Finite Group Databasebeta

← C31×#7927 #21464686

Subgroups — C31×#7927 #21464686

Order 7936.

954 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#407C211yesmaximal, characteristic
2C22×C31×C22⋊C8C211yesmaximal, characteristic
3C31×#2280C211yesmaximal, characteristic
4C31×#1282C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31—21no—
7C23×C8×C31C412yescomplemented
8C2×C31×#117—21no—
9C31×#407—21no—
10C31×#407—21no—
11C31×#407C412yescomplemented
12C31×#407C412yescomplemented
13C2×C31×C22⋊C8—21no—
14C2×C31×C22⋊C8—21no—
15C2×C31×C22⋊C8—21no—
16C2×C31×C22⋊C8—21no—
17C2×C31×C22⋊C8—21no—
18C2×C31×C22⋊C8C412yescomplemented
19C2×C31×C22⋊C8C2212yes—
20C2×C31×C22⋊C8C2212yes—
21C31×#381—21no—
22C31×#380—21no—
23C31×#380C412yes—
24C31×#379C412yes—
25C4×C22⋊C4×C31—21no—
26C4×C22⋊C4×C31C2212yes—
27C25×C31C2×C411yescharacteristic
28C23×C4×C31—44no—
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31D411yescharacteristic
39C23×C4×C31D411yescharacteristic
40C23×C4×C31Q811yescharacteristic
41C23×C4×C31Q811yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C2×M16×C31—22no—
44C2×M16×C31—22no—
45C2×M16×C31—44no—
46C22×C8×C31—22no—
47C22×C8×C31—22no—
48C22×C8×C31—22no—
49C22×C8×C31—44no—
50C22×C8×C31C2×C414yes—
51C31×#117—44no—
52C2×C4⋊C4×C31—22no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31C2×C414yes—
56C2×C42×C31—22no—
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×C22⋊C8—22no—
60C31×C22⋊C8—22no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×C22⋊C8C2×C414yes—
65C31×#95—22no—
66C31×#95—22no—
67C24×C31—24no—
68C24×C31—42no—
69C24×C31—42no—
70C24×C31C4211yescharacteristic
71C24×C31C4211yescharacteristic
72C24×C31C22⋊C411yescharacteristic
73C24×C31C22⋊C411yescharacteristic
74C24×C31C4⋊C411yescharacteristic
75C24×C31C4⋊C411yescharacteristic
76C24×C31C22×C411yescharacteristic
77C22×C4×C31—24no—
78C22×C4×C31—24no—
79C22×C4×C31—24no—
80C22×C4×C31—24no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
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×C31C4211yescharacteristic
93C22×C4×C31C4211yescharacteristic
94C22×C4×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22⋊C411yescharacteristic
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31C22⋊C411yescharacteristic
99C22×C4×C31C22⋊C411yescharacteristic
100C22×C4×C31C22⋊C411yescharacteristic
101C22×C4×C31C22⋊C411yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C4⋊C411yescharacteristic
105C22×C4×C31C4⋊C411yescharacteristic
106C22×C4×C31C4⋊C411yescharacteristic
107C22×C4×C31C4⋊C411yescharacteristic
108C22×C4×C31C4⋊C411yescharacteristic
109C22×C4×C31C4⋊C411yescharacteristic
110C22×C4×C31C4⋊C411yescharacteristic
111C22×C4×C31C4⋊C411yescharacteristic
112C22×C4×C31C4⋊C411yescharacteristic
113C22×C4×C31C4⋊C411yescharacteristic
114C22×C4×C31C22×C411yescharacteristic
115C22×C4×C31C22×C411yescharacteristic
116C22×C4×C31C2×D411yescharacteristic
117C22×C4×C31C2×D411yescharacteristic
118C22×C4×C31C2×D411yescharacteristic
119C22×C4×C31C2×Q811yescharacteristic
120M16×C31—44no—
121M16×C31—44no—
122C2×C8×C31—24no—
123C2×C8×C31—24no—
124C2×C8×C31—44no—
125C2×C8×C31—44no—
126C2×C8×C31—44no—
127C2×C8×C31—44no—
128C4⋊C4×C31—44no—
129C22⋊C4×C31—28no—
130C22⋊C4×C31—44no—
131C22⋊C4×C31—44no—
132C42×C31—44no—
133#7927C3111yesmaximal, characteristic, direct product factor, Sylow
134C23×C31—22no—
135C23×C31—22no—
136C23×C31—22no—
137C23×C31—22no—
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—22no—
141C23×C31—22no—
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—416no—
155C23×C31#9511yescharacteristic
156C23×C31#9511yescharacteristic
157C23×C31#9511yescharacteristic
158C23×C31#9511yescharacteristic
159C23×C31C2×C4211yescharacteristic
160C23×C31C2×C22⋊C411yescharacteristic
161C23×C31C2×C4⋊C411yescharacteristic
162C23×C31#13114yes—
163C2×C4×C31—22no—
164C2×C4×C31—22no—
165C2×C4×C31—22no—
166C2×C4×C31—22no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—22no—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—41no—
189C2×C4×C31—41no—
190C2×C4×C31—44no—
191C2×C4×C31—44no—
192C2×C4×C31—44no—
193C2×C4×C31#9511yescharacteristic
194C2×C4×C31#9511yescharacteristic
195C2×C4×C31#9511yescharacteristic
196C2×C4×C31#9511yescharacteristic
197C2×C4×C31#9914yes—
198C2×C4×C31C2×C22⋊C411yescharacteristic
199C2×C4×C31C2×C22⋊C411yescharacteristic
200C2×C4×C31C2×C4⋊C411yescharacteristic
201C2×C4×C31C2×C4⋊C411yescharacteristic
202C8×C31—44no—
203C8×C31—44no—
204C2×#407C2×C3111yescharacteristic
205C22×C22⋊C8C2×C3111yescharacteristic
206#2280C2×C3111yescharacteristic
207#1282C2×C3114yescomplemented
208C22×C31—28no—
209C22×C31—21no—
210C22×C31—21no—
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—21no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—21no—
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—21no—
220C22×C31—21no—
221C22×C31—21no—
222C22×C31—21no—
223C22×C31—21no—
224C22×C31—21no—
225C22×C31—44no—
226C22×C31—44no—
227C22×C31—44no—
228C22×C31—44no—
229C22×C31—44no—
230C22×C31—44no—
231C22×C31#34212yes—
232C22×C31#34412yes—
233C22×C31C2×#9511yescharacteristic
234C22×C31#40512yes—
235C22×C31#40812yes—
236C22×C31#42412yes—
237C4×C31—21no—
238C4×C31—21no—
239C4×C31—21no—
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—21no—
243C4×C31—84no—
244C4×C31#34212yes—
245C4×C31C2×#9912yes—
246C24×C4C22×C3111yescharacteristic
247C22×M16—21no—
248C23×C8C4×C3112yescomplemented
249C2×#117—21no—
250#407—21no—
251#407—21no—
252#407C4×C3112yescomplemented
253#407C4×C3112yescomplemented
254C2×C22⋊C8—21no—
255C2×C22⋊C8—21no—
256C2×C22⋊C8—21no—
257C2×C22⋊C8—21no—
258C2×C22⋊C8—21no—
259C2×C22⋊C8C4×C3112yescomplemented
260C2×C22⋊C8C22×C3112yes—
261C2×C22⋊C8C22×C3112yes—
262#381—21no—
263#380—21no—
264#380C4×C3112yes—
265#379C4×C3112yes—
266C4×C22⋊C4—21no—
267C4×C22⋊C4C22×C3112yes—
268C2×C31—22no—
269C2×C31—22no—
270C2×C31—22no—
271C2×C31—22no—
272C2×C31—22no—
273C2×C31—41no—
274C2×C31—41no—
275C2×C31#172911yescharacteristic
276C2×C31C2×#34211yescharacteristic
277C2×C31C2×#34411yescharacteristic
278C25C2×C4×C3111yescharacteristic
279C23×C4—44no—
280C23×C4C2×C4×C3111yescharacteristic
281C23×C4C2×C4×C3111yescharacteristic
282C23×C4C2×C4×C3111yescharacteristic
283C23×C4C2×C4×C3111yescharacteristic
284C23×C4C2×C4×C3111yescharacteristic
285C23×C4D4×C3111yescharacteristic
286C23×C4D4×C3111yescharacteristic
287C23×C4D4×C3111yescharacteristic
288C23×C4D4×C3111yescharacteristic
289C23×C4D4×C3111yescharacteristic
290C23×C4D4×C3111yescharacteristic
291C23×C4Q8×C3111yescharacteristic
292C23×C4Q8×C3111yescharacteristic
293C23×C4C23×C3111yescharacteristic
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—44no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—44no—
301C22×C8C2×C4×C3114yes—
302#117—44no—
303C2×C4⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4C2×C4×C3114yes—
307C2×C42—22no—
308C22⋊C8—22no—
309C22⋊C8—22no—
310C22⋊C8—22no—
311C22⋊C8—22no—
312C22⋊C8—22no—
313C22⋊C8—22no—
314C22⋊C8—22no—
315C22⋊C8C2×C4×C3114yes—
316#95—22no—
317#95—22no—
318C31#792711yescharacteristic, direct product factor, Sylow
319C24—24no—
320C24—42no—
321C24—42no—
322C24C42×C3111yescharacteristic
323C24C42×C3111yescharacteristic
324C24C22⋊C4×C3111yescharacteristic
325C24C22⋊C4×C3111yescharacteristic
326C24C4⋊C4×C3111yescharacteristic
327C24C4⋊C4×C3111yescharacteristic
328C24C22×C4×C3111yescharacteristic
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4C42×C3111yescharacteristic
345C22×C4C42×C3111yescharacteristic
346C22×C4C22⋊C4×C3111yescharacteristic
347C22×C4C22⋊C4×C3111yescharacteristic
348C22×C4C22⋊C4×C3111yescharacteristic
349C22×C4C22⋊C4×C3111yescharacteristic
350C22×C4C22⋊C4×C3111yescharacteristic
351C22×C4C22⋊C4×C3111yescharacteristic
352C22×C4C22⋊C4×C3111yescharacteristic
353C22×C4C22⋊C4×C3111yescharacteristic
354C22×C4C22⋊C4×C3111yescharacteristic
355C22×C4C22⋊C4×C3111yescharacteristic
356C22×C4C4⋊C4×C3111yescharacteristic
357C22×C4C4⋊C4×C3111yescharacteristic
358C22×C4C4⋊C4×C3111yescharacteristic
359C22×C4C4⋊C4×C3111yescharacteristic
360C22×C4C4⋊C4×C3111yescharacteristic
361C22×C4C4⋊C4×C3111yescharacteristic
362C22×C4C4⋊C4×C3111yescharacteristic
363C22×C4C4⋊C4×C3111yescharacteristic
364C22×C4C4⋊C4×C3111yescharacteristic
365C22×C4C4⋊C4×C3111yescharacteristic
366C22×C4C22×C4×C3111yescharacteristic
367C22×C4C22×C4×C3111yescharacteristic
368C22×C4C2×D4×C3111yescharacteristic
369C22×C4C2×D4×C3111yescharacteristic
370C22×C4C2×D4×C3111yescharacteristic
371C22×C4C2×Q8×C3111yescharacteristic
372M16—44no—
373M16—44no—
374C2×C8—24no—
375C2×C8—24no—
376C2×C8—44no—
377C2×C8—44no—
378C2×C8—44no—
379C2×C8—44no—
380C4⋊C4—44no—
381C22⋊C4—28no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C42—44no—
385C23—22no—
386C23—22no—
387C23—22no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—416no—
406C23C31×#9511yescharacteristic
407C23C31×#9511yescharacteristic
408C23C31×#9511yescharacteristic
409C23C31×#9511yescharacteristic
410C23C2×C42×C3111yescharacteristic
411C23C2×C22⋊C4×C3111yescharacteristic
412C23C2×C4⋊C4×C3111yescharacteristic
413C23C31×#13114yes—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4C31×#9511yescharacteristic
445C2×C4C31×#9511yescharacteristic
446C2×C4C31×#9511yescharacteristic
447C2×C4C31×#9511yescharacteristic
448C2×C4C31×#9914yes—
449C2×C4C2×C22⋊C4×C3111yescharacteristic
450C2×C4C2×C22⋊C4×C3111yescharacteristic
451C2×C4C2×C4⋊C4×C3111yescharacteristic
452C2×C4C2×C4⋊C4×C3111yescharacteristic
453C8—44no—
454C8—44no—
455C22—28no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—44no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—44no—
478C22C31×#34212yes—
479C22C31×#34412yes—
480C22C2×C31×#9511yescharacteristic
481C22C31×#40512yes—
482C22C31×#40812yes—
483C22C31×#42412yes—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—84no—
491C4C31×#34212yes—
492C4C2×C31×#9912yes—
493C2—22no—
494C2—22no—
495C2—22no—
496C2—22no—
497C2—22no—
498C2—41no—
499C2—41no—
500C2C31×#172911yescharacteristic
501C2C2×C31×#34211yescharacteristic
502C2C2×C31×#34411yescharacteristic
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31C2×#95
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1282C2semidirect
7. C23×C8×C31C4semidirect
11. C31×#407C4semidirect
12. C31×#407C4semidirect
18. C2×C31×C22⋊C8C4semidirect
133. #7927C31direct (N × H)
207. #1282C2×C31semidirect
248. C23×C8C4×C31semidirect
252. #407C4×C31semidirect
253. #407C4×C31semidirect
259. C2×C22⋊C8C4×C31semidirect
318. C31#7927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4072
C22×C31×C22⋊C82
C31×#22802
C31×#12822
#792731