacteristic
21C31×#407C2211yescharacteristic
22C2×C31×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C31—21no—
24C4×C22⋊C4×C31C2211yescharacteristic
25C31×#341—21no—
26C31×#336—21no—
27C31×#328—22no—
28C31×#327—22no—
29C31×#324—22no—
30C31×#323—22no—
31C22×Q8×C31C2×C411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31C2×C411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C2×SD16×C31—21no—
36C2×SD16×C31—21no—
37C2×SD16×C31—42no—
38C2×M16×C31—21no—
39C2×M16×C31—21no—
40C22×C8×C31—21no—
41C22×C8×C31—42no—
42C22×C8×C31C2×C411yescharacteristic
43C22×C8×C31C2×C411yescharacteristic
44C22×C8×C31D411yescharacteristic
45C22×C8×C31D411yescharacteristic
46C22×C8×C31D411yescharacteristic
47C22×C8×C31D411yescharacteristic
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C31×C22⋊Q8—21no—
51C31×C22⋊Q8—21no—
52C31×#121—21no—
53C31×#121—21no—
54C31×#121—21no—
55C31×#121—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31C2×C411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C42×C31—21no—
63C31×#108—42no—
64C31×#106—21no—
65C31×#106—21no—
66C31×#103—21no—
67C31×#103—21no—
68C31×#102—21no—
69C31×#102—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8D412yes—
76C4×C8×C31—42no—
77C31×#95D412yes—
78C24×C31—21no—
79C24×C31#4111yescharacteristic
80C2×Q8×C31—21no—
81C2×Q8×C31—21no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—82no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31C22×C411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4111yescharacteristic
103SD16×C31—42no—
104SD16×C31—42no—
105M16×C31—41no—
106M16×C31—41no—
107M16×C31—41no—
108M16×C31—41no—
109C2×C8×C31—22no—
110C2×C8×C31—22no—
111C2×C8×C31—22no—
112C2×C8×C31—22no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—41no—
118C2×C8×C31—41no—
119C2×C8×C31—41no—
120C2×C8×C31C22⋊C411yescharacteristic
121C2×C8×C31C22⋊C411yescharacteristic
122C2×C8×C31C22⋊C411yescharacteristic
123C2×C8×C31C22⋊C411yescharacteristic
124C4⋊C4×C31—21no—
125C4⋊C4×C31—21no—
126C4⋊C4×C31—21no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—41no—
130C22⋊C4×C31—24no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C42×C31—41no—
136C42×C31—41no—
137#9813C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—42no—
143C23×C31—81no—
144C23×C31—81no—
145C23×C31C4×D411yescharacteristic
146C23×C31#12111yescharacteristic
147C23×C31#12411yescharacteristic
148Q8×C31—41no—
149Q8×C31—41no—
150Q8×C31—81no—
151D4×C31—41no—
152D4×C31—41no—
153D4×C31—81no—
154D4×C31—82no—
155D4×C31—82no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—24no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—42no—
172C2×C4×C31—81no—
173C2×C4×C31—81no—
174C2×C4×C31C2×C22⋊C411yescharacteristic
175C2×C4×C31C4×D411yescharacteristic
176C2×C4×C31#12111yescharacteristic
177C2×C4×C31#12711yescharacteristic
178C8×C31—21no—
179C8×C31—21no—
180C8×C31—21no—
181C8×C31—42no—
182C8×C31—81no—
183C8×C31—81no—
184C8×C31#9912yes—
185C2×#465C2×C3111yescharacteristic
186#1810C2×C3111yescharacteristic, complemented
187C8×C22⋊C4C2×C3111yescharacteristic, complemented
188#1508C2×C3111yescharacteristic, complemented
189#1507C2×C3111yescharacteristic
190#1472C2×C3111yescharacteristic, complemented
191#1471C2×C3111yescharacteristic
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—44no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—162no—
204C22×C31#39011yescharacteristic
205C22×C31#44312yes—
206C22×C31#47112yes—
207C4×C31—21no—
208C4×C31—21no—
209C4×C31—21no—
210C4×C31—44no—
211C4×C31—81no—
212C4×C31—81no—
213C4×C31—81no—
214C4×C31C2×#9911yescharacteristic
215C4×C31#41011yescharacteristic
216C22×SD16C4×C3111yescharacteristic, complemented
217C23×C8C22×C3111yescharacteristic
218C2×C22⋊Q8C22×C3111yescharacteristic
219C2×#121C22×C3111yescharacteristic
220#465—21no—
221#465—21no—
222#465—21no—
223#465—21no—
224C2×#108—21no—
225C2×#106C4×C3111yescharacteristic, complemented
226C2×#103C4×C3111yescharacteristic, complemented
227C2×#102C4×C3111yescharacteristic, complemented
228#407C22×C3111yescharacteristic
229#407C22×C3111yescharacteristic
230C2×C22⋊C8C22×C3111yescharacteristic
231C2×C4×C8—21no—
232C4×C22⋊C4C22×C3111yescharacteristic
233#341—21no—
234#336—21no—
235#328—22no—
236#327—22no—
237#324—22no—
238#323—22no—
239C2×C31—22no—
240C2×C31—22no—
241C2×C31—41no—
242C2×C31—161no—
243C2×C31#196411yescharacteristic
244C2×C31#197411yescharacteristic
245C2×C31#197711yescharacteristic
246C22×Q8C2×C4×C3111yescharacteristic
247C22×D4—21no—
248C22×D4C2×C4×C3111yescharacteristic
249C23×C4C23×C3111yescharacteristic
250C2×SD16—21no—
251C2×SD16—21no—
252C2×SD16—42no—
253C2×M16—21no—
254C2×M16—21no—
255C22×C8—21no—
256C22×C8—42no—
257C22×C8C2×C4×C3111yescharacteristic
258C22×C8C2×C4×C3111yescharacteristic
259C22×C8D4×C3111yescharacteristic
260C22×C8D4×C3111yescharacteristic
261C22×C8D4×C3111yescharacteristic
262C22×C8D4×C3111yescharacteristic
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C2×C4×C3111yescharacteristic
273C2×C4⋊C4C2×C4×C3111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C42—21no—
278#108—42no—
279#106—21no—
280#106—21no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8D4×C3112yes—
291C4×C8—42no—
292#95D4×C3112yes—
293C31#981311yescharacteristic, direct product factor, Sylow
294C24—21no—
295C24#41×C3111yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—82no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C22×C4×C3111yescharacteristic
314C22×C4C2×D4×C3111yescharacteristic
315C22×C4C2×D4×C3111yescharacteristic
316C22×C4C2×D4×C3111yescharacteristic
317C22×C4C2×D4×C3111yescharacteristic
318C22×C4#41×C3111yescharacteristic
319SD16—42no—
320SD16—42no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8C22⋊C4×C3111yescharacteristic
337C2×C8C22⋊C4×C3111yescharacteristic
338C2×C8C22⋊C4×C3111yescharacteristic
339C2×C8C22⋊C4×C3111yescharacteristic
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C22⋊C4—24no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23C4×D4×C3111yescharacteristic
361C23C31×#12111yescharacteristic
362C23C31×#12411yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—81no—
369D4—82no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C2×C22⋊C4×C3111yescharacteristic
390C2×C4C4×D4×C3111yescharacteristic
391C2×C4C31×#12111yescharacteristic
392C2×C4C31×#12711yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—81no—
398C8—81no—
399C8C31×#9912yes—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22C31×#39011yescharacteristic
413C22C31×#44312yes—
414C22C31×#47112yes—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—44no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4C2×C31×#9911yescharacteristic
423C4C31×#41011yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2C31×#196411yescharacteristic
429C2C31×#197411yescharacteristic
430C2C31×#197711yescharacteristic
subgroupG/H
center, socleC22×C31#390
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1810C2semidirect
3. C8×C22⋊C4×C31C2semidirect
4. C31×#1508C2semidirect
6. C31×#1472C2semidirect
8. C22×SD16×C31C4semidirect
17. C2×C31×#106C4semidirect
18. C2×C31×#103C4semidirect
19. C2×C31×#102C4semidirect
137. #9813C31direct (N × H)
186. #1810C2×C31semidirect
187. C8×C22⋊C4C2×C31semidirect
188. #1508C2×C31semidirect
190. #1472C2×C31semidirect
216. C22×SD16C4×C31semidirect
225. C2×#106C4×C31semidirect
226. C2×#103C4×C31semidirect
227. C2×#102C4×C31semidirect
293. C31#9813direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C31×#18102
C8×C22⋊C4×C312
C31×#15082
C31×#15072
C31×#14722
C31×#14712
#981331