Finite Group Databasebeta

← C2×C31×#2121 #21490103

Subgroups — C2×C31×#2121 #21490103

Order 7936.

1494 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#534C211yesmaximal, characteristic
2C22×C31×#100C211yesmaximal, characteristic, complemented
3C22×C31×#99C211yesmaximal, characteristic, complemented
4C31×#2121C218yesmaximal, direct product factor
5C2×C31×#352C212yesmaximal, complemented
6C2×C31×AΣL(1,𝔽16)C212yesmaximal, complemented
7C23×D4×C31C411yescharacteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C22×M16×C31—21no—
10C31×#534—22no—
11C31×#534—22no—
12C31×#534C414yescomplemented
13C31×#534C2214yes—
14C2×C31×#123—21no—
15C2×C31×#123C411yescharacteristic, complemented
16C2×C31×#123C2211yescharacteristic
17C2×C31×#121—21no—
18C2×C31×#121—21no—
19C2×C31×#120—21no—
20C2×C31×#120C411yescharacteristic, complemented
21C2×C31×#120C2211yescharacteristic
22C22×C22⋊C4×C31—21no—
23C22×C22⋊C4×C31C411yescharacteristic, complemented
24C2×C31×#100—22no—
25C2×C31×#100—21no—
26C2×C31×#100C2212yes—
27C2×C31×#100C2214yescomplemented
28C2×C31×#99—22no—
29C2×C31×#99—21no—
30C2×C31×#99C2212yes—
31C2×C31×#99C2214yescomplemented
32C31×#352C2218yescomplemented
33C31×AΣL(1,𝔽16)C2218yescomplemented
34C25×C31C2×C411yescharacteristic
35C25×C31C2×C411yescharacteristic, complemented
36C25×C31D411yescharacteristic
37C22×D4×C31—21no—
38C22×D4×C31—22no—
39C22×D4×C31—21no—
40C22×D4×C31—21no—
41C22×D4×C31—21no—
42C22×D4×C31—41no—
43C22×D4×C31—41no—
44C22×D4×C31—42no—
45C22×D4×C31—42no—
46C22×D4×C31—41no—
47C22×D4×C31—41no—
48C22×D4×C31C2×C411yescharacteristic
49C22×D4×C31C2×C412yes—
50C22×D4×C31C2×C414yescomplemented
51C22×D4×C31D411yescharacteristic
52C22×D4×C31D412yes—
53C22×D4×C31D411yescharacteristic
54C22×D4×C31D412yes—
55C22×D4×C31C2311yescharacteristic
56C22×D4×C31C2312yes—
57C23×C4×C31—21no—
58C23×C4×C31—41no—
59C23×C4×C31C2×C411yescharacteristic, complemented
60C23×C4×C31D411yescharacteristic
61C2×M16×C31—22no—
62C2×M16×C31—24no—
63C2×M16×C31—42no—
64C2×M16×C31—41no—
65C22×C8×C31—41no—
66C31×#123—22no—
67C31×#123—21no—
68C31×#123—21no—
69C31×#123—24no—
70C31×#123—24no—
71C31×#123C2×C414yescomplemented
72C31×#123C2×C412yescomplemented
73C31×#123C2312yes—
74C31×#121—24no—
75C31×#121—24no—
76C31×#121—24no—
77C31×#121—24no—
78C31×#120—24no—
79C31×#120—24no—
80C31×#120—22no—
81C31×#120—21no—
82C31×#120—21no—
83C31×#120C2×C414yescomplemented
84C31×#120C2×C412yescomplemented
85C31×#120C2312yes—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31—21no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31—41no—
98C2×C22⋊C4×C31C2×C411yescharacteristic, complemented
99C2×C22⋊C4×C31C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C31C2×C414yescomplemented
101C31×#100—22no—
102C31×#100—24no—
103C31×#100C2314yes—
104C31×#99—22no—
105C31×#99—24no—
106C31×#99C2314yes—
107C24×C31—21no—
108C24×C31—22no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—41no—
116C24×C31—41no—
117C24×C31—82no—
118C24×C31—82no—
119C24×C31—82no—
120C24×C31C22⋊C411yescharacteristic
121C24×C31C22⋊C411yescharacteristic
122C24×C31C22⋊C412yes—
123C24×C31C22⋊C412yes—
124C24×C31C22⋊C411yescharacteristic
125C24×C31C22×C411yescharacteristic
126C24×C31C22×C412yes—
127C24×C31C22×C412yescomplemented
128C24×C31C2×D411yescharacteristic
129C24×C31C2×D412yes—
130C2×D4×C31—24no—
131C2×D4×C31—24no—
132C2×D4×C31—22no—
133C2×D4×C31—24no—
134C2×D4×C31—22no—
135C2×D4×C31—41no—
136C2×D4×C31—42no—
137C2×D4×C31—42no—
138C2×D4×C31—41no—
139C2×D4×C31—42no—
140C2×D4×C31—41no—
141C2×D4×C31—42no—
142C2×D4×C31—42no—
143C2×D4×C31—41no—
144C2×D4×C31—42no—
145C2×D4×C31—41no—
146C2×D4×C31—41no—
147C2×D4×C31—42no—
148C2×D4×C31—42no—
149C2×D4×C31—41no—
150C2×D4×C31—41no—
151C2×D4×C31—44no—
152C2×D4×C31—44no—
153C2×D4×C31—42no—
154C2×D4×C31—42no—
155C2×D4×C31—42no—
156C2×D4×C31—41no—
157C2×D4×C31—41no—
158C2×D4×C31—44no—
159C2×D4×C31—44no—
160C2×D4×C31—82no—
161C2×D4×C31—82no—
162C2×D4×C31C22⋊C412yes—
163C2×D4×C31C22⋊C412yes—
164C2×D4×C31C22⋊C412yes—
165C2×D4×C31C22×C412yes—
166C2×D4×C31C22×C411yescharacteristic
167C2×D4×C31C2×D411yescharacteristic
168C2×D4×C31C2×D412yes—
169C2×D4×C31C2×D411yescharacteristic
170C2×D4×C31C2×D412yes—
171C2×D4×C31C2411yescharacteristic
172C22×C4×C31—21no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—24no—
180C22×C4×C31—41no—
181C22×C4×C31—41no—
182C22×C4×C31—44no—
183C22×C4×C31—42no—
184C22×C4×C31—82no—
185C22×C4×C31—84no—
186C22×C4×C31C22⋊C411yescharacteristic
187C22×C4×C31C22⋊C412yes—
188C22×C4×C31C22×C412yescomplemented
189C22×C4×C31C2×D411yescharacteristic
190C22×C4×C31C2×D412yes—
191M16×C31—24no—
192M16×C31—42no—
193M16×C31—44no—
194C2×C8×C31—44no—
195C2×C8×C31—42no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C22⋊C4×C31—21no—
200C22⋊C4×C31—21no—
201C22⋊C4×C31—24no—
202C22⋊C4×C31—24no—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—22no—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—24no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—44no—
211C22⋊C4×C31C22×C412yescomplemented
212C22⋊C4×C31C22×C412yescomplemented
213C2×#2121C3111yesmaximal, characteristic, direct product factor, Sylow
214C23×C31—22no—
215C23×C31—21no—
216C23×C31—21no—
217C23×C31—22no—
218C23×C31—21no—
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—21no—
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—44no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—82no—
244C23×C31—82no—
245C23×C31—82no—
246C23×C31—82no—
247C23×C31—82no—
248C23×C31—82no—
249C23×C31—82no—
250C23×C31—82no—
251C23×C31—84no—
252C23×C31—84no—
253C23×C31—82no—
254C23×C31—84no—
255C23×C31—84no—
256C23×C31#9911yescharacteristic
257C23×C31#9911yescharacteristic
258C23×C31#9912yes—
259C23×C31C2×C22⋊C411yescharacteristic
260C23×C31C2×C22⋊C411yescharacteristic
261C23×C31C2×C22⋊C412yes—
262C23×C31C2×C22⋊C411yescharacteristic
263C23×C31C2×C22⋊C412yes—
264C23×C31C2×C22⋊C412yes—
265C23×C31C23×C411yescharacteristic
266C23×C31C22×D411yescharacteristic
267D4×C31—42no—
268D4×C31—42no—
269D4×C31—42no—
270D4×C31—42no—
271D4×C31—41no—
272D4×C31—41no—
273D4×C31—42no—
274D4×C31—41no—
275D4×C31—42no—
276D4×C31—41no—
277D4×C31—48no—
278D4×C31—44no—
279D4×C31—44no—
280D4×C31—84no—
281D4×C31—82no—
282D4×C31—82no—
283C2×C4×C31—22no—
284C2×C4×C31—21no—
285C2×C4×C31—22no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—42no—
300C2×C4×C31—44no—
301C2×C4×C31—84no—
302C2×C4×C31—88no—
303C2×C4×C31—84no—
304C2×C4×C31C2×C22⋊C412yes—
305C2×C4×C31C2×C22⋊C411yescharacteristic
306C2×C4×C31C22×D411yescharacteristic
307C8×C31—44no—
308C2×#534C2×C3111yescharacteristic
309C22×#100C2×C3111yescharacteristic, complemented
310C22×#99C2×C3111yescharacteristic, complemented
311#2121C2×C3118yesdirect product factor
312C2×#352C2×C3112yescomplemented
313C2×AΣL(1,𝔽16)C2×C3112yescomplemented
314C22×C31—22no—
315C22×C31—22no—
316C22×C31—22no—
317C22×C31—21no—
318C22×C31—21no—
319C22×C31—21no—
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—21no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—42no—
326C22×C31—42no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—41no—
331C22×C31—44no—
332C22×C31—42no—
333C22×C31—44no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—42no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—82no—
345C22×C31—82no—
346C22×C31—82no—
347C22×C31—82no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—84no—
352C22×C31—84no—
353C22×C31—82no—
354C22×C31C2×#9911yescharacteristic
355C22×C31C2×#9912yes—
356C22×C31C2×#9912yes—
357C22×C31C2×#9911yescharacteristic
358C22×C31C22×C22⋊C411yescharacteristic
359C4×C31—21no—
360C4×C31—22no—
361C4×C31—21no—
362C4×C31—42no—
363C4×C31—42no—
364C4×C31—42no—
365C4×C31—84no—
366C23×D4C4×C3111yescharacteristic, complemented
367C23×D4C22×C3111yescharacteristic
368C22×M16—21no—
369#534—22no—
370#534—22no—
371#534C4×C3114yescomplemented
372#534C22×C3114yes—
373C2×#123—21no—
374C2×#123C4×C3111yescharacteristic, complemented
375C2×#123C22×C3111yescharacteristic
376C2×#121—21no—
377C2×#121—21no—
378C2×#120—21no—
379C2×#120C4×C3111yescharacteristic, complemented
380C2×#120C22×C3111yescharacteristic
381C22×C22⋊C4—21no—
382C22×C22⋊C4C4×C3111yescharacteristic, complemented
383C2×#100—22no—
384C2×#100—21no—
385C2×#100C22×C3112yes—
386C2×#100C22×C3114yescomplemented
387C2×#99—22no—
388C2×#99—21no—
389C2×#99C22×C3112yes—
390C2×#99C22×C3114yescomplemented
391#352C22×C3118yescomplemented
392AΣL(1,𝔽16)C22×C3118yescomplemented
393C2×C31—21no—
394C2×C31—21no—
395C2×C31—22no—
396C2×C31—22no—
397C2×C31—41no—
398C2×C31—42no—
399C2×C31—41no—
400C2×C31—42no—
401C2×C31—41no—
402C2×C31—41no—
403C2×C31—82no—
404C2×C31#212112yesdirect product factor
405C2×C31C22×#9911yescharacteristic
406C25C2×C4×C3111yescharacteristic
407C25C2×C4×C3111yescharacteristic, complemented
408C25D4×C3111yescharacteristic
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—22no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—41no—
415C22×D4—41no—
416C22×D4—42no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4—42no—
420C22×D4C2×C4×C3111yescharacteristic
421C22×D4C2×C4×C3112yes—
422C22×D4C2×C4×C3114yescomplemented
423C22×D4D4×C3111yescharacteristic
424C22×D4D4×C3112yes—
425C22×D4D4×C3111yescharacteristic
426C22×D4D4×C3112yes—
427C22×D4C23×C3111yescharacteristic
428C22×D4C23×C3112yes—
429C23×C4—21no—
430C23×C4—41no—
431C23×C4C2×C4×C3111yescharacteristic, complemented
432C23×C4D4×C3111yescharacteristic
433C2×M16—22no—
434C2×M16—24no—
435C2×M16—41no—
436C2×M16—42no—
437C22×C8—41no—
438#123—22no—
439#123—21no—
440#123—21no—
441#123—24no—
442#123—24no—
443#123C2×C4×C3114yescomplemented
444#123C2×C4×C3112yescomplemented
445#123C23×C3112yes—
446#121—24no—
447#121—24no—
448#121—24no—
449#121—24no—
450#120—24no—
451#120—24no—
452#120—22no—
453#120—21no—
454#120—21no—
455#120C2×C4×C3114yescomplemented
456#120C2×C4×C3112yescomplemented
457#120C23×C3112yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—41no—
470C2×C22⋊C4C2×C4×C3111yescharacteristic, complemented
471C2×C22⋊C4C2×C4×C3111yescharacteristic, complemented
472C2×C22⋊C4C2×C4×C3114yescomplemented
473#100—22no—
474#100—24no—
475#100C23×C3114yes—
476#99—22no—
477#99—24no—
478#99C23×C3114yes—
479C31C2×#212111yescharacteristic, direct product factor, Sylow
480C24—21no—
481C24—21no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—41no—
489C24—41no—
490C24—82no—
491C24—82no—
492C24—82no—
493C24C22⋊C4×C3111yescharacteristic
494C24C22⋊C4×C3111yescharacteristic
495C24C22⋊C4×C3112yes—
496C24C22⋊C4×C3112yes—
497C24C22⋊C4×C3111yescharacteristic
498C24C22×C4×C3111yescharacteristic
499C24C22×C4×C3112yes—
500C24C22×C4×C3112yescomplemented
501C24C2×D4×C3111yescharacteristic
502C24C2×D4×C3112yes—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—41no—
513C2×D4—42no—
514C2×D4—41no—
515C2×D4—42no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—41no—
519C2×D4—42no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—41no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—42no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—82no—
534C2×D4—82no—
535C2×D4C22⋊C4×C3112yes—
536C2×D4C22⋊C4×C3112yes—
537C2×D4C22⋊C4×C3112yes—
538C2×D4C22×C4×C3112yes—
539C2×D4C22×C4×C3111yescharacteristic
540C2×D4C2×D4×C3111yescharacteristic
541C2×D4C2×D4×C3112yes—
542C2×D4C2×D4×C3111yescharacteristic
543C2×D4C2×D4×C3112yes—
544C2×D4C24×C3111yescharacteristic
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—82no—
558C22×C4—84no—
559C22×C4C22⋊C4×C3111yescharacteristic
560C22×C4C22⋊C4×C3112yes—
561C22×C4C22×C4×C3112yescomplemented
562C22×C4C2×D4×C3111yescharacteristic
563C22×C4C2×D4×C3112yes—
564M16—24no—
565M16—42no—
566M16—44no—
567C2×C8—42no—
568C2×C8—44no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—24no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—24no—
582C22⋊C4—42no—
583C22⋊C4—44no—
584C22⋊C4C22×C4×C3112yescomplemented
585C22⋊C4C22×C4×C3112yescomplemented
586C23—22no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—21no—
594C23—21no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—21no—
601C23—22no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—84no—
624C23—84no—
625C23—82no—
626C23—84no—
627C23—84no—
628C23C31×#9911yescharacteristic
629C23C31×#9911yescharacteristic
630C23C31×#9912yes—
631C23C2×C22⋊C4×C3111yescharacteristic
632C23C2×C22⋊C4×C3111yescharacteristic
633C23C2×C22⋊C4×C3112yes—
634C23C2×C22⋊C4×C3111yescharacteristic
635C23C2×C22⋊C4×C3112yes—
636C23C2×C22⋊C4×C3112yes—
637C23C23×C4×C3111yescharacteristic
638C23C22×D4×C3111yescharacteristic
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—41no—
644D4—41no—
645D4—42no—
646D4—41no—
647D4—42no—
648D4—41no—
649D4—48no—
650D4—44no—
651D4—44no—
652D4—84no—
653D4—82no—
654D4—82no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—84no—
674C2×C4—88no—
675C2×C4—84no—
676C2×C4C2×C22⋊C4×C3112yes—
677C2×C4C2×C22⋊C4×C3111yescharacteristic
678C2×C4C22×D4×C3111yescharacteristic
679C8—44no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—21no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—82no—
717C22—84no—
718C22—84no—
719C22—82no—
720C22C2×C31×#9911yescharacteristic
721C22C2×C31×#9912yes—
722C22C2×C31×#9912yes—
723C22C2×C31×#9911yescharacteristic
724C22C22×C22⋊C4×C3111yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—84no—
732C2—21no—
733C2—21no—
734C2—22no—
735C2—22no—
736C2—41no—
737C2—42no—
738C2—41no—
739C2—41no—
740C2—41no—
741C2—42no—
742C2—82no—
743C2C31×#212112yesdirect product factor
744C2C22×C31×#9911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC23C23×C4×C31
Frattini, cosocleC2×D4C24×C31
prime radicalC2×C31×#534C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C23×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#100C2semidirect
3. C22×C31×#99C2semidirect
4. C31×#2121C2direct (N × H)
5. C2×C31×#352C2semidirect
6. C2×C31×AΣL(1,𝔽16)C2semidirect
7. C23×D4×C31C4semidirect
12. C31×#534C4semidirect
15. C2×C31×#123C4semidirect
20. C2×C31×#120C4semidirect
23. C22×C22⋊C4×C31C4semidirect
27. C2×C31×#100C22semidirect
31. C2×C31×#99C22semidirect
32. C31×#352C22semidirect
33. C31×AΣL(1,𝔽16)C22semidirect
35. C25×C31C2×C4semidirect
50. C22×D4×C31C2×C4semidirect
59. C23×C4×C31C2×C4semidirect
71. C31×#123C2×C4semidirect
72. C31×#123C2×C4semidirect
83. C31×#120C2×C4semidirect
84. C31×#120C2×C4semidirect
98. C2×C22⋊C4×C31C2×C4semidirect
99. C2×C22⋊C4×C31C2×C4semidirect
100. C2×C22⋊C4×C31C2×C4semidirect
127. C24×C31C22×C4semidirect
188. C22×C4×C31C22×C4semidirect
211. C22⋊C4×C31C22×C4semidirect
212. C22⋊C4×C31C22×C4semidirect
213. C2×#2121C31direct (N × H)
309. C22×#100C2×C31semidirect
310. C22×#99C2×C31semidirect
311. #2121C2×C31direct (N × H)
312. C2×#352C2×C31semidirect
313. C2×AΣL(1,𝔽16)C2×C31semidirect
366. C23×D4C4×C31semidirect
371. #534C4×C31semidirect
374. C2×#123C4×C31semidirect
379. C2×#120C4×C31semidirect
382. C22×C22⋊C4C4×C31semidirect
386. C2×#100C22×C31semidirect
390. C2×#99C22×C31semidirect
391. #352C22×C31semidirect
392. AΣL(1,𝔽16)C22×C31semidirect
404. C2×C31#2121direct (N × H)
407. C25C2×C4×C31semidirect
422. C22×D4C2×C4×C31semidirect
431. C23×C4C2×C4×C31semidirect
443. #123C2×C4×C31semidirect
444. #123C2×C4×C31semidirect
455. #120C2×C4×C31semidirect
456. #120C2×C4×C31semidirect
470. C2×C22⋊C4C2×C4×C31semidirect
471. C2×C22⋊C4C2×C4×C31semidirect
472. C2×C22⋊C4C2×C4×C31semidirect
479. C31C2×#2121direct (N × H)
500. C24C22×C4×C31semidirect
561. C22×C4C22×C4×C31semidirect
584. C22⋊C4C22×C4×C31semidirect
585. C22⋊C4C22×C4×C31semidirect
743. C2C31×#2121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5342
C22×C31×#1002
C22×C31×#992
C31×#21212
C2×C31×#3522
C2×C31×AΣL(1,𝔽16)2
C2×#212131