Finite Group Databasebeta

← C31×#9233 #21465992

Subgroups — C31×#9233 #21465992

Order 7936.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3100C211yesmaximal, characteristic
2C42×D4×C31C211yesmaximal, characteristic, complemented
3C31×#1962C211yesmaximal, characteristic, complemented
4C31×#1502C211yesmaximal, characteristic, complemented
5C31×#1486C211yesmaximal, characteristic, complemented
6C31×#1303C211yesmaximal, characteristic, complemented
7C31×#1276C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C4×D4×C31—21no—
10C2×C4×D4×C31C2211yescharacteristic
11C22×C42×C31—21no—
12C31×#480—21no—
13C31×#474C412yescomplemented
14C31×#459C412yescomplemented
15C31×#447—21no—
16C4×D8×C31—22no—
17C31×#431C2211yescharacteristic
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C2×C31×#104—21no—
21C2×C31×#104—21no—
22C4×C4⋊C4×C31—21no—
23C4×C4⋊C4×C31C2211yescharacteristic
24C4×C22⋊C4×C31—21no—
25C4×C22⋊C4×C31—22no—
26C43×C31C2211yescharacteristic
27C31×#327—22no—
28C31×D4⋊C8—22no—
29C2×#41×C31—21no—
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—22no—
32C23×C4×C31—21no—
33C2×D8×C31—22no—
34C2×M16×C31—21no—
35C31×C4⋊Q8C2×C411yescharacteristic, complemented
36C31×#127C2×C411yescharacteristic, complemented
37C31×#124—21no—
38C31×#121—21no—
39C31×#121—21no—
40C4×D4×C31—28no—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C4×D4×C31C2×C412yes—
46C4×D4×C31D412yes—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31—22no—
53C2×C42×C31—21no—
54C2×C42×C31—21no—
55C2×C42×C31—42no—
56C2×C42×C31—42no—
57C2×C42×C31D411yescharacteristic
58C2×C42×C31D411yescharacteristic
59C2×C42×C31C2311yescharacteristic
60C31×#107—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8C2×C412yescomplemented
65C31×#104—42no—
66C31×#104—42no—
67C31×#102—22no—
68C31×#102—22no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C4×C8×C31—21no—
72C4×C8×C31—21no—
73C31×#95—22no—
74C31×#95D412yes—
75C24×C31—21no—
76#41×C31—41no—
77#41×C31—41no—
78#41×C31—41no—
79#41×C31—41no—
80C2×Q8×C31—21no—
81C2×D4×C31—24no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—41no—
87C2×D4×C31C22⋊C412yes—
88C22×C4×C31—21no—
89C22×C4×C31—28no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—44no—
96C22×C4×C31—44no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31—41no—
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105D8×C31—44no—
106M16×C31—41no—
107M16×C31—41no—
108C2×C8×C31—22no—
109C2×C8×C31—41no—
110C2×C8×C31—41no—
111C4⋊C4×C31—24no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31C22⋊C412yes—
116C22⋊C4×C31—28no—
117C22⋊C4×C31—22no—
118C22⋊C4×C31—22no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C42×C31—24no—
122C42×C31—21no—
123C42×C31—21no—
124C42×C31—21no—
125C42×C31—42no—
126C42×C31—44no—
127C42×C31—41no—
128C42×C31—41no—
129C42×C31D812yescomplemented
130C42×C31C22×C411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31#4111yescharacteristic
133C42×C31#4111yescharacteristic
134#9233C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—24no—
136C23×C31—22no—
137C23×C31—42no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31#12011yescharacteristic
142Q8×C31—41no—
143Q8×C31—41no—
144D4×C31—24no—
145D4×C31—22no—
146D4×C31—42no—
147D4×C31—41no—
148D4×C31—41no—
149D4×C31—81no—
150D4×C31—81no—
151D4×C31—81no—
152D4×C31#10414yescomplemented
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—22no—
157C2×C4×C31—22no—
158C2×C4×C31—24no—
159C2×C4×C31—22no—
160C2×C4×C31—41no—
161C2×C4×C31—416no—
162C2×C4×C31—41no—
163C2×C4×C31—42no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—41no—
173C2×C4×C31—81no—
174C2×C4×C31—81no—
175C2×C4×C31C2×C22⋊C411yescharacteristic
176C2×C4×C31C4×D411yescharacteristic
177C2×C4×C31C4×D411yescharacteristic
178C2×C4×C31#12111yescharacteristic
179C2×C4×C31#12111yescharacteristic
180C2×C4×C31#12311yescharacteristic
181C2×C4×C31C2×D811yescharacteristic
182C2×C4×C31#13511yescharacteristic
183C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
185C8×C31—42no—
186C8×C31—81no—
187C8×C31—81no—
188#3100C2×C3111yescharacteristic
189C42×D4C2×C3111yescharacteristic, complemented
190#1962C2×C3111yescharacteristic, complemented
191#1502C2×C3111yescharacteristic, complemented
192#1486C2×C3111yescharacteristic, complemented
193#1303C2×C3111yescharacteristic, complemented
194#1276C2×C3111yescharacteristic, complemented
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—24no—
198C22×C31—44no—
199C22×C31—44no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31#38611yescharacteristic
206C22×C31#44711yescharacteristic
207C22×C31#44911yescharacteristic
208C4×C31—24no—
209C4×C31—21no—
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—42no—
213C4×C31—44no—
214C4×C31—42no—
215C4×C31—81no—
216C4×C31C2×#10412yes—
217C4×C31C4×D811yescharacteristic
218C4×C31#44211yescharacteristic
219C4×C31#45911yescharacteristic
220C4×C31#46311yescharacteristic
221#532C22×C3111yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C22×C3111yescharacteristic
224C22×C42—21no—
225#480—21no—
226#474C4×C3112yescomplemented
227#459C4×C3112yescomplemented
228#447—21no—
229C4×D8—22no—
230#431C22×C3111yescharacteristic
231#431C22×C3111yescharacteristic
232#423C22×C3111yescharacteristic
233C2×#104—21no—
234C2×#104—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4C22×C3111yescharacteristic
237C4×C22⋊C4—21no—
238C4×C22⋊C4—22no—
239C43C22×C3111yescharacteristic
240#327—22no—
241D4⋊C8—22no—
242C2×C31—21no—
243C2×C31—21no—
244C2×C31—44no—
245C2×C31—161no—
246C2×C31#187911yescharacteristic
247C2×C31#189611yescharacteristic
248C2×C31#190611yescharacteristic
249C2×#41—21no—
250C22×D4D4×C3111yescharacteristic
251C23×C4—22no—
252C23×C4—21no—
253C2×D8—22no—
254C2×M16—21no—
255C4⋊Q8C2×C4×C3111yescharacteristic, complemented
256#127C2×C4×C3111yescharacteristic, complemented
257#124—21no—
258#121—21no—
259#121—21no—
260C4×D4—28no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4C2×C4×C3112yes—
266C4×D4D4×C3112yes—
267C2×C4⋊C4—21no—
268C2×C4⋊C4D4×C3111yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C42—21no—
272C2×C42—22no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—42no—
276C2×C42—42no—
277C2×C42D4×C3111yescharacteristic
278C2×C42D4×C3111yescharacteristic
279C2×C42C23×C3111yescharacteristic
280#107—22no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8C2×C4×C3112yescomplemented
285#104—42no—
286#104—42no—
287#102—22no—
288#102—22no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C4×C8—21no—
292C4×C8—21no—
293#95—22no—
294#95D4×C3112yes—
295C31#923311yescharacteristic, direct product factor, Sylow
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4C22⋊C4×C3112yes—
309C22×C4—21no—
310C22×C4—28no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C2×D4×C3111yescharacteristic
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3111yescharacteristic
326D8—44no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊C4×C3112yes—
337C22⋊C4—28no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—24no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—42no—
347C42—44no—
348C42—41no—
349C42—41no—
350C42D8×C3112yescomplemented
351C42C22×C4×C3111yescharacteristic
352C42C2×D4×C3111yescharacteristic
353C42#41×C3111yescharacteristic
354C42#41×C3111yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C31×#12011yescharacteristic
362Q8—41no—
363Q8—41no—
364D4—24no—
365D4—22no—
366D4—42no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4C31×#10414yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—416no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C2×C22⋊C4×C3111yescharacteristic
396C2×C4C4×D4×C3111yescharacteristic
397C2×C4C4×D4×C3111yescharacteristic
398C2×C4C31×#12111yescharacteristic
399C2×C4C31×#12111yescharacteristic
400C2×C4C31×#12311yescharacteristic
401C2×C4C2×D8×C3111yescharacteristic
402C2×C4C31×#13511yescharacteristic
403C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
404C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
405C8—42no—
406C8—81no—
407C8—81no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22C31×#38611yescharacteristic
419C22C31×#44711yescharacteristic
420C22C31×#44911yescharacteristic
421C4—24no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—44no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4C2×C31×#10412yes—
430C4C4×D8×C3111yescharacteristic
431C4C31×#44211yescharacteristic
432C4C31×#45911yescharacteristic
433C4C31×#46311yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—161no—
438C2C31×#187911yescharacteristic
439C2C31×#189611yescharacteristic
440C2C31×#190611yescharacteristic
subgroupG/H
centerC2×C4×C31#121
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#386
prime radicalC31×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C42×D4×C31C2semidirect
3. C31×#1962C2semidirect
4. C31×#1502C2semidirect
5. C31×#1486C2semidirect
6. C31×#1303C2semidirect
7. C31×#1276C2semidirect
13. C31×#474C4semidirect
14. C31×#459C4semidirect
35. C31×C4⋊Q8C2×C4semidirect
36. C31×#127C2×C4semidirect
64. C31×C4⋊C8C2×C4semidirect
129. C42×C31D8semidirect
134. #9233C31direct (N × H)
152. D4×C31#104semidirect
189. C42×D4C2×C31semidirect
190. #1962C2×C31semidirect
191. #1502C2×C31semidirect
192. #1486C2×C31semidirect
193. #1303C2×C31semidirect
194. #1276C2×C31semidirect
226. #474C4×C31semidirect
227. #459C4×C31semidirect
255. C4⋊Q8C2×C4×C31semidirect
256. #127C2×C4×C31semidirect
284. C4⋊C8C2×C4×C31semidirect
295. C31#9233direct (N × H)
350. C42D8×C31semidirect
372. D4C31×#104semidirect

Maximal subgroups

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

subgroupindex
C31×#31002
C42×D4×C312
C31×#19622
C31×#15022
C31×#14862
C31×#13032
C31×#12762
#923331