Finite Group Databasebeta

← C31×#33347 #21490106

Subgroups — C31×#33347 #21490106

Order 7936.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3449C211yesmaximal, characteristic
2C2×C31×#413C211yesmaximal, characteristic, complemented
3C2×C31×#410C211yesmaximal, characteristic, complemented
4C31×#2123C212yesmaximal, complemented
5C31×#2122C212yesmaximal, complemented
6C31×#2121C214yesmaximal, complemented
7C31×#2120C214yesmaximal, complemented
8C22×#41×C31C411yescharacteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C22×M16×C31—21no—
11C31×#537—21no—
12C31×#537—21no—
13C31×#536—21no—
14C31×#536C411yescharacteristic, complemented
15C31×#536C2211yescharacteristic
16C31×#535—21no—
17C31×#535C411yescharacteristic, complemented
18C31×#535C2211yescharacteristic
19C31×#534C412yescomplemented
20C31×#534C2212yes—
21C31×#532—21no—
22C31×#532—21no—
23C31×#525—21no—
24C31×#525—21no—
25C31×#525C412yescomplemented
26C31×#525C2212yes—
27C2×C31×#117—21no—
28C2×C31×#117C411yescharacteristic, complemented
29C31×#413—21no—
30C31×#413—21no—
31C31×#413C2212yes—
32C31×#413C2212yes—
33C2×C31×#101—21no—
34C2×C31×#100C2212yes—
35C31×#410—21no—
36C31×#410—21no—
37C31×#410C2212yes—
38C31×#410C2212yes—
39C2×C31×#99—21no—
40C2×C31×#99C2212yes—
41C31×#352C2218yescomplemented
42C31×AΣL(1,𝔽16)C2218yescomplemented
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—41no—
48C2×#41×C31—41no—
49C2×#41×C31—41no—
50C2×#41×C31—41no—
51C2×#41×C31—41no—
52C2×#41×C31—41no—
53C2×#41×C31—41no—
54C2×#41×C31—41no—
55C2×#41×C31C2×C411yescharacteristic
56C2×#41×C31C2×C411yescharacteristic
57C2×#41×C31D411yescharacteristic
58C2×#41×C31D411yescharacteristic
59C2×#41×C31D411yescharacteristic
60C2×#41×C31D411yescharacteristic
61C2×#41×C31C2311yescharacteristic
62C2×#41×C31C2311yescharacteristic
63C22×Q8×C31C2×C411yescharacteristic, complemented
64C22×Q8×C31D411yescharacteristic
65C22×D4×C31C2×C411yescharacteristic
66C22×D4×C31C2×C412yes—
67C22×D4×C31C2×C411yescharacteristic, complemented
68C22×D4×C31D411yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C23×C4×C31C2×C411yescharacteristic
71C23×C4×C31C2×C412yescomplemented
72C23×C4×C31D411yescharacteristic
73C23×C4×C31D411yescharacteristic
74C2×M16×C31—22no—
75C2×M16×C31—22no—
76C2×M16×C31—22no—
77C2×M16×C31—41no—
78C2×M16×C31—41no—
79C2×M16×C31—41no—
80C22×C8×C31—41no—
81C31×C4⋊Q8—21no—
82C31×C4⋊Q8—21no—
83C31×#127—21no—
84C31×#127—21no—
85C31×#124—21no—
86C31×#124—21no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#123—22no—
90C31×#123—22no—
91C31×#123C2×C412yes—
92C31×#123C2×C412yescomplemented
93C31×#123C2×C412yescomplemented
94C31×#123C2312yes—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—22no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121—21no—
111C31×#120—22no—
112C31×#120—22no—
113C31×#120C2×C412yes—
114C31×#120C2×C412yescomplemented
115C31×#120C2×C412yescomplemented
116C31×#120C2312yes—
117C4×D4×C31—22no—
118C4×D4×C31—22no—
119C4×D4×C31—22no—
120C4×D4×C31—22no—
121C31×#117—21no—
122C31×#117—21no—
123C31×#117—22no—
124C31×#117—22no—
125C31×#117—41no—
126C31×#117—41no—
127C31×#117C2×C412yescomplemented
128C31×#117C2×C411yescharacteristic, complemented
129C31×#117C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—41no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31C2×C412yes—
134C2×C42×C31—21no—
135C2×C42×C31—41no—
136C31×#101—22no—
137C31×#101—22no—
138C31×#100—22no—
139C31×#100C2314yes—
140C31×#99—22no—
141C31×#99—22no—
142C31×#99—22no—
143C31×#99C2314yes—
144C24×C31C22⋊C411yescharacteristic
145C24×C31C22×C411yescharacteristic
146C24×C31C22×C412yes—
147C24×C31C2×D411yescharacteristic
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—41no—
155#41×C31—41no—
156#41×C31—41no—
157#41×C31—41no—
158#41×C31—41no—
159#41×C31—41no—
160#41×C31—41no—
161#41×C31—41no—
162#41×C31—41no—
163#41×C31—41no—
164#41×C31—42no—
165#41×C31—42no—
166#41×C31—42no—
167#41×C31—42no—
168#41×C31—42no—
169#41×C31—42no—
170#41×C31—41no—
171#41×C31—41no—
172#41×C31—41no—
173#41×C31—41no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—41no—
177C2×Q8×C31—41no—
178C2×Q8×C31—41no—
179C2×Q8×C31—41no—
180C2×Q8×C31C22⋊C411yescharacteristic
181C2×Q8×C31C22⋊C411yescharacteristic
182C2×Q8×C31C2×D411yescharacteristic
183C2×Q8×C31C2×D411yescharacteristic
184C2×D4×C31—22no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31—41no—
195C2×D4×C31—41no—
196C2×D4×C31—41no—
197C2×D4×C31—41no—
198C2×D4×C31—41no—
199C2×D4×C31—41no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31C22⋊C411yescharacteristic
203C2×D4×C31C22⋊C411yescharacteristic
204C2×D4×C31C22⋊C411yescharacteristic
205C2×D4×C31C22⋊C411yescharacteristic
206C2×D4×C31C22×C411yescharacteristic
207C2×D4×C31C22×C411yescharacteristic
208C2×D4×C31C22×C411yescharacteristic
209C2×D4×C31C2×D411yescharacteristic
210C2×D4×C31C2×D411yescharacteristic
211C2×D4×C31C2×D411yescharacteristic
212C2×D4×C31C2×D411yescharacteristic
213C2×D4×C31C2411yescharacteristic
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—42no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31C22⋊C411yescharacteristic
233C22×C4×C31C22⋊C411yescharacteristic
234C22×C4×C31C22⋊C411yescharacteristic
235C22×C4×C31C22⋊C411yescharacteristic
236C22×C4×C31C22⋊C411yescharacteristic
237C22×C4×C31C22⋊C411yescharacteristic
238C22×C4×C31C22⋊C411yescharacteristic
239C22×C4×C31C22⋊C411yescharacteristic
240C22×C4×C31C22⋊C411yescharacteristic
241C22×C4×C31C22×C411yescharacteristic
242C22×C4×C31C22×C411yescharacteristic
243C22×C4×C31C22×C412yes—
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249M16×C31—24no—
250M16×C31—42no—
251M16×C31—42no—
252M16×C31—42no—
253C2×C8×C31—42no—
254C2×C8×C31—42no—
255C2×C8×C31—42no—
256C4⋊C4×C31—22no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—22no—
260C4⋊C4×C31—22no—
261C4⋊C4×C31—22no—
262C4⋊C4×C31—22no—
263C4⋊C4×C31—42no—
264C4⋊C4×C31—42no—
265C22⋊C4×C31—22no—
266C22⋊C4×C31—22no—
267C22⋊C4×C31—22no—
268C22⋊C4×C31—22no—
269C22⋊C4×C31—22no—
270C22⋊C4×C31—22no—
271C22⋊C4×C31—22no—
272C22⋊C4×C31—22no—
273C22⋊C4×C31—22no—
274C22⋊C4×C31—24no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31C22×C412yes—
277C22⋊C4×C31C22×C412yes—
278C42×C31—22no—
279C42×C31—21no—
280C42×C31—21no—
281C42×C31—42no—
282C42×C31—42no—
283#33347C3111yesmaximal, characteristic, direct product factor, Sylow
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—22no—
291C23×C31—42no—
292C23×C31—81no—
293C23×C31—81no—
294C23×C31—81no—
295C23×C31—82no—
296C23×C31C2×C22⋊C411yescharacteristic
297C23×C31C2×C22⋊C411yescharacteristic
298C23×C31C2×C22⋊C411yescharacteristic
299C23×C31C2×C22⋊C411yescharacteristic
300C23×C31C2×C22⋊C411yescharacteristic
301C23×C31C23×C411yescharacteristic
302C23×C31C22×D411yescharacteristic
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31—41no—
307Q8×C31—42no—
308Q8×C31—41no—
309Q8×C31—41no—
310D4×C31—41no—
311D4×C31—41no—
312D4×C31—41no—
313D4×C31—41no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—41no—
318D4×C31—41no—
319D4×C31—41no—
320D4×C31—41no—
321D4×C31—41no—
322D4×C31—42no—
323D4×C31—44no—
324D4×C31—42no—
325D4×C31—42no—
326D4×C31—41no—
327D4×C31—41no—
328D4×C31—82no—
329D4×C31—82no—
330D4×C31—82no—
331D4×C31—82no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—21no—
355C2×C4×C31—21no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—44no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—42no—
369C2×C4×C31—44no—
370C2×C4×C31—82no—
371C2×C4×C31—84no—
372C2×C4×C31#9911yescharacteristic
373C2×C4×C31#9911yescharacteristic
374C2×C4×C31#9911yescharacteristic
375C2×C4×C31#9911yescharacteristic
376C2×C4×C31C2×C22⋊C411yescharacteristic
377C2×C4×C31C2×C22⋊C411yescharacteristic
378C2×C4×C31C2×C22⋊C411yescharacteristic
379C2×C4×C31C2×C22⋊C411yescharacteristic
380C2×C4×C31C2×C22⋊C411yescharacteristic
381C2×C4×C31C2×C22⋊C411yescharacteristic
382C2×C4×C31C2×C22⋊C411yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C8×C31—44no—
385#3449C2×C3111yescharacteristic
386C2×#413C2×C3111yescharacteristic, complemented
387C2×#410C2×C3111yescharacteristic, complemented
388#2123C2×C3112yescomplemented
389#2122C2×C3112yescomplemented
390#2121C2×C3114yescomplemented
391#2120C2×C3114yescomplemented
392C22×C31—21no—
393C22×C31—21no—
394C22×C31—21no—
395C22×C31—21no—
396C22×C31—21no—
397C22×C31—21no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31—84no—
415C22×C31C2×#9911yescharacteristic
416C22×C31C2×#9911yescharacteristic
417C22×C31C22×C22⋊C411yescharacteristic
418C4×C31—21no—
419C4×C31—21no—
420C4×C31—21no—
421C4×C31—21no—
422C4×C31—21no—
423C4×C31—21no—
424C4×C31—42no—
425C4×C31—42no—
426C4×C31—42no—
427C4×C31—84no—
428C4×C31C2×#9911yescharacteristic
429C4×C31C2×#9911yescharacteristic
430C4×C31C2×#9911yescharacteristic
431C4×C31C2×#9911yescharacteristic
432C22×#41C4×C3111yescharacteristic, complemented
433C22×#41C22×C3111yescharacteristic
434C22×M16—21no—
435#537—21no—
436#537—21no—
437#536—21no—
438#536C4×C3111yescharacteristic, complemented
439#536C22×C3111yescharacteristic
440#535—21no—
441#535C4×C3111yescharacteristic, complemented
442#535C22×C3111yescharacteristic
443#534C4×C3112yescomplemented
444#534C22×C3112yes—
445#532—21no—
446#532—21no—
447#525—21no—
448#525—21no—
449#525C4×C3112yescomplemented
450#525C22×C3112yes—
451C2×#117—21no—
452C2×#117C4×C3111yescharacteristic, complemented
453#413—21no—
454#413—21no—
455#413C22×C3112yes—
456#413C22×C3112yes—
457C2×#101—21no—
458C2×#100C22×C3112yes—
459#410—21no—
460#410—21no—
461#410C22×C3112yes—
462#410C22×C3112yes—
463C2×#99—21no—
464C2×#99C22×C3112yes—
465#352C22×C3118yescomplemented
466AΣL(1,𝔽16)C22×C3118yescomplemented
467C2×C31—21no—
468C2×C31—21no—
469C2×C31—21no—
470C2×C31—41no—
471C2×C31—41no—
472C2×C31—41no—
473C2×C31—41no—
474C2×C31—41no—
475C2×C31—41no—
476C2×C31—82no—
477C2×C31C22×#9911yescharacteristic
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41C2×C4×C3111yescharacteristic
491C2×#41C2×C4×C3111yescharacteristic
492C2×#41D4×C3111yescharacteristic
493C2×#41D4×C3111yescharacteristic
494C2×#41D4×C3111yescharacteristic
495C2×#41D4×C3111yescharacteristic
496C2×#41C23×C3111yescharacteristic
497C2×#41C23×C3111yescharacteristic
498C22×Q8C2×C4×C3111yescharacteristic, complemented
499C22×Q8D4×C3111yescharacteristic
500C22×D4C2×C4×C3111yescharacteristic
501C22×D4C2×C4×C3112yes—
502C22×D4C2×C4×C3111yescharacteristic, complemented
503C22×D4D4×C3111yescharacteristic
504C22×D4C23×C3111yescharacteristic
505C23×C4C2×C4×C3111yescharacteristic
506C23×C4C2×C4×C3112yescomplemented
507C23×C4D4×C3111yescharacteristic
508C23×C4D4×C3111yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8—41no—
516C4⋊Q8—21no—
517C4⋊Q8—21no—
518#127—21no—
519#127—21no—
520#124—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#123—22no—
525#123—22no—
526#123C2×C4×C3112yes—
527#123C2×C4×C3112yescomplemented
528#123C2×C4×C3112yescomplemented
529#123C23×C3112yes—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—21no—
543#121—21no—
544#121—21no—
545#121—21no—
546#120—22no—
547#120—22no—
548#120C2×C4×C3112yes—
549#120C2×C4×C3112yescomplemented
550#120C2×C4×C3112yescomplemented
551#120C23×C3112yes—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556#117—21no—
557#117—21no—
558#117—22no—
559#117—22no—
560#117—41no—
561#117—41no—
562#117C2×C4×C3112yescomplemented
563#117C2×C4×C3111yescharacteristic, complemented
564#117C2×C4×C3111yescharacteristic, complemented
565C2×C4⋊C4—21no—
566C2×C4⋊C4—41no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4C2×C4×C3112yes—
569C2×C42—21no—
570C2×C42—41no—
571#101—22no—
572#101—22no—
573#100—22no—
574#100C23×C3114yes—
575#99—22no—
576#99—22no—
577#99—22no—
578#99C23×C3114yes—
579C31#3334711yescharacteristic, direct product factor, Sylow
580C24C22⋊C4×C3111yescharacteristic
581C24C22×C4×C3111yescharacteristic
582C24C22×C4×C3112yes—
583C24C2×D4×C3111yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C3111yescharacteristic
617C2×Q8C22⋊C4×C3111yescharacteristic
618C2×Q8C2×D4×C3111yescharacteristic
619C2×Q8C2×D4×C3111yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C3111yescharacteristic
639C2×D4C22⋊C4×C3111yescharacteristic
640C2×D4C22⋊C4×C3111yescharacteristic
641C2×D4C22⋊C4×C3111yescharacteristic
642C2×D4C22×C4×C3111yescharacteristic
643C2×D4C22×C4×C3111yescharacteristic
644C2×D4C22×C4×C3111yescharacteristic
645C2×D4C2×D4×C3111yescharacteristic
646C2×D4C2×D4×C3111yescharacteristic
647C2×D4C2×D4×C3111yescharacteristic
648C2×D4C2×D4×C3111yescharacteristic
649C2×D4C24×C3111yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C3111yescharacteristic
669C22×C4C22⋊C4×C3111yescharacteristic
670C22×C4C22⋊C4×C3111yescharacteristic
671C22×C4C22⋊C4×C3111yescharacteristic
672C22×C4C22⋊C4×C3111yescharacteristic
673C22×C4C22⋊C4×C3111yescharacteristic
674C22×C4C22⋊C4×C3111yescharacteristic
675C22×C4C22⋊C4×C3111yescharacteristic
676C22×C4C22⋊C4×C3111yescharacteristic
677C22×C4C22×C4×C3111yescharacteristic
678C22×C4C22×C4×C3111yescharacteristic
679C22×C4C22×C4×C3112yes—
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4C2×D4×C3111yescharacteristic
683C22×C4C2×D4×C3111yescharacteristic
684C22×C4C2×D4×C3111yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C3112yes—
713C22⋊C4C22×C4×C3112yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C3111yescharacteristic
732C23C2×C22⋊C4×C3111yescharacteristic
733C23C2×C22⋊C4×C3111yescharacteristic
734C23C2×C22⋊C4×C3111yescharacteristic
735C23C2×C22⋊C4×C3111yescharacteristic
736C23C23×C4×C3111yescharacteristic
737C23C22×D4×C3111yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4C31×#9911yescharacteristic
808C2×C4C31×#9911yescharacteristic
809C2×C4C31×#9911yescharacteristic
810C2×C4C31×#9911yescharacteristic
811C2×C4C2×C22⋊C4×C3111yescharacteristic
812C2×C4C2×C22⋊C4×C3111yescharacteristic
813C2×C4C2×C22⋊C4×C3111yescharacteristic
814C2×C4C2×C22⋊C4×C3111yescharacteristic
815C2×C4C2×C22⋊C4×C3111yescharacteristic
816C2×C4C2×C22⋊C4×C3111yescharacteristic
817C2×C4C2×C22⋊C4×C3111yescharacteristic
818C2×C4C22×D4×C3111yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×C31×#9911yescharacteristic
844C22C2×C31×#9911yescharacteristic
845C22C22×C22⋊C4×C3111yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×C31×#9911yescharacteristic
857C4C2×C31×#9911yescharacteristic
858C4C2×C31×#9911yescharacteristic
859C4C2×C31×#9911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×C31×#9911yescharacteristic
subgroupG/H
centerC4×C31C2×#99
commutatorC23C23×C4×C31
Frattini, cosocleC2×D4C24×C31
socleC2×C31C22×#99
prime radicalC31×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C22×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#413C2semidirect
3. C2×C31×#410C2semidirect
4. C31×#2123C2semidirect
5. C31×#2122C2semidirect
6. C31×#2121C2semidirect
7. C31×#2120C2semidirect
8. C22×#41×C31C4semidirect
14. C31×#536C4semidirect
17. C31×#535C4semidirect
19. C31×#534C4semidirect
25. C31×#525C4semidirect
28. C2×C31×#117C4semidirect
41. C31×#352C22semidirect
42. C31×AΣL(1,𝔽16)C22semidirect
63. C22×Q8×C31C2×C4semidirect
67. C22×D4×C31C2×C4semidirect
71. C23×C4×C31C2×C4semidirect
92. C31×#123C2×C4semidirect
93. C31×#123C2×C4semidirect
114. C31×#120C2×C4semidirect
115. C31×#120C2×C4semidirect
127. C31×#117C2×C4semidirect
128. C31×#117C2×C4semidirect
129. C31×#117C2×C4semidirect
283. #33347C31direct (N × H)
386. C2×#413C2×C31semidirect
387. C2×#410C2×C31semidirect
388. #2123C2×C31semidirect
389. #2122C2×C31semidirect
390. #2121C2×C31semidirect
391. #2120C2×C31semidirect
432. C22×#41C4×C31semidirect
438. #536C4×C31semidirect
441. #535C4×C31semidirect
443. #534C4×C31semidirect
449. #525C4×C31semidirect
452. C2×#117C4×C31semidirect
465. #352C22×C31semidirect
466. AΣL(1,𝔽16)C22×C31semidirect
498. C22×Q8C2×C4×C31semidirect
502. C22×D4C2×C4×C31semidirect
506. C23×C4C2×C4×C31semidirect
527. #123C2×C4×C31semidirect
528. #123C2×C4×C31semidirect
549. #120C2×C4×C31semidirect
550. #120C2×C4×C31semidirect
562. #117C2×C4×C31semidirect
563. #117C2×C4×C31semidirect
564. #117C2×C4×C31semidirect
579. C31#33347direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34492
C2×C31×#4132
C2×C31×#4102
C31×#21232
C31×#21222
C31×#21212
C31×#21202
#3334731