Finite Group Databasebeta

← C31×#8561 #21465320

Subgroups — C31×#8561 #21465320

Order 7936.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic, complemented
3C31×#1797C211yesmaximal, characteristic, complemented
4C2×C31×#323C212yesmaximal
5C31×#1280C212yesmaximal, complemented
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C22⋊C4×C31C411yescharacteristic
8C22×C22⋊C4×C31C411yescharacteristic
9C22×C22⋊C4×C31C2211yescharacteristic
10C22×C42×C31C2211yescharacteristic
11C2×C31×C4⋊C8—21no—
12C2×C31×C4⋊C8—21no—
13C2×C31×C22⋊C8C2212yes—
14C2×C31×C22⋊C8C2212yes—
15C31×#388—21no—
16C31×#388—21no—
17C31×#388—21no—
18C31×#388—21no—
19C2×C31×#95C411yescharacteristic
20C2×C31×#95C2211yescharacteristic
21C31×#336—21no—
22C31×#336—21no—
23C31×#323—24no—
24C25×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—42no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—42no—
45C2×C22⋊C4×C31—42no—
46C2×C22⋊C4×C31D412yes—
47C2×C22⋊C4×C31Q812yes—
48C2×C42×C31—42no—
49C2×C42×C31D411yescharacteristic
50C2×C42×C31D411yescharacteristic
51C2×C42×C31D411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C31×C4⋊C8—42no—
54C31×C4⋊C8—42no—
55C31×C22⋊C8—22no—
56C31×C22⋊C8—22no—
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C24×C31—21no—
64C24×C31—21no—
65C24×C31—22no—
66C24×C31—22no—
67C24×C31—41no—
68C24×C31—41no—
69C24×C31—41no—
70C24×C31—41no—
71C24×C31C4⋊C412yes—
72C24×C31C22×C411yescharacteristic
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31C22⋊C411yescharacteristic
94C22×C4×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C4⋊C412yes—
98C22×C4×C31C2×D411yescharacteristic
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—
107C2×C8×C31—42no—
108C2×C8×C31—42no—
109C2×C8×C31—42no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31—42no—
112C22⋊C4×C31—22no—
113C22⋊C4×C31—22no—
114C22⋊C4×C31—22no—
115C22⋊C4×C31—22no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—42no—
118C22⋊C4×C31—42no—
119C22⋊C4×C31—42no—
120C42×C31—22no—
121C42×C31—22no—
122C42×C31—41no—
123C42×C31—41no—
124#8561C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—21no—
129C23×C31—22no—
130C23×C31—24no—
131C23×C31—42no—
132C23×C31—42no—
133C23×C31—42no—
134C23×C31—42no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31—42no—
142C23×C31—82no—
143C23×C31—82no—
144C23×C31—82no—
145C23×C31—82no—
146C23×C31C2×C22⋊C411yescharacteristic
147C23×C31C2×C4⋊C411yescharacteristic
148C23×C31#11711yescharacteristic
149C23×C31#13112yes—
150C23×C31#13112yes—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
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—22no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—44no—
171C2×C4×C31—44no—
172C2×C4×C31—42no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—42no—
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—82no—
183C2×C4×C31—82no—
184C2×C4×C31#9912yes—
185C2×C4×C31#10012yes—
186C2×C4×C31#12111yescharacteristic
187C2×C4×C31#12111yescharacteristic
188C2×C4×C31C22⋊Q811yescharacteristic
189C2×C4×C31C22⋊Q811yescharacteristic
190C8×C31—82no—
191C8×C31—82no—
192C2×#388C2×C3111yescharacteristic
193#1797C2×C3111yescharacteristic, complemented
194#1797C2×C3111yescharacteristic, complemented
195C2×#323C2×C3112yes—
196#1280C2×C3112yescomplemented
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—22no—
202C22×C31—22no—
203C22×C31—22no—
204C22×C31—22no—
205C22×C31—42no—
206C22×C31—42no—
207C22×C31—42no—
208C22×C31—84no—
209C22×C31—84no—
210C22×C31—81no—
211C22×C31—81no—
212C22×C31—81no—
213C22×C31—81no—
214C22×C31#38011yescharacteristic
215C22×C31#40811yescharacteristic
216C22×C31#40811yescharacteristic
217C22×C31C2×#9911yescharacteristic
218C22×C31#41011yescharacteristic
219C22×C31C2×#10011yescharacteristic
220C22×C31#41311yescharacteristic
221C22×C31#42412yes—
222C22×C31#43312yes—
223C4×C31—21no—
224C4×C31—21no—
225C4×C31—21no—
226C4×C31—21no—
227C4×C31—22no—
228C4×C31—22no—
229C4×C31—42no—
230C4×C31—41no—
231C4×C31—41no—
232C4×C31—81no—
233C4×C31—81no—
234C22×C4⋊C4C4×C3111yescharacteristic
235C22×C22⋊C4C4×C3111yescharacteristic
236C22×C22⋊C4C4×C3111yescharacteristic
237C22×C22⋊C4C22×C3111yescharacteristic
238C22×C42C22×C3111yescharacteristic
239C2×C4⋊C8—21no—
240C2×C4⋊C8—21no—
241C2×C22⋊C8C22×C3112yes—
242C2×C22⋊C8C22×C3112yes—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247C2×#95C4×C3111yescharacteristic
248C2×#95C22×C3111yescharacteristic
249#336—21no—
250#336—21no—
251#323—24no—
252C2×C31—22no—
253C2×C31—22no—
254C2×C31—82no—
255C2×C31#146811yescharacteristic
256C2×C31#146911yescharacteristic
257C2×C31#147111yescharacteristic
258C2×C31#147311yescharacteristic
259C2×C31#179811yescharacteristic
260C2×C31#179911yescharacteristic
261C2×C31#180011yescharacteristic
262C25C2×C4×C3111yescharacteristic
263C23×C4C2×C4×C3111yescharacteristic
264C23×C4C2×C4×C3111yescharacteristic
265C23×C4C2×C4×C3111yescharacteristic
266C23×C4C2×C4×C3111yescharacteristic
267C23×C4C2×C4×C3111yescharacteristic
268C23×C4C23×C3111yescharacteristic
269C22×C8—22no—
270C22×C8—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—42no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4D4×C3112yes—
285C2×C22⋊C4Q8×C3112yes—
286C2×C42—42no—
287C2×C42D4×C3111yescharacteristic
288C2×C42D4×C3111yescharacteristic
289C2×C42D4×C3111yescharacteristic
290C2×C42D4×C3111yescharacteristic
291C4⋊C8—42no—
292C4⋊C8—42no—
293C22⋊C8—22no—
294C22⋊C8—22no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301C31#856111yescharacteristic, direct product factor, Sylow
302C24—21no—
303C24—21no—
304C24—22no—
305C24—22no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24—41no—
310C24C4⋊C4×C3112yes—
311C24C22×C4×C3111yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22⋊C4×C3111yescharacteristic
333C22×C4C22⋊C4×C3111yescharacteristic
334C22×C4C22⋊C4×C3111yescharacteristic
335C22×C4C22⋊C4×C3111yescharacteristic
336C22×C4C4⋊C4×C3112yes—
337C22×C4C2×D4×C3111yescharacteristic
338C22×C4C2×D4×C3111yescharacteristic
339C22×C4C2×D4×C3111yescharacteristic
340C22×C4C2×Q8×C3111yescharacteristic
341C22×C4#41×C3111yescharacteristic
342C22×C4#41×C3111yescharacteristic
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C42—22no—
360C42—22no—
361C42—41no—
362C42—41no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—24no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—42no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×C22⋊C4×C3111yescharacteristic
385C23C2×C4⋊C4×C3111yescharacteristic
386C23C31×#11711yescharacteristic
387C23C31×#13112yes—
388C23C31×#13112yes—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4C31×#9912yes—
423C2×C4C31×#10012yes—
424C2×C4C31×#12111yescharacteristic
425C2×C4C31×#12111yescharacteristic
426C2×C4C31×C22⋊Q811yescharacteristic
427C2×C4C31×C22⋊Q811yescharacteristic
428C8—82no—
429C8—82no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22—84no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22C31×#38011yescharacteristic
448C22C31×#40811yescharacteristic
449C22C31×#40811yescharacteristic
450C22C2×C31×#9911yescharacteristic
451C22C31×#41011yescharacteristic
452C22C2×C31×#10011yescharacteristic
453C22C31×#41311yescharacteristic
454C22C31×#42412yes—
455C22C31×#43312yes—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—41no—
464C4—41no—
465C4—81no—
466C4—81no—
467C2—22no—
468C2—22no—
469C2—82no—
470C2C31×#146811yescharacteristic
471C2C31×#146911yescharacteristic
472C2C31×#147111yescharacteristic
473C2C31×#147311yescharacteristic
474C2C31×#179811yescharacteristic
475C2C31×#179911yescharacteristic
476C2C31×#180011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C24 ▷ C2 ▷ 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
3. C31×#1797C2semidirect
5. C31×#1280C2semidirect
124. #8561C31direct (N × H)
193. #1797C2×C31semidirect
194. #1797C2×C31semidirect
196. #1280C2×C31semidirect
301. C31#8561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C31×#17972
C2×C31×#3232
C31×#12802
#856131