Finite Group Databasebeta

← C2×C31×#1472 #21474137

Subgroups — C2×C31×#1472 #21474137

Order 7936.

1426 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic
3C22×C31×C22⋊C8C211yesmaximal, characteristic
4C31×#1472C218yesmaximal, direct product factor
5C2×C31×#324C214yesmaximal, complemented
6C23×Q8×C31C411yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C22×M16×C31—21no—
9C23×C8×C31—21no—
10C2×C31×C22⋊Q8—21no—
11C2×C31×C22⋊Q8—21no—
12C2×C31×C22⋊Q8—22no—
13C2×C31×C22⋊Q8—21no—
14C2×C31×C22⋊Q8—21no—
15C2×C31×C22⋊Q8—22no—
16C2×C31×C22⋊Q8C414yes—
17C2×C31×C22⋊Q8C2214yes—
18C22×C4⋊C4×C31C411yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C412yes—
21C31×#407—22no—
22C31×#407C2214yes—
23C2×C31×C22⋊C8—22no—
24C2×C31×C22⋊C8—21no—
25C2×C31×C22⋊C8—21no—
26C2×C31×C22⋊C8C2212yes—
27C2×C31×C22⋊C8C2214yes—
28C2×C31×C22⋊C8C2212yes—
29C31×#324C22116yescomplemented
30C25×C31C2×C411yescharacteristic
31C22×Q8×C31—22no—
32C22×Q8×C31—21no—
33C22×Q8×C31—21no—
34C22×Q8×C31—44no—
35C22×Q8×C31C2×C414yes—
36C23×C4×C31—44no—
37C23×C4×C31C2×C412yes—
38C23×C4×C31C2×C411yescharacteristic
39C23×C4×C31C2×C412yes—
40C23×C4×C31C2×C412yes—
41C23×C4×C31D411yescharacteristic
42C23×C4×C31D411yescharacteristic
43C23×C4×C31D412yes—
44C23×C4×C31D411yescharacteristic
45C23×C4×C31D411yescharacteristic
46C23×C4×C31D412yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C2×M16×C31—24no—
50C2×M16×C31—44no—
51C22×C8×C31—24no—
52C22×C8×C31—22no—
53C22×C8×C31—22no—
54C22×C8×C31—44no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—24no—
58C31×C22⋊Q8—24no—
59C31×C22⋊Q8—24no—
60C31×C22⋊Q8—24no—
61C31×C22⋊Q8—24no—
62C31×C22⋊Q8—24no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—21no—
65C2×C4⋊C4×C31—21no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31C2×C414yes—
71C2×C4⋊C4×C31C2×C414yes—
72C2×C4⋊C4×C31C2314yes—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31C2×C418yes—
77C31×C22⋊C8—22no—
78C31×C22⋊C8—24no—
79C31×C22⋊C8—24no—
80C31×C22⋊C8—22no—
81C31×C22⋊C8C2314yes—
82C31×C22⋊C8C2314yes—
83C24×C31—24no—
84C24×C31—24no—
85C24×C31—42no—
86C24×C31C22⋊C411yescharacteristic
87C24×C31C22⋊C412yes—
88C24×C31C22⋊C411yescharacteristic
89C24×C31C22×C412yes—
90C24×C31C22×C411yescharacteristic
91C2×Q8×C31—24no—
92C2×Q8×C31—24no—
93C2×Q8×C31—44no—
94C2×Q8×C31—48no—
95C2×Q8×C31—48no—
96C2×Q8×C31—44no—
97C22×C4×C31—24no—
98C22×C4×C31—24no—
99C22×C4×C31—24no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—28no—
105C22×C4×C31—44no—
106C22×C4×C31—44no—
107C22×C4×C31—44no—
108C22×C4×C31—44no—
109C22×C4×C31—42no—
110C22×C4×C31—42no—
111C22×C4×C31—42no—
112C22×C4×C31—44no—
113C22×C4×C31C22⋊C412yes—
114C22×C4×C31C22⋊C412yes—
115C22×C4×C31C22⋊C412yes—
116C22×C4×C31C22⋊C411yescharacteristic
117C22×C4×C31C22⋊C412yes—
118C22×C4×C31C22⋊C412yes—
119C22×C4×C31C22⋊C411yescharacteristic
120C22×C4×C31C22×C414yes—
121C22×C4×C31C22×C412yes—
122C22×C4×C31C22×C414yes—
123C22×C4×C31C22×C411yescharacteristic
124C22×C4×C31C2×D412yes—
125C22×C4×C31C2×D412yes—
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D412yes—
131C22×C4×C31C2×D412yes—
132C22×C4×C31C2411yescharacteristic
133M16×C31—48no—
134C2×C8×C31—24no—
135C2×C8×C31—24no—
136C2×C8×C31—44no—
137C2×C8×C31—48no—
138C2×C8×C31—44no—
139C4⋊C4×C31—24no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—24no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—24no—
144C4⋊C4×C31—24no—
145C22⋊C4×C31—28no—
146C22⋊C4×C31—28no—
147C2×#1472C3111yesmaximal, characteristic, direct product factor, Sylow
148C23×C31—22no—
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—24no—
153C23×C31—24no—
154C23×C31—22no—
155C23×C31—22no—
156C23×C31—24no—
157C23×C31—22no—
158C23×C31—24no—
159C23×C31—42no—
160C23×C31—42no—
161C23×C31—416no—
162C23×C31#10114yes—
163C23×C31C2×C22⋊C412yes—
164C23×C31C2×C22⋊C411yescharacteristic
165C23×C31C2×C22⋊C412yes—
166C23×C31C2×C22⋊C411yescharacteristic
167C23×C31#13114yes—
168C23×C31C23×C411yescharacteristic
169Q8×C31—48no—
170Q8×C31—48no—
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—24no—
175C2×C4×C31—24no—
176C2×C4×C31—24no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—28no—
183C2×C4×C31—42no—
184C2×C4×C31—42no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—42no—
189C2×C4×C31—42no—
190C2×C4×C31—41no—
191C2×C4×C31—44no—
192C2×C4×C31—44no—
193C2×C4×C31—44no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31#9914yes—
197C2×C4×C31C2×C22⋊C411yescharacteristic
198C2×C4×C31C2×C22⋊C411yescharacteristic
199C2×C4×C31C2×C22⋊C412yes—
200C2×C4×C31C2×C22⋊C412yes—
201C2×C4×C31C22×D411yescharacteristic
202C2×C4×C31C22×D411yescharacteristic
203C8×C31—44no—
204C8×C31—44no—
205C22×C22⋊Q8C2×C3111yescharacteristic
206C2×#407C2×C3111yescharacteristic
207C22×C22⋊C8C2×C3111yescharacteristic
208#1472C2×C3118yesdirect product factor
209C2×#324C2×C3114yescomplemented
210C22×C31—22no—
211C22×C31—21no—
212C22×C31—21no—
213C22×C31—22no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—28no—
217C22×C31—28no—
218C22×C31—22no—
219C22×C31—22no—
220C22×C31—22no—
221C22×C31—48no—
222C22×C31—48no—
223C22×C31—44no—
224C22×C31#40812yes—
225C22×C31#40812yes—
226C22×C31C2×#9912yes—
227C22×C31C2×#10114yes—
228C22×C31C2×#10112yes—
229C22×C31C22×C22⋊C411yescharacteristic
230C22×C31C2×#13112yes—
231C4×C31—21no—
232C4×C31—21no—
233C4×C31—21no—
234C4×C31—21no—
235C4×C31—22no—
236C4×C31—44no—
237C4×C31—44no—
238C4×C31C2×#9914yes—
239C23×Q8C4×C3111yescharacteristic
240C24×C4C22×C3111yescharacteristic
241C22×M16—21no—
242C23×C8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—22no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—22no—
249C2×C22⋊Q8C4×C3114yes—
250C2×C22⋊Q8C22×C3114yes—
251C22×C4⋊C4C4×C3111yescharacteristic
252C22×C4⋊C4C22×C3112yes—
253C22×C22⋊C4C4×C3112yes—
254#407—22no—
255#407C22×C3114yes—
256C2×C22⋊C8—22no—
257C2×C22⋊C8—21no—
258C2×C22⋊C8—21no—
259C2×C22⋊C8C22×C3112yes—
260C2×C22⋊C8C22×C3114yes—
261C2×C22⋊C8C22×C3112yes—
262#324C22×C31116yescomplemented
263C2×C31—22no—
264C2×C31—22no—
265C2×C31—24no—
266C2×C31—42no—
267C2×C31#147214yesdirect product factor
268C2×C31C2×#40811yescharacteristic
269C2×C31C22×#9911yescharacteristic
270C2×C31C22×#10111yescharacteristic
271C25C2×C4×C3111yescharacteristic
272C22×Q8—22no—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×Q8—44no—
276C22×Q8C2×C4×C3114yes—
277C23×C4—44no—
278C23×C4C2×C4×C3112yes—
279C23×C4C2×C4×C3111yescharacteristic
280C23×C4C2×C4×C3112yes—
281C23×C4C2×C4×C3112yes—
282C23×C4D4×C3111yescharacteristic
283C23×C4D4×C3111yescharacteristic
284C23×C4D4×C3112yes—
285C23×C4D4×C3111yescharacteristic
286C23×C4D4×C3111yescharacteristic
287C23×C4D4×C3112yes—
288C23×C4C23×C3111yescharacteristic
289C23×C4C23×C3112yes—
290C2×M16—24no—
291C2×M16—44no—
292C22×C8—22no—
293C22×C8—24no—
294C22×C8—22no—
295C22×C8—44no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—24no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4C2×C4×C3114yes—
312C2×C4⋊C4C2×C4×C3114yes—
313C2×C4⋊C4C23×C3114yes—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4C2×C4×C3118yes—
318C22⋊C8—22no—
319C22⋊C8—24no—
320C22⋊C8—24no—
321C22⋊C8—22no—
322C22⋊C8C23×C3114yes—
323C22⋊C8C23×C3114yes—
324C31C2×#147211yescharacteristic, direct product factor, Sylow
325C24—24no—
326C24—24no—
327C24—42no—
328C24C22⋊C4×C3111yescharacteristic
329C24C22⋊C4×C3112yes—
330C24C22⋊C4×C3111yescharacteristic
331C24C22×C4×C3112yes—
332C24C22×C4×C3111yescharacteristic
333C2×Q8—24no—
334C2×Q8—24no—
335C2×Q8—48no—
336C2×Q8—44no—
337C2×Q8—48no—
338C2×Q8—44no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—28no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—44no—
355C22×C4C22⋊C4×C3111yescharacteristic
356C22×C4C22⋊C4×C3112yes—
357C22×C4C22⋊C4×C3112yes—
358C22×C4C22⋊C4×C3112yes—
359C22×C4C22⋊C4×C3112yes—
360C22×C4C22⋊C4×C3112yes—
361C22×C4C22⋊C4×C3111yescharacteristic
362C22×C4C22×C4×C3114yes—
363C22×C4C22×C4×C3112yes—
364C22×C4C22×C4×C3114yes—
365C22×C4C22×C4×C3111yescharacteristic
366C22×C4C2×D4×C3111yescharacteristic
367C22×C4C2×D4×C3111yescharacteristic
368C22×C4C2×D4×C3112yes—
369C22×C4C2×D4×C3112yes—
370C22×C4C2×D4×C3111yescharacteristic
371C22×C4C2×D4×C3111yescharacteristic
372C22×C4C2×D4×C3112yes—
373C22×C4C2×D4×C3112yes—
374C22×C4C24×C3111yescharacteristic
375M16—48no—
376C2×C8—24no—
377C2×C8—24no—
378C2×C8—44no—
379C2×C8—48no—
380C2×C8—44no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—24no—
394C23—22no—
395C23—22no—
396C23—24no—
397C23—22no—
398C23—24no—
399C23—24no—
400C23—42no—
401C23—42no—
402C23—416no—
403C23C31×#10114yes—
404C23C2×C22⋊C4×C3112yes—
405C23C2×C22⋊C4×C3111yescharacteristic
406C23C2×C22⋊C4×C3112yes—
407C23C2×C22⋊C4×C3111yescharacteristic
408C23C31×#13114yes—
409C23C23×C4×C3111yescharacteristic
410Q8—48no—
411Q8—48no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—28no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4C31×#9914yes—
438C2×C4C2×C22⋊C4×C3111yescharacteristic
439C2×C4C2×C22⋊C4×C3111yescharacteristic
440C2×C4C2×C22⋊C4×C3112yes—
441C2×C4C2×C22⋊C4×C3112yes—
442C2×C4C22×D4×C3111yescharacteristic
443C2×C4C22×D4×C3111yescharacteristic
444C8—44no—
445C8—44no—
446C22—22no—
447C22—21no—
448C22—21no—
449C22—22no—
450C22—21no—
451C22—21no—
452C22—28no—
453C22—28no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—48no—
458C22—48no—
459C22—44no—
460C22C31×#40812yes—
461C22C31×#40812yes—
462C22C2×C31×#9912yes—
463C22C2×C31×#10114yes—
464C22C2×C31×#10112yes—
465C22C22×C22⋊C4×C3111yescharacteristic
466C22C2×C31×#13112yes—
467C4—21no—
468C4—21no—
469C4—22no—
470C4—21no—
471C4—21no—
472C4—44no—
473C4—44no—
474C4C2×C31×#9914yes—
475C2—22no—
476C2—24no—
477C2—22no—
478C2—42no—
479C2C31×#147214yesdirect product factor
480C2C2×C31×#40811yescharacteristic
481C2C22×C31×#9911yescharacteristic
482C2C22×C31×#10111yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1472C2direct (N × H)
5. C2×C31×#324C2semidirect
29. C31×#324C22semidirect
147. C2×#1472C31direct (N × H)
208. #1472C2×C31direct (N × H)
209. C2×#324C2×C31semidirect
262. #324C22×C31semidirect
267. C2×C31#1472direct (N × H)
324. C31C2×#1472direct (N × H)
479. C2C31×#1472direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#4072
C22×C31×C22⋊C82
C31×#14722
C2×C31×#3242
C2×#147231