Finite Group Databasebeta

← C31×#12796 #21469555

Subgroups — C31×#12796 #21469555

Order 7936.

512 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2322C211yesmaximal, characteristic
2C2×C31×#352C212yesmaximal
3C31×#1800C211yesmaximal, characteristic
4C31×#1799C211yesmaximal, characteristic
5C31×#1390C212yesmaximal
6C2×C31×#123C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C22×C4⋊C4×C31C411yescharacteristic, complemented
9C31×#423—21no—
10C2×C31×#100C2212yes—
11C2×C31×#99C2212yes—
12C31×#389—21no—
13C31×#388—21no—
14C31×#387—21no—
15C31×#386C2211yescharacteristic
16C31×#385—21no—
17C31×#385C411yescharacteristic, complemented
18C31×#381C411yescharacteristic, complemented
19C31×#380—21no—
20C4×C22⋊C4×C31C411yescharacteristic, complemented
21C31×#352—24no—
22C31×#343—21no—
23C31×#342—21no—
24C22×D4×C31C2311yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C2×M16×C31—22no—
30C31×#123—21no—
31C31×#123—21no—
32C31×#123D412yes—
33C31×#123Q812yes—
34C4×D4×C31—41no—
35C4×D4×C31—41no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—41no—
41C2×C4⋊C4×C31—41no—
42C2×C4⋊C4×C31—41no—
43C2×C4⋊C4×C31D411yescharacteristic
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31C2×C411yescharacteristic
48C2×C22⋊C4×C31C2×C411yescharacteristic
49C2×C22⋊C4×C31C2×C411yescharacteristic
50C2×C22⋊C4×C31D411yescharacteristic
51C2×C42×C31—21no—
52C2×C42×C31D411yescharacteristic
53C31×C4⋊C8—41no—
54C31×C4⋊C8—41no—
55C31×#100—22no—
56C31×#100—22no—
57C31×#99—22no—
58C31×#99—22no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C31×#95—41no—
65C24×C31C22×C411yescharacteristic
66C24×C31C2×D411yescharacteristic
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C2×D4×C31C2×D411yescharacteristic
70C2×D4×C31C2×Q811yescharacteristic
71C2×D4×C31#4111yescharacteristic
72C2×D4×C31#4111yescharacteristic
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—42no—
86C22×C4×C31—81no—
87C22×C4×C31—81no—
88C22×C4×C31—81no—
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C4⋊C412yescomplemented
94C22×C4×C31C2×D411yescharacteristic
95M16×C31—42no—
96M16×C31—42no—
97C2×C8×C31—42no—
98C4⋊C4×C31—22no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—81no—
105C4⋊C4×C31—82no—
106C22⋊C4×C31—21no—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—22no—
109C22⋊C4×C31—41no—
110C22⋊C4×C31—41no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—81no—
115C22⋊C4×C31C4⋊C412yescomplemented
116C42×C31—21no—
117C42×C31—21no—
118C42×C31—81no—
119#12796C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31C2×C22⋊C411yescharacteristic
129C23×C31C2×C4⋊C411yescharacteristic
130C23×C31#11711yescharacteristic
131C23×C31#12111yescharacteristic
132C23×C31C22⋊Q811yescharacteristic
133D4×C31—41no—
134D4×C31—41no—
135D4×C31—41no—
136D4×C31—41no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—41no—
145C2×C4×C31—42no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31—82no—
165C2×C4×C31—82no—
166C2×C4×C31—82no—
167C2×C4×C31—82no—
168C2×C4×C31#9911yescharacteristic
169C2×C4×C31#9911yescharacteristic
170C2×C4×C31#12111yescharacteristic
171C2×C4×C31C22⋊Q811yescharacteristic
172C8×C31—82no—
173#2322C2×C3111yescharacteristic
174C2×#352C2×C3112yes—
175#1800C2×C3111yescharacteristic
176#1799C2×C3111yescharacteristic
177#1390C2×C3112yes—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—41no—
185C22×C31—41no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—42no—
189C22×C31—41no—
190C22×C31—41no—
191C22×C31—41no—
192C22×C31—41no—
193C22×C31—81no—
194C22×C31#38011yescharacteristic
195C22×C31C2×#9911yescharacteristic
196C22×C31#41011yescharacteristic
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—21no—
201C4×C31—42no—
202C4×C31—42no—
203C4×C31—41no—
204C4×C31—41no—
205C4×C31—41no—
206C4×C31—81no—
207C4×C31—81no—
208C4×C31—162no—
209C2×#123C22×C3111yescharacteristic
210C2×C4×D4C22×C3111yescharacteristic
211C22×C4⋊C4C4×C3111yescharacteristic, complemented
212#423—21no—
213C2×#100C22×C3112yes—
214C2×#99C22×C3112yes—
215#389—21no—
216#388—21no—
217#387—21no—
218#386C22×C3111yescharacteristic
219#385—21no—
220#385C4×C3111yescharacteristic, complemented
221#381C4×C3111yescharacteristic, complemented
222#380—21no—
223C4×C22⋊C4C4×C3111yescharacteristic, complemented
224#352—24no—
225#343—21no—
226#342—21no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—41no—
230C2×C31—41no—
231C2×C31—41no—
232C2×C31—41no—
233C2×C31#179911yescharacteristic
234C2×C31#212111yescharacteristic
235C2×C31#212311yescharacteristic
236C22×D4C23×C3111yescharacteristic
237C23×C4C2×C4×C3111yescharacteristic
238C23×C4C2×C4×C3111yescharacteristic
239C23×C4C2×C4×C3111yescharacteristic
240C23×C4D4×C3111yescharacteristic
241C2×M16—22no—
242#123—21no—
243#123—21no—
244#123D4×C3112yes—
245#123Q8×C3112yes—
246C4×D4—41no—
247C4×D4—41no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4D4×C3111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4C2×C4×C3111yescharacteristic
260C2×C22⋊C4C2×C4×C3111yescharacteristic
261C2×C22⋊C4C2×C4×C3111yescharacteristic
262C2×C22⋊C4D4×C3111yescharacteristic
263C2×C42—21no—
264C2×C42D4×C3111yescharacteristic
265C4⋊C8—41no—
266C4⋊C8—41no—
267#100—22no—
268#100—22no—
269#99—22no—
270#99—22no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—41no—
277C31#1279611yescharacteristic, direct product factor, Sylow
278C24C22×C4×C3111yescharacteristic
279C24C2×D4×C3111yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4C2×D4×C3111yescharacteristic
283C2×D4C2×Q8×C3111yescharacteristic
284C2×D4#41×C3111yescharacteristic
285C2×D4#41×C3111yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—81no—
300C22×C4—81no—
301C22×C4—81no—
302C22×C4C22⋊C4×C3111yescharacteristic
303C22×C4C22⋊C4×C3111yescharacteristic
304C22×C4C22⋊C4×C3111yescharacteristic
305C22×C4C22⋊C4×C3111yescharacteristic
306C22×C4C4⋊C4×C3112yescomplemented
307C22×C4C2×D4×C3111yescharacteristic
308M16—42no—
309M16—42no—
310C2×C8—42no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—81no—
318C4⋊C4—82no—
319C22⋊C4—21no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—81no—
328C22⋊C4C4⋊C4×C3112yescomplemented
329C42—21no—
330C42—21no—
331C42—81no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×C22⋊C4×C3111yescharacteristic
341C23C2×C4⋊C4×C3111yescharacteristic
342C23C31×#11711yescharacteristic
343C23C31×#12111yescharacteristic
344C23C31×C22⋊Q811yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4C31×#9911yescharacteristic
381C2×C4C31×#9911yescharacteristic
382C2×C4C31×#12111yescharacteristic
383C2×C4C31×C22⋊Q811yescharacteristic
384C8—82no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22C31×#38011yescharacteristic
402C22C2×C31×#9911yescharacteristic
403C22C31×#41011yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—162no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2C31×#179911yescharacteristic
423C2C31×#212111yescharacteristic
424C2C31×#212311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C4⋊C4×C31C4semidirect
17. C31×#385C4semidirect
18. C31×#381C4semidirect
20. C4×C22⋊C4×C31C4semidirect
93. C22×C4×C31C4⋊C4semidirect
115. C22⋊C4×C31C4⋊C4semidirect
119. #12796C31direct (N × H)
211. C22×C4⋊C4C4×C31semidirect
220. #385C4×C31semidirect
221. #381C4×C31semidirect
223. C4×C22⋊C4C4×C31semidirect
277. C31#12796direct (N × H)
306. C22×C4C4⋊C4×C31semidirect
328. C22⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23222
C2×C31×#3522
C31×#18002
C31×#17992
C31×#13902
#1279631