Finite Group Databasebeta

← C31×#9935 #21466694

Subgroups — C31×#9935 #21466694

Order 7936.

750 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C31×#3195C211yesmaximal, characteristic, complemented
2C31×#3007C211yesmaximal, characteristic
3C31×#2616C211yesmaximal, characteristic
4C31×#1996C211yesmaximal, characteristic, complemented
5C31×#1789C211yesmaximal, characteristic
6C31×#1508C211yesmaximal, characteristic, complemented
7C31×#1305C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C2×C31×#137—21no—
10C2×C31×C22⋊Q8—21no—
11C2×C31×C22⋊Q8C2211yescharacteristic
12C2×C31×C22⋊Q8C2211yescharacteristic
13C31×#483—21no—
14C31×#483—21no—
15C31×#470—22no—
16C31×#452—22no—
17C31×#451—21no—
18C31×#451—21no—
19C31×#451—21no—
20C31×#450—21no—
21C2×C31×#104—22no—
22C31×#417—21no—
23C31×#407C2211yescharacteristic
24C31×#407C2211yescharacteristic
25C31×#395—21no—
26C31×#394—21no—
27C31×#394—22no—
28C31×#380—21no—
29C31×#380C2211yescharacteristic
30C4×C22⋊C4×C31C2211yescharacteristic
31C31×#342—22no—
32C31×#328—22no—
33C2×#41×C31—21no—
34C2×#41×C31—21no—
35C2×#41×C31—21no—
36C2×#41×C31—21no—
37C2×#41×C31—44no—
38C22×Q8×C31D411yescharacteristic
39C22×Q8×C31D411yescharacteristic
40C22×Q8×C31D411yescharacteristic
41C22×D4×C31—21no—
42C22×D4×C31D411yescharacteristic
43C23×C4×C31—21no—
44C23×C4×C31C2311yescharacteristic
45C31×#137—44no—
46C2×Q16×C31—22no—
47C2×Q16×C31—22no—
48C2×SD16×C31—22no—
49C2×M16×C31—21no—
50C2×M16×C31D412yes—
51C31×C22⋊Q8—21no—
52C31×C22⋊Q8—21no—
53C31×C22⋊Q8—21no—
54C31×C22⋊Q8—21no—
55C31×C22⋊Q8—21no—
56C31×C22⋊Q8—21no—
57C31×C22⋊Q8—21no—
58C31×C22⋊Q8—21no—
59C31×C22⋊Q8—44no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31D411yescharacteristic
65C2×C4⋊C4×C31D411yescharacteristic
66C2×C22⋊C4×C31—21no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—21no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31D412yes—
72C2×C42×C31—21no—
73C31×#106—22no—
74C31×#104—44no—
75C31×#103—22no—
76C31×#103—22no—
77C31×#103—22no—
78C31×#102—22no—
79C31×C22⋊C8—21no—
80C31×C22⋊C8—21no—
81C31×C22⋊C8—21no—
82C31×C22⋊C8D412yes—
83C31×#95—22no—
84C31×#95—21no—
85C31×#95—21no—
86C24×C31—21no—
87C24×C31C2×D411yescharacteristic
88#41×C31—24no—
89#41×C31—24no—
90#41×C31—42no—
91#41×C31—42no—
92#41×C31—42no—
93#41×C31—42no—
94#41×C31—42no—
95#41×C31—42no—
96C2×Q8×C31—21no—
97C2×Q8×C31—21no—
98C2×Q8×C31—21no—
99C2×Q8×C31—21no—
100C2×Q8×C31—21no—
101C2×Q8×C31—21no—
102C2×Q8×C31—42no—
103C2×Q8×C31—42no—
104C2×Q8×C31—42no—
105C2×D4×C31—21no—
106C2×D4×C31—21no—
107C2×D4×C31—42no—
108C2×D4×C31—42no—
109C2×D4×C31—42no—
110C2×D4×C31—41no—
111C2×D4×C31—41no—
112C22×C4×C31—24no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—42no—
120C22×C4×C31—42no—
121C22×C4×C31—41no—
122C22×C4×C31—41no—
123C22×C4×C31—41no—
124C22×C4×C31C2×D411yescharacteristic
125C22×C4×C31C2×D411yescharacteristic
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31#4111yescharacteristic
130Q16×C31—44no—
131Q16×C31—82no—
132SD16×C31—44no—
133M16×C31—42no—
134M16×C31—42no—
135C2×C8×C31—22no—
136C2×C8×C31—22no—
137C4⋊C4×C31—21no—
138C4⋊C4×C31—21no—
139C4⋊C4×C31—21no—
140C4⋊C4×C31—21no—
141C4⋊C4×C31—42no—
142C4⋊C4×C31—44no—
143C4⋊C4×C31—41no—
144C4⋊C4×C31—41no—
145C4⋊C4×C31—41no—
146C4⋊C4×C31—41no—
147C22⋊C4×C31—22no—
148C22⋊C4×C31—41no—
149C22⋊C4×C31—44no—
150C22⋊C4×C31—41no—
151C22⋊C4×C31—41no—
152C22⋊C4×C31—41no—
153C22⋊C4×C31—41no—
154C22⋊C4×C31—42no—
155C22⋊C4×C31—82no—
156C42×C31—42no—
157#9935C3111yesmaximal, characteristic, direct product factor, Sylow
158C23×C31—21no—
159C23×C31—21no—
160C23×C31—22no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—41no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31—41no—
167C23×C31—41no—
168C23×C31—41no—
169C23×C31#12011yescharacteristic
170C23×C31#12111yescharacteristic
171C23×C31#12711yescharacteristic
172Q8×C31—22no—
173Q8×C31—22no—
174Q8×C31—41no—
175Q8×C31—41no—
176Q8×C31—42no—
177Q8×C31—42no—
178Q8×C31—42no—
179Q8×C31—81no—
180D4×C31—22no—
181D4×C31—22no—
182D4×C31—41no—
183D4×C31—41no—
184D4×C31—44no—
185D4×C31—44no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—22no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—44no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—44no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—41no—
204C2×C4×C31—41no—
205C2×C4×C31—42no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—81no—
209C2×C4×C31—81no—
210C2×C4×C31—81no—
211C2×C4×C31—81no—
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#12111yescharacteristic
215C2×C4×C31#12111yescharacteristic
216C8×C31—42no—
217C8×C31—42no—
218#3195C2×C3111yescharacteristic, complemented
219#3007C2×C3111yescharacteristic
220#2616C2×C3111yescharacteristic
221#1996C2×C3111yescharacteristic, complemented
222#1789C2×C3111yescharacteristic
223#1508C2×C3111yescharacteristic, complemented
224#1305C2×C3111yescharacteristic, complemented
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—42no—
234C22×C31—42no—
235C22×C31—42no—
236C22×C31—81no—
237C22×C31—81no—
238C22×C31—81no—
239C22×C31—81no—
240C22×C31—81no—
241C22×C31—81no—
242C22×C31#39211yescharacteristic
243C22×C31#45511yescharacteristic
244C22×C31#45611yescharacteristic
245C4×C31—21no—
246C4×C31—21no—
247C4×C31—21no—
248C4×C31—42no—
249C4×C31—82no—
250C4×C31—82no—
251C4×C31—81no—
252C4×C31—81no—
253C4×C31—81no—
254C4×C31—81no—
255C4×C31B(4,𝔽2)12yes—
256C22×#41C22×C3111yescharacteristic
257C2×#137—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C22×C3111yescharacteristic
260C2×C22⋊Q8C22×C3111yescharacteristic
261#483—21no—
262#483—21no—
263#470—22no—
264#452—22no—
265#451—21no—
266#451—21no—
267#451—21no—
268#450—21no—
269C2×#104—22no—
270#417—21no—
271#407C22×C3111yescharacteristic
272#407C22×C3111yescharacteristic
273#395—21no—
274#394—21no—
275#394—22no—
276#380—21no—
277#380C22×C3111yescharacteristic
278C4×C22⋊C4C22×C3111yescharacteristic
279#342—22no—
280#328—22no—
281C2×C31—21no—
282C2×C31—21no—
283C2×C31—41no—
284C2×C31—41no—
285C2×C31—82no—
286C2×C31#200711yescharacteristic
287C2×C31#200911yescharacteristic
288C2×C31#202111yescharacteristic
289C2×#41—21no—
290C2×#41—21no—
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—44no—
294C22×Q8D4×C3111yescharacteristic
295C22×Q8D4×C3111yescharacteristic
296C22×Q8D4×C3111yescharacteristic
297C22×D4—21no—
298C22×D4D4×C3111yescharacteristic
299C23×C4—21no—
300C23×C4C23×C3111yescharacteristic
301#137—44no—
302C2×Q16—22no—
303C2×Q16—22no—
304C2×SD16—22no—
305C2×M16—21no—
306C2×M16D4×C3112yes—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—44no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4D4×C3111yescharacteristic
321C2×C4⋊C4D4×C3111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4D4×C3112yes—
328C2×C42—21no—
329#106—22no—
330#104—44no—
331#103—22no—
332#103—22no—
333#103—22no—
334#102—22no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8D4×C3112yes—
339#95—22no—
340#95—21no—
341#95—21no—
342C31#993511yescharacteristic, direct product factor, Sylow
343C24—21no—
344C24C2×D4×C3111yescharacteristic
345#41—24no—
346#41—24no—
347#41—42no—
348#41—42no—
349#41—42no—
350#41—42no—
351#41—42no—
352#41—42no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4C2×D4×C3111yescharacteristic
382C22×C4C2×D4×C3111yescharacteristic
383C22×C4C2×D4×C3111yescharacteristic
384C22×C4C2×D4×C3111yescharacteristic
385C22×C4C2×D4×C3111yescharacteristic
386C22×C4#41×C3111yescharacteristic
387Q16—44no—
388Q16—82no—
389SD16—44no—
390M16—42no—
391M16—42no—
392C2×C8—22no—
393C2×C8—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—42no—
399C4⋊C4—44no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C22⋊C4—22no—
405C22⋊C4—41no—
406C22⋊C4—44no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—42no—
412C22⋊C4—82no—
413C42—42no—
414C23—21no—
415C23—21no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C31×#12011yescharacteristic
426C23C31×#12111yescharacteristic
427C23C31×#12711yescharacteristic
428Q8—22no—
429Q8—22no—
430Q8—41no—
431Q8—41no—
432Q8—42no—
433Q8—42no—
434Q8—42no—
435Q8—81no—
436D4—22no—
437D4—22no—
438D4—41no—
439D4—41no—
440D4—44no—
441D4—44no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4C31×#12011yescharacteristic
469C2×C4C31×#12011yescharacteristic
470C2×C4C31×#12111yescharacteristic
471C2×C4C31×#12111yescharacteristic
472C8—42no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C31×#39211yescharacteristic
492C22C31×#45511yescharacteristic
493C22C31×#45611yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—42no—
498C4—82no—
499C4—82no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4C31×B(4,𝔽2)12yes—
505C2—21no—
506C2—21no—
507C2—41no—
508C2—41no—
509C2—82no—
510C2C31×#200711yescharacteristic
511C2C31×#200911yescharacteristic
512C2C31×#202111yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3195C2semidirect
4. C31×#1996C2semidirect
6. C31×#1508C2semidirect
7. C31×#1305C2semidirect
157. #9935C31direct (N × H)
218. #3195C2×C31semidirect
221. #1996C2×C31semidirect
223. #1508C2×C31semidirect
224. #1305C2×C31semidirect
342. C31#9935direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31952
C31×#30072
C31×#26162
C31×#19962
C31×#17892
C31×#15082
C31×#13052
#993531