Finite Group Databasebeta

← C31×#9887 #21466646

Subgroups — C31×#9887 #21466646

Order 7936.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2851C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic
3C31×C4⋊#95C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1294C212yesmaximal
6C2×C31×#125C411yescharacteristic, complemented
7C22×C4⋊C4×C31—21no—
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8C2212yes—
10C2×C31×#97—21no—
11C31×#389C411yescharacteristic, complemented
12C31×#389C411yescharacteristic, complemented
13C31×#387—21no—
14C31×#387—21no—
15C31×#385—21no—
16C31×#385—21no—
17C31×#382C411yescharacteristic, complemented
18C31×#380C2211yescharacteristic
19C31×#380C2211yescharacteristic
20C2×C31×#95—21no—
21C2×C31×#95C2212yes—
22C31×#336—21no—
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C31×#125—42no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31—42no—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C42×C31—42no—
43C2×C42×C31C2×C411yescharacteristic
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C31×C22⋊C8—22no—
48C31×C22⋊C8Q814yes—
49C31×#97—42no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—24no—
57C31×#95—42no—
58C24×C31C2×D411yescharacteristic
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—24no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—41no—
71C22×C4×C31—41no—
72C22×C4×C31—41no—
73C22×C4×C31—41no—
74C22×C4×C31—42no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22×C411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31C2×Q812yes—
87C22×C4×C31#4112yes—
88C2×C8×C31—24no—
89C2×C8×C31—42no—
90C2×C8×C31—42no—
91C4⋊C4×C31—42no—
92C4⋊C4×C31—48no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C4⋊C4×C31—41no—
98C4⋊C4×C31—42no—
99C4⋊C4×C31—42no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C42×C31—22no—
105C42×C31—22no—
106C42×C31—41no—
107C42×C31—41no—
108#9887C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31C2×C22⋊C411yescharacteristic
114C23×C31#12411yescharacteristic
115C23×C31C4⋊Q811yescharacteristic
116C23×C31AGL(1,ℤ/8)11yescharacteristic
117C23×C31AGL(1,ℤ/8)11yescharacteristic
118C23×C31#13711yescharacteristic
119C23×C31#13711yescharacteristic
120C2×C4×C31—24no—
121C2×C4×C31—24no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—44no—
141C2×C4×C31—44no—
142C2×C4×C31—44no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—82no—
156C2×C4×C31—82no—
157C2×C4×C31—82no—
158C2×C4×C31—82no—
159C2×C4×C31#9912yes—
160C2×C4×C31#10412yes—
161C2×C4×C31C4×Q812yes—
162C2×C4×C31C22⋊Q812yes—
163C8×C31—44no—
164#2851C2×C3111yescharacteristic
165#1749C2×C3111yescharacteristic
166C4⋊#95C2×C3111yescharacteristic
167#1294C2×C3112yes—
168#1294C2×C3112yes—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31#39111yescharacteristic
182C22×C31C2×#9911yescharacteristic
183C22×C31#41011yescharacteristic
184C22×C31#41711yescharacteristic
185C22×C31#41711yescharacteristic
186C22×C31C2×#10411yescharacteristic
187C22×C31#42111yescharacteristic
188C22×C31#49011yescharacteristic
189C22×C31#49111yescharacteristic
190C22×C31#50111yescharacteristic
191C22×C31#50111yescharacteristic
192C4×C31—22no—
193C4×C31—22no—
194C4×C31—22no—
195C4×C31—22no—
196C4×C31—41no—
197C4×C31—41no—
198C4×C31—84no—
199C4×C31—81no—
200C4×C31—81no—
201C4×C31—81no—
202C4×C31—81no—
203C2×#125C4×C3111yescharacteristic, complemented
204C22×C4⋊C4—21no—
205C22×C42C22×C3111yescharacteristic
206C2×C22⋊C8C22×C3112yes—
207C2×#97—21no—
208#389C4×C3111yescharacteristic, complemented
209#389C4×C3111yescharacteristic, complemented
210#387—21no—
211#387—21no—
212#385—21no—
213#385—21no—
214#382C4×C3111yescharacteristic, complemented
215#380C22×C3111yescharacteristic
216#380C22×C3111yescharacteristic
217C2×#95—21no—
218C2×#95C22×C3112yes—
219#336—21no—
220C2×C31—21no—
221C2×C31—21no—
222C2×C31—21no—
223C2×C31—21no—
224C2×C31#150411yescharacteristic
225C2×C31#150911yescharacteristic
226C2×C31#151211yescharacteristic
227C2×C31#151311yescharacteristic
228C2×C31#198611yescharacteristic
229C2×C31#199211yescharacteristic
230C2×C31#199611yescharacteristic
231C23×C4—22no—
232C23×C4D4×C3111yescharacteristic
233C23×C4D4×C3111yescharacteristic
234C23×C4C23×C3111yescharacteristic
235C22×C8—22no—
236#125—42no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4C2×C4×C3111yescharacteristic
245C2×C4⋊C4C2×C4×C3111yescharacteristic
246C2×C4⋊C4C2×C4×C3111yescharacteristic
247C2×C4⋊C4C2×C4×C3111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42—42no—
251C2×C42C2×C4×C3111yescharacteristic
252C2×C42C2×C4×C3111yescharacteristic
253C2×C42D4×C3111yescharacteristic
254C2×C42D4×C3111yescharacteristic
255C22⋊C8—22no—
256C22⋊C8Q8×C3114yes—
257#97—42no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—24no—
265#95—42no—
266C31#988711yescharacteristic, direct product factor, Sylow
267C24C2×D4×C3111yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C22⋊C4×C3111yescharacteristic
290C22×C4C22⋊C4×C3111yescharacteristic
291C22×C4C22⋊C4×C3111yescharacteristic
292C22×C4C22⋊C4×C3111yescharacteristic
293C22×C4C22×C4×C3111yescharacteristic
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×Q8×C3112yes—
296C22×C4#41×C3112yes—
297C2×C8—24no—
298C2×C8—42no—
299C2×C8—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—48no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—22no—
314C42—22no—
315C42—41no—
316C42—41no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊C4×C3111yescharacteristic
322C23C31×#12411yescharacteristic
323C23C31×C4⋊Q811yescharacteristic
324C23C31×AGL(1,ℤ/8)11yescharacteristic
325C23C31×AGL(1,ℤ/8)11yescharacteristic
326C23C31×#13711yescharacteristic
327C23C31×#13711yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4C31×#9912yes—
368C2×C4C31×#10412yes—
369C2×C4C4×Q8×C3112yes—
370C2×C4C31×C22⋊Q812yes—
371C8—44no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22C31×#39111yescharacteristic
385C22C2×C31×#9911yescharacteristic
386C22C31×#41011yescharacteristic
387C22C31×#41711yescharacteristic
388C22C31×#41711yescharacteristic
389C22C2×C31×#10411yescharacteristic
390C22C31×#42111yescharacteristic
391C22C31×#49011yescharacteristic
392C22C31×#49111yescharacteristic
393C22C31×#50111yescharacteristic
394C22C31×#50111yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—84no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2C31×#150411yescharacteristic
411C2C31×#150911yescharacteristic
412C2C31×#151211yescharacteristic
413C2C31×#151311yescharacteristic
414C2C31×#198611yescharacteristic
415C2C31×#199211yescharacteristic
416C2C31×#199611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C31×#125C4semidirect
11. C31×#389C4semidirect
12. C31×#389C4semidirect
17. C31×#382C4semidirect
108. #9887C31direct (N × H)
203. C2×#125C4×C31semidirect
208. #389C4×C31semidirect
209. #389C4×C31semidirect
214. #382C4×C31semidirect
266. C31#9887direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28512
C31×#17492
C31×C4⋊#952
C31×#12942
#988731