Finite Group Databasebeta

← C31×#60752 #21517511

Subgroups — C31×#60752 #21517511

Order 7936.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic, complemented
2C2×C31×#525C211yesmaximal, characteristic, complemented
3C31×#3197C214yesmaximal, complemented
4C31×#3196C212yesmaximal, complemented
5C31×#3194C212yesmaximal, complemented
6C31×#3191C214yesmaximal, complemented
7C31×#3190C212yesmaximal, complemented
8C31×#3188C212yesmaximal, complemented
9C31×#3095C211yesmaximal, characteristic, complemented
10C31×#3094C211yesmaximal, characteristic, complemented
11C31×#3093C212yesmaximal, complemented
12C31×#3056C212yesmaximal, complemented
13C31×#3055C212yesmaximal, complemented
14C31×#3007C211yesmaximal, characteristic, complemented
15C31×#3006C211yesmaximal, characteristic, complemented
16C31×#3005C212yesmaximal, complemented
17C2×C31×#407C211yesmaximal, characteristic, complemented
18C22×#41×C31C2211yescharacteristic
19C22×#41×C31C2211yescharacteristic, complemented
20C24×C4×C31C2211yescharacteristic
21C2×C31×#137C2212yescomplemented
22C2×C31×AGL(1,ℤ/8)C2212yescomplemented
23C22×M16×C31C2212yescomplemented
24C31×#525—21no—
25C31×#525—21no—
26C31×#525—21no—
27C31×#525—21no—
28C31×#525—21no—
29C31×#525—21no—
30C31×#525—21no—
31C31×#525—21no—
32C31×#525C2212yes—
33C31×#525C2212yes—
34C31×#525C2212yes—
35C31×#525C2212yes—
36C31×#525C2212yescomplemented
37C31×#525C2212yescomplemented
38C31×#525C2212yescomplemented
39C31×#525C2212yescomplemented
40C2×C31×#123—21no—
41C2×C31×#123—21no—
42C2×C31×C22⋊Q8C2211yescharacteristic
43C2×C31×C22⋊Q8C2211yescharacteristic, complemented
44C2×C31×C22⋊Q8C2211yescharacteristic, complemented
45C2×C31×C22⋊Q8C2211yescharacteristic, complemented
46C2×C31×#121C2211yescharacteristic
47C2×C31×#121C2211yescharacteristic, complemented
48C2×C31×#121C2211yescharacteristic, complemented
49C2×C31×#121C2211yescharacteristic, complemented
50C2×C31×#120—21no—
51C2×C31×#120—21no—
52C2×C4×D4×C31—21no—
53C2×C4×D4×C31—21no—
54C2×C4×D4×C31—21no—
55C2×C4×D4×C31—21no—
56C2×C31×#117C2211yescharacteristic
57C2×C31×#117C2211yescharacteristic, complemented
58C31×#485C2214yescomplemented
59C31×#485C2214yescomplemented
60C31×#485C2214yescomplemented
61C31×#484C2212yescomplemented
62C31×#483C2212yescomplemented
63C31×#482C2214yescomplemented
64C31×#482C2214yescomplemented
65C31×#482C2214yescomplemented
66C31×#481C2212yescomplemented
67C31×#480C2212yescomplemented
68C31×#470C2214yescomplemented
69C31×#469C2214yescomplemented
70C31×#468C2214yescomplemented
71C31×#468C2214yescomplemented
72C31×#467C2214yescomplemented
73C31×#466C2214yescomplemented
74C31×#465C2214yescomplemented
75C31×#465C2214yescomplemented
76C31×#452C2214yescomplemented
77C31×#452C2214yescomplemented
78C31×#452C2214yescomplemented
79C31×#451C2212yescomplemented
80C31×#450C2212yescomplemented
81C31×#449C2214yescomplemented
82C31×#449C2214yescomplemented
83C31×#449C2214yescomplemented
84C31×#448C2212yescomplemented
85C31×#447C2212yescomplemented
86C31×#428C2212yescomplemented
87C31×#428C2212yescomplemented
88C31×#419C2212yescomplemented
89C31×#418C2212yescomplemented
90C31×#417C2212yescomplemented
91C31×#417C2212yescomplemented
92C31×#407C2211yescharacteristic
93C31×#407C2211yescharacteristic
94C31×#407C2212yescomplemented
95C31×#407C2212yescomplemented
96C31×#407C2212yescomplemented
97C2×C31×C22⋊C8C2212yescomplemented
98C2×C31×C22⋊C8C2212yescomplemented
99C25×C31D411yescharacteristic
100C2×#41×C31—21no—
101C2×#41×C31—21no—
102C2×#41×C31—21no—
103C2×#41×C31—21no—
104C2×#41×C31—44no—
105C2×#41×C31—44no—
106C2×#41×C31C2312yes—
107C2×#41×C31C2312yes—
108C2×#41×C31C2312yes—
109C2×#41×C31C2312yes—
110C22×Q8×C31C2311yescharacteristic
111C22×Q8×C31C2311yescharacteristic
112C22×D4×C31—21no—
113C22×D4×C31—21no—
114C22×D4×C31—21no—
115C22×D4×C31—21no—
116C22×D4×C31—21no—
117C22×D4×C31—21no—
118C22×D4×C31C2311yescharacteristic
119C22×D4×C31C2311yescharacteristic
120C23×C4×C31—21no—
121C23×C4×C31—21no—
122C23×C4×C31—44no—
123C23×C4×C31D411yescharacteristic
124C23×C4×C31D411yescharacteristic
125C23×C4×C31D411yescharacteristic
126C23×C4×C31D411yescharacteristic
127C23×C4×C31D411yescharacteristic
128C23×C4×C31D411yescharacteristic
129C23×C4×C31D411yescharacteristic
130C23×C4×C31C2311yescharacteristic
131C23×C4×C31C2311yescharacteristic
132C23×C4×C31C2311yescharacteristic
133C23×C4×C31C2311yescharacteristic
134C23×C4×C31C2311yescharacteristic
135C23×C4×C31C2311yescharacteristic
136C23×C4×C31C2311yescharacteristic
137C31×#137—44no—
138C31×AGL(1,ℤ/8)—44no—
139C2×Q16×C31C2314yescomplemented
140C2×SD16×C31C2314yescomplemented
141C2×SD16×C31C2314yescomplemented
142C2×D8×C31C2314yescomplemented
143C2×M16×C31—44no—
144C2×M16×C31C2312yes—
145C2×M16×C31C2312yes—
146C2×M16×C31C2314yes—
147C22×C8×C31C2314yes—
148C31×#123—22no—
149C31×#123—22no—
150C31×#123—22no—
151C31×#123—22no—
152C31×#123—22no—
153C31×#123—22no—
154C31×#123—22no—
155C31×#123—22no—
156C31×C22⋊Q8—21no—
157C31×C22⋊Q8—21no—
158C31×C22⋊Q8—21no—
159C31×C22⋊Q8—21no—
160C31×C22⋊Q8—21no—
161C31×C22⋊Q8—21no—
162C31×C22⋊Q8—21no—
163C31×C22⋊Q8—21no—
164C31×C22⋊Q8C2312yes—
165C31×C22⋊Q8C2312yes—
166C31×C22⋊Q8C2312yes—
167C31×C22⋊Q8C2312yes—
168C31×C22⋊Q8C2312yes—
169C31×C22⋊Q8C2312yes—
170C31×C22⋊Q8C2312yes—
171C31×C22⋊Q8C2312yes—
172C31×#121—21no—
173C31×#121—21no—
174C31×#121—21no—
175C31×#121—21no—
176C31×#121—21no—
177C31×#121—21no—
178C31×#121—21no—
179C31×#121—21no—
180C31×#121C2312yes—
181C31×#121C2312yes—
182C31×#121C2312yes—
183C31×#121C2312yes—
184C31×#121C2312yes—
185C31×#121C2312yes—
186C31×#121C2312yes—
187C31×#121C2312yes—
188C31×#120—22no—
189C31×#120—22no—
190C31×#120—22no—
191C31×#120—22no—
192C31×#120—22no—
193C31×#120—22no—
194C31×#120—22no—
195C31×#120—22no—
196C4×D4×C31—22no—
197C4×D4×C31—22no—
198C4×D4×C31—22no—
199C4×D4×C31—22no—
200C4×D4×C31—22no—
201C4×D4×C31—22no—
202C4×D4×C31—22no—
203C4×D4×C31—22no—
204C4×D4×C31—22no—
205C4×D4×C31—22no—
206C4×D4×C31—22no—
207C4×D4×C31—22no—
208C4×D4×C31—22no—
209C4×D4×C31—22no—
210C4×D4×C31—22no—
211C4×D4×C31—22no—
212C31×#117—21no—
213C31×#117—21no—
214C31×#117—21no—
215C31×#117—21no—
216C31×#117C2312yes—
217C31×#117C2312yes—
218C31×#117C2312yes—
219C31×#117C2312yes—
220C2×C4⋊C4×C31—21no—
221C2×C4⋊C4×C31—21no—
222C2×C4⋊C4×C31—21no—
223C2×C4⋊C4×C31—21no—
224C2×C4⋊C4×C31C2311yescharacteristic
225C2×C4⋊C4×C31C2311yescharacteristic
226C2×C4⋊C4×C31C2311yescharacteristic
227C2×C4⋊C4×C31C2311yescharacteristic
228C2×C22⋊C4×C31—21no—
229C2×C22⋊C4×C31—21no—
230C2×C22⋊C4×C31—21no—
231C2×C22⋊C4×C31—21no—
232C2×C22⋊C4×C31—21no—
233C2×C22⋊C4×C31—21no—
234C2×C22⋊C4×C31—21no—
235C2×C22⋊C4×C31—21no—
236C2×C22⋊C4×C31—21no—
237C2×C22⋊C4×C31—21no—
238C2×C42×C31—21no—
239C2×C42×C31—21no—
240C31×#107C2314yescomplemented
241C31×#107C2314yescomplemented
242C31×#106C2314yescomplemented
243C31×#106C2314yescomplemented
244C31×#103C2314yescomplemented
245C31×#103C2314yescomplemented
246C31×#103C2314yescomplemented
247C31×#103C2314yescomplemented
248C31×#102C2314yescomplemented
249C31×#102C2314yescomplemented
250C31×#102C2314yescomplemented
251C31×#102C2314yescomplemented
252C31×C22⋊C8C2312yes—
253C31×C22⋊C8C2312yes—
254C31×C22⋊C8C2312yes—
255C31×C22⋊C8C2312yes—
256C31×C22⋊C8C2314yes—
257C31×C22⋊C8C2314yes—
258C24×C31—21no—
259C24×C31—21no—
260C24×C31—42no—
261C24×C31—42no—
262C24×C31—42no—
263C24×C31C2×D411yescharacteristic
264C24×C31C2×D411yescharacteristic
265C24×C31C2×D411yescharacteristic
266C24×C31C2×D411yescharacteristic
267C24×C31C2×D411yescharacteristic
268C24×C31C2×D411yescharacteristic
269C24×C31C2×D411yescharacteristic
270#41×C31—24no—
271#41×C31—24no—
272#41×C31—42no—
273#41×C31—44no—
274#41×C31—44no—
275#41×C31—42no—
276#41×C31—44no—
277#41×C31—44no—
278#41×C31—44no—
279#41×C31—44no—
280C2×Q8×C31—21no—
281C2×Q8×C31—21no—
282C2×Q8×C31—24no—
283C2×Q8×C31—42no—
284C2×Q8×C31C2412yes—
285C2×Q8×C31C2412yes—
286C2×D4×C31—22no—
287C2×D4×C31—22no—
288C2×D4×C31—22no—
289C2×D4×C31—22no—
290C2×D4×C31—22no—
291C2×D4×C31—22no—
292C2×D4×C31—22no—
293C2×D4×C31—22no—
294C2×D4×C31—22no—
295C2×D4×C31—22no—
296C2×D4×C31—22no—
297C2×D4×C31—22no—
298C2×D4×C31—21no—
299C2×D4×C31—21no—
300C2×D4×C31—24no—
301C2×D4×C31—42no—
302C2×D4×C31—44no—
303C2×D4×C31—44no—
304C2×D4×C31—44no—
305C2×D4×C31—44no—
306C2×D4×C31—44no—
307C2×D4×C31—44no—
308C2×D4×C31C2412yes—
309C2×D4×C31C2412yes—
310C22×C4×C31—24no—
311C22×C4×C31—24no—
312C22×C4×C31—24no—
313C22×C4×C31—21no—
314C22×C4×C31—21no—
315C22×C4×C31—21no—
316C22×C4×C31—21no—
317C22×C4×C31—21no—
318C22×C4×C31—21no—
319C22×C4×C31—22no—
320C22×C4×C31—22no—
321C22×C4×C31—22no—
322C22×C4×C31—22no—
323C22×C4×C31—42no—
324C22×C4×C31—42no—
325C22×C4×C31—42no—
326C22×C4×C31—42no—
327C22×C4×C31—42no—
328C22×C4×C31—42no—
329C22×C4×C31—42no—
330C22×C4×C31—42no—
331C22×C4×C31—42no—
332C22×C4×C31—42no—
333C22×C4×C31—42no—
334C22×C4×C31—44no—
335C22×C4×C31—44no—
336C22×C4×C31C2×D411yescharacteristic
337C22×C4×C31C2×D411yescharacteristic
338C22×C4×C31C2×D411yescharacteristic
339C22×C4×C31C2×D411yescharacteristic
340C22×C4×C31C2×D411yescharacteristic
341C22×C4×C31C2×D411yescharacteristic
342C22×C4×C31C2×D411yescharacteristic
343C22×C4×C31C2×D411yescharacteristic
344C22×C4×C31C2×D411yescharacteristic
345C22×C4×C31C2×D411yescharacteristic
346C22×C4×C31C2×D411yescharacteristic
347C22×C4×C31C2×D411yescharacteristic
348C22×C4×C31C2×D411yescharacteristic
349C22×C4×C31C2×D411yescharacteristic
350C22×C4×C31C2×D411yescharacteristic
351C22×C4×C31C2×D411yescharacteristic
352C22×C4×C31C2×D411yescharacteristic
353C22×C4×C31C2×D411yescharacteristic
354C22×C4×C31C2×D411yescharacteristic
355C22×C4×C31C2×D411yescharacteristic
356C22×C4×C31C2×D411yescharacteristic
357C22×C4×C31C2411yescharacteristic
358C22×C4×C31C2411yescharacteristic
359C22×C4×C31C2411yescharacteristic
360C22×C4×C31C2411yescharacteristic
361C22×C4×C31C2411yescharacteristic
362C22×C4×C31C2411yescharacteristic
363C22×C4×C31C2411yescharacteristic
364Q16×C31—44no—
365SD16×C31—44no—
366SD16×C31—44no—
367D8×C31—44no—
368M16×C31—24no—
369M16×C31—24no—
370M16×C31—44no—
371C2×C8×C31—44no—
372C2×C8×C31C2414yes—
373C2×C8×C31C2414yes—
374C4⋊C4×C31—22no—
375C4⋊C4×C31—22no—
376C4⋊C4×C31—22no—
377C4⋊C4×C31—22no—
378C4⋊C4×C31—22no—
379C4⋊C4×C31—22no—
380C4⋊C4×C31—22no—
381C4⋊C4×C31—22no—
382C4⋊C4×C31—21no—
383C4⋊C4×C31—21no—
384C4⋊C4×C31—21no—
385C4⋊C4×C31—21no—
386C4⋊C4×C31C2412yes—
387C4⋊C4×C31C2412yes—
388C4⋊C4×C31C2412yes—
389C4⋊C4×C31C2412yes—
390C22⋊C4×C31—22no—
391C22⋊C4×C31—22no—
392C22⋊C4×C31—22no—
393C22⋊C4×C31—22no—
394C22⋊C4×C31—22no—
395C22⋊C4×C31—22no—
396C22⋊C4×C31—22no—
397C22⋊C4×C31—22no—
398C22⋊C4×C31—22no—
399C22⋊C4×C31—22no—
400C22⋊C4×C31—22no—
401C22⋊C4×C31—22no—
402C22⋊C4×C31—22no—
403C22⋊C4×C31—22no—
404C22⋊C4×C31—22no—
405C22⋊C4×C31—22no—
406C22⋊C4×C31—22no—
407C22⋊C4×C31—22no—
408C22⋊C4×C31—22no—
409C22⋊C4×C31—22no—
410C42×C31—22no—
411C42×C31—22no—
412C42×C31—22no—
413C42×C31—22no—
414#60752C3111yesmaximal, characteristic, direct product factor, Sylow
415C23×C31—22no—
416C23×C31—22no—
417C23×C31—22no—
418C23×C31—22no—
419C23×C31—22no—
420C23×C31—22no—
421C23×C31—22no—
422C23×C31—22no—
423C23×C31—22no—
424C23×C31—22no—
425C23×C31—22no—
426C23×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—42no—
439C23×C31—42no—
440C23×C31—42no—
441C23×C31—42no—
442C23×C31—416no—
443C23×C31—42no—
444C23×C31—42no—
445C23×C31C22×D411yescharacteristic
446C23×C31C22×D411yescharacteristic
447C23×C31C22×D411yescharacteristic
448C23×C31C22×D411yescharacteristic
449C23×C31C22×D411yescharacteristic
450C23×C31C22×D411yescharacteristic
451C23×C31C22×D411yescharacteristic
452Q8×C31—22no—
453Q8×C31—24no—
454Q8×C31—22no—
455Q8×C31—42no—
456Q8×C31—42no—
457D4×C31—22no—
458D4×C31—24no—
459D4×C31—22no—
460D4×C31—42no—
461D4×C31—44no—
462D4×C31—44no—
463D4×C31—44no—
464D4×C31—44no—
465D4×C31—44no—
466D4×C31—44no—
467D4×C31—44no—
468D4×C31—44no—
469D4×C31—44no—
470D4×C31—44no—
471D4×C31—44no—
472D4×C31—44no—
473D4×C31—42no—
474C2×C4×C31—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—22no—
491C2×C4×C31—22no—
492C2×C4×C31—22no—
493C2×C4×C31—22no—
494C2×C4×C31—22no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—44no—
508C2×C4×C31—44no—
509C2×C4×C31—44no—
510C2×C4×C31—42no—
511C2×C4×C31—42no—
512C2×C4×C31—42no—
513C2×C4×C31—42no—
514C2×C4×C31—42no—
515C2×C4×C31—42no—
516C2×C4×C31—44no—
517C2×C4×C31C22×D411yescharacteristic
518C2×C4×C31C22×D411yescharacteristic
519C2×C4×C31C22×D411yescharacteristic
520C2×C4×C31C22×D411yescharacteristic
521C2×C4×C31C22×D411yescharacteristic
522C2×C4×C31C22×D411yescharacteristic
523C2×C4×C31C22×D411yescharacteristic
524C2×C4×C31H(5,𝔽2)14yes—
525C2×C4×C31C2511yescharacteristic
526C8×C31—24no—
527C8×C31—24no—
528C2×#525C2×C3111yescharacteristic, complemented
529C2×#525C2×C3111yescharacteristic, complemented
530#3197C2×C3114yescomplemented
531#3196C2×C3112yescomplemented
532#3194C2×C3112yescomplemented
533#3191C2×C3114yescomplemented
534#3190C2×C3112yescomplemented
535#3188C2×C3112yescomplemented
536#3095C2×C3111yescharacteristic, complemented
537#3094C2×C3111yescharacteristic, complemented
538#3093C2×C3112yescomplemented
539#3056C2×C3112yescomplemented
540#3055C2×C3112yescomplemented
541#3007C2×C3111yescharacteristic, complemented
542#3006C2×C3111yescharacteristic, complemented
543#3005C2×C3112yescomplemented
544C2×#407C2×C3111yescharacteristic, complemented
545C22×C31—21no—
546C22×C31—21no—
547C22×C31—21no—
548C22×C31—21no—
549C22×C31—21no—
550C22×C31—21no—
551C22×C31—21no—
552C22×C31—21no—
553C22×C31—21no—
554C22×C31—21no—
555C22×C31—21no—
556C22×C31—21no—
557C22×C31—21no—
558C22×C31—21no—
559C22×C31—21no—
560C22×C31—21no—
561C22×C31—21no—
562C22×C31—21no—
563C22×C31—44no—
564C22×C31—44no—
565C22×C31—44no—
566C22×C31—44no—
567C22×C31—44no—
568C22×C31—44no—
569C22×C31—44no—
570C22×C31—42no—
571C22×C31—42no—
572C22×C31—42no—
573C22×C31—42no—
574C22×C31—42no—
575C22×C31—42no—
576C22×C31—84no—
577C22×C31—84no—
578C22×C31#53412yes—
579C22×C31#57512yes—
580C22×C31#57512yes—
581C22×C31C23×D411yescharacteristic
582C4×C31—21no—
583C4×C31—21no—
584C4×C31—21no—
585C4×C31—21no—
586C4×C31—21no—
587C4×C31—21no—
588C4×C31—42no—
589C4×C31—42no—
590C4×C31—42no—
591C4×C31—42no—
592C4×C31—42no—
593C4×C31—42no—
594C4×C31#53412yes—
595C4×C31C2×H(5,𝔽2)12yes—
596C22×#41C22×C3111yescharacteristic
597C22×#41C22×C3111yescharacteristic, complemented
598C24×C4C22×C3111yescharacteristic
599C2×#137C22×C3112yescomplemented
600C2×AGL(1,ℤ/8)C22×C3112yescomplemented
601C22×M16C22×C3112yescomplemented
602#525—21no—
603#525—21no—
604#525—21no—
605#525—21no—
606#525—21no—
607#525—21no—
608#525—21no—
609#525—21no—
610#525C22×C3112yes—
611#525C22×C3112yes—
612#525C22×C3112yes—
613#525C22×C3112yes—
614#525C22×C3112yescomplemented
615#525C22×C3112yescomplemented
616#525C22×C3112yescomplemented
617#525C22×C3112yescomplemented
618C2×#123—21no—
619C2×#123—21no—
620C2×C22⋊Q8C22×C3111yescharacteristic
621C2×C22⋊Q8C22×C3111yescharacteristic, complemented
622C2×C22⋊Q8C22×C3111yescharacteristic, complemented
623C2×C22⋊Q8C22×C3111yescharacteristic, complemented
624C2×#121C22×C3111yescharacteristic
625C2×#121C22×C3111yescharacteristic, complemented
626C2×#121C22×C3111yescharacteristic, complemented
627C2×#121C22×C3111yescharacteristic, complemented
628C2×#120—21no—
629C2×#120—21no—
630C2×C4×D4—21no—
631C2×C4×D4—21no—
632C2×C4×D4—21no—
633C2×C4×D4—21no—
634C2×#117C22×C3111yescharacteristic
635C2×#117C22×C3111yescharacteristic, complemented
636#485C22×C3114yescomplemented
637#485C22×C3114yescomplemented
638#485C22×C3114yescomplemented
639#484C22×C3112yescomplemented
640#483C22×C3112yescomplemented
641#482C22×C3114yescomplemented
642#482C22×C3114yescomplemented
643#482C22×C3114yescomplemented
644#481C22×C3112yescomplemented
645#480C22×C3112yescomplemented
646#470C22×C3114yescomplemented
647#469C22×C3114yescomplemented
648#468C22×C3114yescomplemented
649#468C22×C3114yescomplemented
650#467C22×C3114yescomplemented
651#466C22×C3114yescomplemented
652#465C22×C3114yescomplemented
653#465C22×C3114yescomplemented
654#452C22×C3114yescomplemented
655#452C22×C3114yescomplemented
656#452C22×C3114yescomplemented
657#451C22×C3112yescomplemented
658#450C22×C3112yescomplemented
659#449C22×C3114yescomplemented
660#449C22×C3114yescomplemented
661#449C22×C3114yescomplemented
662#448C22×C3112yescomplemented
663#447C22×C3112yescomplemented
664#428C22×C3112yescomplemented
665#428C22×C3112yescomplemented
666#419C22×C3112yescomplemented
667#418C22×C3112yescomplemented
668#417C22×C3112yescomplemented
669#417C22×C3112yescomplemented
670#407C22×C3111yescharacteristic
671#407C22×C3111yescharacteristic
672#407C22×C3112yescomplemented
673#407C22×C3112yescomplemented
674#407C22×C3112yescomplemented
675C2×C22⋊C8C22×C3112yescomplemented
676C2×C22⋊C8C22×C3112yescomplemented
677C2×C31—22no—
678C2×C31—22no—
679C2×C31—22no—
680C2×C31—41no—
681C2×C31—41no—
682C2×C31—41no—
683C2×C31—41no—
684C2×C31—82no—
685C2×C31—82no—
686C2×C31C2×#53411yescharacteristic
687C2×C31C2×#57511yescharacteristic
688C2×C31C2×#57511yescharacteristic
689C25D4×C3111yescharacteristic
690C2×#41—21no—
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—21no—
694C2×#41—44no—
695C2×#41—44no—
696C2×#41C23×C3112yes—
697C2×#41C23×C3112yes—
698C2×#41C23×C3112yes—
699C2×#41C23×C3112yes—
700C22×Q8C23×C3111yescharacteristic
701C22×Q8C23×C3111yescharacteristic
702C22×D4—21no—
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—21no—
706C22×D4—21no—
707C22×D4—21no—
708C22×D4C23×C3111yescharacteristic
709C22×D4C23×C3111yescharacteristic
710C23×C4—21no—
711C23×C4—21no—
712C23×C4—44no—
713C23×C4D4×C3111yescharacteristic
714C23×C4D4×C3111yescharacteristic
715C23×C4D4×C3111yescharacteristic
716C23×C4D4×C3111yescharacteristic
717C23×C4D4×C3111yescharacteristic
718C23×C4D4×C3111yescharacteristic
719C23×C4D4×C3111yescharacteristic
720C23×C4C23×C3111yescharacteristic
721C23×C4C23×C3111yescharacteristic
722C23×C4C23×C3111yescharacteristic
723C23×C4C23×C3111yescharacteristic
724C23×C4C23×C3111yescharacteristic
725C23×C4C23×C3111yescharacteristic
726C23×C4C23×C3111yescharacteristic
727#137—44no—
728AGL(1,ℤ/8)—44no—
729C2×Q16C23×C3114yescomplemented
730C2×SD16C23×C3114yescomplemented
731C2×SD16C23×C3114yescomplemented
732C2×D8C23×C3114yescomplemented
733C2×M16—44no—
734C2×M16C23×C3112yes—
735C2×M16C23×C3112yes—
736C2×M16C23×C3114yes—
737C22×C8C23×C3114yes—
738#123—22no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—22no—
744#123—22no—
745#123—22no—
746C22⋊Q8—21no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8—21no—
754C22⋊Q8C23×C3112yes—
755C22⋊Q8C23×C3112yes—
756C22⋊Q8C23×C3112yes—
757C22⋊Q8C23×C3112yes—
758C22⋊Q8C23×C3112yes—
759C22⋊Q8C23×C3112yes—
760C22⋊Q8C23×C3112yes—
761C22⋊Q8C23×C3112yes—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121C23×C3112yes—
771#121C23×C3112yes—
772#121C23×C3112yes—
773#121C23×C3112yes—
774#121C23×C3112yes—
775#121C23×C3112yes—
776#121C23×C3112yes—
777#121C23×C3112yes—
778#120—22no—
779#120—22no—
780#120—22no—
781#120—22no—
782#120—22no—
783#120—22no—
784#120—22no—
785#120—22no—
786C4×D4—22no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—22no—
802#117—21no—
803#117—21no—
804#117—21no—
805#117—21no—
806#117C23×C3112yes—
807#117C23×C3112yes—
808#117C23×C3112yes—
809#117C23×C3112yes—
810C2×C4⋊C4—21no—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—21no—
814C2×C4⋊C4C23×C3111yescharacteristic
815C2×C4⋊C4C23×C3111yescharacteristic
816C2×C4⋊C4C23×C3111yescharacteristic
817C2×C4⋊C4C23×C3111yescharacteristic
818C2×C22⋊C4—21no—
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—21no—
824C2×C22⋊C4—21no—
825C2×C22⋊C4—21no—
826C2×C22⋊C4—21no—
827C2×C22⋊C4—21no—
828C2×C42—21no—
829C2×C42—21no—
830#107C23×C3114yescomplemented
831#107C23×C3114yescomplemented
832#106C23×C3114yescomplemented
833#106C23×C3114yescomplemented
834#103C23×C3114yescomplemented
835#103C23×C3114yescomplemented
836#103C23×C3114yescomplemented
837#103C23×C3114yescomplemented
838#102C23×C3114yescomplemented
839#102C23×C3114yescomplemented
840#102C23×C3114yescomplemented
841#102C23×C3114yescomplemented
842C22⋊C8C23×C3112yes—
843C22⋊C8C23×C3112yes—
844C22⋊C8C23×C3112yes—
845C22⋊C8C23×C3112yes—
846C22⋊C8C23×C3114yes—
847C22⋊C8C23×C3114yes—
848C31#6075211yescharacteristic, direct product factor, Sylow
849C24—21no—
850C24—21no—
851C24—42no—
852C24—42no—
853C24—42no—
854C24C2×D4×C3111yescharacteristic
855C24C2×D4×C3111yescharacteristic
856C24C2×D4×C3111yescharacteristic
857C24C2×D4×C3111yescharacteristic
858C24C2×D4×C3111yescharacteristic
859C24C2×D4×C3111yescharacteristic
860C24C2×D4×C3111yescharacteristic
861#41—24no—
862#41—24no—
863#41—42no—
864#41—44no—
865#41—44no—
866#41—42no—
867#41—44no—
868#41—44no—
869#41—44no—
870#41—44no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—24no—
874C2×Q8—42no—
875C2×Q8C24×C3112yes—
876C2×Q8C24×C3112yes—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—24no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4C24×C3112yes—
900C2×D4C24×C3112yes—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4C2×D4×C3111yescharacteristic
928C22×C4C2×D4×C3111yescharacteristic
929C22×C4C2×D4×C3111yescharacteristic
930C22×C4C2×D4×C3111yescharacteristic
931C22×C4C2×D4×C3111yescharacteristic
932C22×C4C2×D4×C3111yescharacteristic
933C22×C4C2×D4×C3111yescharacteristic
934C22×C4C2×D4×C3111yescharacteristic
935C22×C4C2×D4×C3111yescharacteristic
936C22×C4C2×D4×C3111yescharacteristic
937C22×C4C2×D4×C3111yescharacteristic
938C22×C4C2×D4×C3111yescharacteristic
939C22×C4C2×D4×C3111yescharacteristic
940C22×C4C2×D4×C3111yescharacteristic
941C22×C4C2×D4×C3111yescharacteristic
942C22×C4C2×D4×C3111yescharacteristic
943C22×C4C2×D4×C3111yescharacteristic
944C22×C4C2×D4×C3111yescharacteristic
945C22×C4C2×D4×C3111yescharacteristic
946C22×C4C2×D4×C3111yescharacteristic
947C22×C4C2×D4×C3111yescharacteristic
948C22×C4C24×C3111yescharacteristic
949C22×C4C24×C3111yescharacteristic
950C22×C4C24×C3111yescharacteristic
951C22×C4C24×C3111yescharacteristic
952C22×C4C24×C3111yescharacteristic
953C22×C4C24×C3111yescharacteristic
954C22×C4C24×C3111yescharacteristic
955Q16—44no—
956SD16—44no—
957SD16—44no—
958D8—44no—
959M16—24no—
960M16—24no—
961M16—44no—
962C2×C8—44no—
963C2×C8C24×C3114yes—
964C2×C8C24×C3114yes—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4C24×C3112yes—
978C4⋊C4C24×C3112yes—
979C4⋊C4C24×C3112yes—
980C4⋊C4C24×C3112yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—416no—
1033C23—42no—
1034C23—42no—
1035C23C22×D4×C3111yescharacteristic
1036C23C22×D4×C3111yescharacteristic
1037C23C22×D4×C3111yescharacteristic
1038C23C22×D4×C3111yescharacteristic
1039C23C22×D4×C3111yescharacteristic
1040C23C22×D4×C3111yescharacteristic
1041C23C22×D4×C3111yescharacteristic
1042Q8—22no—
1043Q8—24no—
1044Q8—22no—
1045Q8—42no—
1046Q8—42no—
1047D4—22no—
1048D4—24no—
1049D4—22no—
1050D4—42no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—44no—
1055D4—44no—
1056D4—44no—
1057D4—44no—
1058D4—44no—
1059D4—44no—
1060D4—44no—
1061D4—44no—
1062D4—44no—
1063D4—42no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—44no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—44no—
1107C2×C4C22×D4×C3111yescharacteristic
1108C2×C4C22×D4×C3111yescharacteristic
1109C2×C4C22×D4×C3111yescharacteristic
1110C2×C4C22×D4×C3111yescharacteristic
1111C2×C4C22×D4×C3111yescharacteristic
1112C2×C4C22×D4×C3111yescharacteristic
1113C2×C4C22×D4×C3111yescharacteristic
1114C2×C4C31×H(5,𝔽2)14yes—
1115C2×C4C25×C3111yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—84no—
1150C22—84no—
1151C22C31×#53412yes—
1152C22C31×#57512yes—
1153C22C31×#57512yes—
1154C22C23×D4×C3111yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4C31×#53412yes—
1168C4C2×C31×H(5,𝔽2)12yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—82no—
1178C2C2×C31×#53411yescharacteristic
1179C2C2×C31×#57511yescharacteristic
1180C2C2×C31×#57511yescharacteristic
subgroupG/H
center, socleC22×C31C23×D4
commutator, Frattini, cosocleC2×C4C25×C31
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#525C2semidirect
2. C2×C31×#525C2semidirect
3. C31×#3197C2semidirect
4. C31×#3196C2semidirect
5. C31×#3194C2semidirect
6. C31×#3191C2semidirect
7. C31×#3190C2semidirect
8. C31×#3188C2semidirect
9. C31×#3095C2semidirect
10. C31×#3094C2semidirect
11. C31×#3093C2semidirect
12. C31×#3056C2semidirect
13. C31×#3055C2semidirect
14. C31×#3007C2semidirect
15. C31×#3006C2semidirect
16. C31×#3005C2semidirect
17. C2×C31×#407C2semidirect
19. C22×#41×C31C22semidirect
21. C2×C31×#137C22semidirect
22. C2×C31×AGL(1,ℤ/8)C22semidirect
23. C22×M16×C31C22semidirect
36. C31×#525C22semidirect
37. C31×#525C22semidirect
38. C31×#525C22semidirect
39. C31×#525C22semidirect
43. C2×C31×C22⋊Q8C22semidirect
44. C2×C31×C22⋊Q8C22semidirect
45. C2×C31×C22⋊Q8C22semidirect
47. C2×C31×#121C22semidirect
48. C2×C31×#121C22semidirect
49. C2×C31×#121C22semidirect
57. C2×C31×#117C22semidirect
58. C31×#485C22semidirect
59. C31×#485C22semidirect
60. C31×#485C22semidirect
61. C31×#484C22semidirect
62. C31×#483C22semidirect
63. C31×#482C22semidirect
64. C31×#482C22semidirect
65. C31×#482C22semidirect
66. C31×#481C22semidirect
67. C31×#480C22semidirect
68. C31×#470C22semidirect
69. C31×#469C22semidirect
70. C31×#468C22semidirect
71. C31×#468C22semidirect
72. C31×#467C22semidirect
73. C31×#466C22semidirect
74. C31×#465C22semidirect
75. C31×#465C22semidirect
76. C31×#452C22semidirect
77. C31×#452C22semidirect
78. C31×#452C22semidirect
79. C31×#451C22semidirect
80. C31×#450C22semidirect
81. C31×#449C22semidirect
82. C31×#449C22semidirect
83. C31×#449C22semidirect
84. C31×#448C22semidirect
85. C31×#447C22semidirect
86. C31×#428C22semidirect
87. C31×#428C22semidirect
88. C31×#419C22semidirect
89. C31×#418C22semidirect
90. C31×#417C22semidirect
91. C31×#417C22semidirect
94. C31×#407C22semidirect
95. C31×#407C22semidirect
96. C31×#407C22semidirect
97. C2×C31×C22⋊C8C22semidirect
98. C2×C31×C22⋊C8C22semidirect
139. C2×Q16×C31C23semidirect
140. C2×SD16×C31C23semidirect
141. C2×SD16×C31C23semidirect
142. C2×D8×C31C23semidirect
240. C31×#107C23semidirect
241. C31×#107C23semidirect
242. C31×#106C23semidirect
243. C31×#106C23semidirect
244. C31×#103C23semidirect
245. C31×#103C23semidirect
246. C31×#103C23semidirect
247. C31×#103C23semidirect
248. C31×#102C23semidirect
249. C31×#102C23semidirect
250. C31×#102C23semidirect
251. C31×#102C23semidirect
414. #60752C31direct (N × H)
528. C2×#525C2×C31semidirect
529. C2×#525C2×C31semidirect
530. #3197C2×C31semidirect
531. #3196C2×C31semidirect
532. #3194C2×C31semidirect
533. #3191C2×C31semidirect
534. #3190C2×C31semidirect
535. #3188C2×C31semidirect
536. #3095C2×C31semidirect
537. #3094C2×C31semidirect
538. #3093C2×C31semidirect
539. #3056C2×C31semidirect
540. #3055C2×C31semidirect
541. #3007C2×C31semidirect
542. #3006C2×C31semidirect
543. #3005C2×C31semidirect
544. C2×#407C2×C31semidirect
597. C22×#41C22×C31semidirect
599. C2×#137C22×C31semidirect
600. C2×AGL(1,ℤ/8)C22×C31semidirect
601. C22×M16C22×C31semidirect
614. #525C22×C31semidirect
615. #525C22×C31semidirect
616. #525C22×C31semidirect
617. #525C22×C31semidirect
621. C2×C22⋊Q8C22×C31semidirect
622. C2×C22⋊Q8C22×C31semidirect
623. C2×C22⋊Q8C22×C31semidirect
625. C2×#121C22×C31semidirect
626. C2×#121C22×C31semidirect
627. C2×#121C22×C31semidirect
635. C2×#117C22×C31semidirect
636. #485C22×C31semidirect
637. #485C22×C31semidirect
638. #485C22×C31semidirect
639. #484C22×C31semidirect
640. #483C22×C31semidirect
641. #482C22×C31semidirect
642. #482C22×C31semidirect
643. #482C22×C31semidirect
644. #481C22×C31semidirect
645. #480C22×C31semidirect
646. #470C22×C31semidirect
647. #469C22×C31semidirect
648. #468C22×C31semidirect
649. #468C22×C31semidirect
650. #467C22×C31semidirect
651. #466C22×C31semidirect
652. #465C22×C31semidirect
653. #465C22×C31semidirect
654. #452C22×C31semidirect
655. #452C22×C31semidirect
656. #452C22×C31semidirect
657. #451C22×C31semidirect
658. #450C22×C31semidirect
659. #449C22×C31semidirect
660. #449C22×C31semidirect
661. #449C22×C31semidirect
662. #448C22×C31semidirect
663. #447C22×C31semidirect
664. #428C22×C31semidirect
665. #428C22×C31semidirect
666. #419C22×C31semidirect
667. #418C22×C31semidirect
668. #417C22×C31semidirect
669. #417C22×C31semidirect
672. #407C22×C31semidirect
673. #407C22×C31semidirect
674. #407C22×C31semidirect
675. C2×C22⋊C8C22×C31semidirect
676. C2×C22⋊C8C22×C31semidirect
729. C2×Q16C23×C31semidirect
730. C2×SD16C23×C31semidirect
731. C2×SD16C23×C31semidirect
732. C2×D8C23×C31semidirect
830. #107C23×C31semidirect
831. #107C23×C31semidirect
832. #106C23×C31semidirect
833. #106C23×C31semidirect
834. #103C23×C31semidirect
835. #103C23×C31semidirect
836. #103C23×C31semidirect
837. #103C23×C31semidirect
838. #102C23×C31semidirect
839. #102C23×C31semidirect
840. #102C23×C31semidirect
841. #102C23×C31semidirect
848. C31#60752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C31×#31972
C31×#31962
C31×#31942
C31×#31912
C31×#31902
C31×#31882
C31×#30952
C31×#30942
C31×#30932
C31×#30562
C31×#30552
C31×#30072
C31×#30062
C31×#30052
C2×C31×#4072
#6075231