Finite Group Databasebeta

← C31×#33551 #21490310

Subgroups — C31×#33551 #21490310

Order 7936.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3532C211yesmaximal, characteristic, complemented
2C31×#3026C211yesmaximal, characteristic, complemented
3C2×C31×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C31×#3019C211yesmaximal, characteristic, complemented
5C31×#2200C212yesmaximal, complemented
6C31×#2199C212yesmaximal, complemented
7C31×#2197C212yesmaximal, complemented
8C31×#2196C212yesmaximal, complemented
9C31×#2127C211yesmaximal, characteristic, complemented
10C31×#2121C211yesmaximal, characteristic, complemented
11C2×C31×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
12C2×C31×H(5,𝔽2)C2211yescharacteristic, complemented
13C31×#575—21no—
14C31×H(3,𝔽4)C2211yescharacteristic, complemented
15C31×#560—21no—
16C31×#560C2211yescharacteristic, complemented
17C31×#551—21no—
18C31×#551C2211yescharacteristic, complemented
19C31×#546—21no—
20C31×#546—21no—
21C31×#546—21no—
22D42×C31—21no—
23D42×C31C2211yescharacteristic, complemented
24C31×#538—21no—
25C31×#538—21no—
26C31×#538—21no—
27C31×#535—21no—
28C31×#535C2211yescharacteristic
29C31×#534—21no—
30C31×#534—21no—
31C31×#534C2211yescharacteristic
32C2×C31×#120—21no—
33C2×C31×#120—21no—
34C2×C31×#120C2211yescharacteristic
35C31×#458—21no—
36C31×#458C2212yescomplemented
37C31×B(4,𝔽2)—21no—
38C31×B(4,𝔽2)—21no—
39C31×B(4,𝔽2)—21no—
40C31×B(4,𝔽2)C2212yes—
41C31×B(4,𝔽2)C2212yescomplemented
42C31×B(4,𝔽2)C2212yescomplemented
43C31×#455—21no—
44C31×#455C2212yescomplemented
45C31×#453—21no—
46C31×#453C2212yescomplemented
47C31×#421—21no—
48C2×C31×#100C2211yescharacteristic, complemented
49C2×C31×#99—21no—
50C2×C31×#99—21no—
51C2×C31×#99C2211yescharacteristic, complemented
52C2×C31×#99C2211yescharacteristic, complemented
53C31×#354C2212yescomplemented
54C31×#353C2212yescomplemented
55C31×#352C2212yescomplemented
56C31×AΣL(1,𝔽16)C2212yescomplemented
57C31×AΣL(1,𝔽16)C2212yescomplemented
58C31×AΣL(1,𝔽16)C2212yescomplemented
59C25×C31D411yescharacteristic, complemented
60C31×H(5,𝔽2)—21no—
61C31×H(5,𝔽2)—21no—
62C31×H(5,𝔽2)—21no—
63C31×H(5,𝔽2)—42no—
64C31×H(5,𝔽2)C2312yes—
65C2×#41×C31—21no—
66C2×#41×C31—21no—
67C2×#41×C31—41no—
68C2×#41×C31D411yescharacteristic, complemented
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31D411yescharacteristic, complemented
79C22×D4×C31C2311yescharacteristic
80C31×#137—22no—
81C31×#137—41no—
82C31×AGL(1,ℤ/8)—22no—
83C31×AGL(1,ℤ/8)—41no—
84C31×#135—42no—
85C2×M16×C31—21no—
86C31×#127—21no—
87C31×#127D411yescharacteristic, complemented
88C31×#127C2311yescharacteristic
89C31×#126—21no—
90C31×#126—21no—
91C31×#126—21no—
92C31×#126—21no—
93C31×#124—21no—
94C31×#124—21no—
95C31×#124—21no—
96C31×#124—21no—
97C31×#124—21no—
98C31×#124D411yescharacteristic, complemented
99C31×#124C2311yescharacteristic
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—22no—
109C31×#123—41no—
110C31×#123D411yescharacteristic, complemented
111C31×#123C2311yescharacteristic
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121—42no—
131C31×#120—21no—
132C31×#120—21no—
133C31×#120—21no—
134C31×#120—21no—
135C31×#120—21no—
136C31×#120—21no—
137C31×#120—21no—
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C31×#120—21no—
144C31×#120—21no—
145C31×#120—22no—
146C31×#120—22no—
147C31×#120—22no—
148C31×#120—42no—
149C31×#120—41no—
150C31×#120D411yescharacteristic, complemented
151C31×#120D411yescharacteristic, complemented
152C31×#120D411yescharacteristic, complemented
153C31×#120C2311yescharacteristic
154C31×#120C2311yescharacteristic
155C31×#120C2311yescharacteristic
156C4×D4×C31—21no—
157C4×D4×C31—21no—
158C4×D4×C31—21no—
159C4×D4×C31—21no—
160C4×D4×C31—21no—
161C4×D4×C31—21no—
162C31×#117—21no—
163C31×#117D411yescharacteristic, complemented
164C2×C22⋊C4×C31—21no—
165C2×C22⋊C4×C31—21no—
166C2×C22⋊C4×C31—21no—
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, complemented
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×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—41no—
192C24×C31—41no—
193C24×C31—82no—
194C24×C31C2×D411yescharacteristic
195C24×C31C2×D411yescharacteristic
196C24×C31C2×D411yescharacteristic
197C24×C31C2×D411yescharacteristic
198C24×C31C2×D411yescharacteristic, complemented
199#41×C31—22no—
200#41×C31—22no—
201#41×C31—42no—
202#41×C31—41no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—41no—
206#41×C31—41no—
207#41×C31—42no—
208#41×C31—41no—
209#41×C31—82no—
210C2×Q8×C31—21no—
211C2×Q8×C31—21no—
212C2×Q8×C31C2×D411yescharacteristic, complemented
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31—22no—
217C2×D4×C31—22no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—22no—
222C2×D4×C31—22no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—41no—
239C2×D4×C31—41no—
240C2×D4×C31—42no—
241C2×D4×C31—42no—
242C2×D4×C31—41no—
243C2×D4×C31—41no—
244C2×D4×C31—41no—
245C2×D4×C31—41no—
246C2×D4×C31—42no—
247C2×D4×C31—42no—
248C2×D4×C31—41no—
249C2×D4×C31—41no—
250C2×D4×C31—41no—
251C2×D4×C31—41no—
252C2×D4×C31—41no—
253C2×D4×C31—42no—
254C2×D4×C31—42no—
255C2×D4×C31—42no—
256C2×D4×C31—82no—
257C2×D4×C31—82no—
258C2×D4×C31—82no—
259C2×D4×C31—82no—
260C2×D4×C31—81no—
261C2×D4×C31—81no—
262C2×D4×C31—84no—
263C2×D4×C31C2×D411yescharacteristic
264C2×D4×C31C2×D411yescharacteristic
265C2×D4×C31C2×D411yescharacteristic
266C2×D4×C31C2×D411yescharacteristic, complemented
267C2×D4×C31C2411yescharacteristic
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—41no—
279C22×C4×C31—41no—
280C22×C4×C31—41no—
281C22×C4×C31C2×D411yescharacteristic
282C22×C4×C31C2×D411yescharacteristic, complemented
283Q16×C31—42no—
284SD16×C31—42no—
285SD16×C31—42no—
286D8×C31—42no—
287M16×C31—22no—
288M16×C31—41no—
289C2×C8×C31—41no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—42no—
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—21no—
317C22⋊C4×C31—21no—
318C22⋊C4×C31—21no—
319C22⋊C4×C31—21no—
320C22⋊C4×C31—21no—
321C22⋊C4×C31—21no—
322C22⋊C4×C31—21no—
323C22⋊C4×C31—21no—
324C22⋊C4×C31—21no—
325C22⋊C4×C31—22no—
326C22⋊C4×C31—22no—
327C22⋊C4×C31—42no—
328C22⋊C4×C31—42no—
329C22⋊C4×C31—42no—
330C22⋊C4×C31—41no—
331C22⋊C4×C31—41no—
332C22⋊C4×C31—42no—
333C22⋊C4×C31C2×D411yescharacteristic
334C22⋊C4×C31C2×D411yescharacteristic
335C22⋊C4×C31C2×D411yescharacteristic, complemented
336C22⋊C4×C31C2×D411yescharacteristic, complemented
337C42×C31—21no—
338C42×C31—21no—
339C42×C31C2×D411yescharacteristic, complemented
340C42×C31C2×D411yescharacteristic, complemented
341#33551C3111yesmaximal, characteristic, direct product factor, Sylow
342C23×C31—21no—
343C23×C31—21no—
344C23×C31—21no—
345C23×C31—21no—
346C23×C31—21no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—21no—
350C23×C31—21no—
351C23×C31—21no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—42no—
355C23×C31—42no—
356C23×C31—42no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—42no—
360C23×C31—41no—
361C23×C31—44no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—81no—
366C23×C31—81no—
367C23×C31—81no—
368C23×C31—81no—
369C23×C31—81no—
370C23×C31—81no—
371C23×C31—81no—
372C23×C31—81no—
373C23×C31—81no—
374C23×C31—82no—
375C23×C31—82no—
376C23×C31—82no—
377C23×C31—82no—
378C23×C31—161no—
379C23×C31#12011yescharacteristic
380C23×C31#12011yescharacteristic
381C23×C31#12011yescharacteristic
382C23×C31C22×D411yescharacteristic
383C23×C31C22×D411yescharacteristic
384Q8×C31—22no—
385Q8×C31—41no—
386Q8×C31—41no—
387Q8×C31—81no—
388D4×C31—22no—
389D4×C31—41no—
390D4×C31—41no—
391D4×C31—41no—
392D4×C31—41no—
393D4×C31—41no—
394D4×C31—41no—
395D4×C31—42no—
396D4×C31—42no—
397D4×C31—42no—
398D4×C31—42no—
399D4×C31—42no—
400D4×C31—42no—
401D4×C31—42no—
402D4×C31—42no—
403D4×C31—42no—
404D4×C31—42no—
405D4×C31—41no—
406D4×C31—41no—
407D4×C31—41no—
408D4×C31—41no—
409D4×C31—81no—
410D4×C31—81no—
411D4×C31—81no—
412D4×C31—81no—
413D4×C31—81no—
414D4×C31—81no—
415D4×C31—81no—
416D4×C31—81no—
417D4×C31—81no—
418D4×C31—81no—
419D4×C31—81no—
420D4×C31—81no—
421D4×C31—81no—
422D4×C31—81no—
423D4×C31—84no—
424D4×C31—84no—
425D4×C31—162no—
426C2×C4×C31—21no—
427C2×C4×C31—21no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—21no—
431C2×C4×C31—21no—
432C2×C4×C31—21no—
433C2×C4×C31—21no—
434C2×C4×C31—21no—
435C2×C4×C31—21no—
436C2×C4×C31—21no—
437C2×C4×C31—21no—
438C2×C4×C31—42no—
439C2×C4×C31—42no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—42no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—42no—
446C2×C4×C31—42no—
447C2×C4×C31—81no—
448C2×C4×C31—81no—
449C2×C4×C31—81no—
450C2×C4×C31—81no—
451C2×C4×C31—81no—
452C2×C4×C31—81no—
453C2×C4×C31—81no—
454C2×C4×C31—82no—
455C2×C4×C31—161no—
456C2×C4×C31#12011yescharacteristic
457C2×C4×C31C22×D411yescharacteristic
458C8×C31—42no—
459#3532C2×C3111yescharacteristic, complemented
460#3026C2×C3111yescharacteristic, complemented
461C2×B(4,𝔽2)C2×C3111yescharacteristic, complemented
462#3019C2×C3111yescharacteristic, complemented
463#2200C2×C3112yescomplemented
464#2199C2×C3112yescomplemented
465#2197C2×C3112yescomplemented
466#2196C2×C3112yescomplemented
467#2127C2×C3111yescharacteristic, complemented
468#2121C2×C3111yescharacteristic, complemented
469C2×AΣL(1,𝔽16)C2×C3111yescharacteristic, complemented
470C22×C31—22no—
471C22×C31—21no—
472C22×C31—21no—
473C22×C31—21no—
474C22×C31—21no—
475C22×C31—41no—
476C22×C31—41no—
477C22×C31—41no—
478C22×C31—41no—
479C22×C31—41no—
480C22×C31—41no—
481C22×C31—42no—
482C22×C31—41no—
483C22×C31—41no—
484C22×C31—41no—
485C22×C31—41no—
486C22×C31—41no—
487C22×C31—41no—
488C22×C31—42no—
489C22×C31—41no—
490C22×C31—42no—
491C22×C31—42no—
492C22×C31—41no—
493C22×C31—41no—
494C22×C31—41no—
495C22×C31—81no—
496C22×C31—81no—
497C22×C31—81no—
498C22×C31—82no—
499C22×C31—82no—
500C22×C31—82no—
501C22×C31—81no—
502C22×C31—84no—
503C22×C31—82no—
504C22×C31—82no—
505C22×C31—82no—
506C22×C31—81no—
507C22×C31—162no—
508C22×C31—161no—
509C22×C31—161no—
510C22×C31B(4,𝔽2)11yescharacteristic
511C22×C31B(4,𝔽2)11yescharacteristic
512C22×C31C2×#12011yescharacteristic
513C4×C31—21no—
514C4×C31—21no—
515C4×C31—41no—
516C4×C31—41no—
517C4×C31—41no—
518C4×C31—41no—
519C4×C31—41no—
520C4×C31—41no—
521C4×C31—42no—
522C4×C31—41no—
523C4×C31—41no—
524C4×C31—82no—
525C4×C31—82no—
526C2×H(5,𝔽2)C22×C3111yescharacteristic, complemented
527#575—21no—
528H(3,𝔽4)C22×C3111yescharacteristic, complemented
529#560—21no—
530#560C22×C3111yescharacteristic, complemented
531#551—21no—
532#551C22×C3111yescharacteristic, complemented
533#546—21no—
534#546—21no—
535#546—21no—
536D42—21no—
537D42C22×C3111yescharacteristic, complemented
538#538—21no—
539#538—21no—
540#538—21no—
541#535—21no—
542#535C22×C3111yescharacteristic
543#534—21no—
544#534—21no—
545#534C22×C3111yescharacteristic
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C3111yescharacteristic
549#458—21no—
550#458C22×C3112yescomplemented
551B(4,𝔽2)—21no—
552B(4,𝔽2)—21no—
553B(4,𝔽2)—21no—
554B(4,𝔽2)C22×C3112yes—
555B(4,𝔽2)C22×C3112yescomplemented
556B(4,𝔽2)C22×C3112yescomplemented
557#455—21no—
558#455C22×C3112yescomplemented
559#453—21no—
560#453C22×C3112yescomplemented
561#421—21no—
562C2×#100C22×C3111yescharacteristic, complemented
563C2×#99—21no—
564C2×#99—21no—
565C2×#99C22×C3111yescharacteristic, complemented
566C2×#99C22×C3111yescharacteristic, complemented
567#354C22×C3112yescomplemented
568#353C22×C3112yescomplemented
569#352C22×C3112yescomplemented
570AΣL(1,𝔽16)C22×C3112yescomplemented
571AΣL(1,𝔽16)C22×C3112yescomplemented
572AΣL(1,𝔽16)C22×C3112yescomplemented
573C2×C31—21no—
574C2×C31—21no—
575C2×C31—21no—
576C2×C31—41no—
577C2×C31—41no—
578C2×C31—42no—
579C2×C31—41no—
580C2×C31—41no—
581C2×C31—81no—
582C2×C31—81no—
583C2×C31—81no—
584C2×C31—82no—
585C2×C31C2×B(4,𝔽2)11yescharacteristic
586C25D4×C3111yescharacteristic, complemented
587H(5,𝔽2)—21no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—42no—
591H(5,𝔽2)C23×C3112yes—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—41no—
595C2×#41D4×C3111yescharacteristic, complemented
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4D4×C3111yescharacteristic, complemented
606C22×D4C23×C3111yescharacteristic
607#137—22no—
608#137—41no—
609AGL(1,ℤ/8)—22no—
610AGL(1,ℤ/8)—41no—
611#135—42no—
612C2×M16—21no—
613#127—21no—
614#127D4×C3111yescharacteristic, complemented
615#127C23×C3111yescharacteristic
616#126—21no—
617#126—21no—
618#126—21no—
619#126—21no—
620#124—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124D4×C3111yescharacteristic, complemented
626#124C23×C3111yescharacteristic
627#123—21no—
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—22no—
636#123—41no—
637#123D4×C3111yescharacteristic, complemented
638#123C23×C3111yescharacteristic
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—42no—
658#120—21no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—22no—
673#120—22no—
674#120—22no—
675#120—42no—
676#120—41no—
677#120D4×C3111yescharacteristic, complemented
678#120D4×C3111yescharacteristic, complemented
679#120D4×C3111yescharacteristic, complemented
680#120C23×C3111yescharacteristic
681#120C23×C3111yescharacteristic
682#120C23×C3111yescharacteristic
683C4×D4—21no—
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689#117—21no—
690#117D4×C3111yescharacteristic, complemented
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4D4×C3111yescharacteristic, complemented
700C2×C22⋊C4D4×C3111yescharacteristic, complemented
701#104—22no—
702#104—22no—
703#100—21no—
704#100C23×C3112yes—
705#99—21no—
706#99—21no—
707#99—22no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99C23×C3112yes—
712#99C23×C3112yes—
713C31#3355111yescharacteristic, direct product factor, Sylow
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C3111yescharacteristic
723C24C2×D4×C3111yescharacteristic
724C24C2×D4×C3111yescharacteristic
725C24C2×D4×C3111yescharacteristic
726C24C2×D4×C3111yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C3111yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C3111yescharacteristic
792C2×D4C2×D4×C3111yescharacteristic
793C2×D4C2×D4×C3111yescharacteristic
794C2×D4C2×D4×C3111yescharacteristic, complemented
795C2×D4C24×C3111yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C3111yescharacteristic
810C22×C4C2×D4×C3111yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C3111yescharacteristic
862C22⋊C4C2×D4×C3111yescharacteristic
863C22⋊C4C2×D4×C3111yescharacteristic, complemented
864C22⋊C4C2×D4×C3111yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C3111yescharacteristic, complemented
868C42C2×D4×C3111yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23C31×#12011yescharacteristic
907C23C31×#12011yescharacteristic
908C23C31×#12011yescharacteristic
909C23C22×D4×C3111yescharacteristic
910C23C22×D4×C3111yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4C31×#12011yescharacteristic
984C2×C4C22×D4×C3111yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22C31×B(4,𝔽2)11yescharacteristic
1027C22C31×B(4,𝔽2)11yescharacteristic
1028C22C2×C31×#12011yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×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×#3532C2semidirect
2. C31×#3026C2semidirect
3. C2×C31×B(4,𝔽2)C2semidirect
4. C31×#3019C2semidirect
5. C31×#2200C2semidirect
6. C31×#2199C2semidirect
7. C31×#2197C2semidirect
8. C31×#2196C2semidirect
9. C31×#2127C2semidirect
10. C31×#2121C2semidirect
11. C2×C31×AΣL(1,𝔽16)C2semidirect
12. C2×C31×H(5,𝔽2)C22semidirect
14. C31×H(3,𝔽4)C22semidirect
16. C31×#560C22semidirect
18. C31×#551C22semidirect
23. D42×C31C22semidirect
36. C31×#458C22semidirect
41. C31×B(4,𝔽2)C22semidirect
42. C31×B(4,𝔽2)C22semidirect
44. C31×#455C22semidirect
46. C31×#453C22semidirect
48. C2×C31×#100C22semidirect
51. C2×C31×#99C22semidirect
52. C2×C31×#99C22semidirect
53. C31×#354C22semidirect
54. C31×#353C22semidirect
55. C31×#352C22semidirect
56. C31×AΣL(1,𝔽16)C22semidirect
57. C31×AΣL(1,𝔽16)C22semidirect
58. C31×AΣL(1,𝔽16)C22semidirect
59. C25×C31D4semidirect
68. C2×#41×C31D4semidirect
78. C22×D4×C31D4semidirect
87. C31×#127D4semidirect
98. C31×#124D4semidirect
110. C31×#123D4semidirect
150. C31×#120D4semidirect
151. C31×#120D4semidirect
152. C31×#120D4semidirect
163. C31×#117D4semidirect
172. C2×C22⋊C4×C31D4semidirect
173. C2×C22⋊C4×C31D4semidirect
198. C24×C31C2×D4semidirect
212. C2×Q8×C31C2×D4semidirect
266. C2×D4×C31C2×D4semidirect
282. C22×C4×C31C2×D4semidirect
335. C22⋊C4×C31C2×D4semidirect
336. C22⋊C4×C31C2×D4semidirect
339. C42×C31C2×D4semidirect
340. C42×C31C2×D4semidirect
341. #33551C31direct (N × H)
459. #3532C2×C31semidirect
460. #3026C2×C31semidirect
461. C2×B(4,𝔽2)C2×C31semidirect
462. #3019C2×C31semidirect
463. #2200C2×C31semidirect
464. #2199C2×C31semidirect
465. #2197C2×C31semidirect
466. #2196C2×C31semidirect
467. #2127C2×C31semidirect
468. #2121C2×C31semidirect
469. C2×AΣL(1,𝔽16)C2×C31semidirect
526. C2×H(5,𝔽2)C22×C31semidirect
528. H(3,𝔽4)C22×C31semidirect
530. #560C22×C31semidirect
532. #551C22×C31semidirect
537. D42C22×C31semidirect
550. #458C22×C31semidirect
555. B(4,𝔽2)C22×C31semidirect
556. B(4,𝔽2)C22×C31semidirect
558. #455C22×C31semidirect
560. #453C22×C31semidirect
562. C2×#100C22×C31semidirect
565. C2×#99C22×C31semidirect
566. C2×#99C22×C31semidirect
567. #354C22×C31semidirect
568. #353C22×C31semidirect
569. #352C22×C31semidirect
570. AΣL(1,𝔽16)C22×C31semidirect
571. AΣL(1,𝔽16)C22×C31semidirect
572. AΣL(1,𝔽16)C22×C31semidirect
586. C25D4×C31semidirect
595. C2×#41D4×C31semidirect
605. C22×D4D4×C31semidirect
614. #127D4×C31semidirect
625. #124D4×C31semidirect
637. #123D4×C31semidirect
677. #120D4×C31semidirect
678. #120D4×C31semidirect
679. #120D4×C31semidirect
690. #117D4×C31semidirect
699. C2×C22⋊C4D4×C31semidirect
700. C2×C22⋊C4D4×C31semidirect
713. C31#33551direct (N × H)
726. C24C2×D4×C31semidirect
740. C2×Q8C2×D4×C31semidirect
794. C2×D4C2×D4×C31semidirect
810. C22×C4C2×D4×C31semidirect
863. C22⋊C4C2×D4×C31semidirect
864. C22⋊C4C2×D4×C31semidirect
867. C42C2×D4×C31semidirect
868. C42C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35322
C31×#30262
C2×C31×B(4,𝔽2)2
C31×#30192
C31×#22002
C31×#21992
C31×#21972
C31×#21962
C31×#21272
C31×#21212
C2×C31×AΣL(1,𝔽16)2
#3355131