Finite Group Databasebeta

← C31×#21462 #21478221

Subgroups — C31×#21462 #21478221

Order 7936.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#519C211yesmaximal, characteristic, complemented
2C2×C31×#448C211yesmaximal, characteristic
3C2×C31×#440C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2324C211yesmaximal, characteristic
6C31×#1880C211yesmaximal, characteristic, complemented
7C31×#1880C211yesmaximal, characteristic, complemented
8C31×#1875C211yesmaximal, characteristic
9C31×#1865C211yesmaximal, characteristic, complemented
10C31×#1863C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1787C211yesmaximal, characteristic, complemented
13C31×#1763C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C31×#1750C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C31×#519—24no—
21C31×#519—24no—
22C2×C4×Q8×C31—21no—
23C2×C4×Q8×C31—21no—
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117—21no—
30C2×C31×#117—21no—
31C2×C31×#117C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C31×#448C418yescomplemented
34C31×#440—24no—
35C4×SD16×C31—24no—
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic
49C2×C4×C8×C31C2211yescharacteristic
50C31×#390—21no—
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#386—21no—
55C31×#385—21no—
56C31×#380C2211yescharacteristic
57C4×C4⋊C4×C31C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—22no—
67C22×Q8×C31—22no—
68C22×Q8×C31—21no—
69C22×Q8×C31—22no—
70C22×Q8×C31C2×C414yescomplemented
71C22×Q8×C31C2311yescharacteristic
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31C2×C414yes—
83C2×SD16×C31C2×C414yes—
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C31×#121—22no—
89C31×#121C2×C414yes—
90C4×Q8×C31—28no—
91C4×Q8×C31—28no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31—22no—
98C4×Q8×C31D414yescomplemented
99C4×Q8×C31D414yescomplemented
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C31×#117—28no—
103C31×#117—28no—
104C31×#117—22no—
105C31×#117—22no—
106C31×#117—22no—
107C31×#117—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31D411yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31—21no—
132C2×C42×C31—21no—
133C2×C42×C31—21no—
134C2×C42×C31C2311yescharacteristic
135C2×C42×C31C2311yescharacteristic
136C31×#107—22no—
137C31×#106—22no—
138C31×#103—22no—
139C31×#103—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103C2×C414yescomplemented
143C31×#103C2×C414yescomplemented
144C31×#102—22no—
145C31×#102—22no—
146C31×C22⋊C8—22no—
147C31×C22⋊C8C2×C414yescomplemented
148C31×#97—22no—
149C4×C8×C31—22no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C24×C31—21no—
154C24×C31C2×D411yescharacteristic
155C2×Q8×C31—24no—
156C2×Q8×C31—28no—
157C2×Q8×C31—28no—
158C2×Q8×C31—24no—
159C2×Q8×C31—28no—
160C2×Q8×C31—28no—
161C2×Q8×C31—24no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31C22×C412yes—
169C2×Q8×C31C22×C412yes—
170C2×Q8×C31C2×D412yes—
171C2×Q8×C31C2×D412yes—
172C2×Q8×C31#4112yes—
173C2×Q8×C31#4112yes—
174C2×D4×C31—24no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—81no—
181C2×D4×C31—81no—
182C2×D4×C31C22×C412yes—
183C22×C4×C31—24no—
184C22×C4×C31—24no—
185C22×C4×C31—24no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—42no—
198C22×C4×C31—81no—
199C22×C4×C31—81no—
200C22×C4×C31C22×C412yes—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31#4112yes—
207C22×C4×C31C2411yescharacteristic
208SD16×C31—28no—
209SD16×C31—28no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31C22×C412yes—
221C2×C8×C31C22×C412yes—
222C4⋊C4×C31—24no—
223C4⋊C4×C31—24no—
224C4⋊C4×C31—24no—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—81no—
236C4⋊C4×C31C22×C412yes—
237C4⋊C4×C31C2×D412yes—
238C4⋊C4×C31C2×D412yes—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—81no—
245C22⋊C4×C31—81no—
246C22⋊C4×C31—81no—
247C42×C31—24no—
248C42×C31—24no—
249C42×C31—24no—
250C42×C31—24no—
251C42×C31—24no—
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—81no—
255C42×C31C2×D412yes—
256C42×C31C2×D412yes—
257#21462C3111yesmaximal, characteristic, direct product factor, Sylow
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31C4×D412yes—
272C23×C31C22×D411yescharacteristic
273Q8×C31—216no—
274Q8×C31—22no—
275Q8×C31—22no—
276Q8×C31—22no—
277Q8×C31—22no—
278Q8×C31—22no—
279Q8×C31—22no—
280Q8×C31C4×D414yes—
281Q8×C31C4×D414yes—
282D4×C31—22no—
283D4×C31—22no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—84no—
287C2×C4×C31—216no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—21no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
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—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
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—41no—
325C2×C4×C31—84no—
326C2×C4×C31C4×D412yes—
327C2×C4×C31#12012yes—
328C2×C4×C31#12012yes—
329C2×C4×C31C23×C411yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C22×D411yescharacteristic
332C2×C4×C31C2×#4111yescharacteristic
333C2×C4×C31C2×#4111yescharacteristic
334C2×C4×C31C2×#4111yescharacteristic
335C8×C31—22no—
336C8×C31—22no—
337C8×C31—41no—
338C8×C31—41no—
339C2×#519C2×C3111yescharacteristic, complemented
340C2×#448C2×C3111yescharacteristic
341C2×#440C2×C3111yescharacteristic, complemented
342C2×C4×SD16C2×C3111yescharacteristic, complemented
343#2324C2×C3111yescharacteristic
344#1880C2×C3111yescharacteristic, complemented
345#1880C2×C3111yescharacteristic, complemented
346#1875C2×C3111yescharacteristic
347#1865C2×C3111yescharacteristic, complemented
348#1863C2×C3111yescharacteristic, complemented
349#1854C2×C3111yescharacteristic, complemented
350#1787C2×C3111yescharacteristic, complemented
351#1763C2×C3111yescharacteristic, complemented
352C4×#103C2×C3111yescharacteristic, complemented
353#1750C2×C3111yescharacteristic, complemented
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31C2×C4×D411yescharacteristic
369C22×C31C2×#12011yescharacteristic
370C22×C31#52511yescharacteristic
371C22×C31#57711yescharacteristic
372C22×C31#57711yescharacteristic
373C22×C31#57711yescharacteristic
374C22×C31#57811yescharacteristic
375C4×C31—22no—
376C4×C31—22no—
377C4×C31—24no—
378C4×C31—24no—
379C4×C31—22no—
380C4×C31—42no—
381C4×C31—41no—
382C4×C31—42no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31C2×C4×D411yescharacteristic
388C4×C31C2×C4×D411yescharacteristic
389C4×C31#52511yescharacteristic
390C4×C31#52511yescharacteristic
391C23×Q8C22×C3111yescharacteristic
392C22×SD16C22×C3111yescharacteristic
393C22×SD16C22×C3111yescharacteristic
394C2×#121C22×C3111yescharacteristic
395#519—24no—
396#519—24no—
397C2×C4×Q8—21no—
398C2×C4×Q8—21no—
399C2×C4×Q8C22×C3111yescharacteristic
400C2×C4×Q8C22×C3111yescharacteristic
401C2×C4×Q8C22×C3111yescharacteristic
402C2×C4×Q8C22×C3111yescharacteristic
403C2×C4×D4C22×C3111yescharacteristic
404C2×#117—21no—
405C2×#117—21no—
406C2×#117C22×C3111yescharacteristic
407C2×#117C22×C3111yescharacteristic
408#448C4×C3118yescomplemented
409#440—24no—
410C4×SD16—24no—
411C2×#107C22×C3111yescharacteristic
412C2×#106C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#103C22×C3111yescharacteristic
415C2×#103C22×C3111yescharacteristic
416C2×#103C22×C3111yescharacteristic
417C2×#103C22×C3111yescharacteristic
418C2×#103C22×C3111yescharacteristic
419C2×#102C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×C22⋊C8C22×C3111yescharacteristic
422C2×C22⋊C8C22×C3111yescharacteristic
423C2×#97C22×C3111yescharacteristic
424C2×C4×C8C22×C3111yescharacteristic
425#390—21no—
426#390C22×C3111yescharacteristic
427#389C22×C3111yescharacteristic
428#388—21no—
429#386—21no—
430#385—21no—
431#380C22×C3111yescharacteristic
432C4×C4⋊C4C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic
434#340C22×C3111yescharacteristic
435#340C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#336C22×C3111yescharacteristic
438#336C22×C3111yescharacteristic
439C2×C31—42no—
440C2×C31—82no—
441C2×C31C4×#12011yescharacteristic
442C2×C31#294711yescharacteristic
443C2×C31#294911yescharacteristic
444C2×C31#301011yescharacteristic
445C2×C31#301311yescharacteristic
446C2×C31#312111yescharacteristic
447C2×C31#312611yescharacteristic
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—21no—
453C22×Q8—22no—
454C22×Q8C2×C4×C3114yescomplemented
455C22×Q8C23×C3111yescharacteristic
456C22×Q8C23×C3111yescharacteristic
457C22×D4—21no—
458C22×D4C23×C3111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C3111yescharacteristic
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16C2×C4×C3114yes—
467C2×SD16C2×C4×C3114yes—
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472#121—22no—
473#121C2×C4×C3114yes—
474C4×Q8—28no—
475C4×Q8—28no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8D4×C3114yescomplemented
483C4×Q8D4×C3114yescomplemented
484C4×D4—22no—
485C4×D4—22no—
486#117—28no—
487#117—28no—
488#117—22no—
489#117—22no—
490#117—22no—
491#117—22no—
492C2×C4⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
511C2×C22⋊C4D4×C3111yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42C23×C3111yescharacteristic
519C2×C42C23×C3111yescharacteristic
520#107—22no—
521#106—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#103—22no—
526#103C2×C4×C3114yescomplemented
527#103C2×C4×C3114yescomplemented
528#102—22no—
529#102—22no—
530C22⋊C8—22no—
531C22⋊C8C2×C4×C3114yescomplemented
532#97—22no—
533C4×C8—22no—
534#95—21no—
535#95—21no—
536#95—21no—
537C31#2146211yescharacteristic, direct product factor, Sylow
538C24—21no—
539C24C2×D4×C3111yescharacteristic
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C22×C4×C3112yes—
554C2×Q8C22×C4×C3112yes—
555C2×Q8C2×D4×C3112yes—
556C2×Q8C2×D4×C3112yes—
557C2×Q8#41×C3112yes—
558C2×Q8#41×C3112yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4C22×C4×C3112yes—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4C22×C4×C3112yes—
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4#41×C3112yes—
592C22×C4C24×C3111yescharacteristic
593SD16—28no—
594SD16—28no—
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—21no—
605C2×C8C22×C4×C3112yes—
606C2×C8C22×C4×C3112yes—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—81no—
621C4⋊C4C22×C4×C3112yes—
622C4⋊C4C2×D4×C3112yes—
623C4⋊C4C2×D4×C3112yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—81no—
640C42C2×D4×C3112yes—
641C42C2×D4×C3112yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C4×D4×C3112yes—
656C23C22×D4×C3111yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8C4×D4×C3114yes—
665Q8C4×D4×C3114yes—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
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—84no—
710C2×C4C4×D4×C3112yes—
711C2×C4C31×#12012yes—
712C2×C4C31×#12012yes—
713C2×C4C23×C4×C3111yescharacteristic
714C2×C4C22×D4×C3111yescharacteristic
715C2×C4C22×D4×C3111yescharacteristic
716C2×C4C2×#41×C3111yescharacteristic
717C2×C4C2×#41×C3111yescharacteristic
718C2×C4C2×#41×C3111yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×C4×D4×C3111yescharacteristic
738C22C2×C31×#12011yescharacteristic
739C22C31×#52511yescharacteristic
740C22C31×#57711yescharacteristic
741C22C31×#57711yescharacteristic
742C22C31×#57711yescharacteristic
743C22C31×#57811yescharacteristic
744C4—22no—
745C4—22no—
746C4—24no—
747C4—24no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4C2×C4×D4×C3111yescharacteristic
757C4C2×C4×D4×C3111yescharacteristic
758C4C31×#52511yescharacteristic
759C4C31×#52511yescharacteristic
760C2—42no—
761C2—82no—
762C2C4×C31×#12011yescharacteristic
763C2C31×#294711yescharacteristic
764C2C31×#294911yescharacteristic
765C2C31×#301011yescharacteristic
766C2C31×#301311yescharacteristic
767C2C31×#312111yescharacteristic
768C2C31×#312611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C2×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×#519C2semidirect
3. C2×C31×#440C2semidirect
4. C2×C4×SD16×C31C2semidirect
6. C31×#1880C2semidirect
7. C31×#1880C2semidirect
9. C31×#1865C2semidirect
10. C31×#1863C2semidirect
11. C31×#1854C2semidirect
12. C31×#1787C2semidirect
13. C31×#1763C2semidirect
14. C4×C31×#103C2semidirect
15. C31×#1750C2semidirect
33. C31×#448C4semidirect
70. C22×Q8×C31C2×C4semidirect
98. C4×Q8×C31D4semidirect
99. C4×Q8×C31D4semidirect
142. C31×#103C2×C4semidirect
143. C31×#103C2×C4semidirect
147. C31×C22⋊C8C2×C4semidirect
257. #21462C31direct (N × H)
339. C2×#519C2×C31semidirect
341. C2×#440C2×C31semidirect
342. C2×C4×SD16C2×C31semidirect
344. #1880C2×C31semidirect
345. #1880C2×C31semidirect
347. #1865C2×C31semidirect
348. #1863C2×C31semidirect
349. #1854C2×C31semidirect
350. #1787C2×C31semidirect
351. #1763C2×C31semidirect
352. C4×#103C2×C31semidirect
353. #1750C2×C31semidirect
408. #448C4×C31semidirect
454. C22×Q8C2×C4×C31semidirect
482. C4×Q8D4×C31semidirect
483. C4×Q8D4×C31semidirect
526. #103C2×C4×C31semidirect
527. #103C2×C4×C31semidirect
531. C22⋊C8C2×C4×C31semidirect
537. C31#21462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5192
C2×C31×#4482
C2×C31×#4402
C2×C4×SD16×C312
C31×#23242
C31×#18802
C31×#18752
C31×#18652
C31×#18632
C31×#18542
C31×#17872
C31×#17632
C4×C31×#1032
C31×#17502
#2146231