Finite Group Databasebeta

← C31×#9381 #21466140

Subgroups — C31×#9381 #21466140

Order 7936.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3213C211yesmaximal, characteristic
2C31×#2337C211yesmaximal, characteristic, complemented
3C31×#1980C211yesmaximal, characteristic, complemented
4C31×#1527C211yesmaximal, characteristic, complemented
5C31×#1514C211yesmaximal, characteristic, complemented
6C31×#1288C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×#124C2211yescharacteristic
10C31×#496C412yescomplemented
11C31×#489C412yescomplemented
12C31×#463—22no—
13C31×#448—21no—
14C31×#447—21no—
15C31×#432C2211yescharacteristic
16C31×#432C2211yescharacteristic
17C2×C31×#104—21no—
18C2×C31×#104—21no—
19C4×M16×C31C2211yescharacteristic
20C31×#391—21no—
21C31×#388—21no—
22C31×#388—21no—
23C31×#386—21no—
24C31×#385—21no—
25C31×#383C2211yescharacteristic
26C4×C4⋊C4×C31C2211yescharacteristic
27C4×C22⋊C4×C31—21no—
28C31×#329—22no—
29C31×#327—21no—
30C31×#327—21no—
31C2×#41×C31—21no—
32C22×Q8×C31D411yescharacteristic
33C22×D4×C31D411yescharacteristic
34C23×C4×C31—21no—
35C2×SD16×C31—22no—
36C2×D8×C31—22no—
37C2×M16×C31—21no—
38C31×C4⋊Q8C2×C411yescharacteristic, complemented
39C31×#127C2×C411yescharacteristic, complemented
40C31×#124—21no—
41C31×#124—21no—
42C31×#124—21no—
43C31×#124C2×C412yes—
44C31×#124D412yes—
45C31×#121—21no—
46C31×#121—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C42×C31—21no—
57C2×C42×C31D411yescharacteristic
58C2×C42×C31D411yescharacteristic
59C2×C42×C31C2311yescharacteristic
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×#104—42no—
63C31×#104—42no—
64C31×#103—22no—
65C31×#102—22no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C31×#97—21no—
69C31×#97—21no—
70C31×#97C2×C412yescomplemented
71C4×C8×C31—21no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95—21no—
77C31×#95D411yescharacteristic
78C31×#95D411yescharacteristic
79C24×C31—21no—
80#41×C31—41no—
81#41×C31—41no—
82#41×C31—41no—
83#41×C31—41no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—81no—
87C2×Q8×C31C22⋊C412yes—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—41no—
93C2×D4×C31—81no—
94C2×D4×C31C22⋊C412yes—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—42no—
101C22×C4×C31—41no—
102C22×C4×C31—81no—
103C22×C4×C31—81no—
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31C2×D411yescharacteristic
107SD16×C31—82no—
108D8×C31—82no—
109M16×C31—22no—
110M16×C31—41no—
111C2×C8×C31—22no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—42no—
117C4⋊C4×C31—81no—
118C22⋊C4×C31—22no—
119C22⋊C4×C31—22no—
120C22⋊C4×C31—22no—
121C22⋊C4×C31—22no—
122C22⋊C4×C31—42no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—81no—
126C22⋊C4×C31—81no—
127C42×C31—41no—
128C42×C31—41no—
129C42×C31—81no—
130C42×C31C22×C411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31#4111yescharacteristic
133C42×C31#4111yescharacteristic
134#9381C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—22no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—41no—
143C23×C31#12011yescharacteristic
144Q8×C31—42no—
145Q8×C31—41no—
146Q8×C31—41no—
147Q8×C31—81no—
148D4×C31—42no—
149D4×C31—42no—
150D4×C31—41no—
151D4×C31—41no—
152D4×C31—81no—
153D4×C31—81no—
154D4×C31—81no—
155D4×C31—81no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—22no—
159C2×C4×C31—22no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—81no—
177C2×C4×C31—81no—
178C2×C4×C31—84no—
179C2×C4×C31C2×C22⋊C411yescharacteristic
180C2×C4×C31C4×D411yescharacteristic
181C2×C4×C31C4×D411yescharacteristic
182C2×C4×C31#12111yescharacteristic
183C2×C4×C31#12111yescharacteristic
184C2×C4×C31#12311yescharacteristic
185C8×C31—42no—
186C8×C31—42no—
187C8×C31—81no—
188#3213C2×C3111yescharacteristic
189#2337C2×C3111yescharacteristic, complemented
190#1980C2×C3111yescharacteristic, complemented
191#1527C2×C3111yescharacteristic, complemented
192#1514C2×C3111yescharacteristic, complemented
193#1288C2×C3111yescharacteristic, complemented
194#1285C2×C3111yescharacteristic, complemented
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—42no—
198C22×C31—42no—
199C22×C31—42no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31#38611yescharacteristic
208C22×C31#45311yescharacteristic
209C22×C31#45411yescharacteristic
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—21no—
215C4×C31—21no—
216C4×C31—42no—
217C4×C31—42no—
218C4×C31—81no—
219C4×C31—81no—
220C4×C31—81no—
221C4×C31—81no—
222#532C22×C3111yescharacteristic
223C2×#124C22×C3111yescharacteristic
224#496C4×C3112yescomplemented
225#489C4×C3112yescomplemented
226#463—22no—
227#448—21no—
228#447—21no—
229#432C22×C3111yescharacteristic
230#432C22×C3111yescharacteristic
231C2×#104—21no—
232C2×#104—21no—
233C4×M16C22×C3111yescharacteristic
234#391—21no—
235#388—21no—
236#388—21no—
237#386—21no—
238#385—21no—
239#383C22×C3111yescharacteristic
240C4×C4⋊C4C22×C3111yescharacteristic
241C4×C22⋊C4—21no—
242#329—22no—
243#327—21no—
244#327—21no—
245C2×C31—21no—
246C2×C31—21no—
247C2×C31—82no—
248C2×C31—161no—
249C2×C31#188311yescharacteristic
250C2×C31#190611yescharacteristic
251C2×C31#191111yescharacteristic
252C2×#41—21no—
253C22×Q8D4×C3111yescharacteristic
254C22×D4D4×C3111yescharacteristic
255C23×C4—21no—
256C2×SD16—22no—
257C2×D8—22no—
258C2×M16—21no—
259C4⋊Q8C2×C4×C3111yescharacteristic, complemented
260#127C2×C4×C3111yescharacteristic, complemented
261#124—21no—
262#124—21no—
263#124—21no—
264#124C2×C4×C3112yes—
265#124D4×C3112yes—
266#121—21no—
267#121—21no—
268C4×D4—21no—
269C4×D4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C42—21no—
278C2×C42D4×C3111yescharacteristic
279C2×C42D4×C3111yescharacteristic
280C2×C42C23×C3111yescharacteristic
281C4⋊C8—21no—
282C4⋊C8—21no—
283#104—42no—
284#104—42no—
285#103—22no—
286#102—22no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289#97—21no—
290#97—21no—
291#97C2×C4×C3112yescomplemented
292C4×C8—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95D4×C3111yescharacteristic
299#95D4×C3111yescharacteristic
300C31#938111yescharacteristic, direct product factor, Sylow
301C24—21no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—41no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—81no—
309C2×Q8C22⋊C4×C3112yes—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—81no—
316C2×D4C22⋊C4×C3112yes—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—81no—
325C22×C4—81no—
326C22×C4C2×D4×C3111yescharacteristic
327C22×C4C2×D4×C3111yescharacteristic
328C22×C4C2×D4×C3111yescharacteristic
329SD16—82no—
330D8—82no—
331M16—22no—
332M16—41no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—42no—
339C4⋊C4—81no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—42no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—81no—
348C22⋊C4—81no—
349C42—41no—
350C42—41no—
351C42—81no—
352C42C22×C4×C3111yescharacteristic
353C42C2×D4×C3111yescharacteristic
354C42#41×C3111yescharacteristic
355C42#41×C3111yescharacteristic
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23C31×#12011yescharacteristic
365Q8—42no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369D4—42no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—84no—
400C2×C4C2×C22⋊C4×C3111yescharacteristic
401C2×C4C4×D4×C3111yescharacteristic
402C2×C4C4×D4×C3111yescharacteristic
403C2×C4C31×#12111yescharacteristic
404C2×C4C31×#12111yescharacteristic
405C2×C4C31×#12311yescharacteristic
406C8—42no—
407C8—42no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C31×#38611yescharacteristic
422C22C31×#45311yescharacteristic
423C22C31×#45411yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—81no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2C31×#188311yescharacteristic
441C2C31×#190611yescharacteristic
442C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3213C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2337C2semidirect
3. C31×#1980C2semidirect
4. C31×#1527C2semidirect
5. C31×#1514C2semidirect
6. C31×#1288C2semidirect
7. C31×#1285C2semidirect
10. C31×#496C4semidirect
11. C31×#489C4semidirect
38. C31×C4⋊Q8C2×C4semidirect
39. C31×#127C2×C4semidirect
70. C31×#97C2×C4semidirect
134. #9381C31direct (N × H)
189. #2337C2×C31semidirect
190. #1980C2×C31semidirect
191. #1527C2×C31semidirect
192. #1514C2×C31semidirect
193. #1288C2×C31semidirect
194. #1285C2×C31semidirect
224. #496C4×C31semidirect
225. #489C4×C31semidirect
259. C4⋊Q8C2×C4×C31semidirect
260. #127C2×C4×C31semidirect
291. #97C2×C4×C31semidirect
300. C31#9381direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32132
C31×#23372
C31×#19802
C31×#15272
C31×#15142
C31×#12882
C31×#12852
#938131