Finite Group Databasebeta

← C2×C31×#1905 #21477756

Subgroups — C2×C31×#1905 #21477756

Order 7936.

1678 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic
2C2×C31×#519C211yesmaximal, characteristic, complemented
3C2×C31×#421C211yesmaximal, characteristic
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C2×C31×#410C211yesmaximal, characteristic
6C31×#1905C218yesmaximal, direct product factor
7C2×C31×#344C211yesmaximal, characteristic, complemented
8C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C23×Q8×C31C2211yescharacteristic
11C2×C31×#137—22no—
12C2×C31×#137—22no—
13C2×C31×#137—22no—
14C2×C31×#137—22no—
15C2×C31×#137C414yescomplemented
16C2×C31×#137C2214yes—
17C22×Q16×C31C412yescomplemented
18C22×SD16×C31C412yescomplemented
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C31×#519—22no—
22C31×#519—22no—
23C31×#519—22no—
24C31×#519C2214yescomplemented
25C2×C4×Q8×C31—22no—
26C2×C4×Q8×C31—22no—
27C2×C31×#117—22no—
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C31×#421—22no—
32C31×#421C2214yes—
33C2×C31×#104—22no—
34C31×#419—22no—
35C31×#419C2214yescomplemented
36C2×C31×#103—22no—
37C31×#410—22no—
38C31×#410C2214yes—
39C2×C31×#99—22no—
40C31×#344C2214yescomplemented
41C31×H(3,ℤ/4)C2214yescomplemented
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31C2×C412yes—
53C2×#41×C31C2312yes—
54C22×Q8×C31—21no—
55C22×Q8×C31—21no—
56C22×Q8×C31—21no—
57C22×Q8×C31—21no—
58C22×Q8×C31—21no—
59C22×Q8×C31—21no—
60C22×Q8×C31—21no—
61C22×Q8×C31C2×C411yescharacteristic
62C22×Q8×C31C2×C412yes—
63C22×Q8×C31C2×C412yes—
64C22×Q8×C31D412yes—
65C22×Q8×C31D412yes—
66C22×Q8×C31D412yes—
67C22×Q8×C31D412yes—
68C22×Q8×C31C2312yes—
69C22×D4×C31—21no—
70C22×D4×C31C2×C411yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C31×#137—28no—
75C31×#137—28no—
76C31×#137—28no—
77C31×#137—28no—
78C2×Q16×C31—24no—
79C2×Q16×C31—24no—
80C2×Q16×C31C2×C418yescomplemented
81C2×SD16×C31—24no—
82C2×SD16×C31—24no—
83C2×SD16×C31C2×C418yescomplemented
84C2×M16×C31—21no—
85C2×M16×C31—21no—
86C2×M16×C31—21no—
87C2×M16×C31—21no—
88C2×M16×C31—21no—
89C2×M16×C31—21no—
90C2×M16×C31—21no—
91C2×M16×C31—21no—
92C2×M16×C31—21no—
93C2×M16×C31C2×C412yes—
94C2×M16×C31C2312yes—
95C2×M16×C31C2312yes—
96C22×C8×C31—21no—
97C22×C8×C31C2×C412yes—
98C4×Q8×C31—28no—
99C4×Q8×C31—28no—
100C4×Q8×C31—28no—
101C4×Q8×C31—28no—
102C31×#117—28no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—28no—
108C31×#117—21no—
109C31×#117—21no—
110C31×#117—21no—
111C31×#117D412yes—
112C31×#117D412yes—
113C31×#117C2312yes—
114C31×#117C2312yes—
115C31×#117C2312yes—
116C2×C4⋊C4×C31—24no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31D412yes—
123C2×C42×C31—24no—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31D412yes—
127C31×#104—28no—
128C31×#103—28no—
129C31×#99—28no—
130C24×C31—21no—
131C24×C31C2×D411yescharacteristic
132#41×C31—22no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31—22no—
136#41×C31—22no—
137#41×C31—22no—
138#41×C31—22no—
139#41×C31—22no—
140#41×C31—41no—
141#41×C31—41no—
142#41×C31—41no—
143#41×C31—41no—
144#41×C31—41no—
145#41×C31—41no—
146#41×C31—41no—
147#41×C31—41no—
148C2×Q8×C31—22no—
149C2×Q8×C31—22no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31—22no—
153C2×Q8×C31—22no—
154C2×Q8×C31—21no—
155C2×Q8×C31—22no—
156C2×Q8×C31—22no—
157C2×Q8×C31—22no—
158C2×Q8×C31—22no—
159C2×Q8×C31—22no—
160C2×Q8×C31—22no—
161C2×Q8×C31—22no—
162C2×Q8×C31—22no—
163C2×Q8×C31—22no—
164C2×Q8×C31—22no—
165C2×Q8×C31—22no—
166C2×Q8×C31—22no—
167C2×Q8×C31—22no—
168C2×Q8×C31—22no—
169C2×Q8×C31—22no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31C22⋊C414yes—
175C2×Q8×C31C22⋊C414yes—
176C2×Q8×C31C22⋊C414yes—
177C2×Q8×C31C22⋊C414yes—
178C2×Q8×C31C22×C412yes—
179C2×Q8×C31C22×C414yes—
180C2×Q8×C31C2×D414yes—
181C2×Q8×C31C2×D414yes—
182C2×D4×C31—22no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—41no—
192C2×D4×C31—41no—
193C2×D4×C31C22×C412yes—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—21no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31C22×C411yescharacteristic
212C22×C4×C31C22×C411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31#4111yescharacteristic
221C22×C4×C31#4111yescharacteristic
222C22×C4×C31#4111yescharacteristic
223C22×C4×C31#4111yescharacteristic
224C22×C4×C31C2411yescharacteristic
225Q16×C31—216no—
226SD16×C31—216no—
227M16×C31—22no—
228M16×C31—22no—
229M16×C31—22no—
230M16×C31—22no—
231M16×C31—22no—
232M16×C31—22no—
233M16×C31—41no—
234M16×C31—41no—
235C2×C8×C31—22no—
236C2×C8×C31—22no—
237C2×C8×C31—22no—
238C2×C8×C31—41no—
239C2×C8×C31—41no—
240C2×C8×C31C22×C414yes—
241C4⋊C4×C31—216no—
242C4⋊C4×C31—22no—
243C4⋊C4×C31—22no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—41no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—41no—
253C22⋊C4×C31C2×D414yes—
254C42×C31—216no—
255C42×C31—22no—
256C42×C31—22no—
257C42×C31—22no—
258C42×C31—22no—
259C42×C31—41no—
260C42×C31C2×D414yes—
261C2×#1905C3111yesmaximal, characteristic, direct product factor, Sylow
262C23×C31—22no—
263C23×C31—42no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—82no—
267C23×C31C4×D411yescharacteristic
268C23×C31C4×D411yescharacteristic
269C23×C31#12011yescharacteristic
270C23×C31#12011yescharacteristic
271C23×C31#12111yescharacteristic
272C23×C31#12111yescharacteristic
273C23×C31C22×D411yescharacteristic
274Q8×C31—24no—
275Q8×C31—24no—
276Q8×C31—24no—
277Q8×C31—24no—
278Q8×C31—24no—
279Q8×C31—24no—
280Q8×C31—24no—
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—41no—
284Q8×C31—41no—
285Q8×C31C2×C22⋊C418yes—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—42no—
289D4×C31—42no—
290D4×C31—42no—
291D4×C31—42no—
292D4×C31—41no—
293D4×C31—41no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—24no—
300C2×C4×C31—24no—
301C2×C4×C31—22no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—44no—
305C2×C4×C31—44no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—82no—
314C2×C4×C31C2×C22⋊C411yescharacteristic
315C2×C4×C31C2×C22⋊C411yescharacteristic
316C2×C4×C31C2×C22⋊C411yescharacteristic
317C2×C4×C31C2×C22⋊C411yescharacteristic
318C2×C4×C31C4×D411yescharacteristic
319C2×C4×C31C4×D411yescharacteristic
320C2×C4×C31C4×D411yescharacteristic
321C2×C4×C31C4×D411yescharacteristic
322C2×C4×C31C4×D411yescharacteristic
323C2×C4×C31C4×D411yescharacteristic
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31#12111yescharacteristic
327C2×C4×C31#12111yescharacteristic
328C2×C4×C31#12111yescharacteristic
329C2×C4×C31#12111yescharacteristic
330C2×C4×C31#12111yescharacteristic
331C2×C4×C31#12111yescharacteristic
332C2×C4×C31#12311yescharacteristic
333C2×C4×C31#12311yescharacteristic
334C2×C4×C31#12311yescharacteristic
335C2×C4×C31#12311yescharacteristic
336C2×C4×C31C23×C411yescharacteristic
337C2×C4×C31C22×D411yescharacteristic
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C8×C31—24no—
343C8×C31—42no—
344C22×#137C2×C3111yescharacteristic
345C2×#519C2×C3111yescharacteristic, complemented
346C2×#421C2×C3111yescharacteristic
347C2×#419C2×C3111yescharacteristic, complemented
348C2×#410C2×C3111yescharacteristic
349#1905C2×C3118yesdirect product factor
350C2×#344C2×C3111yescharacteristic, complemented
351C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
352C22×C31—22no—
353C22×C31—22no—
354C22×C31—22no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—42no—
360C22×C31—82no—
361C22×C31—82no—
362C22×C31—82no—
363C22×C31#38611yescharacteristic
364C22×C31#38611yescharacteristic
365C22×C31#38611yescharacteristic
366C22×C31#38611yescharacteristic
367C22×C31C2×C4×D411yescharacteristic
368C22×C31C2×#12011yescharacteristic
369C22×C31C2×#12111yescharacteristic
370C4×C31—28no—
371C4×C31—44no—
372C4×C31—44no—
373C4×C31—42no—
374C4×C31—82no—
375C4×C31#38611yescharacteristic
376C4×C31#38611yescharacteristic
377C4×C31#38611yescharacteristic
378C4×C31#38611yescharacteristic
379C4×C31C22×C22⋊C411yescharacteristic
380C4×C31C2×C4×D411yescharacteristic
381C4×C31C2×#12111yescharacteristic
382C4×C31C2×#12311yescharacteristic
383C22×#41C22×C3111yescharacteristic
384C23×Q8C22×C3111yescharacteristic
385C2×#137—22no—
386C2×#137—22no—
387C2×#137—22no—
388C2×#137—22no—
389C2×#137C4×C3114yescomplemented
390C2×#137C22×C3114yes—
391C22×Q16C4×C3112yescomplemented
392C22×SD16C4×C3112yescomplemented
393C22×M16C22×C3111yescharacteristic
394C22×M16C22×C3111yescharacteristic
395#519—22no—
396#519—22no—
397#519—22no—
398#519C22×C3114yescomplemented
399C2×C4×Q8—22no—
400C2×C4×Q8—22no—
401C2×#117—22no—
402C2×#117C22×C3111yescharacteristic
403C2×#117C22×C3111yescharacteristic
404C2×#117C22×C3111yescharacteristic
405#421—22no—
406#421C22×C3114yes—
407C2×#104—22no—
408#419—22no—
409#419C22×C3114yescomplemented
410C2×#103—22no—
411#410—22no—
412#410C22×C3114yes—
413C2×#99—22no—
414#344C22×C3114yescomplemented
415H(3,ℤ/4)C22×C3114yescomplemented
416C2×C31—21no—
417C2×C31—21no—
418C2×C31—21no—
419C2×C31—21no—
420C2×C31—21no—
421C2×C31—21no—
422C2×C31—82no—
423C2×C31#190512yesdirect product factor
424C2×C31C2×#38611yescharacteristic
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41C2×C4×C3112yes—
436C2×#41C23×C3112yes—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8C2×C4×C3111yescharacteristic
445C22×Q8C2×C4×C3112yes—
446C22×Q8C2×C4×C3112yes—
447C22×Q8D4×C3112yes—
448C22×Q8D4×C3112yes—
449C22×Q8D4×C3112yes—
450C22×Q8D4×C3112yes—
451C22×Q8C23×C3112yes—
452C22×D4—21no—
453C22×D4C2×C4×C3111yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4C23×C3111yescharacteristic
457#137—28no—
458#137—28no—
459#137—28no—
460#137—28no—
461C2×Q16—24no—
462C2×Q16—24no—
463C2×Q16C2×C4×C3118yescomplemented
464C2×SD16—24no—
465C2×SD16—24no—
466C2×SD16C2×C4×C3118yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16C2×C4×C3112yes—
477C2×M16C23×C3112yes—
478C2×M16C23×C3112yes—
479C22×C8—21no—
480C22×C8C2×C4×C3112yes—
481C4×Q8—28no—
482C4×Q8—28no—
483C4×Q8—28no—
484C4×Q8—28no—
485#117—28no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—28no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117D4×C3112yes—
495#117D4×C3112yes—
496#117C23×C3112yes—
497#117C23×C3112yes—
498#117C23×C3112yes—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C3112yes—
506C2×C42—24no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42D4×C3112yes—
510#104—28no—
511#103—28no—
512#99—28no—
513C31C2×#190511yescharacteristic, direct product factor, Sylow
514C24—21no—
515C24C2×D4×C3111yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C22⋊C4×C3114yes—
559C2×Q8C22⋊C4×C3114yes—
560C2×Q8C22⋊C4×C3114yes—
561C2×Q8C22⋊C4×C3114yes—
562C2×Q8C22×C4×C3112yes—
563C2×Q8C22×C4×C3114yes—
564C2×Q8C2×D4×C3114yes—
565C2×Q8C2×D4×C3114yes—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4C22×C4×C3112yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C22×C4×C3111yescharacteristic
596C22×C4C22×C4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C2×D4×C3111yescharacteristic
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4#41×C3111yescharacteristic
605C22×C4#41×C3111yescharacteristic
606C22×C4#41×C3111yescharacteristic
607C22×C4#41×C3111yescharacteristic
608C22×C4C24×C3111yescharacteristic
609Q16—216no—
610SD16—216no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—22no—
617M16—41no—
618M16—41no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8C22×C4×C3114yes—
625C4⋊C4—216no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—41no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4C2×D4×C3114yes—
638C42—216no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—41no—
644C42C2×D4×C3114yes—
645C23—22no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—82no—
650C23C4×D4×C3111yescharacteristic
651C23C4×D4×C3111yescharacteristic
652C23C31×#12011yescharacteristic
653C23C31×#12011yescharacteristic
654C23C31×#12111yescharacteristic
655C23C31×#12111yescharacteristic
656C23C22×D4×C3111yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668Q8C2×C22⋊C4×C3118yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—82no—
697C2×C4C2×C22⋊C4×C3111yescharacteristic
698C2×C4C2×C22⋊C4×C3111yescharacteristic
699C2×C4C2×C22⋊C4×C3111yescharacteristic
700C2×C4C2×C22⋊C4×C3111yescharacteristic
701C2×C4C4×D4×C3111yescharacteristic
702C2×C4C4×D4×C3111yescharacteristic
703C2×C4C4×D4×C3111yescharacteristic
704C2×C4C4×D4×C3111yescharacteristic
705C2×C4C4×D4×C3111yescharacteristic
706C2×C4C4×D4×C3111yescharacteristic
707C2×C4C31×#12011yescharacteristic
708C2×C4C31×#12011yescharacteristic
709C2×C4C31×#12111yescharacteristic
710C2×C4C31×#12111yescharacteristic
711C2×C4C31×#12111yescharacteristic
712C2×C4C31×#12111yescharacteristic
713C2×C4C31×#12111yescharacteristic
714C2×C4C31×#12111yescharacteristic
715C2×C4C31×#12311yescharacteristic
716C2×C4C31×#12311yescharacteristic
717C2×C4C31×#12311yescharacteristic
718C2×C4C31×#12311yescharacteristic
719C2×C4C23×C4×C3111yescharacteristic
720C2×C4C22×D4×C3111yescharacteristic
721C2×C4C22×D4×C3111yescharacteristic
722C2×C4C22×D4×C3111yescharacteristic
723C2×C4C2×#41×C3111yescharacteristic
724C2×C4C2×#41×C3111yescharacteristic
725C8—24no—
726C8—42no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22C31×#38611yescharacteristic
739C22C31×#38611yescharacteristic
740C22C31×#38611yescharacteristic
741C22C31×#38611yescharacteristic
742C22C2×C4×D4×C3111yescharacteristic
743C22C2×C31×#12011yescharacteristic
744C22C2×C31×#12111yescharacteristic
745C4—28no—
746C4—44no—
747C4—44no—
748C4—42no—
749C4—82no—
750C4C31×#38611yescharacteristic
751C4C31×#38611yescharacteristic
752C4C31×#38611yescharacteristic
753C4C31×#38611yescharacteristic
754C4C22×C22⋊C4×C3111yescharacteristic
755C4C2×C4×D4×C3111yescharacteristic
756C4C2×C31×#12111yescharacteristic
757C4C2×C31×#12311yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—82no—
765C2C31×#190512yesdirect product factor
766C2C2×C31×#38611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#519C2semidirect
4. C2×C31×#419C2semidirect
6. C31×#1905C2direct (N × H)
7. C2×C31×#344C2semidirect
8. C2×C31×H(3,ℤ/4)C2semidirect
15. C2×C31×#137C4semidirect
17. C22×Q16×C31C4semidirect
18. C22×SD16×C31C4semidirect
24. C31×#519C22semidirect
35. C31×#419C22semidirect
40. C31×#344C22semidirect
41. C31×H(3,ℤ/4)C22semidirect
80. C2×Q16×C31C2×C4semidirect
83. C2×SD16×C31C2×C4semidirect
261. C2×#1905C31direct (N × H)
345. C2×#519C2×C31semidirect
347. C2×#419C2×C31semidirect
349. #1905C2×C31direct (N × H)
350. C2×#344C2×C31semidirect
351. C2×H(3,ℤ/4)C2×C31semidirect
389. C2×#137C4×C31semidirect
391. C22×Q16C4×C31semidirect
392. C22×SD16C4×C31semidirect
398. #519C22×C31semidirect
409. #419C22×C31semidirect
414. #344C22×C31semidirect
415. H(3,ℤ/4)C22×C31semidirect
423. C2×C31#1905direct (N × H)
463. C2×Q16C2×C4×C31semidirect
466. C2×SD16C2×C4×C31semidirect
513. C31C2×#1905direct (N × H)
765. C2C31×#1905direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×C31×#5192
C2×C31×#4212
C2×C31×#4192
C2×C31×#4102
C31×#19052
C2×C31×#3442
C2×C31×H(3,ℤ/4)2
C2×#190531