Finite Group Databasebeta

← C31×#26984 #21483743

Subgroups — C31×#26984 #21483743

Order 7936.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#469C211yesmaximal, characteristic, complemented
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C31×#2428C211yesmaximal, characteristic, complemented
4C31×#2422C211yesmaximal, characteristic, complemented
5C31×#2084C211yesmaximal, characteristic, complemented
6C31×#2034C211yesmaximal, characteristic, complemented
7C31×#2011C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1957C211yesmaximal, characteristic, complemented
10C31×#1936C211yesmaximal, characteristic, complemented
11C31×#1934C211yesmaximal, characteristic, complemented
12C31×#1895C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C31×#123—21no—
21C2×C31×#121—21no—
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C31×#469—24no—
28C31×#442—24no—
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#397—21no—
43C31×#394—21no—
44C31×#394—21no—
45C31×#392—21no—
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#386—21no—
51C31×#385—21no—
52C31×#384C2211yescharacteristic
53C31×#380C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31C2311yescharacteristic
72C2×D8×C31—22no—
73C2×D8×C31—22no—
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—41no—
78C2×M16×C31—22no—
79C2×M16×C31—22no—
80C2×M16×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#127—22no—
86C31×#127—41no—
87C31×#123—44no—
88C31×#121—22no—
89C31×#121—22no—
90C31×#121—22no—
91C31×#121—44no—
92C31×#121—41no—
93C31×#121—41no—
94C31×#121—41no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C2×C42×C31C2311yescharacteristic
122C31×#106—22no—
123C31×#106—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—41no—
129C31×#102—41no—
130C31×#102—41no—
131C31×#102D414yescomplemented
132C31×C22⋊C8—22no—
133C31×#97—22no—
134C4×C8×C31—41no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95D411yescharacteristic
139C31×#95D411yescharacteristic
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31C2×D411yescharacteristic
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—42no—
161C2×D4×C31—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—81no—
171C2×D4×C31—81no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31C2×D412yes—
176C2×D4×C31#4112yes—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2411yescharacteristic
200D8×C31—28no—
201D8×C31—44no—
202M16×C31—44no—
203C2×C8×C31—21no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31C2×D412yes—
213C2×C8×C31#4112yes—
214C2×C8×C31#4112yes—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31—81no—
228C4⋊C4×C31C2×D412yes—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—81no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245#26984C3111yesmaximal, characteristic, direct product factor, Sylow
246C23×C31—21no—
247C23×C31—22no—
248C23×C31—21no—
249C23×C31—22no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31C22×D411yescharacteristic
275D4×C31—22no—
276D4×C31—22no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—41no—
280D4×C31—41no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—84no—
288D4×C31—84no—
289D4×C31—84no—
290D4×C31—84no—
291D4×C31—84no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—84no—
325C2×C4×C31—84no—
326C2×C4×C31AGL(1,ℤ/8)12yes—
327C2×C4×C31AGL(1,ℤ/8)12yes—
328C2×C4×C31C22×D411yescharacteristic
329C2×C4×C31C2×#4111yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31H(5,𝔽2)11yescharacteristic
333C2×C4×C31H(5,𝔽2)11yescharacteristic
334C8×C31—22no—
335C8×C31—22no—
336C8×C31—22no—
337C8×C31—41no—
338C2×#469C2×C3111yescharacteristic, complemented
339C2×#442C2×C3111yescharacteristic, complemented
340#2428C2×C3111yescharacteristic, complemented
341#2422C2×C3111yescharacteristic, complemented
342#2084C2×C3111yescharacteristic, complemented
343#2034C2×C3111yescharacteristic, complemented
344#2011C2×C3111yescharacteristic, complemented
345#1999C2×C3111yescharacteristic, complemented
346#1957C2×C3111yescharacteristic, complemented
347#1936C2×C3111yescharacteristic, complemented
348#1934C2×C3111yescharacteristic, complemented
349#1895C2×C3111yescharacteristic, complemented
350#1879C2×C3111yescharacteristic, complemented
351#1864C2×C3111yescharacteristic, complemented
352#1753C2×C3111yescharacteristic, complemented
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—41no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—42no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—81no—
377C22×C31—81no—
378C22×C31—81no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31#53211yescharacteristic
382C22×C31D4211yescharacteristic
383C22×C31#54611yescharacteristic
384C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C31#57611yescharacteristic
387C22×C31#57711yescharacteristic
388C4×C31—22no—
389C4×C31—22no—
390C4×C31—41no—
391C4×C31—41no—
392C4×C31—42no—
393C4×C31—41no—
394C4×C31—81no—
395C4×C31—81no—
396C4×C31—81no—
397C4×C31—81no—
398C4×C31#52511yescharacteristic
399C4×C31#54011yescharacteristic
400C4×C31#54611yescharacteristic
401C4×C31#55311yescharacteristic
402C22×D8C22×C3111yescharacteristic
403C22×D8C22×C3111yescharacteristic
404C22×M16C22×C3111yescharacteristic
405C2×#127C22×C3111yescharacteristic
406C2×#123—21no—
407C2×#121—21no—
408C2×#121C22×C3111yescharacteristic
409C2×#121C22×C3111yescharacteristic
410C2×#121C22×C3111yescharacteristic
411C2×C4×D4C22×C3111yescharacteristic
412C2×C4×D4C22×C3111yescharacteristic
413#469—24no—
414#442—24no—
415C2×#106C22×C3111yescharacteristic
416C2×#106C22×C3111yescharacteristic
417C2×#102C22×C3111yescharacteristic
418C2×#102C22×C3111yescharacteristic
419C2×#102C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×C22⋊C8C22×C3111yescharacteristic
426C2×#97C22×C3111yescharacteristic
427C2×C4×C8C22×C3111yescharacteristic
428#397—21no—
429#394—21no—
430#394—21no—
431#392—21no—
432#390C22×C3111yescharacteristic
433#390C22×C3111yescharacteristic
434#389C22×C3111yescharacteristic
435#389C22×C3111yescharacteristic
436#386—21no—
437#385—21no—
438#384C22×C3111yescharacteristic
439#380C22×C3111yescharacteristic
440C4×C22⋊C4C22×C3111yescharacteristic
441#340C22×C3111yescharacteristic
442#340C22×C3111yescharacteristic
443#340C22×C3111yescharacteristic
444#340C22×C3111yescharacteristic
445#336C22×C3111yescharacteristic
446#336C22×C3111yescharacteristic
447C2×C31—81no—
448C2×C31—82no—
449C2×C31—82no—
450C2×C31—161no—
451C2×C31#246411yescharacteristic
452C2×C31#317911yescharacteristic
453C2×C31#318411yescharacteristic
454C2×C31#327211yescharacteristic
455C2×C31#327411yescharacteristic
456C2×C31#330611yescharacteristic
457C2×C31#331811yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C3111yescharacteristic
464C22×D4C23×C3111yescharacteristic
465C22×D4C23×C3111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4C23×C3111yescharacteristic
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—41no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—41no—
478C22×C8C23×C3111yescharacteristic
479C22×C8C23×C3111yescharacteristic
480C22×C8C23×C3111yescharacteristic
481C22×C8C23×C3111yescharacteristic
482#127—22no—
483#127—41no—
484#123—44no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—44no—
489#121—41no—
490#121—41no—
491#121—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4C23×C3111yescharacteristic
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4D4×C3111yescharacteristic
516C2×C22⋊C4D4×C3111yescharacteristic
517C2×C42C23×C3111yescharacteristic
518C2×C42C23×C3111yescharacteristic
519#106—22no—
520#106—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102D4×C3114yescomplemented
529C22⋊C8—22no—
530#97—22no—
531C4×C8—41no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95D4×C3111yescharacteristic
536#95D4×C3111yescharacteristic
537C31#2698411yescharacteristic, direct product factor, Sylow
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C3111yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C3112yes—
574C2×D4#41×C3112yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C24×C3111yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C3112yes—
611C2×C8#41×C3112yes—
612C2×C8#41×C3112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C3112yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C3111yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4C31×AGL(1,ℤ/8)12yes—
724C2×C4C31×AGL(1,ℤ/8)12yes—
725C2×C4C22×D4×C3111yescharacteristic
726C2×C4C2×#41×C3111yescharacteristic
727C2×C4C2×#41×C3111yescharacteristic
728C2×C4C2×#41×C3111yescharacteristic
729C2×C4C31×H(5,𝔽2)11yescharacteristic
730C2×C4C31×H(5,𝔽2)11yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C31×#53211yescharacteristic
764C22D42×C3111yescharacteristic
765C22C31×#54611yescharacteristic
766C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
767C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
768C22C31×#57611yescharacteristic
769C22C31×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4C31×#52511yescharacteristic
781C4C31×#54011yescharacteristic
782C4C31×#54611yescharacteristic
783C4C31×#55311yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C31×#246411yescharacteristic
789C2C31×#317911yescharacteristic
790C2C31×#318411yescharacteristic
791C2C31×#327211yescharacteristic
792C2C31×#327411yescharacteristic
793C2C31×#330611yescharacteristic
794C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×C31×#469C2semidirect
2. C2×C31×#442C2semidirect
3. C31×#2428C2semidirect
4. C31×#2422C2semidirect
5. C31×#2084C2semidirect
6. C31×#2034C2semidirect
7. C31×#2011C2semidirect
8. C31×#1999C2semidirect
9. C31×#1957C2semidirect
10. C31×#1936C2semidirect
11. C31×#1934C2semidirect
12. C31×#1895C2semidirect
13. C31×#1879C2semidirect
14. C31×#1864C2semidirect
15. C31×#1753C2semidirect
131. C31×#102D4semidirect
245. #26984C31direct (N × H)
338. C2×#469C2×C31semidirect
339. C2×#442C2×C31semidirect
340. #2428C2×C31semidirect
341. #2422C2×C31semidirect
342. #2084C2×C31semidirect
343. #2034C2×C31semidirect
344. #2011C2×C31semidirect
345. #1999C2×C31semidirect
346. #1957C2×C31semidirect
347. #1936C2×C31semidirect
348. #1934C2×C31semidirect
349. #1895C2×C31semidirect
350. #1879C2×C31semidirect
351. #1864C2×C31semidirect
352. #1753C2×C31semidirect
528. #102D4×C31semidirect
537. C31#26984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4692
C2×C31×#4422
C31×#24282
C31×#24222
C31×#20842
C31×#20342
C31×#20112
C31×#19992
C31×#19572
C31×#19362
C31×#19342
C31×#18952
C31×#18792
C31×#18642
C31×#17532
#2698431