Finite Group Databasebeta

← C31×#11796 #21468555

Subgroups — C31×#11796 #21468555

Order 7936.

1068 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic, complemented
3C31×#1462C211yesmaximal, characteristic, complemented
4C31×#1343C214yesmaximal, complemented
5C23×D4×C31—21no—
6C23×D4×C31C411yescharacteristic, complemented
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31C2211yescharacteristic
9C31×#407—21no—
10C31×#392—21no—
11C31×#392—21no—
12C31×#392C412yescomplemented
13C31×#392C2212yes—
14C31×#379—21no—
15C2×C31×#95C411yescharacteristic, complemented
16C31×#342—21no—
17C31×#342C2212yescomplemented
18C31×#323—21no—
19C31×#323C2212yescomplemented
20C25×C31—21no—
21C25×C31D411yescharacteristic
22C22×D4×C31—22no—
23C22×D4×C31—22no—
24C22×D4×C31—21no—
25C22×D4×C31—44no—
26C22×D4×C31—41no—
27C22×D4×C31—41no—
28C22×D4×C31—44no—
29C22×D4×C31—44no—
30C22×D4×C31—44no—
31C22×D4×C31C2×C412yes—
32C23×C4×C31—21no—
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C2×M16×C31—41no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—41no—
40C2×C22⋊C4×C31—41no—
41C2×C22⋊C4×C31—44no—
42C2×C22⋊C4×C31—41no—
43C2×C22⋊C4×C31—41no—
44C2×C22⋊C4×C31C2×C411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C22⋊C4×C31C2311yescharacteristic
48C31×C22⋊C8—22no—
49C31×C22⋊C8—41no—
50C31×#95—21no—
51C31×#95C2×C412yes—
52C24×C31—24no—
53C24×C31—22no—
54C24×C31—22no—
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—41no—
58C24×C31—42no—
59C24×C31—42no—
60C24×C31—42no—
61C24×C31—42no—
62C24×C31—42no—
63C24×C31—42no—
64C24×C31—42no—
65C24×C31—41no—
66C24×C31—41no—
67C24×C31C22⋊C411yescharacteristic
68C24×C31C22⋊C411yescharacteristic
69C24×C31C2×D411yescharacteristic
70C2×D4×C31—44no—
71C2×D4×C31—44no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C2×D4×C31—44no—
75C2×D4×C31—44no—
76C2×D4×C31—44no—
77C2×D4×C31—44no—
78C2×D4×C31—48no—
79C2×D4×C31—432no—
80C2×D4×C31—44no—
81C2×D4×C31—44no—
82C2×D4×C31—44no—
83C2×D4×C31—44no—
84C22×C4×C31—24no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22×C411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99M16×C31—82no—
100C2×C8×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—44no—
106C22⋊C4×C31—44no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—82no—
110C22⋊C4×C31—82no—
111#11796C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—24no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—42no—
123C23×C31—42no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—42no—
129C23×C31—48no—
130C23×C31—48no—
131C23×C31—42no—
132C23×C31—44no—
133C23×C31—42no—
134C23×C31—48no—
135C23×C31—42no—
136C23×C31—44no—
137C23×C31—42no—
138C23×C31—42no—
139C23×C31—42no—
140C23×C31—42no—
141C23×C31—81no—
142C23×C31—81no—
143C23×C31—84no—
144C23×C31—84no—
145C23×C31—84no—
146C23×C31—82no—
147C23×C31—82no—
148C23×C31—82no—
149C23×C31—82no—
150C23×C31#9911yescharacteristic
151C23×C31#9911yescharacteristic
152C23×C31C2×C22⋊C411yescharacteristic
153C23×C31AGL(1,ℤ/8)12yes—
154D4×C31—44no—
155D4×C31—416no—
156D4×C31—416no—
157D4×C31—48no—
158D4×C31—44no—
159C2×C4×C31—24no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—48no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—81no—
175C2×C4×C31—82no—
176C2×C4×C31—82no—
177C2×C4×C31—82no—
178C8×C31—82no—
179C2×#392C2×C3111yescharacteristic
180#1819C2×C3111yescharacteristic, complemented
181#1462C2×C3111yescharacteristic, complemented
182#1343C2×C3114yescomplemented
183C22×C31—24no—
184C22×C31—24no—
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—22no—
192C22×C31—42no—
193C22×C31—42no—
194C22×C31—44no—
195C22×C31—44no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—44no—
199C22×C31—41no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—81no—
203C22×C31—84no—
204C22×C31—84no—
205C22×C31—81no—
206C22×C31—82no—
207C22×C31—82no—
208C22×C31—88no—
209C22×C31—88no—
210C22×C31—82no—
211C22×C31—82no—
212C22×C31AΣL(1,𝔽16)12yes—
213C22×C31#35312yes—
214C22×C31C2×#9911yescharacteristic
215C22×C31#41811yescharacteristic
216C22×C31#42111yescharacteristic
217C4×C31—44no—
218C4×C31—41no—
219C4×C31—41no—
220C4×C31—41no—
221C4×C31—41no—
222C4×C31—162no—
223C23×D4—21no—
224C23×D4C4×C3111yescharacteristic, complemented
225C22×C22⋊C4—21no—
226C22×C22⋊C4C22×C3111yescharacteristic
227#407—21no—
228#392—21no—
229#392—21no—
230#392C4×C3112yescomplemented
231#392C22×C3112yes—
232#379—21no—
233C2×#95C4×C3111yescharacteristic, complemented
234#342—21no—
235#342C22×C3112yescomplemented
236#323—21no—
237#323C22×C3112yescomplemented
238C2×C31—21no—
239C2×C31—21no—
240C2×C31—22no—
241C2×C31—22no—
242C2×C31—42no—
243C2×C31—81no—
244C2×C31—84no—
245C2×C31#151011yescharacteristic
246C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
247C2×C31C2×#35311yescharacteristic
248C25—21no—
249C25D4×C3111yescharacteristic
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4—41no—
254C22×D4—41no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4C2×C4×C3112yes—
260C23×C4—21no—
261C23×C4C2×C4×C3111yescharacteristic
262C23×C4D4×C3111yescharacteristic
263C2×M16—41no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—41no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4—44no—
270C2×C22⋊C4—41no—
271C2×C22⋊C4—41no—
272C2×C22⋊C4C2×C4×C3111yescharacteristic
273C2×C22⋊C4D4×C3111yescharacteristic
274C2×C22⋊C4D4×C3111yescharacteristic
275C2×C22⋊C4C23×C3111yescharacteristic
276C22⋊C8—22no—
277C22⋊C8—41no—
278#95—21no—
279#95C2×C4×C3112yes—
280C31#1179611yescharacteristic, direct product factor, Sylow
281C24—24no—
282C24—22no—
283C24—22no—
284C24—21no—
285C24—21no—
286C24—41no—
287C24—42no—
288C24—42no—
289C24—42no—
290C24—42no—
291C24—42no—
292C24—42no—
293C24—42no—
294C24—41no—
295C24—41no—
296C24C22⋊C4×C3111yescharacteristic
297C24C22⋊C4×C3111yescharacteristic
298C24C2×D4×C3111yescharacteristic
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—42no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C2×D4—44no—
308C2×D4—48no—
309C2×D4—432no—
310C2×D4—44no—
311C2×D4—44no—
312C2×D4—44no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4C22⋊C4×C3111yescharacteristic
325C22×C4C22⋊C4×C3111yescharacteristic
326C22×C4C22×C4×C3111yescharacteristic
327C22×C4C2×D4×C3111yescharacteristic
328M16—82no—
329C2×C8—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—44no—
335C22⋊C4—44no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—82no—
339C22⋊C4—82no—
340C23—21no—
341C23—21no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—21no—
346C23—24no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—48no—
358C23—48no—
359C23—42no—
360C23—44no—
361C23—42no—
362C23—48no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—84no—
374C23—82no—
375C23—82no—
376C23—82no—
377C23—82no—
378C23C31×#9911yescharacteristic
379C23C31×#9911yescharacteristic
380C23C2×C22⋊C4×C3111yescharacteristic
381C23C31×AGL(1,ℤ/8)12yes—
382D4—44no—
383D4—416no—
384D4—416no—
385D4—44no—
386D4—48no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—48no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—81no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C8—82no—
407C22—24no—
408C22—24no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—44no—
420C22—41no—
421C22—41no—
422C22—44no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—84no—
428C22—84no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—88no—
433C22—88no—
434C22—82no—
435C22—82no—
436C22C31×AΣL(1,𝔽16)12yes—
437C22C31×#35312yes—
438C22C2×C31×#9911yescharacteristic
439C22C31×#41811yescharacteristic
440C22C31×#42111yescharacteristic
441C4—44no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—162no—
447C2—21no—
448C2—21no—
449C2—22no—
450C2—22no—
451C2—42no—
452C2—81no—
453C2—84no—
454C2C31×#151011yescharacteristic
455C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
456C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC2×C31×#392C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1819C2semidirect
3. C31×#1462C2semidirect
4. C31×#1343C2semidirect
6. C23×D4×C31C4semidirect
12. C31×#392C4semidirect
15. C2×C31×#95C4semidirect
17. C31×#342C22semidirect
19. C31×#323C22semidirect
111. #11796C31direct (N × H)
180. #1819C2×C31semidirect
181. #1462C2×C31semidirect
182. #1343C2×C31semidirect
224. C23×D4C4×C31semidirect
230. #392C4×C31semidirect
233. C2×#95C4×C31semidirect
235. #342C22×C31semidirect
237. #323C22×C31semidirect
280. C31#11796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3922
C31×#18192
C31×#14622
C31×#13432
#1179631