Finite Group Databasebeta

← C31×#9921 #21466680

Subgroups — C31×#9921 #21466680

Order 7936.

672 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#481C211yesmaximal, characteristic
2C31×#2618C211yesmaximal, characteristic
3C2×C31×#400C211yesmaximal, characteristic, complemented
4C31×#1824C211yesmaximal, characteristic, complemented
5C2×C31×#327C211yesmaximal, characteristic
6C2×C31×#324C211yesmaximal, characteristic, complemented
7C31×#1294C211yesmaximal, characteristic, complemented
8C2×C31×#123—21no—
9C2×C31×#121C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic
12C31×#481—22no—
13C31×#481—22no—
14C2×C31×#106—21no—
15C2×C31×#102—21no—
16C2×C31×C22⋊C8C2211yescharacteristic
17C2×C31×C22⋊C8C2211yescharacteristic
18C31×#400—22no—
19C31×#400—22no—
20C31×#398—21no—
21C31×#396—22no—
22C31×#394—21no—
23C31×#386—21no—
24C31×#380C2211yescharacteristic
25C2×C31×#95—21no—
26C2×C31×#95—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#327—22no—
30C31×#324—22no—
31C22×D4×C31—21no—
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31D411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31C2311yescharacteristic
38C22×C8×C31—21no—
39C22×C8×C31—21no—
40C31×#123—42no—
41C31×#123—42no—
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×C31—22no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C4⋊C4×C31D412yes—
60C2×C4⋊C4×C31D412yes—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—22no—
65C31×#106—24no—
66C31×#102—24no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8D412yes—
71C31×#95—22no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95D412yes—
77C24×C31—21no—
78C24×C31C2×D411yescharacteristic
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—42no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—42no—
102C22×C4×C31—42no—
103C22×C4×C31—42no—
104C22×C4×C31—42no—
105C22×C4×C31—44no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31—41no—
109C22×C4×C31—41no—
110C22×C4×C31SD1612yes—
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31C2×D411yescharacteristic
114C22×C4×C31C2×D411yescharacteristic
115C22×C4×C31C2×D411yescharacteristic
116C22×C4×C31#4111yescharacteristic
117C2×C8×C31—22no—
118C2×C8×C31—42no—
119C2×C8×C31—42no—
120C2×C8×C31—41no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—22no—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—44no—
126C4⋊C4×C31—42no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31—41no—
132C4⋊C4×C31—41no—
133C22⋊C4×C31—44no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—82no—
139#9921C3111yesmaximal, characteristic, direct product factor, Sylow
140C23×C31—22no—
141C23×C31—22no—
142C23×C31—41no—
143C23×C31—41no—
144C23×C31—41no—
145C23×C31—42no—
146C23×C31—42no—
147C23×C31#12011yescharacteristic
148C23×C31#12011yescharacteristic
149C23×C31#12111yescharacteristic
150C23×C31C2×SD1611yescharacteristic
151C23×C31#13511yescharacteristic
152C23×C31AGL(1,ℤ/8)11yescharacteristic
153C23×C31#13711yescharacteristic
154D4×C31—42no—
155D4×C31—81no—
156D4×C31—81no—
157D4×C31—81no—
158D4×C31—81no—
159D4×C31—81no—
160C2×C4×C31—22no—
161C2×C4×C31—22no—
162C2×C4×C31—22no—
163C2×C4×C31—22no—
164C2×C4×C31—22no—
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—42no—
174C2×C4×C31—42no—
175C2×C4×C31—44no—
176C2×C4×C31—42no—
177C2×C4×C31—41no—
178C2×C4×C31—42no—
179C2×C4×C31—41no—
180C2×C4×C31—42no—
181C2×C4×C31—42no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—42no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—82no—
188C2×C4×C31—82no—
189C2×C4×C31—82no—
190C2×C4×C31—82no—
191C2×C4×C31—81no—
192C2×C4×C31#12011yescharacteristic
193C2×C4×C31#12111yescharacteristic
194C2×C4×C31#12111yescharacteristic
195C2×C4×C31#12711yescharacteristic
196C8×C31—42no—
197C8×C31—81no—
198C2×#481C2×C3111yescharacteristic
199#2618C2×C3111yescharacteristic
200C2×#400C2×C3111yescharacteristic, complemented
201#1824C2×C3111yescharacteristic, complemented
202C2×#327C2×C3111yescharacteristic
203C2×#324C2×C3111yescharacteristic, complemented
204#1294C2×C3111yescharacteristic, complemented
205C22×C31—22no—
206C22×C31—22no—
207C22×C31—22no—
208C22×C31—22no—
209C22×C31—21no—
210C22×C31—21no—
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—82no—
214C22×C31—82no—
215C22×C31—81no—
216C22×C31—81no—
217C22×C31—81no—
218C22×C31#39211yescharacteristic
219C22×C31#44811yescharacteristic
220C22×C31#44911yescharacteristic
221C22×C31#45011yescharacteristic
222C22×C31#45211yescharacteristic
223C22×C31#45412yes—
224C22×C31#45812yes—
225C22×C31#46511yescharacteristic
226C22×C31#46811yescharacteristic
227C4×C31—21no—
228C4×C31—21no—
229C4×C31—21no—
230C4×C31—21no—
231C4×C31—42no—
232C4×C31—82no—
233C4×C31—82no—
234C4×C31—81no—
235C4×C31—82no—
236C4×C31—81no—
237C2×#123—21no—
238C2×#121C22×C3111yescharacteristic
239C22×C4⋊C4C22×C3111yescharacteristic
240C22×C4⋊C4C22×C3111yescharacteristic
241#481—22no—
242#481—22no—
243C2×#106—21no—
244C2×#102—21no—
245C2×C22⋊C8C22×C3111yescharacteristic
246C2×C22⋊C8C22×C3111yescharacteristic
247#400—22no—
248#400—22no—
249#398—21no—
250#396—22no—
251#394—21no—
252#386—21no—
253#380C22×C3111yescharacteristic
254C2×#95—21no—
255C2×#95—21no—
256C2×#95C22×C3111yescharacteristic
257#340—22no—
258#327—22no—
259#324—22no—
260C2×C31—21no—
261C2×C31—21no—
262C2×C31—21no—
263C2×C31—21no—
264C2×C31—161no—
265C2×C31#161512yes—
266C2×C31#161612yes—
267C2×C31#200011yescharacteristic
268C2×C31#200311yescharacteristic
269C2×C31#202211yescharacteristic
270C22×D4—21no—
271C22×D4D4×C3111yescharacteristic
272C23×C4—21no—
273C23×C4—21no—
274C23×C4D4×C3111yescharacteristic
275C23×C4D4×C3111yescharacteristic
276C23×C4C23×C3111yescharacteristic
277C22×C8—21no—
278C22×C8—21no—
279#123—42no—
280#123—42no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C3112yes—
298C2×C4⋊C4D4×C3111yescharacteristic
299C2×C4⋊C4D4×C3112yes—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304#106—24no—
305#102—24no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8D4×C3112yes—
310#95—24no—
311#95—24no—
312#95—22no—
313#95—21no—
314#95—21no—
315#95D4×C3112yes—
316C31#992111yescharacteristic, direct product factor, Sylow
317C24—21no—
318C24C2×D4×C3111yescharacteristic
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—44no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4SD16×C3112yes—
351C22×C4C2×D4×C3111yescharacteristic
352C22×C4C2×D4×C3111yescharacteristic
353C22×C4C2×D4×C3111yescharacteristic
354C22×C4C2×D4×C3111yescharacteristic
355C22×C4C2×D4×C3111yescharacteristic
356C22×C4#41×C3111yescharacteristic
357C2×C8—22no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—41no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—42no—
366C4⋊C4—44no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C22⋊C4—44no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—82no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23—41no—
386C23C31×#12011yescharacteristic
387C23C31×#12011yescharacteristic
388C23C31×#12111yescharacteristic
389C23C2×SD16×C3111yescharacteristic
390C23C31×#13511yescharacteristic
391C23C31×AGL(1,ℤ/8)11yescharacteristic
392C23C31×#13711yescharacteristic
393D4—42no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—81no—
398D4—81no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4C31×#12011yescharacteristic
432C2×C4C31×#12111yescharacteristic
433C2×C4C31×#12111yescharacteristic
434C2×C4C31×#12711yescharacteristic
435C8—42no—
436C8—81no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—82no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C31×#39211yescharacteristic
451C22C31×#44811yescharacteristic
452C22C31×#44911yescharacteristic
453C22C31×#45011yescharacteristic
454C22C31×#45211yescharacteristic
455C22C31×#45412yes—
456C22C31×#45812yes—
457C22C31×#46511yescharacteristic
458C22C31×#46811yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4—81no—
467C4—82no—
468C4—81no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—161no—
474C2C31×#161512yes—
475C2C31×#161612yes—
476C2C31×#200011yescharacteristic
477C2C31×#200311yescharacteristic
478C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
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
3. C2×C31×#400C2semidirect
4. C31×#1824C2semidirect
6. C2×C31×#324C2semidirect
7. C31×#1294C2semidirect
139. #9921C31direct (N × H)
200. C2×#400C2×C31semidirect
201. #1824C2×C31semidirect
203. C2×#324C2×C31semidirect
204. #1294C2×C31semidirect
316. C31#9921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4812
C31×#26182
C2×C31×#4002
C31×#18242
C2×C31×#3272
C2×C31×#3242
C31×#12942
#992131