Finite Group Databasebeta

← C31×#14291 #21471050

Subgroups — C31×#14291 #21471050

Order 7936.

1610 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#126C211yesmaximal, characteristic
2C2×C31×#382C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
4C31×#1441C212yesmaximal, complemented
5C31×#1441C212yesmaximal, complemented
6C31×#1439C212yesmaximal
7C31×#1439C212yesmaximal
8C31×#1437C212yesmaximal
9C31×#1436C212yesmaximal, complemented
10C2×C31×#126—24no—
11C2×C31×#126—24no—
12C2×C31×#126C418yescomplemented
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2214yes—
22C22×C42×C31C2212yes—
23C22×C42×C31C2211yescharacteristic
24C31×#382—24no—
25C4×C4⋊C4×C31—24no—
26C2×C31×#95C2212yes—
27C2×C31×#95C2214yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2214yes—
31C2×C31×#95C2214yes—
32C25×C31C2311yescharacteristic
33C23×C4×C31C2314yes—
34C23×C4×C31C2311yescharacteristic
35C23×C4×C31C2311yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C23×C4×C31C2314yes—
38C23×C4×C31C2311yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C31×#126—232no—
42C2×C4⋊C4×C31—22no—
43C2×C4⋊C4×C31—22no—
44C2×C4⋊C4×C31—22no—
45C2×C4⋊C4×C31—22no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31—28no—
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—44no—
52C2×C4⋊C4×C31C2×C414yes—
53C2×C4⋊C4×C31C2×C414yes—
54C2×C4⋊C4×C31C2×C414yes—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—22no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—28no—
62C2×C22⋊C4×C31—44no—
63C2×C22⋊C4×C31—44no—
64C2×C22⋊C4×C31C2×C414yes—
65C2×C22⋊C4×C31C2×C414yes—
66C2×C22⋊C4×C31C2×C414yes—
67C2×C42×C31—24no—
68C2×C42×C31—44no—
69C2×C42×C31C2×C414yes—
70C2×C42×C31D414yes—
71C2×C42×C31D414yes—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—28no—
76C31×#95—44no—
77C31×#95—44no—
78C24×C31—21no—
79C24×C31—21no—
80C24×C31—24no—
81C24×C31—22no—
82C24×C31—22no—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31C22×C412yes—
86C24×C31C2411yescharacteristic
87C22×C4×C31—24no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—24no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—24no—
100C22×C4×C31—24no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—24no—
104C22×C4×C31—24no—
105C22×C4×C31—24no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—24no—
109C22×C4×C31—24no—
110C22×C4×C31—24no—
111C22×C4×C31—24no—
112C22×C4×C31—24no—
113C22×C4×C31—24no—
114C22×C4×C31—24no—
115C22×C4×C31—24no—
116C22×C4×C31C22×C412yes—
117C22×C4×C31C22×C412yes—
118C22×C4×C31C22×C412yes—
119C22×C4×C31C22×C412yes—
120C22×C4×C31C22×C412yes—
121C22×C4×C31C22×C412yes—
122C22×C4×C31C2×D412yes—
123C22×C4×C31C2×D412yes—
124C22×C4×C31C2×D412yes—
125C22×C4×C31C2×D412yes—
126C22×C4×C31C2×D412yes—
127C22×C4×C31C2×D412yes—
128C22×C4×C31#4118yes—
129C4⋊C4×C31—216no—
130C4⋊C4×C31—28no—
131C4⋊C4×C31—28no—
132C4⋊C4×C31—28no—
133C4⋊C4×C31—48no—
134C22⋊C4×C31—28no—
135C22⋊C4×C31—28no—
136C22⋊C4×C31—28no—
137C22⋊C4×C31—416no—
138C42×C31—48no—
139C42×C31C22⋊C4116yescomplemented
140#14291C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—22no—
142C23×C31—24no—
143C23×C31—24no—
144C23×C31—24no—
145C23×C31—42no—
146C23×C31—42no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—42no—
152C23×C31—42no—
153C23×C31—44no—
154C23×C31—44no—
155C23×C31—44no—
156C23×C31—44no—
157C23×C31C23×C411yescharacteristic
158C23×C31C22×D411yescharacteristic
159C23×C31C22×D411yescharacteristic
160C23×C31C2×#4114yes—
161C23×C31H(5,𝔽2)12yes—
162C23×C31H(5,𝔽2)12yes—
163C23×C312−1+412yes—
164C23×C312−1+412yes—
165C2×C4×C31—24no—
166C2×C4×C31—24no—
167C2×C4×C31—24no—
168C2×C4×C31—24no—
169C2×C4×C31—24no—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—24no—
175C2×C4×C31—24no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—28no—
183C2×C4×C31—28no—
184C2×C4×C31—28no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—44no—
188C2×C4×C31—41no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31—44no—
197C2×C4×C31—44no—
198C2×C4×C31—44no—
199C2×C4×C31—44no—
200C2×C4×C31—44no—
201C2×C4×C31—44no—
202C2×C4×C31—44no—
203C2×C4×C31—44no—
204C2×C4×C31C2×C22⋊C414yes—
205C2×C4×C31C2×C22⋊C414yes—
206C2×C4×C31C2×C22⋊C414yes—
207C22×#126C2×C3111yescharacteristic
208C2×#382C2×C3111yescharacteristic, complemented
209C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
210#1441C2×C3112yescomplemented
211#1441C2×C3112yescomplemented
212#1439C2×C3112yes—
213#1439C2×C3112yes—
214#1437C2×C3112yes—
215#1436C2×C3112yescomplemented
216C22×C31—42no—
217C22×C31—42no—
218C22×C31—48no—
219C22×C31—42no—
220C22×C31—82no—
221C22×C31—82no—
222C22×C31—82no—
223C22×C31—82no—
224C22×C31C22×C22⋊C411yescharacteristic
225C22×C31C4×#4112yes—
226C22×C31#52012yes—
227C22×C31#52012yes—
228C22×C31#52512yes—
229C22×C31#53212yes—
230C22×C31#53511yescharacteristic
231C22×C31#53511yescharacteristic
232C22×C31#53611yescharacteristic
233C22×C31#53611yescharacteristic
234C22×C31#53712yes—
235C22×C31#53712yes—
236C22×C31#53814yes—
237C22×C31#53914yes—
238C22×C31#54114yes—
239C22×C31#54214yes—
240C4×C31—24no—
241C4×C31—24no—
242C4×C31—24no—
243C4×C31—42no—
244C4×C31—42no—
245C4×C31—48no—
246C4×C31—42no—
247C4×C31—84no—
248C2×#126—24no—
249C2×#126—24no—
250C2×#126C4×C3118yescomplemented
251C22×C4⋊C4C22×C3112yes—
252C22×C4⋊C4C22×C3111yescharacteristic
253C22×C4⋊C4C22×C3111yescharacteristic
254C22×C4⋊C4C22×C3111yescharacteristic
255C22×C4⋊C4C22×C3112yes—
256C22×C22⋊C4C22×C3111yescharacteristic
257C22×C22⋊C4C22×C3111yescharacteristic
258C22×C22⋊C4C22×C3111yescharacteristic
259C22×C22⋊C4C22×C3114yes—
260C22×C42C22×C3112yes—
261C22×C42C22×C3111yescharacteristic
262#382—24no—
263C4×C4⋊C4—24no—
264C2×#95C22×C3112yes—
265C2×#95C22×C3114yes—
266C2×#95C22×C3112yes—
267C2×#95C22×C3112yes—
268C2×#95C22×C3114yes—
269C2×#95C22×C3114yes—
270C2×C31—82no—
271C2×C31#229711yescharacteristic
272C2×C31#231111yescharacteristic
273C2×C31#231111yescharacteristic
274C2×C31#233414yes—
275C2×C31#263612yes—
276C2×C31#263712yes—
277C2×C31#266212yes—
278C2×C31#266412yes—
279C25C23×C3111yescharacteristic
280C23×C4C23×C3114yes—
281C23×C4C23×C3111yescharacteristic
282C23×C4C23×C3111yescharacteristic
283C23×C4C23×C3111yescharacteristic
284C23×C4C23×C3114yes—
285C23×C4C23×C3111yescharacteristic
286C23×C4C23×C3111yescharacteristic
287C23×C4C23×C3111yescharacteristic
288#126—232no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4C2×C4×C3114yes—
300C2×C4⋊C4C2×C4×C3114yes—
301C2×C4⋊C4C2×C4×C3114yes—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4C2×C4×C3114yes—
312C2×C22⋊C4C2×C4×C3114yes—
313C2×C22⋊C4C2×C4×C3114yes—
314C2×C42—24no—
315C2×C42—44no—
316C2×C42C2×C4×C3114yes—
317C2×C42D4×C3114yes—
318C2×C42D4×C3114yes—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—28no—
323#95—44no—
324#95—44no—
325C31#1429111yescharacteristic, direct product factor, Sylow
326C24—21no—
327C24—21no—
328C24—24no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24C22×C4×C3112yes—
334C24C24×C3111yescharacteristic
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4C22×C4×C3112yes—
365C22×C4C22×C4×C3112yes—
366C22×C4C22×C4×C3112yes—
367C22×C4C22×C4×C3112yes—
368C22×C4C22×C4×C3112yes—
369C22×C4C22×C4×C3112yes—
370C22×C4C2×D4×C3112yes—
371C22×C4C2×D4×C3112yes—
372C22×C4C2×D4×C3112yes—
373C22×C4C2×D4×C3112yes—
374C22×C4C2×D4×C3112yes—
375C22×C4C2×D4×C3112yes—
376C22×C4#41×C3118yes—
377C4⋊C4—216no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—48no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—416no—
386C42—48no—
387C42C22⋊C4×C31116yescomplemented
388C23—22no—
389C23—24no—
390C23—24no—
391C23—24no—
392C23—42no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—42no—
400C23—44no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23C23×C4×C3111yescharacteristic
405C23C22×D4×C3111yescharacteristic
406C23C22×D4×C3111yescharacteristic
407C23C2×#41×C3114yes—
408C23C31×H(5,𝔽2)12yes—
409C23C31×H(5,𝔽2)12yes—
410C23C31×2−1+412yes—
411C23C31×2−1+412yes—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—28no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4C2×C22⋊C4×C3114yes—
452C2×C4C2×C22⋊C4×C3114yes—
453C2×C4C2×C22⋊C4×C3114yes—
454C22—42no—
455C22—42no—
456C22—48no—
457C22—42no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22C22×C22⋊C4×C3111yescharacteristic
463C22C4×#41×C3112yes—
464C22C31×#52012yes—
465C22C31×#52012yes—
466C22C31×#52512yes—
467C22C31×#53212yes—
468C22C31×#53511yescharacteristic
469C22C31×#53511yescharacteristic
470C22C31×#53611yescharacteristic
471C22C31×#53611yescharacteristic
472C22C31×#53712yes—
473C22C31×#53712yes—
474C22C31×#53814yes—
475C22C31×#53914yes—
476C22C31×#54114yes—
477C22C31×#54214yes—
478C4—24no—
479C4—24no—
480C4—24no—
481C4—42no—
482C4—42no—
483C4—48no—
484C4—42no—
485C4—84no—
486C2—82no—
487C2C31×#229711yescharacteristic
488C2C31×#231111yescharacteristic
489C2C31×#231111yescharacteristic
490C2C31×#233414yes—
491C2C31×#263612yes—
492C2C31×#263712yes—
493C2C31×#266212yes—
494C2C31×#266412yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#382C2semidirect
3. C2×C4×C4⋊C4×C31C2semidirect
4. C31×#1441C2semidirect
5. C31×#1441C2semidirect
9. C31×#1436C2semidirect
12. C2×C31×#126C4semidirect
139. C42×C31C22⋊C4semidirect
140. #14291C31direct (N × H)
208. C2×#382C2×C31semidirect
209. C2×C4×C4⋊C4C2×C31semidirect
210. #1441C2×C31semidirect
211. #1441C2×C31semidirect
215. #1436C2×C31semidirect
250. C2×#126C4×C31semidirect
325. C31#14291direct (N × H)
387. C42C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1262
C2×C31×#3822
C2×C4×C4⋊C4×C312
C31×#14412
C31×#14392
C31×#14372
C31×#14362
#1429131