Finite Group Databasebeta

← C31×#9929 #21466688

Subgroups — C31×#9929 #21466688

Order 7936.

610 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#484C211yesmaximal, characteristic
2C31×#2627C211yesmaximal, characteristic
3C2×C31×#400C211yesmaximal, characteristic
4C31×#1824C211yesmaximal, characteristic
5C2×C31×#328C211yesmaximal, characteristic
6C2×C31×#324C211yesmaximal, characteristic
7C31×#1294C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C31×#484—22no—
12C31×#484—22no—
13C2×C31×#107—21no—
14C2×C31×#103—21no—
15C2×C31×C22⋊C8C2211yescharacteristic
16C2×C31×C22⋊C8C2211yescharacteristic
17C31×#400—21no—
18C31×#400—22no—
19C31×#400—22no—
20C31×#398—22no—
21C31×#395—21no—
22C31×#385—21no—
23C31×#381—21no—
24C31×#380C2211yescharacteristic
25C2×C31×#95—21no—
26C2×C31×#95—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#328—22no—
30C31×#324—22no—
31C22×Q8×C31D411yescharacteristic
32C23×C4×C31—21no—
33C23×C4×C31—21no—
34C23×C4×C31D411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C4⋊C4×C31D412yes—
58C2×C4⋊C4×C31D412yes—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C31×#107—24no—
62C31×#103—24no—
63C31×C22⋊C8—21no—
64C31×C22⋊C8—21no—
65C31×C22⋊C8—21no—
66C31×C22⋊C8D412yes—
67C31×#95—22no—
68C31×#95—22no—
69C31×#95—22no—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95D412yes—
75C24×C31C2×D411yescharacteristic
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—42no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—22no—
86C22×C4×C31—21no—
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—22no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31—42no—
97C22×C4×C31—44no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31—41no—
102C22×C4×C31Q1612yes—
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31C2×D411yescharacteristic
107C22×C4×C31C2×D411yescharacteristic
108C22×C4×C31#4111yescharacteristic
109C2×C8×C31—22no—
110C2×C8×C31—42no—
111C2×C8×C31—42no—
112C2×C8×C31—41no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—22no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—42no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—82no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—41no—
131#9929C3111yesmaximal, characteristic, direct product factor, Sylow
132C23×C31—22no—
133C23×C31—22no—
134C23×C31#12011yescharacteristic
135C23×C31#12011yescharacteristic
136C23×C31#12111yescharacteristic
137C23×C31C2×Q1611yescharacteristic
138C23×C31#13511yescharacteristic
139C23×C31#13711yescharacteristic
140C23×C31#13711yescharacteristic
141Q8×C31—42no—
142Q8×C31—81no—
143C2×C4×C31—22no—
144C2×C4×C31—22no—
145C2×C4×C31—22no—
146C2×C4×C31—22no—
147C2×C4×C31—22no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—44no—
159C2×C4×C31—42no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—42no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—82no—
172C2×C4×C31—82no—
173C2×C4×C31—82no—
174C2×C4×C31—82no—
175C2×C4×C31—81no—
176C2×C4×C31#12011yescharacteristic
177C2×C4×C31#12111yescharacteristic
178C2×C4×C31#12111yescharacteristic
179C2×C4×C31#12711yescharacteristic
180C8×C31—42no—
181C8×C31—81no—
182C2×#484C2×C3111yescharacteristic
183#2627C2×C3111yescharacteristic
184C2×#400C2×C3111yescharacteristic
185#1824C2×C3111yescharacteristic
186C2×#328C2×C3111yescharacteristic
187C2×#324C2×C3111yescharacteristic
188#1294C2×C3111yescharacteristic
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—22no—
192C22×C31—22no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31#39211yescharacteristic
198C22×C31#45111yescharacteristic
199C22×C31#45111yescharacteristic
200C22×C31#45211yescharacteristic
201C22×C31#45211yescharacteristic
202C22×C31#45412yes—
203C22×C31#45812yes—
204C22×C31#46711yescharacteristic
205C22×C31#47011yescharacteristic
206C4×C31—21no—
207C4×C31—21no—
208C4×C31—21no—
209C4×C31—21no—
210C4×C31—42no—
211C4×C31—82no—
212C4×C31—82no—
213C4×C31—81no—
214C4×C31—82no—
215C4×C31—81no—
216C4×C31—81no—
217C2×C22⋊Q8C22×C3111yescharacteristic
218C22×C4⋊C4C22×C3111yescharacteristic
219C22×C4⋊C4C22×C3111yescharacteristic
220#484—22no—
221#484—22no—
222C2×#107—21no—
223C2×#103—21no—
224C2×C22⋊C8C22×C3111yescharacteristic
225C2×C22⋊C8C22×C3111yescharacteristic
226#400—21no—
227#400—22no—
228#400—22no—
229#398—22no—
230#395—21no—
231#385—21no—
232#381—21no—
233#380C22×C3111yescharacteristic
234C2×#95—21no—
235C2×#95—21no—
236C2×#95C22×C3111yescharacteristic
237#340—22no—
238#328—22no—
239#324—22no—
240C2×C31—21no—
241C2×C31—21no—
242C2×C31—21no—
243C2×C31—21no—
244C2×C31#161512yes—
245C2×C31#161712yes—
246C2×C31#200111yescharacteristic
247C2×C31#200311yescharacteristic
248C2×C31#202211yescharacteristic
249C22×Q8D4×C3111yescharacteristic
250C23×C4—21no—
251C23×C4—21no—
252C23×C4D4×C3111yescharacteristic
253C23×C4D4×C3111yescharacteristic
254C23×C4C23×C3111yescharacteristic
255C22×C8—21no—
256C22×C8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4D4×C3112yes—
275C2×C4⋊C4D4×C3111yescharacteristic
276C2×C4⋊C4D4×C3112yes—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279#107—24no—
280#103—24no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8D4×C3112yes—
285#95—24no—
286#95—24no—
287#95—22no—
288#95—22no—
289#95—22no—
290#95—21no—
291#95—21no—
292#95D4×C3112yes—
293C31#992911yescharacteristic, direct product factor, Sylow
294C24C2×D4×C3111yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—44no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4Q16×C3112yes—
322C22×C4C2×D4×C3111yescharacteristic
323C22×C4C2×D4×C3111yescharacteristic
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3111yescharacteristic
326C22×C4C2×D4×C3111yescharacteristic
327C22×C4#41×C3111yescharacteristic
328C2×C8—22no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—41no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—82no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C23—22no—
351C23—22no—
352C23C31×#12011yescharacteristic
353C23C31×#12011yescharacteristic
354C23C31×#12111yescharacteristic
355C23C2×Q16×C3111yescharacteristic
356C23C31×#13511yescharacteristic
357C23C31×#13711yescharacteristic
358C23C31×#13711yescharacteristic
359Q8—42no—
360Q8—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—81no—
394C2×C4C31×#12011yescharacteristic
395C2×C4C31×#12111yescharacteristic
396C2×C4C31×#12111yescharacteristic
397C2×C4C31×#12711yescharacteristic
398C8—42no—
399C8—81no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22C31×#39211yescharacteristic
409C22C31×#45111yescharacteristic
410C22C31×#45111yescharacteristic
411C22C31×#45211yescharacteristic
412C22C31×#45211yescharacteristic
413C22C31×#45412yes—
414C22C31×#45812yes—
415C22C31×#46711yescharacteristic
416C22C31×#47011yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—82no—
423C4—82no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4—81no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2C31×#161512yes—
433C2C31×#161712yes—
434C2C31×#200111yescharacteristic
435C2C31×#200311yescharacteristic
436C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
131. #9929C31direct (N × H)
293. C31#9929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4842
C31×#26272
C2×C31×#4002
C31×#18242
C2×C31×#3282
C2×C31×#3242
C31×#12942
#992931