Finite Group Databasebeta

← C31×#8573 #21465332

Subgroups — C31×#8573 #21465332

Order 7936.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#121C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic, complemented
3C2×C31×#327C212yesmaximal
4C31×#1434C211yesmaximal, characteristic, complemented
5C31×#1294C212yesmaximal, complemented
6C2×C31×#121C2211yescharacteristic
7C2×C4×D4×C31—21no—
8C2×C4×D4×C31C411yescharacteristic, complemented
9C22×C42×C31C2211yescharacteristic
10C2×C31×C4⋊C8—21no—
11C2×C31×C22⋊C8C2212yes—
12C31×#390C411yescharacteristic, complemented
13C31×#389C411yescharacteristic, complemented
14C31×#388—21no—
15C31×#386—21no—
16C31×#380C2211yescharacteristic
17C4×C4⋊C4×C31C411yescharacteristic, complemented
18C4×C22⋊C4×C31—21no—
19C2×C31×#95—21no—
20C2×C31×#95—21no—
21C2×C31×#95C2212yes—
22C31×#336—21no—
23C31×#327—24no—
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31—22no—
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C31×#121—21no—
33C31×#121—21no—
34C31×#121D412yes—
35C31×#121Q812yes—
36C4×D4×C31—42no—
37C4×D4×C31—44no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C42×C31—21no—
48C2×C42×C31—42no—
49C2×C42×C31C2×C411yescharacteristic
50C2×C42×C31C2×C411yescharacteristic
51C2×C42×C31D411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C31×C4⋊C8—42no—
54C31×C22⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×#95—24no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—22no—
61C31×#95—22no—
62C31×#95—42no—
63C24×C31—21no—
64C24×C31C2×D411yescharacteristic
65C2×D4×C31—22no—
66C2×D4×C31—22no—
67C2×D4×C31—21no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—42no—
71C2×D4×C31—42no—
72C2×D4×C31C4⋊C412yes—
73C22×C4×C31—21no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—24no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31C22×C411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×Q811yescharacteristic
102C22×C4×C31#4111yescharacteristic
103C22×C4×C31#4111yescharacteristic
104C2×C8×C31—42no—
105C2×C8×C31—42no—
106C2×C8×C31—42no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31C4⋊C412yes—
112C22⋊C4×C31—22no—
113C22⋊C4×C31—22no—
114C22⋊C4×C31—42no—
115C22⋊C4×C31—42no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—42no—
118C42×C31—22no—
119C42×C31—22no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31—42no—
123#8573C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—22no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31C2×C22⋊C411yescharacteristic
136C23×C31#12111yescharacteristic
137C23×C31C22⋊Q811yescharacteristic
138C23×C31#13512yes—
139C23×C31AGL(1,ℤ/8)12yes—
140D4×C31—42no—
141D4×C31—42no—
142D4×C31—44no—
143D4×C31—44no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—44no—
164C2×C4×C31—44no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—44no—
168C2×C4×C31—44no—
169C2×C4×C31—44no—
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—84no—
177C2×C4×C31—82no—
178C2×C4×C31—82no—
179C2×C4×C31—82no—
180C2×C4×C31—82no—
181C2×C4×C31#9912yes—
182C2×C4×C31#10412yes—
183C2×C4×C31C2×C4⋊C411yescharacteristic
184C2×C4×C31#11711yescharacteristic
185C2×C4×C31#12111yescharacteristic
186C2×C4×C31C22⋊Q811yescharacteristic
187C8×C31—82no—
188C4×#121C2×C3111yescharacteristic
189#1797C2×C3111yescharacteristic, complemented
190C2×#327C2×C3112yes—
191#1434C2×C3111yescharacteristic, complemented
192#1294C2×C3112yescomplemented
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—22no—
198C22×C31—22no—
199C22×C31—22no—
200C22×C31—22no—
201C22×C31—42no—
202C22×C31—42no—
203C22×C31—42no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31—81no—
208C22×C31#38011yescharacteristic
209C22×C31C2×#9911yescharacteristic
210C22×C31#41011yescharacteristic
211C22×C31#41611yescharacteristic
212C22×C31#41811yescharacteristic
213C22×C31C2×#10411yescharacteristic
214C22×C31#42111yescharacteristic
215C22×C31#46312yes—
216C22×C31#47812yes—
217C4×C31—21no—
218C4×C31—21no—
219C4×C31—21no—
220C4×C31—21no—
221C4×C31—22no—
222C4×C31—22no—
223C4×C31—42no—
224C4×C31—41no—
225C4×C31—41no—
226C4×C31—84no—
227C4×C31—81no—
228C4×C31—81no—
229C2×#121C22×C3111yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4C4×C3111yescharacteristic, complemented
232C22×C42C22×C3111yescharacteristic
233C2×C4⋊C8—21no—
234C2×C22⋊C8C22×C3112yes—
235#390C4×C3111yescharacteristic, complemented
236#389C4×C3111yescharacteristic, complemented
237#388—21no—
238#386—21no—
239#380C22×C3111yescharacteristic
240C4×C4⋊C4C4×C3111yescharacteristic, complemented
241C4×C22⋊C4—21no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95C22×C3112yes—
245#336—21no—
246#327—24no—
247C2×C31—22no—
248C2×C31—22no—
249C2×C31—82no—
250C2×C31#150011yescharacteristic
251C2×C31#150711yescharacteristic
252C2×C31#151411yescharacteristic
253C2×C31#151611yescharacteristic
254C2×C31#179911yescharacteristic
255C2×C31#180411yescharacteristic
256C2×C31#180611yescharacteristic
257C22×D4—21no—
258C22×D4C2×C4×C3111yescharacteristic
259C23×C4—22no—
260C23×C4—21no—
261C23×C4D4×C3111yescharacteristic
262C23×C4D4×C3111yescharacteristic
263C23×C4C23×C3111yescharacteristic
264C22×C8—22no—
265#121—21no—
266#121—21no—
267#121D4×C3112yes—
268#121Q8×C3112yes—
269C4×D4—42no—
270C4×D4—44no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C2×C4×C3111yescharacteristic
273C2×C4⋊C4C2×C4×C3111yescharacteristic
274C2×C4⋊C4C2×C4×C3111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—21no—
281C2×C42—42no—
282C2×C42C2×C4×C3111yescharacteristic
283C2×C42C2×C4×C3111yescharacteristic
284C2×C42D4×C3111yescharacteristic
285C2×C42D4×C3111yescharacteristic
286C4⋊C8—42no—
287C22⋊C8—22no—
288C22⋊C8—22no—
289#95—24no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—22no—
294#95—22no—
295#95—42no—
296C31#857311yescharacteristic, direct product factor, Sylow
297C24—21no—
298C24C2×D4×C3111yescharacteristic
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4C4⋊C4×C3112yes—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C22⋊C4×C3111yescharacteristic
329C22×C4C22⋊C4×C3111yescharacteristic
330C22×C4C22⋊C4×C3111yescharacteristic
331C22×C4C22⋊C4×C3111yescharacteristic
332C22×C4C22×C4×C3111yescharacteristic
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4C2×D4×C3111yescharacteristic
335C22×C4C2×Q8×C3111yescharacteristic
336C22×C4#41×C3111yescharacteristic
337C22×C4#41×C3111yescharacteristic
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—42no—
345C4⋊C4C4⋊C4×C3112yes—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C42—22no—
353C42—22no—
354C42—41no—
355C42—41no—
356C42—42no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23C2×C22⋊C4×C3111yescharacteristic
369C23C31×#12111yescharacteristic
370C23C31×C22⋊Q811yescharacteristic
371C23C31×#13512yes—
372C23C31×AGL(1,ℤ/8)12yes—
373D4—42no—
374D4—42no—
375D4—44no—
376D4—44no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—84no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4C31×#9912yes—
415C2×C4C31×#10412yes—
416C2×C4C2×C4⋊C4×C3111yescharacteristic
417C2×C4C31×#11711yescharacteristic
418C2×C4C31×#12111yescharacteristic
419C2×C4C31×C22⋊Q811yescharacteristic
420C8—82no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22C31×#38011yescharacteristic
437C22C2×C31×#9911yescharacteristic
438C22C31×#41011yescharacteristic
439C22C31×#41611yescharacteristic
440C22C31×#41811yescharacteristic
441C22C2×C31×#10411yescharacteristic
442C22C31×#42111yescharacteristic
443C22C31×#46312yes—
444C22C31×#47812yes—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—22no—
450C4—22no—
451C4—42no—
452C4—41no—
453C4—41no—
454C4—84no—
455C4—81no—
456C4—81no—
457C2—22no—
458C2—22no—
459C2—82no—
460C2C31×#150011yescharacteristic
461C2C31×#150711yescharacteristic
462C2C31×#151411yescharacteristic
463C2C31×#151611yescharacteristic
464C2C31×#179911yescharacteristic
465C2C31×#180411yescharacteristic
466C2C31×#180611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1797C2semidirect
4. C31×#1434C2semidirect
5. C31×#1294C2semidirect
8. C2×C4×D4×C31C4semidirect
12. C31×#390C4semidirect
13. C31×#389C4semidirect
17. C4×C4⋊C4×C31C4semidirect
123. #8573C31direct (N × H)
189. #1797C2×C31semidirect
191. #1434C2×C31semidirect
192. #1294C2×C31semidirect
231. C2×C4×D4C4×C31semidirect
235. #390C4×C31semidirect
236. #389C4×C31semidirect
240. C4×C4⋊C4C4×C31semidirect
296. C31#8573direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1212
C31×#17972
C2×C31×#3272
C31×#14342
C31×#12942
#857331