Finite Group Databasebeta

← C31×#13232 #21469991

Subgroups — C31×#13232 #21469991

Order 7936.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3057C211yesmaximal, characteristic
2C31×#2135C211yesmaximal, characteristic, complemented
3C31×#2134C211yesmaximal, characteristic
4C31×#2123C211yesmaximal, characteristic, complemented
5C31×#2122C211yesmaximal, characteristic
6C31×#1813C211yesmaximal, characteristic, complemented
7C31×#1757C211yesmaximal, characteristic, complemented
8C22×SD16×C31C411yescharacteristic, complemented
9C2×C31×#131C2211yescharacteristic
10C31×#536C2211yescharacteristic
11C31×#535C2211yescharacteristic
12C31×#468—21no—
13C31×#468—21no—
14C31×#465—21no—
15C31×#465—21no—
16C2×C31×#108—21no—
17C31×#427C411yescharacteristic, complemented
18C31×#419C411yescharacteristic, complemented
19C31×#418C411yescharacteristic, complemented
20C31×#413C2211yescharacteristic
21C31×#413C2211yescharacteristic
22C31×#413C2211yescharacteristic
23C31×#410C2211yescharacteristic
24C31×#405—21no—
25C31×#356—22no—
26C31×#355—22no—
27C31×#352—22no—
28C31×AΣL(1,𝔽16)—22no—
29C31×#344—21no—
30C31×#338—21no—
31C2×#41×C31C2311yescharacteristic
32C22×Q8×C31C2×C411yescharacteristic
33C22×D4×C31C2×C411yescharacteristic
34C2×SD16×C31—21no—
35C2×SD16×C31—21no—
36C2×SD16×C31—41no—
37C2×SD16×C31—41no—
38C31×#131—41no—
39C31×#131—41no—
40C2×M16×C31—21no—
41C2×M16×C31—21no—
42C2×M16×C31—21no—
43C2×M16×C31C2×C411yescharacteristic
44C2×M16×C31D411yescharacteristic
45C2×M16×C31D411yescharacteristic
46C22×C8×C31C2×C411yescharacteristic
47C22×C8×C31D411yescharacteristic
48C22×C8×C31D411yescharacteristic
49C31×C4⋊Q8—21no—
50C31×#127—21no—
51C31×#124—21no—
52C31×#124—21no—
53C31×#123—21no—
54C31×#123—21no—
55C31×C22⋊Q8—21no—
56C31×C22⋊Q8—21no—
57C31×#121—21no—
58C31×#121—21no—
59C31×#120—21no—
60C31×#120—21no—
61C31×#117—21no—
62C31×#117C2×C411yescharacteristic
63C31×#117C2×C411yescharacteristic
64C31×#108—41no—
65C31×#108—41no—
66C31×#107—21no—
67C31×#106—21no—
68C31×#103—21no—
69C31×#103—21no—
70C31×#102—21no—
71C31×#102—21no—
72C31×#101—21no—
73C31×#101—21no—
74C31×#101D412yes—
75C31×#100—21no—
76C31×#100—21no—
77C31×#100—21no—
78C31×#99—21no—
79C31×#99D412yes—
80C31×#97—41no—
81C4×C8×C31—41no—
82C24×C31—21no—
83#41×C31—41no—
84#41×C31—41no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—41no—
88C2×Q8×C31—41no—
89C2×Q8×C31C2×D411yescharacteristic
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31C2×D411yescharacteristic
97C2×D4×C31#4111yescharacteristic
98C2×D4×C31#4111yescharacteristic
99C22×C4×C31—21no—
100C22×C4×C31C22×C411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103SD16×C31—42no—
104SD16×C31—41no—
105SD16×C31—41no—
106M16×C31—22no—
107M16×C31—41no—
108M16×C31—41no—
109M16×C31—41no—
110M16×C31—41no—
111M16×C31—41no—
112M16×C31—41no—
113M16×C31—41no—
114M16×C31—41no—
115C2×C8×C31—21no—
116C2×C8×C31—21no—
117C2×C8×C31—21no—
118C2×C8×C31—21no—
119C2×C8×C31—21no—
120C2×C8×C31—21no—
121C2×C8×C31—41no—
122C2×C8×C31—41no—
123C2×C8×C31—41no—
124C2×C8×C31C22⋊C411yescharacteristic
125C2×C8×C31C22⋊C411yescharacteristic
126C2×C8×C31C22⋊C411yescharacteristic
127C2×C8×C31C22⋊C411yescharacteristic
128C4⋊C4×C31—21no—
129C4⋊C4×C31—21no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31—41no—
132C4⋊C4×C31—41no—
133C22⋊C4×C31—21no—
134C22⋊C4×C31—21no—
135C22⋊C4×C31—22no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—41no—
139C22⋊C4×C31—41no—
140C42×C31—21no—
141C42×C31—21no—
142C42×C31—41no—
143#13232C3111yesmaximal, characteristic, direct product factor, Sylow
144C23×C31—41no—
145C23×C31—81no—
146C23×C31—161no—
147C23×C31C4×D411yescharacteristic
148C23×C31#12111yescharacteristic
149C23×C31#12411yescharacteristic
150Q8×C31—41no—
151Q8×C31—41no—
152Q8×C31—41no—
153Q8×C31—81no—
154D4×C31—41no—
155D4×C31—41no—
156D4×C31—41no—
157D4×C31—41no—
158D4×C31—41no—
159D4×C31—81no—
160D4×C31—161no—
161D4×C31—161no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—21no—
168C2×C4×C31—42no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—81no—
173C2×C4×C31C2×C22⋊C411yescharacteristic
174C2×C4×C31C4×D411yescharacteristic
175C2×C4×C31#12111yescharacteristic
176C2×C4×C31#12711yescharacteristic
177C8×C31—21no—
178C8×C31—21no—
179C8×C31—21no—
180C8×C31—42no—
181C8×C31—81no—
182C8×C31—81no—
183C8×C31#9911yescharacteristic
184C8×C31#9911yescharacteristic
185#3057C2×C3111yescharacteristic
186#2135C2×C3111yescharacteristic, complemented
187#2134C2×C3111yescharacteristic
188#2123C2×C3111yescharacteristic, complemented
189#2122C2×C3111yescharacteristic
190#1813C2×C3111yescharacteristic, complemented
191#1757C2×C3111yescharacteristic, complemented
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—41no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—81no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—162no—
202C22×C31#39011yescharacteristic
203C4×C31—21no—
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—81no—
207C4×C31—81no—
208C4×C31—82no—
209C4×C31—81no—
210C4×C31C2×#9911yescharacteristic
211C4×C31#41011yescharacteristic
212C22×SD16C4×C3111yescharacteristic, complemented
213C2×#131C22×C3111yescharacteristic
214#536C22×C3111yescharacteristic
215#535C22×C3111yescharacteristic
216#468—21no—
217#468—21no—
218#465—21no—
219#465—21no—
220C2×#108—21no—
221#427C4×C3111yescharacteristic, complemented
222#419C4×C3111yescharacteristic, complemented
223#418C4×C3111yescharacteristic, complemented
224#413C22×C3111yescharacteristic
225#413C22×C3111yescharacteristic
226#413C22×C3111yescharacteristic
227#410C22×C3111yescharacteristic
228#405—21no—
229#356—22no—
230#355—22no—
231#352—22no—
232AΣL(1,𝔽16)—22no—
233#344—21no—
234#338—21no—
235C2×C31—21no—
236C2×C31—41no—
237C2×C31—41no—
238C2×C31—41no—
239C2×C31—161no—
240C2×C31#196411yescharacteristic
241C2×#41C23×C3111yescharacteristic
242C22×Q8C2×C4×C3111yescharacteristic
243C22×D4C2×C4×C3111yescharacteristic
244C2×SD16—21no—
245C2×SD16—21no—
246C2×SD16—41no—
247C2×SD16—41no—
248#131—41no—
249#131—41no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16C2×C4×C3111yescharacteristic
254C2×M16D4×C3111yescharacteristic
255C2×M16D4×C3111yescharacteristic
256C22×C8C2×C4×C3111yescharacteristic
257C22×C8D4×C3111yescharacteristic
258C22×C8D4×C3111yescharacteristic
259C4⋊Q8—21no—
260#127—21no—
261#124—21no—
262#124—21no—
263#123—21no—
264#123—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267#121—21no—
268#121—21no—
269#120—21no—
270#120—21no—
271#117—21no—
272#117C2×C4×C3111yescharacteristic
273#117C2×C4×C3111yescharacteristic
274#108—41no—
275#108—41no—
276#107—21no—
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#101—21no—
283#101—21no—
284#101D4×C3112yes—
285#100—21no—
286#100—21no—
287#100—21no—
288#99—21no—
289#99D4×C3112yes—
290#97—41no—
291C4×C8—41no—
292C31#1323211yescharacteristic, direct product factor, Sylow
293C24—21no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8C2×D4×C3111yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4C2×D4×C3111yescharacteristic
308C2×D4#41×C3111yescharacteristic
309C2×D4#41×C3111yescharacteristic
310C22×C4—21no—
311C22×C4C22×C4×C3111yescharacteristic
312C22×C4C2×D4×C3111yescharacteristic
313C22×C4C2×D4×C3111yescharacteristic
314SD16—42no—
315SD16—41no—
316SD16—41no—
317M16—22no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8C22⋊C4×C3111yescharacteristic
336C2×C8C22⋊C4×C3111yescharacteristic
337C2×C8C22⋊C4×C3111yescharacteristic
338C2×C8C22⋊C4×C3111yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—21no—
352C42—21no—
353C42—41no—
354C23—41no—
355C23—81no—
356C23—161no—
357C23C4×D4×C3111yescharacteristic
358C23C31×#12111yescharacteristic
359C23C31×#12411yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4C2×C22⋊C4×C3111yescharacteristic
384C2×C4C4×D4×C3111yescharacteristic
385C2×C4C31×#12111yescharacteristic
386C2×C4C31×#12711yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—42no—
391C8—81no—
392C8—81no—
393C8C31×#9911yescharacteristic
394C8C31×#9911yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22C31×#39011yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—81no—
413C4C2×C31×#9911yescharacteristic
414C4C31×#41011yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2C31×#196411yescharacteristic
subgroupG/H
center, socleC2×C31#1964
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×#41C23×C31
prime radicalC31×#535C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×C31×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2135C2semidirect
4. C31×#2123C2semidirect
6. C31×#1813C2semidirect
7. C31×#1757C2semidirect
8. C22×SD16×C31C4semidirect
17. C31×#427C4semidirect
18. C31×#419C4semidirect
19. C31×#418C4semidirect
143. #13232C31direct (N × H)
186. #2135C2×C31semidirect
188. #2123C2×C31semidirect
190. #1813C2×C31semidirect
191. #1757C2×C31semidirect
212. C22×SD16C4×C31semidirect
221. #427C4×C31semidirect
222. #419C4×C31semidirect
223. #418C4×C31semidirect
292. C31#13232direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30572
C31×#21352
C31×#21342
C31×#21232
C31×#21222
C31×#18132
C31×#17572
#1323231