Finite Group Databasebeta

← C2×C31×#1996 #21478090

Subgroups — C2×C31×#1996 #21478090

Order 7936.

1698 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#380C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1996C218yesmaximal, direct product factor
5C2×C31×#342C214yesmaximal
6C23×Q8×C31C411yescharacteristic, complemented
7C24×C4×C31C2211yescharacteristic
8C2×C31×C22⋊Q8—21no—
9C2×C31×C22⋊Q8—21no—
10C2×C31×C22⋊Q8—21no—
11C2×C31×C22⋊Q8—21no—
12C2×C31×C22⋊Q8—22no—
13C2×C31×C22⋊Q8—22no—
14C2×C31×C22⋊Q8C414yescomplemented
15C2×C31×C22⋊Q8C2214yes—
16C22×C4⋊C4×C31—21no—
17C22×C4⋊C4×C31C411yescharacteristic, complemented
18C22×C4⋊C4×C31C412yescomplemented
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31—21no—
23C31×#380—22no—
24C31×#380C2214yes—
25C4×C22⋊C4×C31—22no—
26C4×C22⋊C4×C31C2214yes—
27C2×C31×#95—21no—
28C2×C31×#95—21no—
29C31×#342C22116yes—
30C25×C31C2311yescharacteristic
31C22×Q8×C31—22no—
32C22×Q8×C31—21no—
33C22×Q8×C31—21no—
34C22×Q8×C31—44no—
35C22×Q8×C31C2×C414yescomplemented
36C23×C4×C31—22no—
37C23×C4×C31—22no—
38C23×C4×C31—44no—
39C23×C4×C31C2×C411yescharacteristic
40C23×C4×C31C2×C412yes—
41C23×C4×C31C2×C412yes—
42C23×C4×C31C2×C411yescharacteristic
43C23×C4×C31C2×C412yes—
44C23×C4×C31D411yescharacteristic
45C23×C4×C31D411yescharacteristic
46C23×C4×C31D411yescharacteristic
47C23×C4×C31D411yescharacteristic
48C23×C4×C31D412yes—
49C23×C4×C31D412yes—
50C23×C4×C31C2312yes—
51C31×C22⋊Q8—24no—
52C31×C22⋊Q8—24no—
53C31×C22⋊Q8—24no—
54C31×C22⋊Q8—24no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—24no—
58C31×C22⋊Q8—24no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—44no—
67C2×C4⋊C4×C31C2×C414yescomplemented
68C2×C4⋊C4×C31C2×C418yescomplemented
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—28no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31C2×C414yes—
78C2×C22⋊C4×C31Q818yescomplemented
79C2×C22⋊C4×C31C2314yes—
80C2×C22⋊C4×C31C2314yes—
81C2×C22⋊C4×C31C2314yes—
82C2×C42×C31—24no—
83C2×C42×C31—44no—
84C31×#95—24no—
85C31×#95—24no—
86C24×C31—42no—
87C24×C31—42no—
88C24×C31C22×C411yescharacteristic
89C24×C31C22×C411yescharacteristic
90C24×C31C2×D411yescharacteristic
91C24×C31C2×D411yescharacteristic
92C24×C31C2×D411yescharacteristic
93C24×C31C2×D411yescharacteristic
94C24×C31C2×Q814yes—
95C24×C31#4114yes—
96C24×C31C2411yescharacteristic
97C2×Q8×C31—24no—
98C2×Q8×C31—24no—
99C2×Q8×C31—44no—
100C2×Q8×C31—48no—
101C2×Q8×C31—48no—
102C2×Q8×C31—44no—
103C22×C4×C31—24no—
104C22×C4×C31—24no—
105C22×C4×C31—24no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—28no—
111C22×C4×C31—24no—
112C22×C4×C31—24no—
113C22×C4×C31—44no—
114C22×C4×C31—44no—
115C22×C4×C31—44no—
116C22×C4×C31—44no—
117C22×C4×C31—42no—
118C22×C4×C31—42no—
119C22×C4×C31—42no—
120C22×C4×C31—44no—
121C22×C4×C31—44no—
122C22×C4×C31—44no—
123C22×C4×C31—44no—
124C22×C4×C31—44no—
125C22×C4×C31—44no—
126C22×C4×C31—44no—
127C22×C4×C31C22⋊C412yes—
128C22×C4×C31C22⋊C412yes—
129C22×C4×C31C22⋊C412yes—
130C22×C4×C31C22⋊C411yescharacteristic
131C22×C4×C31C22⋊C411yescharacteristic
132C22×C4×C31C22⋊C411yescharacteristic
133C22×C4×C31C22⋊C412yes—
134C22×C4×C31C22⋊C412yes—
135C22×C4×C31C22⋊C412yes—
136C22×C4×C31C22⋊C411yescharacteristic
137C22×C4×C31C22×C412yes—
138C22×C4×C31C22×C414yes—
139C22×C4×C31C22×C414yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C4⋊C4×C31—24no—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—28no—
148C4⋊C4×C31—28no—
149C4⋊C4×C31—48no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—24no—
152C22⋊C4×C31—28no—
153C22⋊C4×C31—24no—
154C22⋊C4×C31—24no—
155C22⋊C4×C31—24no—
156C22⋊C4×C31—28no—
157C22⋊C4×C31—44no—
158C22⋊C4×C31C2×Q818yescomplemented
159C42×C31—48no—
160C2×#1996C3111yesmaximal, characteristic, direct product factor, Sylow
161C23×C31—22no—
162C23×C31—22no—
163C23×C31—22no—
164C23×C31—22no—
165C23×C31—22no—
166C23×C31—22no—
167C23×C31—41no—
168C23×C31—41no—
169C23×C31—41no—
170C23×C31—41no—
171C23×C31—41no—
172C23×C31—41no—
173C23×C31—41no—
174C23×C31—48no—
175C23×C31—48no—
176C23×C31—41no—
177C23×C31C2×C22⋊C411yescharacteristic
178C23×C31C2×C22⋊C411yescharacteristic
179C23×C31C2×C22⋊C411yescharacteristic
180C23×C31C2×C22⋊C411yescharacteristic
181C23×C31C4×Q814yes—
182C23×C31C4×Q814yes—
183C23×C31C22⋊Q814yes—
184C23×C31C22⋊Q814yes—
185C23×C31#12412yes—
186C23×C31#12412yes—
187C23×C31C4⋊Q812yes—
188C23×C31C4⋊Q812yes—
189C23×C31C23×C411yescharacteristic
190C23×C31C22×D411yescharacteristic
191C23×C31C22×D411yescharacteristic
192C23×C31C22×Q812yes—
193C23×C31C2×#4112yes—
194Q8×C31—48no—
195Q8×C31—48no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—24no—
200C2×C4×C31—24no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—28no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—44no—
215C2×C4×C31—44no—
216C2×C4×C31—416no—
217C2×C4×C31—44no—
218C2×C4×C31—44no—
219C2×C4×C31—44no—
220C2×C4×C31—44no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31—44no—
226C2×C4×C31—88no—
227C2×C4×C31#9914yes—
228C2×C4×C31C2×C22⋊C412yes—
229C2×C4×C31C2×C22⋊C412yes—
230C2×C4×C31C2×C22⋊C412yes—
231C2×C4×C31C2×C22⋊C412yes—
232C22×C22⋊Q8C2×C3111yescharacteristic
233C2×#380C2×C3111yescharacteristic
234C2×C4×C22⋊C4C2×C3111yescharacteristic
235#1996C2×C3118yesdirect product factor
236C2×#342C2×C3114yes—
237C22×C31—21no—
238C22×C31—21no—
239C22×C31—21no—
240C22×C31—21no—
241C22×C31—21no—
242C22×C31—21no—
243C22×C31—21no—
244C22×C31—21no—
245C22×C31—21no—
246C22×C31—21no—
247C22×C31—21no—
248C22×C31—21no—
249C22×C31—28no—
250C22×C31—24no—
251C22×C31—28no—
252C22×C31—24no—
253C22×C31—44no—
254C22×C31—44no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31#39112yes—
260C22×C31#39112yes—
261C22×C31#39112yes—
262C22×C31#39112yes—
263C22×C31C2×#9912yes—
264C22×C31#41012yes—
265C22×C31C22×C22⋊C411yescharacteristic
266C22×C31C2×C4×Q812yes—
267C22×C31C2×C22⋊Q812yes—
268C22×C31C2×#12411yescharacteristic
269C22×C31C2×C4⋊Q811yescharacteristic
270C4×C31—22no—
271C4×C31—22no—
272C4×C31—22no—
273C4×C31—48no—
274C4×C31—44no—
275C4×C31—44no—
276C4×C31—84no—
277C4×C31C2×#9914yes—
278C23×Q8C4×C3111yescharacteristic, complemented
279C24×C4C22×C3111yescharacteristic
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8—21no—
283C2×C22⋊Q8—21no—
284C2×C22⋊Q8—22no—
285C2×C22⋊Q8—22no—
286C2×C22⋊Q8C4×C3114yescomplemented
287C2×C22⋊Q8C22×C3114yes—
288C22×C4⋊C4—21no—
289C22×C4⋊C4C4×C3111yescharacteristic, complemented
290C22×C4⋊C4C4×C3112yescomplemented
291C22×C22⋊C4C22×C3112yes—
292C22×C22⋊C4C22×C3112yes—
293C22×C22⋊C4C22×C3112yes—
294C22×C42—21no—
295#380—22no—
296#380C22×C3114yes—
297C4×C22⋊C4—22no—
298C4×C22⋊C4C22×C3114yes—
299C2×#95—21no—
300C2×#95—21no—
301#342C22×C31116yes—
302C2×C31—22no—
303C2×C31—21no—
304C2×C31—22no—
305C2×C31—21no—
306C2×C31—22no—
307C2×C31—22no—
308C2×C31—22no—
309C2×C31#199614yesdirect product factor
310C2×C31C2×#39111yescharacteristic
311C2×C31C22×#9911yescharacteristic
312C2×C31C2×#41011yescharacteristic
313C25C23×C3111yescharacteristic
314C22×Q8—22no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—44no—
318C22×Q8C2×C4×C3114yescomplemented
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—44no—
322C23×C4C2×C4×C3111yescharacteristic
323C23×C4C2×C4×C3112yes—
324C23×C4C2×C4×C3112yes—
325C23×C4C2×C4×C3111yescharacteristic
326C23×C4C2×C4×C3112yes—
327C23×C4D4×C3111yescharacteristic
328C23×C4D4×C3111yescharacteristic
329C23×C4D4×C3111yescharacteristic
330C23×C4D4×C3111yescharacteristic
331C23×C4D4×C3112yes—
332C23×C4D4×C3112yes—
333C23×C4C23×C3112yes—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4C2×C4×C3114yescomplemented
351C2×C4⋊C4C2×C4×C3118yescomplemented
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4C2×C4×C3114yes—
361C2×C22⋊C4Q8×C3118yescomplemented
362C2×C22⋊C4C23×C3114yes—
363C2×C22⋊C4C23×C3114yes—
364C2×C22⋊C4C23×C3114yes—
365C2×C42—24no—
366C2×C42—44no—
367#95—24no—
368#95—24no—
369C31C2×#199611yescharacteristic, direct product factor, Sylow
370C24—42no—
371C24—42no—
372C24C22×C4×C3111yescharacteristic
373C24C22×C4×C3111yescharacteristic
374C24C2×D4×C3111yescharacteristic
375C24C2×D4×C3111yescharacteristic
376C24C2×D4×C3111yescharacteristic
377C24C2×D4×C3111yescharacteristic
378C24C2×Q8×C3114yes—
379C24#41×C3114yes—
380C24C24×C3111yescharacteristic
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—48no—
384C2×Q8—44no—
385C2×Q8—48no—
386C2×Q8—44no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—28no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4C22⋊C4×C3111yescharacteristic
412C22×C4C22⋊C4×C3111yescharacteristic
413C22×C4C22⋊C4×C3111yescharacteristic
414C22×C4C22⋊C4×C3112yes—
415C22×C4C22⋊C4×C3112yes—
416C22×C4C22⋊C4×C3112yes—
417C22×C4C22⋊C4×C3112yes—
418C22×C4C22⋊C4×C3112yes—
419C22×C4C22⋊C4×C3112yes—
420C22×C4C22⋊C4×C3111yescharacteristic
421C22×C4C22×C4×C3112yes—
422C22×C4C22×C4×C3114yes—
423C22×C4C22×C4×C3114yes—
424C22×C4C22×C4×C3112yes—
425C22×C4C2×D4×C3112yes—
426C22×C4C2×D4×C3112yes—
427C22×C4C2×D4×C3112yes—
428C22×C4C2×D4×C3112yes—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—28no—
432C4⋊C4—28no—
433C4⋊C4—48no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—28no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—28no—
441C22⋊C4—44no—
442C22⋊C4C2×Q8×C3118yescomplemented
443C42—48no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—48no—
458C23—48no—
459C23—41no—
460C23C2×C22⋊C4×C3111yescharacteristic
461C23C2×C22⋊C4×C3111yescharacteristic
462C23C2×C22⋊C4×C3111yescharacteristic
463C23C2×C22⋊C4×C3111yescharacteristic
464C23C4×Q8×C3114yes—
465C23C4×Q8×C3114yes—
466C23C31×C22⋊Q814yes—
467C23C31×C22⋊Q814yes—
468C23C31×#12412yes—
469C23C31×#12412yes—
470C23C31×C4⋊Q812yes—
471C23C31×C4⋊Q812yes—
472C23C23×C4×C3111yescharacteristic
473C23C22×D4×C3111yescharacteristic
474C23C22×D4×C3111yescharacteristic
475C23C22×Q8×C3112yes—
476C23C2×#41×C3112yes—
477Q8—48no—
478Q8—48no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—28no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—416no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—88no—
510C2×C4C31×#9914yes—
511C2×C4C2×C22⋊C4×C3112yes—
512C2×C4C2×C22⋊C4×C3112yes—
513C2×C4C2×C22⋊C4×C3112yes—
514C2×C4C2×C22⋊C4×C3112yes—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—28no—
528C22—24no—
529C22—28no—
530C22—24no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22C31×#39112yes—
538C22C31×#39112yes—
539C22C31×#39112yes—
540C22C31×#39112yes—
541C22C2×C31×#9912yes—
542C22C31×#41012yes—
543C22C22×C22⋊C4×C3111yescharacteristic
544C22C2×C4×Q8×C3112yes—
545C22C2×C31×C22⋊Q812yes—
546C22C2×C31×#12411yescharacteristic
547C22C2×C31×C4⋊Q811yescharacteristic
548C4—22no—
549C4—22no—
550C4—22no—
551C4—48no—
552C4—44no—
553C4—44no—
554C4—84no—
555C4C2×C31×#9914yes—
556C2—22no—
557C2—21no—
558C2—22no—
559C2—21no—
560C2—22no—
561C2—22no—
562C2—22no—
563C2C31×#199614yesdirect product factor
564C2C2×C31×#39111yescharacteristic
565C2C22×C31×#9911yescharacteristic
566C2C2×C31×#41011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
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×#1996C2direct (N × H)
6. C23×Q8×C31C4semidirect
14. C2×C31×C22⋊Q8C4semidirect
17. C22×C4⋊C4×C31C4semidirect
18. C22×C4⋊C4×C31C4semidirect
35. C22×Q8×C31C2×C4semidirect
67. C2×C4⋊C4×C31C2×C4semidirect
68. C2×C4⋊C4×C31C2×C4semidirect
78. C2×C22⋊C4×C31Q8semidirect
158. C22⋊C4×C31C2×Q8semidirect
160. C2×#1996C31direct (N × H)
235. #1996C2×C31direct (N × H)
278. C23×Q8C4×C31semidirect
286. C2×C22⋊Q8C4×C31semidirect
289. C22×C4⋊C4C4×C31semidirect
290. C22×C4⋊C4C4×C31semidirect
309. C2×C31#1996direct (N × H)
318. C22×Q8C2×C4×C31semidirect
350. C2×C4⋊C4C2×C4×C31semidirect
351. C2×C4⋊C4C2×C4×C31semidirect
361. C2×C22⋊C4Q8×C31semidirect
369. C31C2×#1996direct (N × H)
442. C22⋊C4C2×Q8×C31semidirect
563. C2C31×#1996direct (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×#3802
C2×C4×C22⋊C4×C312
C31×#19962
C2×C31×#3422
C2×#199631