Finite Group Databasebeta

← C31×#33553 #21490312

Subgroups — C31×#33553 #21490312

Order 7936.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic, complemented
2C31×#3027C211yesmaximal, characteristic, complemented
3C31×#3025C211yesmaximal, characteristic, complemented
4C31×#3021C211yesmaximal, characteristic, complemented
5C31×#2200C214yesmaximal, complemented
6C31×#2196C214yesmaximal, complemented
7C31×#2128C211yesmaximal, characteristic, complemented
8C31×#2122C211yesmaximal, characteristic, complemented
9C31×#2120C211yesmaximal, characteristic, complemented
10C31×#585C2211yescharacteristic, complemented
11C2×C31×AGL(1,ℤ/8)—21no—
12C31×#560—21no—
13C31×#560C2212yescomplemented
14C31×#553—21no—
15C31×#553—21no—
16D42×C31—21no—
17D42×C31—21no—
18D42×C31—21no—
19D42×C31C2212yescomplemented
20C31×#540—21no—
21C31×#538—22no—
22C31×#535—21no—
23C31×#535C2211yescharacteristic
24C31×#535C2211yescharacteristic
25C31×#534—22no—
26C31×#525—21no—
27C31×#525C2211yescharacteristic
28C2×C31×#121—21no—
29C31×#458—21no—
30C31×#458C2212yescomplemented
31C31×B(4,𝔽2)—21no—
32C31×B(4,𝔽2)—22no—
33C31×B(4,𝔽2)C2212yescomplemented
34C31×B(4,𝔽2)C2214yescomplemented
35C31×#454—22no—
36C31×#453C2214yescomplemented
37C31×#421—21no—
38C31×#413C2211yescharacteristic, complemented
39C31×#410—21no—
40C31×#410—21no—
41C31×#410C2211yescharacteristic, complemented
42C31×#410C2211yescharacteristic, complemented
43C31×#353C2214yescomplemented
44C31×#352C2212yescomplemented
45C31×AΣL(1,𝔽16)C2212yescomplemented
46C31×AΣL(1,𝔽16)C2214yescomplemented
47C31×2−1+4—21no—
48C31×2−1+4—41no—
49C31×H(5,𝔽2)—21no—
50C31×H(5,𝔽2)—21no—
51C31×H(5,𝔽2)—41no—
52C31×H(5,𝔽2)C2312yes—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—42no—
57C2×#41×C31C2311yescharacteristic
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31D411yescharacteristic, complemented
63C22×D4×C31D411yescharacteristic, complemented
64C23×C4×C31D411yescharacteristic, complemented
65C31×AGL(1,ℤ/8)—24no—
66C31×AGL(1,ℤ/8)—42no—
67C2×SD16×C31—41no—
68C2×D8×C31—41no—
69C2×M16×C31—21no—
70C31×#127—21no—
71C31×#127—21no—
72C31×#127—41no—
73C31×#127C2312yes—
74C31×#126—22no—
75C31×#126—22no—
76C31×#125—21no—
77C31×#124—21no—
78C31×#124—41no—
79C31×#124D412yescomplemented
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×#123—22no—
85C31×#123D411yescharacteristic, complemented
86C31×#123C2311yescharacteristic
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—41no—
89C31×#121—22no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—21no—
95C31×#121—22no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—22no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—42no—
105C31×#121—41no—
106C31×#120—22no—
107C31×#120—22no—
108C31×#120—22no—
109C31×#120—21no—
110C31×#120—21no—
111C31×#120—22no—
112C31×#120—22no—
113C31×#120—24no—
114C31×#120D411yescharacteristic, complemented
115C31×#120D412yescomplemented
116C31×#120C2311yescharacteristic
117C31×#120C2312yes—
118C4×D4×C31—22no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—21no—
123C4×D4×C31—22no—
124C4×D4×C31—42no—
125C31×#117—21no—
126C31×#117—21no—
127C31×#117D411yescharacteristic, complemented
128C31×#117D411yescharacteristic, complemented
129C31×#117D411yescharacteristic, complemented
130C2×C4⋊C4×C31—21no—
131C2×C22⋊C4×C31—22no—
132C31×#104—24no—
133C31×#101—21no—
134C31×#100C2312yes—
135C31×#99—21no—
136C31×#99—21no—
137C31×#99—24no—
138C31×#99—22no—
139C31×#99—22no—
140C31×#99C2312yes—
141C31×#99C2312yes—
142C24×C31—22no—
143C24×C31—21no—
144C24×C31C2×D411yescharacteristic
145C24×C31C2×D412yes—
146#41×C31—22no—
147#41×C31—22no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—42no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154#41×C31—41no—
155#41×C31—41no—
156#41×C31—42no—
157#41×C31—42no—
158#41×C31—42no—
159#41×C31—41no—
160#41×C31—41no—
161#41×C31—41no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—42no—
166C2×Q8×C31C2×D411yescharacteristic
167C2×D4×C31—21no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—21no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—22no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—41no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—41no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—42no—
193C2×D4×C31—41no—
194C2×D4×C31—42no—
195C2×D4×C31—44no—
196C2×D4×C31—81no—
197C2×D4×C31—81no—
198C2×D4×C31—84no—
199C2×D4×C31—84no—
200C2×D4×C31—84no—
201C2×D4×C31C2×D411yescharacteristic
202C2×D4×C31C2×D411yescharacteristic
203C2×D4×C31C2×D412yes—
204C2×D4×C31C2411yescharacteristic
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—41no—
213C22×C4×C31—41no—
214C22×C4×C31—41no—
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219SD16×C31—44no—
220D8×C31—44no—
221M16×C31—22no—
222M16×C31—41no—
223C2×C8×C31—41no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—41no—
233C4⋊C4×C31—41no—
234C4⋊C4×C31—42no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—21no—
240C22⋊C4×C31—21no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—44no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31C2×D412yes—
254C22⋊C4×C31C2×D411yescharacteristic
255C22⋊C4×C31C2×D411yescharacteristic
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—41no—
259C42×C31—41no—
260C42×C31C2×D412yes—
261#33553C3111yesmaximal, characteristic, direct product factor, Sylow
262C23×C31—21no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—41no—
268C23×C31—42no—
269C23×C31—41no—
270C23×C31—44no—
271C23×C31—42no—
272C23×C31—81no—
273C23×C31—82no—
274C23×C31—82no—
275C23×C31—82no—
276C23×C31—82no—
277C23×C31#12011yescharacteristic
278C23×C31C22×D411yescharacteristic
279C23×C31C22×D411yescharacteristic
280Q8×C31—22no—
281Q8×C31—41no—
282Q8×C31—41no—
283Q8×C31—41no—
284Q8×C31—41no—
285D4×C31—22no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—42no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—42no—
295D4×C31—42no—
296D4×C31—44no—
297D4×C31—44no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—41no—
305D4×C31—81no—
306D4×C31—82no—
307D4×C31—82no—
308D4×C31—82no—
309D4×C31—82no—
310D4×C31—82no—
311D4×C31—82no—
312D4×C31—82no—
313D4×C31—84no—
314D4×C31—164no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—22no—
327C2×C4×C31—21no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—41no—
332C2×C4×C31—42no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—81no—
339C2×C4×C31—82no—
340C2×C4×C31—82no—
341C2×C4×C31—82no—
342C2×C4×C31#12011yescharacteristic
343C2×C4×C31#12011yescharacteristic
344C2×C4×C31#12011yescharacteristic
345C2×C4×C31C22×D411yescharacteristic
346C8×C31—42no—
347#3537C2×C3111yescharacteristic, complemented
348#3027C2×C3111yescharacteristic, complemented
349#3025C2×C3111yescharacteristic, complemented
350#3021C2×C3111yescharacteristic, complemented
351#2200C2×C3114yescomplemented
352#2196C2×C3114yescomplemented
353#2128C2×C3111yescharacteristic, complemented
354#2122C2×C3111yescharacteristic, complemented
355#2120C2×C3111yescharacteristic, complemented
356C22×C31—22no—
357C22×C31—21no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—41no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—81no—
374C22×C31—82no—
375C22×C31—82no—
376C22×C31—84no—
377C22×C31—161no—
378C22×C31—164no—
379C22×C31—162no—
380C22×C31C2×#12011yescharacteristic
381C4×C31—21no—
382C4×C31—21no—
383C4×C31—21no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—42no—
388C4×C31—42no—
389C4×C31—41no—
390C4×C31—82no—
391C4×C31—82no—
392C4×C31B(4,𝔽2)11yescharacteristic
393C4×C31B(4,𝔽2)11yescharacteristic
394#585C22×C3111yescharacteristic, complemented
395C2×AGL(1,ℤ/8)—21no—
396#560—21no—
397#560C22×C3112yescomplemented
398#553—21no—
399#553—21no—
400D42—21no—
401D42—21no—
402D42—21no—
403D42C22×C3112yescomplemented
404#540—21no—
405#538—22no—
406#535—21no—
407#535C22×C3111yescharacteristic
408#535C22×C3111yescharacteristic
409#534—22no—
410#525—21no—
411#525C22×C3111yescharacteristic
412C2×#121—21no—
413#458—21no—
414#458C22×C3112yescomplemented
415B(4,𝔽2)—21no—
416B(4,𝔽2)—22no—
417B(4,𝔽2)C22×C3112yescomplemented
418B(4,𝔽2)C22×C3114yescomplemented
419#454—22no—
420#453C22×C3114yescomplemented
421#421—21no—
422#413C22×C3111yescharacteristic, complemented
423#410—21no—
424#410—21no—
425#410C22×C3111yescharacteristic, complemented
426#410C22×C3111yescharacteristic, complemented
427#353C22×C3114yescomplemented
428#352C22×C3112yescomplemented
429AΣL(1,𝔽16)C22×C3112yescomplemented
430AΣL(1,𝔽16)C22×C3114yescomplemented
431C2×C31—21no—
432C2×C31—41no—
433C2×C31—41no—
434C2×C31—42no—
435C2×C31—41no—
436C2×C31—82no—
437C2×C31—82no—
438C2×C31—82no—
439C2×C31C2×B(4,𝔽2)11yescharacteristic
4402−1+4—21no—
4412−1+4—41no—
442H(5,𝔽2)—21no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—41no—
445H(5,𝔽2)C23×C3112yes—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—42no—
450C2×#41C23×C3111yescharacteristic
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4D4×C3111yescharacteristic, complemented
456C22×D4D4×C3111yescharacteristic, complemented
457C23×C4D4×C3111yescharacteristic, complemented
458AGL(1,ℤ/8)—24no—
459AGL(1,ℤ/8)—42no—
460C2×SD16—41no—
461C2×D8—41no—
462C2×M16—21no—
463#127—21no—
464#127—21no—
465#127—41no—
466#127C23×C3112yes—
467#126—22no—
468#126—22no—
469#125—21no—
470#124—21no—
471#124—41no—
472#124D4×C3112yescomplemented
473#123—22no—
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123D4×C3111yescharacteristic, complemented
479#123C23×C3111yescharacteristic
480C22⋊Q8—21no—
481C22⋊Q8—41no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—22no—
486#121—22no—
487#121—21no—
488#121—22no—
489#121—21no—
490#121—21no—
491#121—22no—
492#121—21no—
493#121—21no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121—42no—
498#121—41no—
499#120—22no—
500#120—22no—
501#120—22no—
502#120—21no—
503#120—21no—
504#120—22no—
505#120—22no—
506#120—24no—
507#120D4×C3111yescharacteristic, complemented
508#120D4×C3112yescomplemented
509#120C23×C3111yescharacteristic
510#120C23×C3112yes—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—22no—
517C4×D4—42no—
518#117—21no—
519#117—21no—
520#117D4×C3111yescharacteristic, complemented
521#117D4×C3111yescharacteristic, complemented
522#117D4×C3111yescharacteristic, complemented
523C2×C4⋊C4—21no—
524C2×C22⋊C4—22no—
525#104—24no—
526#101—21no—
527#100C23×C3112yes—
528#99—21no—
529#99—21no—
530#99—24no—
531#99—22no—
532#99—22no—
533#99C23×C3112yes—
534#99C23×C3112yes—
535C31#3355311yescharacteristic, direct product factor, Sylow
536C24—22no—
537C24—21no—
538C24C2×D4×C3111yescharacteristic
539C24C2×D4×C3112yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C3111yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C3111yescharacteristic
596C2×D4C2×D4×C3111yescharacteristic
597C2×D4C2×D4×C3112yes—
598C2×D4C24×C3111yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C3112yes—
648C22⋊C4C2×D4×C3111yescharacteristic
649C22⋊C4C2×D4×C3111yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C3112yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23C31×#12011yescharacteristic
671C23C22×D4×C3111yescharacteristic
672C23C22×D4×C3111yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4C31×#12011yescharacteristic
736C2×C4C31×#12011yescharacteristic
737C2×C4C31×#12011yescharacteristic
738C2×C4C22×D4×C3111yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×C31×#12011yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C31×B(4,𝔽2)11yescharacteristic
777C4C31×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×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 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3537C2semidirect
2. C31×#3027C2semidirect
3. C31×#3025C2semidirect
4. C31×#3021C2semidirect
5. C31×#2200C2semidirect
6. C31×#2196C2semidirect
7. C31×#2128C2semidirect
8. C31×#2122C2semidirect
9. C31×#2120C2semidirect
10. C31×#585C22semidirect
13. C31×#560C22semidirect
19. D42×C31C22semidirect
30. C31×#458C22semidirect
33. C31×B(4,𝔽2)C22semidirect
34. C31×B(4,𝔽2)C22semidirect
36. C31×#453C22semidirect
38. C31×#413C22semidirect
41. C31×#410C22semidirect
42. C31×#410C22semidirect
43. C31×#353C22semidirect
44. C31×#352C22semidirect
45. C31×AΣL(1,𝔽16)C22semidirect
46. C31×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C31D4semidirect
63. C22×D4×C31D4semidirect
64. C23×C4×C31D4semidirect
79. C31×#124D4semidirect
85. C31×#123D4semidirect
114. C31×#120D4semidirect
115. C31×#120D4semidirect
127. C31×#117D4semidirect
128. C31×#117D4semidirect
129. C31×#117D4semidirect
261. #33553C31direct (N × H)
347. #3537C2×C31semidirect
348. #3027C2×C31semidirect
349. #3025C2×C31semidirect
350. #3021C2×C31semidirect
351. #2200C2×C31semidirect
352. #2196C2×C31semidirect
353. #2128C2×C31semidirect
354. #2122C2×C31semidirect
355. #2120C2×C31semidirect
394. #585C22×C31semidirect
397. #560C22×C31semidirect
403. D42C22×C31semidirect
414. #458C22×C31semidirect
417. B(4,𝔽2)C22×C31semidirect
418. B(4,𝔽2)C22×C31semidirect
420. #453C22×C31semidirect
422. #413C22×C31semidirect
425. #410C22×C31semidirect
426. #410C22×C31semidirect
427. #353C22×C31semidirect
428. #352C22×C31semidirect
429. AΣL(1,𝔽16)C22×C31semidirect
430. AΣL(1,𝔽16)C22×C31semidirect
455. C22×D4D4×C31semidirect
456. C22×D4D4×C31semidirect
457. C23×C4D4×C31semidirect
472. #124D4×C31semidirect
478. #123D4×C31semidirect
507. #120D4×C31semidirect
508. #120D4×C31semidirect
520. #117D4×C31semidirect
521. #117D4×C31semidirect
522. #117D4×C31semidirect
535. C31#33553direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35372
C31×#30272
C31×#30252
C31×#30212
C31×#22002
C31×#21962
C31×#21282
C31×#21222
C31×#21202
#3355331