Finite Group Databasebeta

← C31×#24365 #21481124

Subgroups — C31×#24365 #21481124

Order 7936.

1454 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C2×C31×#452C211yesmaximal, characteristic, complemented
5C31×#2432C211yesmaximal, characteristic, complemented
6C31×#2339C211yesmaximal, characteristic, complemented
7C31×#2056C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2016C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1892C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, 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×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C31×#463—24no—
34C31×#461—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×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#386—21no—
54C31×#386—21no—
55C31×#385—21no—
56C31×#385—21no—
57C31×#381—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31C2211yescharacteristic
60C2×C31×#95—21no—
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×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C31×#135—232no—
90C2×Q16×C31—22no—
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31—22no—
94C2×Q16×C31—41no—
95C2×Q16×C31—41no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—22no—
104C2×SD16×C31D414yes—
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×D8×C31D414yes—
108C22×C8×C31—22no—
109C22×C8×C31—22no—
110C22×C8×C31—22no—
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C22×C8×C31C2311yescharacteristic
115C31×C4⋊Q8—22no—
116C31×C4⋊Q8—41no—
117C31×#124—22no—
118C31×#124—41no—
119C31×C22⋊Q8—22no—
120C31×C22⋊Q8—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C4×D4×C31—41no—
124C4×D4×C31—41no—
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×C31D411yescharacteristic
140C2×C22⋊C4×C31D411yescharacteristic
141C2×C42×C31C2311yescharacteristic
142C2×C42×C31C2311yescharacteristic
143C31×C4⋊C8—22no—
144C31×C4⋊C8—22no—
145C31×#103—22no—
146C31×#103—22no—
147C31×#103—22no—
148C31×#103—22no—
149C31×#103—41no—
150C31×#102—22no—
151C31×#102—22no—
152C31×#102—41no—
153C31×C22⋊C8—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
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×C31—21no—
189C2×Q8×C31—21no—
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—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31C2×D412yes—
207C2×D4×C31C2×D412yes—
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×C31—42no—
227C22×C4×C31—42no—
228C22×C4×C31—42no—
229C22×C4×C31—42no—
230C22×C4×C31—81no—
231C22×C4×C31—81no—
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D412yes—
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31#4112yes—
239C22×C4×C31C2411yescharacteristic
240Q16×C31—28no—
241Q16×C31—44no—
242SD16×C31—28no—
243SD16×C31—28no—
244SD16×C31—44no—
245D8×C31—28no—
246C2×C8×C31—28no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31C2×D412yes—
258C2×C8×C31C2×D412yes—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—42no—
266C4⋊C4×C31—42no—
267C4⋊C4×C31—42no—
268C22⋊C4×C31—22no—
269C22⋊C4×C31—41no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—42no—
274C22⋊C4×C31—42no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—42no—
277C22⋊C4×C31—81no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31—21no—
281C42×C31—21no—
282#24365C3111yesmaximal, characteristic, direct product factor, Sylow
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—22no—
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—41no—
310Q8×C31—41no—
311Q8×C31—41no—
312Q8×C31—41no—
313Q8×C31—41no—
314Q8×C31—41no—
315Q8×C31—41no—
316Q8×C31—41no—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—22no—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—48no—
323D4×C31—48no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31#12014yes—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—22no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—48no—
347C2×C4×C31—48no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
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—84no—
365C2×C4×C31—84no—
366C2×C4×C31#12112yes—
367C2×C4×C31#13512yescomplemented
368C2×C4×C31C22×D411yescharacteristic
369C2×C4×C31C22×D411yescharacteristic
370C2×C4×C31C22×D411yescharacteristic
371C2×C4×C31C2×#4111yescharacteristic
372C2×C4×C31H(5,𝔽2)11yescharacteristic
373C2×C4×C31H(5,𝔽2)11yescharacteristic
374C8×C31—22no—
375C8×C31—22no—
376C8×C31—41no—
377C8×C31—41no—
378C22×#135C2×C3111yescharacteristic
379C2×#463C2×C3111yescharacteristic, complemented
380C2×#461C2×C3111yescharacteristic, complemented
381C2×#452C2×C3111yescharacteristic, complemented
382#2432C2×C3111yescharacteristic, complemented
383#2339C2×C3111yescharacteristic, complemented
384#2056C2×C3111yescharacteristic, complemented
385#2055C2×C3111yescharacteristic, complemented
386#2016C2×C3111yescharacteristic, complemented
387#2015C2×C3111yescharacteristic, complemented
388#1892C2×C3111yescharacteristic, complemented
389#1879C2×C3111yescharacteristic, complemented
390#1877C2×C3111yescharacteristic, complemented
391#1850C2×C3111yescharacteristic, complemented
392#1788C2×C3111yescharacteristic, complemented
393C22×C31—22no—
394C22×C31—24no—
395C22×C31—22no—
396C22×C31—22no—
397C22×C31—42no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31—81no—
413C22×C31—81no—
414C22×C31C2×#12111yescharacteristic
415C22×C31D4211yescharacteristic
416C22×C31D4211yescharacteristic
417C22×C31C2×#13511yescharacteristic
418C22×C31#57511yescharacteristic
419C22×C31#57711yescharacteristic
420C22×C31#57811yescharacteristic
421C4×C31—22no—
422C4×C31—22no—
423C4×C31—42no—
424C4×C31—42no—
425C4×C31—41no—
426C4×C31—41no—
427C4×C31—41no—
428C4×C31—81no—
429C4×C31—81no—
430C4×C31—81no—
431C4×C31—81no—
432C4×C31C2×#12011yescharacteristic
433C4×C31#53411yescharacteristic
434C4×C31#54611yescharacteristic
435C4×C31#54611yescharacteristic
436C22×#41C22×C3111yescharacteristic
437C22×#41C22×C3111yescharacteristic
438C2×#135—24no—
439C2×#135—24no—
440C2×#135—24no—
441C22×Q16C22×C3111yescharacteristic
442C22×Q16C22×C3111yescharacteristic
443C22×SD16C22×C3111yescharacteristic
444C22×SD16C22×C3111yescharacteristic
445C22×SD16C22×C3111yescharacteristic
446C22×D8C22×C3111yescharacteristic
447C23×C8C22×C3111yescharacteristic
448C2×C4⋊Q8C22×C3111yescharacteristic
449C2×#124C22×C3111yescharacteristic
450C2×C22⋊Q8C22×C3111yescharacteristic
451C2×C4×D4C22×C3111yescharacteristic
452C2×C4×D4C22×C3111yescharacteristic
453#463—24no—
454#461—24no—
455#452—24no—
456C2×C4⋊C8C22×C3111yescharacteristic
457C2×C4⋊C8C22×C3111yescharacteristic
458C2×#103C22×C3111yescharacteristic
459C2×#103C22×C3111yescharacteristic
460C2×#103C22×C3111yescharacteristic
461C2×#103C22×C3111yescharacteristic
462C2×#103C22×C3111yescharacteristic
463C2×#102C22×C3111yescharacteristic
464C2×#102C22×C3111yescharacteristic
465C2×#102C22×C3111yescharacteristic
466C2×C22⋊C8C22×C3111yescharacteristic
467#394—21no—
468#394—21no—
469#391C22×C3111yescharacteristic
470#391C22×C3111yescharacteristic
471#391C22×C3111yescharacteristic
472#390C22×C3111yescharacteristic
473#386—21no—
474#386—21no—
475#385—21no—
476#385—21no—
477#381—21no—
478#380C22×C3111yescharacteristic
479C4×C22⋊C4C22×C3111yescharacteristic
480C2×#95—21no—
481#340C22×C3111yescharacteristic
482#340C22×C3111yescharacteristic
483#336C22×C3111yescharacteristic
484#336C22×C3111yescharacteristic
485C2×C31—42no—
486C2×C31—44no—
487C2×C31—82no—
488C2×C31#241011yescharacteristic
489C2×C31#303511yescharacteristic
490C2×C31#304611yescharacteristic
491C2×C31#326711yescharacteristic
492C2×C31#326911yescharacteristic
493C2×C31#328211yescharacteristic
494C2×C31#328311yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C3114yes—
507C22×Q8C23×C3111yescharacteristic
508C22×Q8C23×C3111yescharacteristic
509C22×Q8C23×C3111yescharacteristic
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C23×C3111yescharacteristic
513C22×D4C23×C3111yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C23×C3111yescharacteristic
519#135—232no—
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—22no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16D4×C3114yes—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8D4×C3114yes—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8C23×C3111yescharacteristic
542C22×C8C23×C3111yescharacteristic
543C22×C8C23×C3111yescharacteristic
544C22×C8C23×C3111yescharacteristic
545C4⋊Q8—22no—
546C4⋊Q8—41no—
547#124—22no—
548#124—41no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—41no—
554C4×D4—41no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4C23×C3111yescharacteristic
559C2×C4⋊C4C23×C3111yescharacteristic
560C2×C4⋊C4C23×C3111yescharacteristic
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×C42C23×C3111yescharacteristic
572C2×C42C23×C3111yescharacteristic
573C4⋊C8—22no—
574C4⋊C8—22no—
575#103—22no—
576#103—22no—
577#103—22no—
578#103—22no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583C22⋊C8—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95D4×C3111yescharacteristic
592#95D4×C3111yescharacteristic
593C31#2436511yescharacteristic, direct product factor, Sylow
594C24—21no—
595C24—21no—
596C24C2×D4×C3111yescharacteristic
597#41—28no—
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
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×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×D4×C3112yes—
622C2×Q8C2×D4×C3112yes—
623C2×D4—24no—
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—
639C2×D4C2×D4×C3112yes—
640C2×D4C2×D4×C3112yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C3111yescharacteristic
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4C2×D4×C3111yescharacteristic
666C22×C4C2×D4×C3111yescharacteristic
667C22×C4C2×D4×C3112yes—
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4#41×C3112yes—
670C22×C4C24×C3111yescharacteristic
671Q16—28no—
672Q16—44no—
673SD16—28no—
674SD16—28no—
675SD16—44no—
676D8—28no—
677C2×C8—28no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8C2×D4×C3112yes—
689C2×C8C2×D4×C3112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C22⋊C4—22no—
700C22⋊C4—41no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—81no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23C31×#12112yes—
734C23C22×D4×C3111yescharacteristic
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—48no—
753D4—48no—
754D4—41no—
755D4—41no—
756D4C31×#12014yes—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
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×C4—41no—
793C2×C4—41no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4C31×#12112yes—
797C2×C4C31×#13512yescomplemented
798C2×C4C22×D4×C3111yescharacteristic
799C2×C4C22×D4×C3111yescharacteristic
800C2×C4C22×D4×C3111yescharacteristic
801C2×C4C2×#41×C3111yescharacteristic
802C2×C4C31×H(5,𝔽2)11yescharacteristic
803C2×C4C31×H(5,𝔽2)11yescharacteristic
804C8—22no—
805C8—22no—
806C8—41no—
807C8—41no—
808C22—22no—
809C22—24no—
810C22—22no—
811C22—22no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22C2×C31×#12111yescharacteristic
830C22D42×C3111yescharacteristic
831C22D42×C3111yescharacteristic
832C22C2×C31×#13511yescharacteristic
833C22C31×#57511yescharacteristic
834C22C31×#57711yescharacteristic
835C22C31×#57811yescharacteristic
836C4—22no—
837C4—22no—
838C4—42no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4C2×C31×#12011yescharacteristic
848C4C31×#53411yescharacteristic
849C4C31×#54611yescharacteristic
850C4C31×#54611yescharacteristic
851C2—42no—
852C2—44no—
853C2—82no—
854C2C31×#241011yescharacteristic
855C2C31×#303511yescharacteristic
856C2C31×#304611yescharacteristic
857C2C31×#326711yescharacteristic
858C2C31×#326911yescharacteristic
859C2C31×#328211yescharacteristic
860C2C31×#328311yescharacteristic
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×#463C2semidirect
3. C2×C31×#461C2semidirect
4. C2×C31×#452C2semidirect
5. C31×#2432C2semidirect
6. C31×#2339C2semidirect
7. C31×#2056C2semidirect
8. C31×#2055C2semidirect
9. C31×#2016C2semidirect
10. C31×#2015C2semidirect
11. C31×#1892C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1850C2semidirect
15. C31×#1788C2semidirect
282. #24365C31direct (N × H)
367. C2×C4×C31#135semidirect
379. C2×#463C2×C31semidirect
380. C2×#461C2×C31semidirect
381. C2×#452C2×C31semidirect
382. #2432C2×C31semidirect
383. #2339C2×C31semidirect
384. #2056C2×C31semidirect
385. #2055C2×C31semidirect
386. #2016C2×C31semidirect
387. #2015C2×C31semidirect
388. #1892C2×C31semidirect
389. #1879C2×C31semidirect
390. #1877C2×C31semidirect
391. #1850C2×C31semidirect
392. #1788C2×C31semidirect
593. C31#24365direct (N × H)
797. 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×#4632
C2×C31×#4612
C2×C31×#4522
C31×#24322
C31×#23392
C31×#20562
C31×#20552
C31×#20162
C31×#20152
C31×#18922
C31×#18792
C31×#18772
C31×#18502
C31×#17882
#2436531