Finite Group Databasebeta

← C31×#9344 #21466103

Subgroups — C31×#9344 #21466103

Order 7936.

520 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3193C211yesmaximal, characteristic
2C31×#2378C211yesmaximal, characteristic, complemented
3C31×#1964C211yesmaximal, characteristic
4C31×#1510C211yesmaximal, characteristic
5C31×#1508C211yesmaximal, characteristic, complemented
6C31×#1305C211yesmaximal, characteristic, complemented
7C31×#1284C211yesmaximal, characteristic, complemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C2×C31×#121C2211yescharacteristic
10C31×#484C412yescomplemented
11C31×#480—21no—
12C31×#468—22no—
13C31×#450C412yescomplemented
14C31×#448—21no—
15C2×C31×#99—21no—
16C2×C31×#99—21no—
17C31×#407C2211yescharacteristic
18C31×#407C2211yescharacteristic
19C31×#391—21no—
20C31×#389—21no—
21C31×#388—21no—
22C31×#388—21no—
23C31×#387—21no—
24C31×#387—21no—
25C31×#381C2211yescharacteristic
26C31×#380C2211yescharacteristic
27C4×C22⋊C4×C31C2211yescharacteristic
28C31×#328—22no—
29C31×#327—21no—
30C31×#327—21no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31C2×C411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C2×SD16×C31—22no—
36C2×M16×C31—21no—
37C2×M16×C31—21no—
38C31×C22⋊Q8—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8C2×C412yes—
41C31×C22⋊Q8D412yes—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#121—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31C2×C411yescharacteristic
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31D411yescharacteristic
57C2×C22⋊C4×C31D411yescharacteristic
58C2×C42×C31—21no—
59C2×C42×C31—21no—
60C2×C42×C31—21no—
61C31×#107—22no—
62C31×#103—22no—
63C31×#102—22no—
64C31×#99—42no—
65C31×#99—42no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8C2×C412yes—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95—21no—
77C31×#95D411yescharacteristic
78C31×#95D411yescharacteristic
79C24×C31—21no—
80C24×C31C2×D411yescharacteristic
81C2×Q8×C31—21no—
82C2×Q8×C31—81no—
83C2×Q8×C31C22⋊C412yes—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—41no—
92C2×D4×C31—81no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—41no—
101C22×C4×C31—81no—
102C22×C4×C31C22×C411yescharacteristic
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31#4111yescharacteristic
107C22×C4×C31#4111yescharacteristic
108SD16×C31—82no—
109M16×C31—81no—
110M16×C31—81no—
111C2×C8×C31—22no—
112C2×C8×C31—41no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—22no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—81no—
119C4⋊C4×C31—81no—
120C4⋊C4×C31—81no—
121C4⋊C4×C31C22⋊C412yes—
122C22⋊C4×C31—22no—
123C22⋊C4×C31—22no—
124C22⋊C4×C31—22no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—81no—
131C42×C31—81no—
132C42×C31—81no—
133C42×C31—81no—
134#9344C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—21no—
136C23×C31—21no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—81no—
143C23×C31—81no—
144C23×C31C4×D411yescharacteristic
145C23×C31#12011yescharacteristic
146C23×C31#12111yescharacteristic
147Q8×C31—42no—
148Q8×C31—81no—
149D4×C31—42no—
150D4×C31—81no—
151D4×C31—81no—
152D4×C31—81no—
153D4×C31—81no—
154D4×C31—81no—
155C2×C4×C31—22no—
156C2×C4×C31—22no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
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—42no—
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—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—81no—
184C2×C4×C31—81no—
185C2×C4×C31C2×C22⋊C411yescharacteristic
186C2×C4×C31C4×D411yescharacteristic
187C2×C4×C31#12111yescharacteristic
188C2×C4×C31#12311yescharacteristic
189C8×C31—42no—
190C8×C31—81no—
191#3193C2×C3111yescharacteristic
192#2378C2×C3111yescharacteristic, complemented
193#1964C2×C3111yescharacteristic
194#1510C2×C3111yescharacteristic
195#1508C2×C3111yescharacteristic, complemented
196#1305C2×C3111yescharacteristic, complemented
197#1284C2×C3111yescharacteristic, complemented
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—81no—
207C22×C31—81no—
208C22×C31—81no—
209C22×C31—81no—
210C22×C31—81no—
211C22×C31—161no—
212C22×C31—161no—
213C22×C31#38611yescharacteristic
214C22×C31#45311yescharacteristic
215C22×C31#45411yescharacteristic
216C4×C31—21no—
217C4×C31—21no—
218C4×C31—21no—
219C4×C31—21no—
220C4×C31—42no—
221C4×C31—42no—
222C4×C31—81no—
223C4×C31—81no—
224C4×C31—81no—
225C4×C31—81no—
226C4×C31—82no—
227C4×C31—81no—
228C2×C22⋊Q8C22×C3111yescharacteristic
229C2×#121C22×C3111yescharacteristic
230#484C4×C3112yescomplemented
231#480—21no—
232#468—22no—
233#450C4×C3112yescomplemented
234#448—21no—
235C2×#99—21no—
236C2×#99—21no—
237#407C22×C3111yescharacteristic
238#407C22×C3111yescharacteristic
239#391—21no—
240#389—21no—
241#388—21no—
242#388—21no—
243#387—21no—
244#387—21no—
245#381C22×C3111yescharacteristic
246#380C22×C3111yescharacteristic
247C4×C22⋊C4C22×C3111yescharacteristic
248#328—22no—
249#327—21no—
250#327—21no—
251C2×C31—21no—
252C2×C31—21no—
253C2×C31—41no—
254C2×C31—41no—
255C2×C31—161no—
256C2×C31#188311yescharacteristic
257C2×C31#190511yescharacteristic
258C2×C31#191311yescharacteristic
259C22×Q8D4×C3111yescharacteristic
260C22×D4—21no—
261C22×D4C2×C4×C3111yescharacteristic
262C23×C4C23×C3111yescharacteristic
263C2×SD16—22no—
264C2×M16—21no—
265C2×M16—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8C2×C4×C3112yes—
269C22⋊Q8D4×C3112yes—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C2×C4×C3111yescharacteristic
279C2×C4⋊C4D4×C3111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4D4×C3111yescharacteristic
285C2×C22⋊C4D4×C3111yescharacteristic
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289#107—22no—
290#103—22no—
291#102—22no—
292#99—42no—
293#99—42no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8C2×C4×C3112yes—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95D4×C3111yescharacteristic
306#95D4×C3111yescharacteristic
307C31#934411yescharacteristic, direct product factor, Sylow
308C24—21no—
309C24C2×D4×C3111yescharacteristic
310C2×Q8—21no—
311C2×Q8—81no—
312C2×Q8C22⋊C4×C3112yes—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4C22×C4×C3111yescharacteristic
332C22×C4C2×D4×C3111yescharacteristic
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4#41×C3111yescharacteristic
336C22×C4#41×C3111yescharacteristic
337SD16—82no—
338M16—81no—
339M16—81no—
340C2×C8—22no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—81no—
348C4⋊C4—81no—
349C4⋊C4—81no—
350C4⋊C4C22⋊C4×C3112yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—81no—
360C42—81no—
361C42—81no—
362C42—81no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×D4×C3111yescharacteristic
373C23C31×#12011yescharacteristic
374C23C31×#12111yescharacteristic
375Q8—42no—
376Q8—81no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—22no—
384C2×C4—22no—
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—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C3111yescharacteristic
414C2×C4C4×D4×C3111yescharacteristic
415C2×C4C31×#12111yescharacteristic
416C2×C4C31×#12311yescharacteristic
417C8—42no—
418C8—81no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22C31×#38611yescharacteristic
435C22C31×#45311yescharacteristic
436C22C31×#45411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—82no—
448C4—81no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2C31×#188311yescharacteristic
455C2C31×#190511yescharacteristic
456C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2378C2semidirect
5. C31×#1508C2semidirect
6. C31×#1305C2semidirect
7. C31×#1284C2semidirect
10. C31×#484C4semidirect
13. C31×#450C4semidirect
134. #9344C31direct (N × H)
192. #2378C2×C31semidirect
195. #1508C2×C31semidirect
196. #1305C2×C31semidirect
197. #1284C2×C31semidirect
230. #484C4×C31semidirect
233. #450C4×C31semidirect
307. C31#9344direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31932
C31×#23782
C31×#19642
C31×#15102
C31×#15082
C31×#13052
C31×#12842
#934431