Finite Group Databasebeta

← C4×C31×#398 #21470622

Subgroups — C4×C31×#398 #21470622

Order 7936.

1574 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C212yesmaximal
5C31×#1445C211yesmaximal, characteristic
6C31×#1444C211yesmaximal, characteristic
7C31×#1442C212yesmaximal
8C31×#1441C212yesmaximal
9C31×#1441C211yesmaximal, characteristic
10C4×C31×#95C212yesmaximal
11C4×C31×#95C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2212yes—
23C31×#398C418yesdirect product factor
24C4×C4⋊C4×C31—24no—
25C4×C4⋊C4×C31—28no—
26C4×C4⋊C4×C31—24no—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2212yes—
38C2×C31×#95C2211yescharacteristic
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—24no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31C2×C414yes—
65C2×C4⋊C4×C31C2×C414yes—
66C2×C4⋊C4×C31C2×C418yes—
67C2×C42×C31—22no—
68C2×C42×C31—24no—
69C2×C42×C31—22no—
70C2×C42×C31—24no—
71C2×C42×C31—24no—
72C2×C42×C31—24no—
73C2×C42×C31—24no—
74C2×C42×C31—22no—
75C2×C42×C31—24no—
76C2×C42×C31—24no—
77C2×C42×C31D414yes—
78C2×C42×C31D414yes—
79C2×C42×C31Q818yes—
80C31×#95—22no—
81C31×#95—24no—
82C31×#95—24no—
83C31×#95—22no—
84C31×#95—24no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—22no—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95C2×C418yes—
91C31×#95C2×C414yes—
92C24×C31C2411yescharacteristic
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—21no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31C22×C412yes—
138C22×C4×C31C22×C414yes—
139C22×C4×C31C22×C412yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C22×C414yes—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×Q814yes—
149C22×C4×C31C2×Q814yes—
150C22×C4×C31C2×Q814yes—
151C22×C4×C31#4112yes—
152C22×C4×C31#4114yes—
153C22×C4×C31#4112yes—
154C22×C4×C31#4112yes—
155C22×C4×C31#4114yes—
156C22×C4×C31#4112yes—
157C22×C4×C31#4114yes—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—28no—
160C4⋊C4×C31—216no—
161C4⋊C4×C31—28no—
162C4⋊C4×C31—216no—
163C4⋊C4×C31—28no—
164C42×C31—28no—
165C42×C31—216no—
166C42×C31—28no—
167C42×C31—48no—
168C42×C31—44no—
169C4×#398C3111yesmaximal, characteristic, direct product factor, Sylow
170C23×C31C23×C411yescharacteristic
171C23×C31C22×D411yescharacteristic
172C23×C31C22×D411yescharacteristic
173C23×C31C22×Q812yes—
174C23×C31C2×#4111yescharacteristic
175C23×C31C2×#4111yescharacteristic
176C23×C31C2×#4112yes—
177C23×C31C2×#4111yescharacteristic
178C23×C31C2×#4112yes—
179C23×C31C2×#4112yes—
180C23×C31C2×#4111yescharacteristic
181C2×C4×C31—22no—
182C2×C4×C31—24no—
183C2×C4×C31—22no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—22no—
187C2×C4×C31—24no—
188C2×C4×C31—22no—
189C2×C4×C31—22no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—22no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—22no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—22no—
200C2×C4×C31—24no—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—24no—
204C2×C4×C31—22no—
205C2×C4×C31—24no—
206C2×C4×C31—22no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—22no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—41no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—41no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31C4×D414yes—
239C2×C4×C31C4×D414yes—
240C2×C4×C31C4×Q818yes—
241C2×C4×C31#12114yes—
242C2×C4×C31C22⋊Q818yes—
243C2×C4×C31#12314yes—
244C2×C4×C31#12518yes—
245C2×C4×C31C4⋊Q814yes—
246C2×#398C2×C3111yescharacteristic
247C2×C4×C4⋊C4C2×C3111yescharacteristic
248C2×C4×C4⋊C4C2×C3111yescharacteristic
249C2×C4×C4⋊C4C2×C3112yes—
250#1445C2×C3111yescharacteristic
251#1444C2×C3111yescharacteristic
252#1442C2×C3112yes—
253#1441C2×C3112yes—
254#1441C2×C3111yescharacteristic
255C4×#95C2×C3111yescharacteristic
256C4×#95C2×C3112yes—
257C22×C31C2×C4×D411yescharacteristic
258C22×C31C2×C4×D411yescharacteristic
259C22×C31C2×C4×Q812yes—
260C22×C31C4×#4111yescharacteristic
261C22×C31C4×#4112yes—
262C22×C31C2×#12111yescharacteristic
263C22×C31C2×C22⋊Q812yes—
264C22×C31C2×#12311yescharacteristic
265C22×C31#52512yes—
266C22×C31#52511yescharacteristic
267C22×C31#52511yescharacteristic
268C22×C31C2×#12512yes—
269C22×C31#52912yes—
270C22×C31#52912yes—
271C22×C31#52912yes—
272C22×C31#52912yes—
273C22×C31#52911yescharacteristic
274C22×C31C2×C4⋊Q811yescharacteristic
275C22×C31#53211yescharacteristic
276C22×C31#53211yescharacteristic
277C22×C31#53312yes—
278C22×C31#53312yes—
279C22×C31#53312yes—
280C4×C31—24no—
281C4×C31—24no—
282C4×C31—28no—
283C4×C31—42no—
284C4×C31—44no—
285C4×C31—42no—
286C4×C31—42no—
287C4×C31—44no—
288C4×C31—44no—
289C4×C31—42no—
290C4×C31#39818yesdirect product factor
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C4⋊C4C22×C3111yescharacteristic
293C22×C4⋊C4C22×C3112yes—
294C22×C4⋊C4C22×C3112yes—
295C22×C4⋊C4C22×C3111yescharacteristic
296C22×C4⋊C4C22×C3111yescharacteristic
297C22×C42C22×C3111yescharacteristic
298C22×C42C22×C3112yes—
299C22×C42C22×C3111yescharacteristic
300C22×C42C22×C3111yescharacteristic
301C22×C42C22×C3112yes—
302#398C4×C3118yesdirect product factor
303C4×C4⋊C4—24no—
304C4×C4⋊C4—28no—
305C4×C4⋊C4—24no—
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×#95C22×C3112yes—
310C2×#95C22×C3111yescharacteristic
311C2×#95C22×C3112yes—
312C2×#95C22×C3112yes—
313C2×#95C22×C3111yescharacteristic
314C2×#95C22×C3112yes—
315C2×#95C22×C3111yescharacteristic
316C2×#95C22×C3112yes—
317C2×#95C22×C3111yescharacteristic
318C2×C31C4×#12111yescharacteristic
319C2×C31C4×#12311yescharacteristic
320C2×C31C4×C22⋊Q812yes—
321C2×C31C4×#12512yes—
322C2×C31C4×C4⋊Q811yescharacteristic
323C2×C31C2×#39811yescharacteristic
324C2×C31#239211yescharacteristic
325C2×C31#239511yescharacteristic
326C2×C31#239612yes—
327C2×C31#239911yescharacteristic
328C2×C31#240212yes—
329C23×C4C23×C3112yes—
330C23×C4C23×C3111yescharacteristic
331C23×C4C23×C3111yescharacteristic
332C23×C4C23×C3111yescharacteristic
333C23×C4C23×C3112yes—
334C23×C4C23×C3112yes—
335C23×C4C23×C3111yescharacteristic
336C23×C4C23×C3111yescharacteristic
337C23×C4C23×C3111yescharacteristic
338C23×C4C23×C3112yes—
339C23×C4C23×C3111yescharacteristic
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4C2×C4×C3114yes—
355C2×C4⋊C4C2×C4×C3114yes—
356C2×C4⋊C4C2×C4×C3118yes—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42D4×C3114yes—
368C2×C42D4×C3114yes—
369C2×C42Q8×C3118yes—
370#95—22no—
371#95—24no—
372#95—24no—
373#95—22no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—22no—
378#95—24no—
379#95—24no—
380#95C2×C4×C3118yes—
381#95C2×C4×C3114yes—
382C31C4×#39811yescharacteristic, direct product factor, Sylow
383C24C24×C3111yescharacteristic
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4C22×C4×C3112yes—
429C22×C4C22×C4×C3114yes—
430C22×C4C22×C4×C3112yes—
431C22×C4C22×C4×C3112yes—
432C22×C4C22×C4×C3114yes—
433C22×C4C2×D4×C3112yes—
434C22×C4C2×D4×C3112yes—
435C22×C4C2×D4×C3112yes—
436C22×C4C2×D4×C3112yes—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3112yes—
439C22×C4C2×Q8×C3114yes—
440C22×C4C2×Q8×C3114yes—
441C22×C4C2×Q8×C3114yes—
442C22×C4#41×C3112yes—
443C22×C4#41×C3114yes—
444C22×C4#41×C3112yes—
445C22×C4#41×C3112yes—
446C22×C4#41×C3114yes—
447C22×C4#41×C3112yes—
448C22×C4#41×C3114yes—
449C4⋊C4—28no—
450C4⋊C4—28no—
451C4⋊C4—216no—
452C4⋊C4—28no—
453C4⋊C4—216no—
454C4⋊C4—28no—
455C42—28no—
456C42—216no—
457C42—28no—
458C42—48no—
459C42—44no—
460C23C23×C4×C3111yescharacteristic
461C23C22×D4×C3111yescharacteristic
462C23C22×D4×C3111yescharacteristic
463C23C22×Q8×C3112yes—
464C23C2×#41×C3111yescharacteristic
465C23C2×#41×C3111yescharacteristic
466C23C2×#41×C3112yes—
467C23C2×#41×C3111yescharacteristic
468C23C2×#41×C3112yes—
469C23C2×#41×C3112yes—
470C23C2×#41×C3111yescharacteristic
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4C4×D4×C3114yes—
529C2×C4C4×D4×C3114yes—
530C2×C4C4×Q8×C3118yes—
531C2×C4C31×#12114yes—
532C2×C4C31×C22⋊Q818yes—
533C2×C4C31×#12314yes—
534C2×C4C31×#12518yes—
535C2×C4C31×C4⋊Q814yes—
536C22C2×C4×D4×C3111yescharacteristic
537C22C2×C4×D4×C3111yescharacteristic
538C22C2×C4×Q8×C3112yes—
539C22C4×#41×C3111yescharacteristic
540C22C4×#41×C3112yes—
541C22C2×C31×#12111yescharacteristic
542C22C2×C31×C22⋊Q812yes—
543C22C2×C31×#12311yescharacteristic
544C22C31×#52512yes—
545C22C31×#52511yescharacteristic
546C22C31×#52511yescharacteristic
547C22C2×C31×#12512yes—
548C22C31×#52912yes—
549C22C31×#52912yes—
550C22C31×#52912yes—
551C22C31×#52912yes—
552C22C31×#52911yescharacteristic
553C22C2×C31×C4⋊Q811yescharacteristic
554C22C31×#53211yescharacteristic
555C22C31×#53211yescharacteristic
556C22C31×#53312yes—
557C22C31×#53312yes—
558C22C31×#53312yes—
559C4—24no—
560C4—24no—
561C4—28no—
562C4—42no—
563C4—44no—
564C4—42no—
565C4—42no—
566C4—44no—
567C4—44no—
568C4—42no—
569C4C31×#39818yesdirect product factor
570C2C4×C31×#12111yescharacteristic
571C2C4×C31×#12311yescharacteristic
572C2C4×C31×C22⋊Q812yes—
573C2C4×C31×#12512yes—
574C2C4×C31×C4⋊Q811yescharacteristic
575C2C2×C31×#39811yescharacteristic
576C2C31×#239211yescharacteristic
577C2C31×#239511yescharacteristic
578C2C31×#239612yes—
579C2C31×#239911yescharacteristic
580C2C31×#240212yes—
subgroupG/H
centerC23×C4×C31C23
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
socle, prime radicalC24×C31C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
23. C31×#398C4direct (N × H)
169. C4×#398C31direct (N × H)
290. C4×C31#398direct (N × H)
302. #398C4×C31direct (N × H)
382. C31C4×#398direct (N × H)
569. C4C31×#398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14442
C31×#14422
C31×#14412
C4×C31×#952
C4×#39831