Finite Group Databasebeta

← C31×#24363 #21481122

Subgroups — C31×#24363 #21481122

Order 7936.

1426 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C2×C31×#452C211yesmaximal, characteristic, complemented
5C31×#2432C211yesmaximal, characteristic, complemented
6C31×#2341C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2013C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1892C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1850C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×#135—24no—
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C22×Q16×C31C2211yescharacteristic
22C22×Q16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C23×C8×C31C2211yescharacteristic
28C2×C31×C4⋊Q8C2211yescharacteristic
29C2×C31×#124C2211yescharacteristic
30C2×C31×C22⋊Q8C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C31×#464—24no—
34C31×#462—24no—
35C31×#452—24no—
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#394—21no—
48C31×#394—21no—
49C31×#391C2211yescharacteristic
50C31×#390—21no—
51C31×#390—21no—
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic
54C31×#390C2211yescharacteristic
55C31×#385—21no—
56C31×#385—21no—
57C31×#380—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31D414yes—
77C22×Q8×C31C2311yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31C2311yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31C2311yescharacteristic
87C31×#135—232no—
88C2×Q16×C31—22no—
89C2×Q16×C31—22no—
90C2×Q16×C31—22no—
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31D414yes—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—41no—
101C2×SD16×C31—41no—
102C2×SD16×C31D414yes—
103C2×D8×C31—22no—
104C2×D8×C31—22no—
105C2×D8×C31—22no—
106C22×C8×C31—22no—
107C22×C8×C31—22no—
108C22×C8×C31—22no—
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C31×C4⋊Q8—22no—
114C31×C4⋊Q8—41no—
115C31×#124—22no—
116C31×#124—41no—
117C31×C22⋊Q8—22no—
118C31×C22⋊Q8—22no—
119C4×Q8×C31—22no—
120C4×Q8×C31—22no—
121C4×Q8×C31—41no—
122C4×Q8×C31—41no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31D411yescharacteristic
142C2×C22⋊C4×C31D411yescharacteristic
143C2×C42×C31—21no—
144C2×C42×C31—21no—
145C2×C42×C31C2311yescharacteristic
146C2×C42×C31C2311yescharacteristic
147C31×C4⋊C8—22no—
148C31×C4⋊C8—22no—
149C31×#103—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—41no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—41no—
157C31×C22⋊C8—22no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95D411yescharacteristic
162C31×#95D411yescharacteristic
163C24×C31—21no—
164C24×C31—21no—
165C24×C31C2×D411yescharacteristic
166#41×C31—28no—
167#41×C31—28no—
168#41×C31—44no—
169#41×C31—44no—
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31C2×D412yes—
189C2×Q8×C31C2×D412yes—
190C2×Q8×C31C2×D412yes—
191C2×Q8×C31C2×D412yes—
192C2×D4×C31—24no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31C2×D412yes—
209C2×D4×C31C2×D412yes—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—24no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31#4112yes—
233C22×C4×C31C2411yescharacteristic
234Q16×C31—28no—
235Q16×C31—44no—
236SD16×C31—28no—
237SD16×C31—28no—
238SD16×C31—44no—
239D8×C31—28no—
240C2×C8×C31—28no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31C2×D412yes—
252C2×C8×C31C2×D412yes—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—42no—
260C4⋊C4×C31—42no—
261C4⋊C4×C31—42no—
262C4⋊C4×C31—42no—
263C4⋊C4×C31—42no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—41no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—81no—
274C22⋊C4×C31—81no—
275C22⋊C4×C31—81no—
276C42×C31—21no—
277C42×C31—21no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31—42no—
281C42×C31—42no—
282#24363C3111yesmaximal, characteristic, direct product factor, Sylow
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31#12112yes—
304C23×C31C22×D411yescharacteristic
305Q8×C31—22no—
306Q8×C31—22no—
307Q8×C31—22no—
308Q8×C31—22no—
309Q8×C31—22no—
310Q8×C31—41no—
311Q8×C31—41no—
312Q8×C31—41no—
313Q8×C31—41no—
314Q8×C31—41no—
315Q8×C31—41no—
316Q8×C31#12014yes—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—22no—
320D4×C31—22no—
321D4×C31—48no—
322D4×C31—48no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31—41no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—22no—
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—48no—
349C2×C4×C31—48no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31#12112yes—
365C2×C4×C31#13512yescomplemented
366C2×C4×C31C22×D411yescharacteristic
367C2×C4×C31C22×D411yescharacteristic
368C2×C4×C31C22×D411yescharacteristic
369C2×C4×C31C2×#4111yescharacteristic
370C2×C4×C31H(5,𝔽2)11yescharacteristic
371C2×C4×C31H(5,𝔽2)11yescharacteristic
372C8×C31—22no—
373C8×C31—22no—
374C8×C31—41no—
375C8×C31—41no—
376C22×#135C2×C3111yescharacteristic
377C2×#464C2×C3111yescharacteristic, complemented
378C2×#462C2×C3111yescharacteristic, complemented
379C2×#452C2×C3111yescharacteristic, complemented
380#2432C2×C3111yescharacteristic, complemented
381#2341C2×C3111yescharacteristic, complemented
382#2055C2×C3111yescharacteristic, complemented
383#2054C2×C3111yescharacteristic, complemented
384#2013C2×C3111yescharacteristic, complemented
385#2012C2×C3111yescharacteristic, complemented
386#1892C2×C3111yescharacteristic, complemented
387#1880C2×C3111yescharacteristic, complemented
388#1878C2×C3111yescharacteristic, complemented
389#1850C2×C3111yescharacteristic, complemented
390#1788C2×C3111yescharacteristic, complemented
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—22no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31—81no—
408C22×C31—81no—
409C22×C31—81no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31C2×#12111yescharacteristic
413C22×C31D4211yescharacteristic
414C22×C31D4211yescharacteristic
415C22×C31C2×#13511yescharacteristic
416C22×C31#57511yescharacteristic
417C22×C31#57711yescharacteristic
418C22×C31#57811yescharacteristic
419C4×C31—22no—
420C4×C31—24no—
421C4×C31—22no—
422C4×C31—42no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31—41no—
426C4×C31—81no—
427C4×C31—81no—
428C4×C31—81no—
429C4×C31—81no—
430C4×C31C2×#12011yescharacteristic
431C4×C31#53411yescharacteristic
432C4×C31#54611yescharacteristic
433C4×C31#54611yescharacteristic
434C22×#41C22×C3111yescharacteristic
435C22×#41C22×C3111yescharacteristic
436C2×#135—24no—
437C2×#135—24no—
438C2×#135—24no—
439C22×Q16C22×C3111yescharacteristic
440C22×Q16C22×C3111yescharacteristic
441C22×SD16C22×C3111yescharacteristic
442C22×SD16C22×C3111yescharacteristic
443C22×SD16C22×C3111yescharacteristic
444C22×D8C22×C3111yescharacteristic
445C23×C8C22×C3111yescharacteristic
446C2×C4⋊Q8C22×C3111yescharacteristic
447C2×#124C22×C3111yescharacteristic
448C2×C22⋊Q8C22×C3111yescharacteristic
449C2×C4×Q8C22×C3111yescharacteristic
450C2×C4×Q8C22×C3111yescharacteristic
451#464—24no—
452#462—24no—
453#452—24no—
454C2×C4⋊C8C22×C3111yescharacteristic
455C2×C4⋊C8C22×C3111yescharacteristic
456C2×#103C22×C3111yescharacteristic
457C2×#103C22×C3111yescharacteristic
458C2×#103C22×C3111yescharacteristic
459C2×#103C22×C3111yescharacteristic
460C2×#103C22×C3111yescharacteristic
461C2×#102C22×C3111yescharacteristic
462C2×#102C22×C3111yescharacteristic
463C2×#102C22×C3111yescharacteristic
464C2×C22⋊C8C22×C3111yescharacteristic
465#394—21no—
466#394—21no—
467#391C22×C3111yescharacteristic
468#390—21no—
469#390—21no—
470#390C22×C3111yescharacteristic
471#390C22×C3111yescharacteristic
472#390C22×C3111yescharacteristic
473#385—21no—
474#385—21no—
475#380—21no—
476#380C22×C3111yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4C22×C3111yescharacteristic
479#340C22×C3111yescharacteristic
480#340C22×C3111yescharacteristic
481#336C22×C3111yescharacteristic
482#336C22×C3111yescharacteristic
483C2×C31—42no—
484C2×C31—82no—
485C2×C31—82no—
486C2×C31#241011yescharacteristic
487C2×C31#303511yescharacteristic
488C2×C31#304611yescharacteristic
489C2×C31#326911yescharacteristic
490C2×C31#327111yescharacteristic
491C2×C31#328411yescharacteristic
492C2×C31#328511yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41D4×C3114yes—
505C22×Q8C23×C3111yescharacteristic
506C22×Q8C23×C3111yescharacteristic
507C22×Q8C23×C3111yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4C23×C3111yescharacteristic
511C22×D4C23×C3111yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C23×C3111yescharacteristic
515#135—232no—
516C2×Q16—22no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16D4×C3114yes—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16D4×C3114yes—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8C23×C3111yescharacteristic
538C22×C8C23×C3111yescharacteristic
539C22×C8C23×C3111yescharacteristic
540C22×C8C23×C3111yescharacteristic
541C4⋊Q8—22no—
542C4⋊Q8—41no—
543#124—22no—
544#124—41no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—41no—
550C4×Q8—41no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4C23×C3111yescharacteristic
557C2×C4⋊C4C23×C3111yescharacteristic
558C2×C4⋊C4C23×C3111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4D4×C3111yescharacteristic
570C2×C22⋊C4D4×C3111yescharacteristic
571C2×C42—21no—
572C2×C42—21no—
573C2×C42C23×C3111yescharacteristic
574C2×C42C23×C3111yescharacteristic
575C4⋊C8—22no—
576C4⋊C8—22no—
577#103—22no—
578#103—22no—
579#103—22no—
580#103—22no—
581#103—41no—
582#102—22no—
583#102—22no—
584#102—41no—
585C22⋊C8—22no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95D4×C3111yescharacteristic
590#95D4×C3111yescharacteristic
591C31#2436311yescharacteristic, direct product factor, Sylow
592C24—21no—
593C24—21no—
594C24C2×D4×C3111yescharacteristic
595#41—28no—
596#41—28no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—44no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C2×D4×C3112yes—
618C2×Q8C2×D4×C3112yes—
619C2×Q8C2×D4×C3112yes—
620C2×Q8C2×D4×C3112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4C2×D4×C3112yes—
638C2×D4C2×D4×C3112yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4C2×D4×C3111yescharacteristic
656C22×C4C2×D4×C3111yescharacteristic
657C22×C4C2×D4×C3111yescharacteristic
658C22×C4C2×D4×C3111yescharacteristic
659C22×C4C2×D4×C3112yes—
660C22×C4C2×D4×C3111yescharacteristic
661C22×C4#41×C3112yes—
662C22×C4C24×C3111yescharacteristic
663Q16—28no—
664Q16—44no—
665SD16—28no—
666SD16—28no—
667SD16—44no—
668D8—28no—
669C2×C8—28no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8C2×D4×C3112yes—
681C2×C8C2×D4×C3112yes—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C22⋊C4—22no—
694C22⋊C4—41no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—42no—
710C42—42no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—22no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23C31×#12112yes—
732C23C22×D4×C3111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8C31×#12014yes—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—48no—
750D4—48no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—48no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4C31×#12112yes—
793C2×C4C31×#13512yescomplemented
794C2×C4C22×D4×C3111yescharacteristic
795C2×C4C22×D4×C3111yescharacteristic
796C2×C4C22×D4×C3111yescharacteristic
797C2×C4C2×#41×C3111yescharacteristic
798C2×C4C31×H(5,𝔽2)11yescharacteristic
799C2×C4C31×H(5,𝔽2)11yescharacteristic
800C8—22no—
801C8—22no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×C31×#12111yescharacteristic
826C22D42×C3111yescharacteristic
827C22D42×C3111yescharacteristic
828C22C2×C31×#13511yescharacteristic
829C22C31×#57511yescharacteristic
830C22C31×#57711yescharacteristic
831C22C31×#57811yescharacteristic
832C4—22no—
833C4—24no—
834C4—22no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4C2×C31×#12011yescharacteristic
844C4C31×#53411yescharacteristic
845C4C31×#54611yescharacteristic
846C4C31×#54611yescharacteristic
847C2—42no—
848C2—82no—
849C2—82no—
850C2C31×#241011yescharacteristic
851C2C31×#303511yescharacteristic
852C2C31×#304611yescharacteristic
853C2C31×#326911yescharacteristic
854C2C31×#327111yescharacteristic
855C2C31×#328411yescharacteristic
856C2C31×#328511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#135C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#464C2semidirect
3. C2×C31×#462C2semidirect
4. C2×C31×#452C2semidirect
5. C31×#2432C2semidirect
6. C31×#2341C2semidirect
7. C31×#2055C2semidirect
8. C31×#2054C2semidirect
9. C31×#2013C2semidirect
10. C31×#2012C2semidirect
11. C31×#1892C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1850C2semidirect
15. C31×#1788C2semidirect
282. #24363C31direct (N × H)
365. C2×C4×C31#135semidirect
377. C2×#464C2×C31semidirect
378. C2×#462C2×C31semidirect
379. C2×#452C2×C31semidirect
380. #2432C2×C31semidirect
381. #2341C2×C31semidirect
382. #2055C2×C31semidirect
383. #2054C2×C31semidirect
384. #2013C2×C31semidirect
385. #2012C2×C31semidirect
386. #1892C2×C31semidirect
387. #1880C2×C31semidirect
388. #1878C2×C31semidirect
389. #1850C2×C31semidirect
390. #1788C2×C31semidirect
591. C31#24363direct (N × H)
793. C2×C4C31×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1352
C2×C31×#4642
C2×C31×#4622
C2×C31×#4522
C31×#24322
C31×#23412
C31×#20552
C31×#20542
C31×#20132
C31×#20122
C31×#18922
C31×#18802
C31×#18782
C31×#18502
C31×#17882
#2436331