Finite Group Databasebeta

← C31×#33552 #21490311

Subgroups — C31×#33552 #21490311

Order 7936.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3533C211yesmaximal, characteristic, complemented
2C31×#3026C211yesmaximal, characteristic, complemented
3C2×C31×#458C211yesmaximal, characteristic, complemented
4C31×#3019C211yesmaximal, characteristic, complemented
5C31×#2201C212yesmaximal, complemented
6C31×#2200C212yesmaximal, complemented
7C31×#2198C212yesmaximal, complemented
8C31×#2197C212yesmaximal, complemented
9C31×#2127C211yesmaximal, characteristic, complemented
10C31×#2121C211yesmaximal, characteristic, complemented
11C2×C31×#352C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic
13C31×#575—21no—
14C31×#563C2211yescharacteristic, complemented
15C31×#562—21no—
16C31×#560C2211yescharacteristic, complemented
17C31×#559C2211yescharacteristic, complemented
18C31×#553—21no—
19C31×#552—21no—
20C31×#551—21no—
21C31×#551C2211yescharacteristic, complemented
22C31×#547—21no—
23C31×#546—21no—
24C31×#542—21no—
25C31×#540—21no—
26C31×#539—21no—
27C31×#538—21no—
28C31×#538—21no—
29C31×#535C2211yescharacteristic
30C31×#534—21no—
31C31×#534C2211yescharacteristic
32C31×#525—21no—
33C2×C31×#123—21no—
34C2×C31×#123C2211yescharacteristic
35C31×#458—21no—
36C31×#458—21no—
37C31×#458—21no—
38C31×#458C2212yes—
39C31×#458C2212yes—
40C31×#458C2212yes—
41C31×B(4,𝔽2)—21no—
42C31×B(4,𝔽2)C2212yes—
43C31×#455—21no—
44C31×#455C2212yes—
45C31×#453—21no—
46C31×#453C2212yes—
47C31×#421—21no—
48C2×C31×#100C2211yescharacteristic
49C2×C31×#99—21no—
50C2×C31×#99—21no—
51C2×C31×#99C2211yescharacteristic
52C2×C31×#99C2211yescharacteristic
53C31×#354C2212yescomplemented
54C31×#353C2212yescomplemented
55C31×#352C2212yescomplemented
56C31×#352C2212yescomplemented
57C31×#352C2212yescomplemented
58C31×AΣL(1,𝔽16)C2212yescomplemented
59C31×H(5,𝔽2)—21no—
60C31×H(5,𝔽2)—21no—
61C31×H(5,𝔽2)—21no—
62C31×H(5,𝔽2)—42no—
63C31×H(5,𝔽2)C2312yes—
64C2×#41×C31—21no—
65C2×#41×C31—21no—
66C2×#41×C31—41no—
67C2×#41×C31D411yescharacteristic, complemented
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—41no—
71C22×D4×C31D411yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31D411yescharacteristic, complemented
74C31×#137—22no—
75C31×#137—41no—
76C31×AGL(1,ℤ/8)—22no—
77C31×AGL(1,ℤ/8)—41no—
78C31×#135—42no—
79C2×M16×C31—21no—
80C31×C4⋊Q8—21no—
81C31×#127D411yescharacteristic, complemented
82C31×#127C2311yescharacteristic
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#125—21no—
90C31×#125—21no—
91C31×#125—21no—
92C31×#124—21no—
93C31×#124—21no—
94C31×#124—21no—
95C31×#124—21no—
96C31×#124D411yescharacteristic, complemented
97C31×#124C2311yescharacteristic
98C31×#123—21no—
99C31×#123—21no—
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×#123—22no—
111C31×#123—22no—
112C31×#123—22no—
113C31×#123—41no—
114C31×#123—42no—
115C31×#123D411yescharacteristic
116C31×#123D411yescharacteristic, complemented
117C31×#123D411yescharacteristic, complemented
118C31×#123C2311yescharacteristic
119C31×#123C2311yescharacteristic
120C31×#123C2311yescharacteristic
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×#121—21no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121—21no—
138C31×#121—21no—
139C31×#121—21no—
140C31×#121—21no—
141C31×#121—42no—
142C31×#120—21no—
143C31×#120—21no—
144C31×#120—21no—
145C31×#120—21no—
146C31×#120—22no—
147C31×#120—41no—
148C31×#120D411yescharacteristic
149C31×#120C2311yescharacteristic
150C4×Q8×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C4×D4×C31—21no—
155C4×D4×C31—21no—
156C4×D4×C31—21no—
157C4×D4×C31—21no—
158C4×D4×C31—21no—
159C4×D4×C31—21no—
160C31×#117—21no—
161C31×#117—21no—
162C31×#117—21no—
163C31×#117D411yescharacteristic, complemented
164C2×C4⋊C4×C31—21no—
165C2×C4⋊C4×C31—21no—
166C2×C4⋊C4×C31—41no—
167C2×C22⋊C4×C31—21no—
168C2×C22⋊C4×C31—21no—
169C2×C22⋊C4×C31—21no—
170C2×C22⋊C4×C31—21no—
171C2×C22⋊C4×C31—41no—
172C2×C22⋊C4×C31D411yescharacteristic
173C2×C22⋊C4×C31D411yescharacteristic, complemented
174C31×#104—22no—
175C31×#104—22no—
176C31×#100—21no—
177C31×#100C2312yes—
178C31×#99—21no—
179C31×#99—21no—
180C31×#99—22no—
181C31×#99—22no—
182C31×#99—22no—
183C31×#99—22no—
184C31×#99C2312yes—
185C31×#99C2312yes—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31C2×D411yescharacteristic
189C24×C31C2×D411yescharacteristic
190C24×C31C2×D411yescharacteristic
191#41×C31—22no—
192#41×C31—22no—
193#41×C31—42no—
194#41×C31—41no—
195#41×C31—42no—
196#41×C31—42no—
197#41×C31—41no—
198#41×C31—41no—
199#41×C31—42no—
200#41×C31—41no—
201#41×C31—81no—
202#41×C31—81no—
203C2×Q8×C31—21no—
204C2×Q8×C31—21no—
205C2×Q8×C31—21no—
206C2×Q8×C31C2×D411yescharacteristic
207C2×D4×C31—21no—
208C2×D4×C31—22no—
209C2×D4×C31—22no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—22no—
213C2×D4×C31—22no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—41no—
224C2×D4×C31—41no—
225C2×D4×C31—42no—
226C2×D4×C31—42no—
227C2×D4×C31—41no—
228C2×D4×C31—41no—
229C2×D4×C31—41no—
230C2×D4×C31—41no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—41no—
234C2×D4×C31—41no—
235C2×D4×C31—41no—
236C2×D4×C31—41no—
237C2×D4×C31—41no—
238C2×D4×C31—42no—
239C2×D4×C31C2×D411yescharacteristic
240C2×D4×C31C2×D411yescharacteristic
241C2×D4×C31C2×D411yescharacteristic
242C2×D4×C31C2×D411yescharacteristic
243C2×D4×C31C2411yescharacteristic
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—41no—
256C22×C4×C31—41no—
257C22×C4×C31—41no—
258C22×C4×C31—41no—
259C22×C4×C31—41no—
260C22×C4×C31C2×D411yescharacteristic
261C22×C4×C31C2×D411yescharacteristic
262C22×C4×C31C2×D411yescharacteristic
263C22×C4×C31C2×D411yescharacteristic
264Q16×C31—42no—
265SD16×C31—42no—
266SD16×C31—42no—
267D8×C31—42no—
268M16×C31—22no—
269M16×C31—41no—
270C2×C8×C31—41no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—42no—
291C4⋊C4×C31—42no—
292C4⋊C4×C31—42no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—21no—
302C22⋊C4×C31—21no—
303C22⋊C4×C31—21no—
304C22⋊C4×C31—21no—
305C22⋊C4×C31—21no—
306C22⋊C4×C31—21no—
307C22⋊C4×C31—21no—
308C22⋊C4×C31—21no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—21no—
315C22⋊C4×C31—21no—
316C22⋊C4×C31—22no—
317C22⋊C4×C31—22no—
318C22⋊C4×C31—42no—
319C22⋊C4×C31—41no—
320C22⋊C4×C31—41no—
321C22⋊C4×C31—42no—
322C22⋊C4×C31—42no—
323C22⋊C4×C31—42no—
324C22⋊C4×C31C2×D411yescharacteristic
325C22⋊C4×C31C2×D411yescharacteristic
326C22⋊C4×C31C2×D411yescharacteristic
327C22⋊C4×C31C2×D411yescharacteristic
328C42×C31—21no—
329C42×C31—21no—
330C42×C31—21no—
331C42×C31—21no—
332C42×C31C2×D411yescharacteristic
333C42×C31C2×D411yescharacteristic
334#33552C3111yesmaximal, characteristic, direct product factor, Sylow
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—21no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—21no—
342C23×C31—21no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—81no—
348C23×C31—81no—
349C23×C31—81no—
350C23×C31—82no—
351C23×C31—161no—
352C23×C31#12011yescharacteristic
353C23×C31#12011yescharacteristic
354C23×C31#12011yescharacteristic
355C23×C31C22×D411yescharacteristic
356C23×C31C22×D411yescharacteristic
357Q8×C31—22no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31—81no—
361Q8×C31—81no—
362D4×C31—22no—
363D4×C31—41no—
364D4×C31—41no—
365D4×C31—41no—
366D4×C31—41no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—42no—
370D4×C31—42no—
371D4×C31—42no—
372D4×C31—42no—
373D4×C31—42no—
374D4×C31—42no—
375D4×C31—41no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—41no—
379D4×C31—81no—
380D4×C31—81no—
381D4×C31—81no—
382D4×C31—81no—
383D4×C31—81no—
384D4×C31—81no—
385D4×C31—81no—
386D4×C31—81no—
387D4×C31—81no—
388D4×C31—162no—
389C2×C4×C31—21no—
390C2×C4×C31—21no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
398C2×C4×C31—21no—
399C2×C4×C31—21no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—21no—
403C2×C4×C31—42no—
404C2×C4×C31—42no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—42no—
414C2×C4×C31—42no—
415C2×C4×C31—81no—
416C2×C4×C31—81no—
417C2×C4×C31—81no—
418C2×C4×C31—81no—
419C2×C4×C31—81no—
420C2×C4×C31—81no—
421C2×C4×C31—81no—
422C2×C4×C31—81no—
423C2×C4×C31—82no—
424C2×C4×C31—161no—
425C2×C4×C31#12011yescharacteristic
426C2×C4×C31C22×D411yescharacteristic
427C8×C31—42no—
428#3533C2×C3111yescharacteristic, complemented
429#3026C2×C3111yescharacteristic, complemented
430C2×#458C2×C3111yescharacteristic, complemented
431#3019C2×C3111yescharacteristic, complemented
432#2201C2×C3112yescomplemented
433#2200C2×C3112yescomplemented
434#2198C2×C3112yescomplemented
435#2197C2×C3112yescomplemented
436#2127C2×C3111yescharacteristic, complemented
437#2121C2×C3111yescharacteristic, complemented
438C2×#352C2×C3111yescharacteristic, complemented
439C22×C31—21no—
440C22×C31—21no—
441C22×C31—21no—
442C22×C31—21no—
443C22×C31—41no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—42no—
449C22×C31—41no—
450C22×C31—41no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—42no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—82no—
460C22×C31—82no—
461C22×C31—82no—
462C22×C31—82no—
463C22×C31—161no—
464C22×C31—161no—
465C22×C31B(4,𝔽2)11yescharacteristic
466C22×C31B(4,𝔽2)11yescharacteristic
467C22×C31C2×#12011yescharacteristic
468C4×C31—21no—
469C4×C31—21no—
470C4×C31—41no—
471C4×C31—41no—
472C4×C31—41no—
473C4×C31—41no—
474C4×C31—41no—
475C4×C31—41no—
476C4×C31—42no—
477C4×C31—41no—
478C4×C31—41no—
479C4×C31—41no—
480C4×C31—41no—
481C4×C31—82no—
482C4×C31—82no—
483C2×H(5,𝔽2)C22×C3111yescharacteristic
484#575—21no—
485#563C22×C3111yescharacteristic, complemented
486#562—21no—
487#560C22×C3111yescharacteristic, complemented
488#559C22×C3111yescharacteristic, complemented
489#553—21no—
490#552—21no—
491#551—21no—
492#551C22×C3111yescharacteristic, complemented
493#547—21no—
494#546—21no—
495#542—21no—
496#540—21no—
497#539—21no—
498#538—21no—
499#538—21no—
500#535C22×C3111yescharacteristic
501#534—21no—
502#534C22×C3111yescharacteristic
503#525—21no—
504C2×#123—21no—
505C2×#123C22×C3111yescharacteristic
506#458—21no—
507#458—21no—
508#458—21no—
509#458C22×C3112yes—
510#458C22×C3112yes—
511#458C22×C3112yes—
512B(4,𝔽2)—21no—
513B(4,𝔽2)C22×C3112yes—
514#455—21no—
515#455C22×C3112yes—
516#453—21no—
517#453C22×C3112yes—
518#421—21no—
519C2×#100C22×C3111yescharacteristic
520C2×#99—21no—
521C2×#99—21no—
522C2×#99C22×C3111yescharacteristic
523C2×#99C22×C3111yescharacteristic
524#354C22×C3112yescomplemented
525#353C22×C3112yescomplemented
526#352C22×C3112yescomplemented
527#352C22×C3112yescomplemented
528#352C22×C3112yescomplemented
529AΣL(1,𝔽16)C22×C3112yescomplemented
530C2×C31—21no—
531C2×C31—21no—
532C2×C31—21no—
533C2×C31—41no—
534C2×C31—41no—
535C2×C31—41no—
536C2×C31—41no—
537C2×C31—81no—
538C2×C31—81no—
539C2×C31—82no—
540C2×C31C2×B(4,𝔽2)11yescharacteristic
541H(5,𝔽2)—21no—
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—42no—
545H(5,𝔽2)C23×C3112yes—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—41no—
549C2×#41D4×C3111yescharacteristic, complemented
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—41no—
553C22×D4D4×C3111yescharacteristic
554C22×D4C23×C3111yescharacteristic
555C23×C4D4×C3111yescharacteristic, complemented
556#137—22no—
557#137—41no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—41no—
560#135—42no—
561C2×M16—21no—
562C4⋊Q8—21no—
563#127D4×C3111yescharacteristic, complemented
564#127C23×C3111yescharacteristic
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#125—21no—
572#125—21no—
573#125—21no—
574#124—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124D4×C3111yescharacteristic, complemented
579#124C23×C3111yescharacteristic
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—22no—
593#123—22no—
594#123—22no—
595#123—41no—
596#123—42no—
597#123D4×C3111yescharacteristic
598#123D4×C3111yescharacteristic, complemented
599#123D4×C3111yescharacteristic, complemented
600#123C23×C3111yescharacteristic
601#123C23×C3111yescharacteristic
602#123C23×C3111yescharacteristic
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—42no—
624#120—21no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—22no—
629#120—41no—
630#120D4×C3111yescharacteristic
631#120C23×C3111yescharacteristic
632C4×Q8—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642#117—21no—
643#117—21no—
644#117—21no—
645#117D4×C3111yescharacteristic, complemented
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—41no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4D4×C3111yescharacteristic
655C2×C22⋊C4D4×C3111yescharacteristic, complemented
656#104—22no—
657#104—22no—
658#100—21no—
659#100C23×C3112yes—
660#99—21no—
661#99—21no—
662#99—22no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99C23×C3112yes—
667#99C23×C3112yes—
668C31#3355211yescharacteristic, direct product factor, Sylow
669C24—21no—
670C24—21no—
671C24C2×D4×C3111yescharacteristic
672C24C2×D4×C3111yescharacteristic
673C24C2×D4×C3111yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C3111yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C3111yescharacteristic
723C2×D4C2×D4×C3111yescharacteristic
724C2×D4C2×D4×C3111yescharacteristic
725C2×D4C2×D4×C3111yescharacteristic
726C2×D4C24×C3111yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C3111yescharacteristic
744C22×C4C2×D4×C3111yescharacteristic
745C22×C4C2×D4×C3111yescharacteristic
746C22×C4C2×D4×C3111yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C3111yescharacteristic
808C22⋊C4C2×D4×C3111yescharacteristic
809C22⋊C4C2×D4×C3111yescharacteristic
810C22⋊C4C2×D4×C3111yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C3111yescharacteristic
816C42C2×D4×C3111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23C31×#12011yescharacteristic
835C23C31×#12011yescharacteristic
836C23C31×#12011yescharacteristic
837C23C22×D4×C3111yescharacteristic
838C23C22×D4×C3111yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4C31×#12011yescharacteristic
908C2×C4C22×D4×C3111yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22C31×B(4,𝔽2)11yescharacteristic
937C22C31×B(4,𝔽2)11yescharacteristic
938C22C2×C31×#12011yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C31C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C31
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3533C2semidirect
2. C31×#3026C2semidirect
3. C2×C31×#458C2semidirect
4. C31×#3019C2semidirect
5. C31×#2201C2semidirect
6. C31×#2200C2semidirect
7. C31×#2198C2semidirect
8. C31×#2197C2semidirect
9. C31×#2127C2semidirect
10. C31×#2121C2semidirect
11. C2×C31×#352C2semidirect
14. C31×#563C22semidirect
16. C31×#560C22semidirect
17. C31×#559C22semidirect
21. C31×#551C22semidirect
53. C31×#354C22semidirect
54. C31×#353C22semidirect
55. C31×#352C22semidirect
56. C31×#352C22semidirect
57. C31×#352C22semidirect
58. C31×AΣL(1,𝔽16)C22semidirect
67. C2×#41×C31D4semidirect
73. C23×C4×C31D4semidirect
81. C31×#127D4semidirect
96. C31×#124D4semidirect
116. C31×#123D4semidirect
117. C31×#123D4semidirect
163. C31×#117D4semidirect
173. C2×C22⋊C4×C31D4semidirect
334. #33552C31direct (N × H)
428. #3533C2×C31semidirect
429. #3026C2×C31semidirect
430. C2×#458C2×C31semidirect
431. #3019C2×C31semidirect
432. #2201C2×C31semidirect
433. #2200C2×C31semidirect
434. #2198C2×C31semidirect
435. #2197C2×C31semidirect
436. #2127C2×C31semidirect
437. #2121C2×C31semidirect
438. C2×#352C2×C31semidirect
485. #563C22×C31semidirect
487. #560C22×C31semidirect
488. #559C22×C31semidirect
492. #551C22×C31semidirect
524. #354C22×C31semidirect
525. #353C22×C31semidirect
526. #352C22×C31semidirect
527. #352C22×C31semidirect
528. #352C22×C31semidirect
529. AΣL(1,𝔽16)C22×C31semidirect
549. C2×#41D4×C31semidirect
555. C23×C4D4×C31semidirect
563. #127D4×C31semidirect
578. #124D4×C31semidirect
598. #123D4×C31semidirect
599. #123D4×C31semidirect
645. #117D4×C31semidirect
655. C2×C22⋊C4D4×C31semidirect
668. C31#33552direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35332
C31×#30262
C2×C31×#4582
C31×#30192
C31×#22012
C31×#22002
C31×#21982
C31×#21972
C31×#21272
C31×#21212
C2×C31×#3522
#3355231