Finite Group Databasebeta

← C31×#23583 #21480342

Subgroups — C31×#23583 #21480342

Order 7936.

1178 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#542C211yesmaximal, characteristic, complemented
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2324C211yesmaximal, characteristic, complemented
5C31×#2058C211yesmaximal, characteristic, complemented
6C31×#2042C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2023C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#2000C211yesmaximal, characteristic, complemented
12C31×#1999C211yesmaximal, characteristic
13C31×#1763C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C31×#1750C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C31×#542—24no—
19C31×#542—24no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#126—21no—
22C2×C31×#124—21no—
23C2×C31×#124C2211yescharacteristic
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C31×#442—24no—
34C4×SD16×C31—24no—
35C2×C31×#106C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×#97C2211yescharacteristic
48C2×C4×C8×C31C2211yescharacteristic
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#386—21no—
54C31×#385—21no—
55C31×#380C2211yescharacteristic
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31C2311yescharacteristic
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C31×C4⋊Q8—22no—
83C31×C4⋊Q8—22no—
84C31×#126—28no—
85C31×#124—28no—
86C31×#124—22no—
87C31×#124—22no—
88C31×#123—28no—
89C31×C22⋊Q8—28no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×#121—22no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31D414yescomplemented
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31D414yescomplemented
102C31×#117—22no—
103C31×#117—22no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31D411yescharacteristic
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31D411yescharacteristic
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C42×C31—21no—
128C2×C42×C31—21no—
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#106—22no—
132C31×#106—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×C22⋊C8—22no—
143C31×#97—22no—
144C4×C8×C31—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31C2×D411yescharacteristic
151C2×Q8×C31—24no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—81no—
158C2×Q8×C31—81no—
159C2×Q8×C31C2×D412yes—
160C2×D4×C31—24no—
161C2×D4×C31—24no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31C2×D412yes—
177C2×D4×C31#4112yes—
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—24no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—42no—
192C22×C4×C31—81no—
193C22×C4×C31—81no—
194C22×C4×C31—81no—
195C22×C4×C31—81no—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2411yescharacteristic
202SD16×C31—28no—
203D8×C31—28no—
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×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31#4112yes—
215C2×C8×C31#4112yes—
216C4⋊C4×C31—24no—
217C4⋊C4×C31—24no—
218C4⋊C4×C31—24no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—81no—
229C4⋊C4×C31C2×D412yes—
230C4⋊C4×C31C2×D412yes—
231C4⋊C4×C31#4112yes—
232C22⋊C4×C31—24no—
233C22⋊C4×C31—24no—
234C22⋊C4×C31—24no—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—24no—
237C22⋊C4×C31—24no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—81no—
242C22⋊C4×C31—81no—
243C22⋊C4×C31—81no—
244C42×C31—24no—
245C42×C31—21no—
246C42×C31—21no—
247C42×C31—81no—
248C42×C31C2×D412yes—
249C42×C31C2×D412yes—
250#23583C3111yesmaximal, characteristic, direct product factor, Sylow
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
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×C31C22×D411yescharacteristic
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—84no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—84no—
287D4×C31—84no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—22no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
298C2×C4×C31—21no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—41no—
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—84no—
324C2×C4×C31—84no—
325C2×C4×C31#12012yes—
326C2×C4×C31#12012yes—
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C22×D411yescharacteristic
329C2×C4×C31C2×#4111yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31C2×#4111yescharacteristic
333C8×C31—22no—
334C8×C31—22no—
335C8×C31—41no—
336C8×C31—41no—
337C2×#542C2×C3111yescharacteristic, complemented
338C2×#442C2×C3111yescharacteristic, complemented
339C2×C4×SD16C2×C3111yescharacteristic, complemented
340#2324C2×C3111yescharacteristic, complemented
341#2058C2×C3111yescharacteristic, complemented
342#2042C2×C3111yescharacteristic, complemented
343#2035C2×C3111yescharacteristic, complemented
344#2034C2×C3111yescharacteristic, complemented
345#2023C2×C3111yescharacteristic, complemented
346#2012C2×C3111yescharacteristic, complemented
347#2000C2×C3111yescharacteristic, complemented
348#1999C2×C3111yescharacteristic
349#1763C2×C3111yescharacteristic, complemented
350C4×#102C2×C3111yescharacteristic, complemented
351#1750C2×C3111yescharacteristic, complemented
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—42no—
356C22×C31—41no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—41no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31C2×#12011yescharacteristic
374C22×C31#52511yescharacteristic
375C22×C31#53211yescharacteristic
376C22×C31#57611yescharacteristic
377C22×C31#57711yescharacteristic
378C22×C31#57711yescharacteristic
379C22×C31#57711yescharacteristic
380C4×C31—22no—
381C4×C31—22no—
382C4×C31—42no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—42no—
388C4×C31—42no—
389C4×C31—81no—
390C4×C31—81no—
391C4×C31#52511yescharacteristic
392C4×C31#52511yescharacteristic
393C4×C31#53211yescharacteristic
394C4×C31#53211yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396C22×D8C22×C3111yescharacteristic
397#542—24no—
398#542—24no—
399C2×C4⋊Q8C22×C3111yescharacteristic
400C2×#126—21no—
401C2×#124—21no—
402C2×#124C22×C3111yescharacteristic
403C2×#123—21no—
404C2×C22⋊Q8—21no—
405C2×C22⋊Q8C22×C3111yescharacteristic
406C2×#121C22×C3111yescharacteristic
407C2×#121C22×C3111yescharacteristic
408C2×C4×Q8C22×C3111yescharacteristic
409C2×C4×D4C22×C3111yescharacteristic
410C2×C4×D4C22×C3111yescharacteristic
411C2×#117C22×C3111yescharacteristic
412#442—24no—
413C4×SD16—24no—
414C2×#106C22×C3111yescharacteristic
415C2×#106C22×C3111yescharacteristic
416C2×#103C22×C3111yescharacteristic
417C2×#103C22×C3111yescharacteristic
418C2×#103C22×C3111yescharacteristic
419C2×#102C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×C22⋊C8C22×C3111yescharacteristic
425C2×C22⋊C8C22×C3111yescharacteristic
426C2×#97C22×C3111yescharacteristic
427C2×C4×C8C22×C3111yescharacteristic
428#390—21no—
429#390C22×C3111yescharacteristic
430#389C22×C3111yescharacteristic
431#388—21no—
432#386—21no—
433#385—21no—
434#380C22×C3111yescharacteristic
435C4×C4⋊C4C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#340C22×C3111yescharacteristic
438#340C22×C3111yescharacteristic
439#340C22×C3111yescharacteristic
440#336C22×C3111yescharacteristic
441#336C22×C3111yescharacteristic
442C2×C31—81no—
443C2×C31—82no—
444C2×C31—82no—
445C2×C31#238811yescharacteristic
446C2×C31#301011yescharacteristic
447C2×C31#301211yescharacteristic
448C2×C31#311811yescharacteristic
449C2×C31#312511yescharacteristic
450C2×C31#317311yescharacteristic
451C2×C31#317911yescharacteristic
452C22×Q8—21no—
453C22×Q8C23×C3111yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4C23×C3111yescharacteristic
457C22×D4C23×C3111yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4C23×C3111yescharacteristic
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C22×C8C23×C3111yescharacteristic
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8—22no—
473#126—28no—
474#124—28no—
475#124—22no—
476#124—22no—
477#123—28no—
478C22⋊Q8—28no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485C4×Q8—22no—
486C4×Q8D4×C3114yescomplemented
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4D4×C3114yescomplemented
491#117—22no—
492#117—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4D4×C3111yescharacteristic
498C2×C4⋊C4D4×C3111yescharacteristic
499C2×C4⋊C4C23×C3111yescharacteristic
500C2×C4⋊C4C23×C3111yescharacteristic
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C22⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
515C2×C22⋊C4D4×C3111yescharacteristic
516C2×C42—21no—
517C2×C42—21no—
518C2×C42C23×C3111yescharacteristic
519C2×C42C23×C3111yescharacteristic
520#106—22no—
521#106—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532#97—22no—
533C4×C8—22no—
534#95—21no—
535#95—21no—
536#95—21no—
537C31#2358311yescharacteristic, direct product factor, Sylow
538C24—21no—
539C24—21no—
540C24C2×D4×C3111yescharacteristic
541C2×Q8—24no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—81no—
548C2×Q8—81no—
549C2×Q8C2×D4×C3112yes—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4C2×D4×C3112yes—
567C2×D4#41×C3112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C24×C3111yescharacteristic
592SD16—28no—
593D8—28no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8#41×C3112yes—
605C2×C8#41×C3112yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—81no—
619C4⋊C4C2×D4×C3112yes—
620C4⋊C4C2×D4×C3112yes—
621C4⋊C4#41×C3112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C42—24no—
635C42—21no—
636C42—21no—
637C42—81no—
638C42C2×D4×C3112yes—
639C42C2×D4×C3112yes—
640C23—21no—
641C23—22no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C22×D4×C3111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666Q8—84no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—84no—
713C2×C4—84no—
714C2×C4C31×#12012yes—
715C2×C4C31×#12012yes—
716C2×C4C22×D4×C3111yescharacteristic
717C2×C4C22×D4×C3111yescharacteristic
718C2×C4C2×#41×C3111yescharacteristic
719C2×C4C2×#41×C3111yescharacteristic
720C2×C4C2×#41×C3111yescharacteristic
721C2×C4C2×#41×C3111yescharacteristic
722C8—22no—
723C8—22no—
724C8—41no—
725C8—41no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22C2×C31×#12011yescharacteristic
748C22C31×#52511yescharacteristic
749C22C31×#53211yescharacteristic
750C22C31×#57611yescharacteristic
751C22C31×#57711yescharacteristic
752C22C31×#57711yescharacteristic
753C22C31×#57711yescharacteristic
754C4—22no—
755C4—22no—
756C4—42no—
757C4—41no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—42no—
762C4—42no—
763C4—81no—
764C4—81no—
765C4C31×#52511yescharacteristic
766C4C31×#52511yescharacteristic
767C4C31×#53211yescharacteristic
768C4C31×#53211yescharacteristic
769C2—81no—
770C2—82no—
771C2—82no—
772C2C31×#238811yescharacteristic
773C2C31×#301011yescharacteristic
774C2C31×#301211yescharacteristic
775C2C31×#311811yescharacteristic
776C2C31×#312511yescharacteristic
777C2C31×#317311yescharacteristic
778C2C31×#317911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#542C2semidirect
2. C2×C31×#442C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2324C2semidirect
5. C31×#2058C2semidirect
6. C31×#2042C2semidirect
7. C31×#2035C2semidirect
8. C31×#2034C2semidirect
9. C31×#2023C2semidirect
10. C31×#2012C2semidirect
11. C31×#2000C2semidirect
13. C31×#1763C2semidirect
14. C4×C31×#102C2semidirect
15. C31×#1750C2semidirect
97. C4×Q8×C31D4semidirect
101. C4×D4×C31D4semidirect
250. #23583C31direct (N × H)
337. C2×#542C2×C31semidirect
338. C2×#442C2×C31semidirect
339. C2×C4×SD16C2×C31semidirect
340. #2324C2×C31semidirect
341. #2058C2×C31semidirect
342. #2042C2×C31semidirect
343. #2035C2×C31semidirect
344. #2034C2×C31semidirect
345. #2023C2×C31semidirect
346. #2012C2×C31semidirect
347. #2000C2×C31semidirect
349. #1763C2×C31semidirect
350. C4×#102C2×C31semidirect
351. #1750C2×C31semidirect
486. C4×Q8D4×C31semidirect
490. C4×D4D4×C31semidirect
537. C31#23583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5422
C2×C31×#4422
C2×C4×SD16×C312
C31×#23242
C31×#20582
C31×#20422
C31×#20352
C31×#20342
C31×#20232
C31×#20122
C31×#20002
C31×#19992
C31×#17632
C4×C31×#1022
C31×#17502
#2358331