Finite Group Databasebeta

← C31×#60559 #21517318

Subgroups — C31×#60559 #21517318

Order 7936.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3444C211yesmaximal, characteristic, complemented
2C2×C4×#41×C31C211yesmaximal, characteristic, complemented
3C31×#3116C212yesmaximal, complemented
4C31×#3115C212yesmaximal, complemented
5C31×#3111C214yesmaximal, complemented
6C31×#3107C212yesmaximal, complemented
7C31×#3106C212yesmaximal, complemented
8C31×#3102C214yesmaximal, complemented
9C31×#3093C212yesmaximal, complemented
10C31×#3078C211yesmaximal, characteristic, complemented
11C31×#3077C211yesmaximal, characteristic, complemented
12C31×#3037C211yesmaximal, characteristic, complemented
13C31×#3036C211yesmaximal, characteristic, complemented
14C31×#3005C212yesmaximal, complemented
15C4×C31×#137C212yesmaximal, complemented
16C4×C31×AGL(1,ℤ/8)C212yesmaximal, complemented
17C31×#2920C211yesmaximal, characteristic, complemented
18C22×#41×C31C2211yescharacteristic
19C2×C31×#137C2212yes—
20C2×C31×AGL(1,ℤ/8)C2212yes—
21C31×#533C2211yescharacteristic
22C31×#533C2211yescharacteristic, complemented
23C31×#533C2211yescharacteristic, complemented
24C31×#532C2211yescharacteristic
25C31×#532C2211yescharacteristic, complemented
26C31×#532C2211yescharacteristic, complemented
27C31×#529—21no—
28C31×#529—21no—
29C31×#529—21no—
30C31×#529—21no—
31C31×#529C2212yescomplemented
32C31×#529C2212yescomplemented
33C31×#525—21no—
34C31×#525—21no—
35C31×#525C2212yes—
36C4×#41×C31—21no—
37C4×#41×C31—21no—
38C4×#41×C31—21no—
39C4×#41×C31—21no—
40C4×#41×C31—21no—
41C4×#41×C31—21no—
42C4×#41×C31C2212yes—
43C4×#41×C31C2212yes—
44C4×#41×C31C2212yes—
45C4×#41×C31C2212yes—
46C4×#41×C31C2212yes—
47C2×C4×Q8×C31C2211yescharacteristic
48C2×C4×Q8×C31C2211yescharacteristic
49C2×C4×D4×C31—21no—
50C2×C4×D4×C31—21no—
51C2×C4×D4×C31C2211yescharacteristic
52C2×C4×D4×C31C2211yescharacteristic
53C2×C31×#117—21no—
54C2×C31×#117C2211yescharacteristic
55C22×C42×C31—21no—
56C22×C42×C31C2211yescharacteristic
57C31×#485C2214yescomplemented
58C31×#485C2214yescomplemented
59C31×#482C2214yescomplemented
60C31×#482C2214yescomplemented
61C31×#479C2214yescomplemented
62C31×#478C2214yescomplemented
63C31×#477C2212yescomplemented
64C31×#476C2212yescomplemented
65C31×#475C2212yescomplemented
66C31×#474C2212yescomplemented
67C31×#464C2214yescomplemented
68C31×#463C2214yescomplemented
69C31×#462C2212yescomplemented
70C31×#461C2212yescomplemented
71C31×#460C2212yescomplemented
72C31×#459C2212yescomplemented
73C31×#452C2214yes—
74C31×#452C2214yes—
75C31×#449C2214yes—
76C31×#449C2214yes—
77C31×#442C2214yescomplemented
78C31×#441C2214yescomplemented
79C31×#440C2214yescomplemented
80C31×#440C2214yescomplemented
81C4×Q16×C31C2214yescomplemented
82C4×SD16×C31C2214yescomplemented
83C4×SD16×C31C2214yescomplemented
84C4×D8×C31C2214yescomplemented
85C31×#432C2212yescomplemented
86C31×#432C2212yescomplemented
87C31×#431C2212yescomplemented
88C31×#431C2212yescomplemented
89C31×#428C2212yes—
90C31×#428C2212yes—
91C31×#423C2211yescharacteristic
92C31×#423C2211yescharacteristic
93C31×#419C2212yes—
94C31×#418C2212yes—
95C31×#417C2212yes—
96C31×#417C2212yes—
97C31×#407C2212yes—
98C4×M16×C31C2212yes—
99C2×#41×C31—24no—
100C2×#41×C31—24no—
101C2×#41×C31—21no—
102C2×#41×C31—21no—
103C2×#41×C31—21no—
104C2×#41×C31—21no—
105C2×#41×C31C2312yes—
106C2×#41×C31C2312yes—
107C2×#41×C31C2312yes—
108C22×Q8×C31C2311yescharacteristic
109C22×D4×C31—21no—
110C22×D4×C31C2311yescharacteristic
111C23×C4×C31—21no—
112C23×C4×C31—21no—
113C23×C4×C31—21no—
114C23×C4×C31D411yescharacteristic
115C23×C4×C31D411yescharacteristic
116C23×C4×C31C2311yescharacteristic
117C31×#137—28no—
118C31×AGL(1,ℤ/8)—28no—
119C2×Q16×C31C2314yes—
120C2×SD16×C31C2314yes—
121C2×SD16×C31C2314yes—
122C2×D8×C31C2314yes—
123C2×M16×C31C2312yes—
124C2×M16×C31C2312yes—
125C31×C4⋊Q8C2311yescharacteristic
126C31×C4⋊Q8C2311yescharacteristic
127C31×C4⋊Q8C2311yescharacteristic
128C31×#127C2311yescharacteristic
129C31×#126—22no—
130C31×#126—22no—
131C31×#125—21no—
132C31×#125—21no—
133C31×#125C2312yes—
134C31×#124—21no—
135C31×#124—21no—
136C31×#124C2312yes—
137C31×#123—22no—
138C31×#123—22no—
139C31×#123—22no—
140C31×C22⋊Q8—21no—
141C31×C22⋊Q8—21no—
142C31×C22⋊Q8—21no—
143C31×C22⋊Q8—21no—
144C31×C22⋊Q8C2312yes—
145C31×C22⋊Q8C2312yes—
146C31×#121—21no—
147C31×#121—21no—
148C31×#121—21no—
149C31×#121—21no—
150C31×#121C2312yes—
151C31×#121C2312yes—
152C31×#120—22no—
153C4×Q8×C31—21no—
154C4×Q8×C31—21no—
155C4×Q8×C31—21no—
156C4×Q8×C31—21no—
157C4×Q8×C31—21no—
158C4×Q8×C31—21no—
159C4×Q8×C31—21no—
160C4×Q8×C31—21no—
161C4×Q8×C31C2312yes—
162C4×Q8×C31C2312yes—
163C4×Q8×C31C2312yes—
164C4×Q8×C31C2312yes—
165C4×Q8×C31C2312yes—
166C4×Q8×C31C2312yes—
167C4×D4×C31—22no—
168C4×D4×C31—22no—
169C4×D4×C31—22no—
170C4×D4×C31—22no—
171C4×D4×C31—22no—
172C4×D4×C31—22no—
173C4×D4×C31—22no—
174C4×D4×C31—22no—
175C4×D4×C31—22no—
176C4×D4×C31—22no—
177C4×D4×C31—22no—
178C4×D4×C31—22no—
179C4×D4×C31—22no—
180C4×D4×C31—22no—
181C4×D4×C31—21no—
182C4×D4×C31—21no—
183C4×D4×C31—21no—
184C4×D4×C31—21no—
185C4×D4×C31—21no—
186C4×D4×C31—21no—
187C4×D4×C31—21no—
188C4×D4×C31—21no—
189C4×D4×C31C2312yes—
190C4×D4×C31C2312yes—
191C4×D4×C31C2312yes—
192C4×D4×C31C2312yes—
193C4×D4×C31C2312yes—
194C4×D4×C31C2312yes—
195C31×#117—21no—
196C31×#117—21no—
197C31×#117—21no—
198C31×#117—21no—
199C31×#117—22no—
200C31×#117—22no—
201C31×#117—22no—
202C31×#117—22no—
203C31×#117—22no—
204C31×#117—22no—
205C31×#117—22no—
206C31×#117C2312yes—
207C31×#117C2312yes—
208C31×#117C2312yes—
209C2×C4⋊C4×C31—21no—
210C2×C4⋊C4×C31—21no—
211C2×C4⋊C4×C31C2311yescharacteristic
212C2×C4⋊C4×C31C2311yescharacteristic
213C2×C22⋊C4×C31—21no—
214C2×C22⋊C4×C31—21no—
215C2×C22⋊C4×C31—21no—
216C2×C42×C31—21no—
217C2×C42×C31—21no—
218C2×C42×C31—21no—
219C2×C42×C31—22no—
220C2×C42×C31—22no—
221C2×C42×C31—22no—
222C2×C42×C31—22no—
223C2×C42×C31—22no—
224C2×C42×C31D411yescharacteristic
225C2×C42×C31D411yescharacteristic
226C2×C42×C31D411yescharacteristic
227C2×C42×C31D411yescharacteristic
228C2×C42×C31D411yescharacteristic
229C2×C42×C31D411yescharacteristic
230C2×C42×C31C2311yescharacteristic
231C2×C42×C31C2311yescharacteristic
232C2×C42×C31C2311yescharacteristic
233C2×C42×C31C2311yescharacteristic
234C2×C42×C31C2311yescharacteristic
235C2×C42×C31C2311yescharacteristic
236C31×#107C2314yes—
237C31×#107C2314yes—
238C31×#106C2314yes—
239C31×#106C2314yes—
240C31×C4⋊C8C2312yes—
241C31×C4⋊C8C2312yes—
242C31×C4⋊C8C2312yes—
243C31×C4⋊C8C2312yes—
244C31×#103C2314yes—
245C31×#103C2314yes—
246C31×#103C2314yes—
247C31×#103C2314yes—
248C31×#102C2314yes—
249C31×#102C2314yes—
250C31×#102C2314yes—
251C31×#102C2314yes—
252C31×C22⋊C8C2314yes—
253C31×C22⋊C8C2314yes—
254C31×#97C2314yes—
255C4×C8×C31C2314yes—
256C24×C31—21no—
257C24×C31C2×D411yescharacteristic
258#41×C31—28no—
259#41×C31—28no—
260#41×C31—24no—
261#41×C31—24no—
262#41×C31—24no—
263#41×C31—24no—
264#41×C31—24no—
265#41×C31—24no—
266#41×C31—44no—
267#41×C31—44no—
268C2×Q8×C31—21no—
269C2×Q8×C31—21no—
270C2×Q8×C31—21no—
271C2×Q8×C31—22no—
272C2×Q8×C31#4114yescomplemented
273C2×Q8×C31C2412yes—
274C2×Q8×C31C2412yes—
275C2×D4×C31—28no—
276C2×D4×C31—22no—
277C2×D4×C31—22no—
278C2×D4×C31—22no—
279C2×D4×C31—22no—
280C2×D4×C31—22no—
281C2×D4×C31—21no—
282C2×D4×C31—21no—
283C2×D4×C31—21no—
284C2×D4×C31—22no—
285C2×D4×C31#4114yescomplemented
286C2×D4×C31C2412yes—
287C2×D4×C31C2412yes—
288C22×C4×C31—28no—
289C22×C4×C31—21no—
290C22×C4×C31—22no—
291C22×C4×C31—22no—
292C22×C4×C31—22no—
293C22×C4×C31—22no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—22no—
297C22×C4×C31—22no—
298C22×C4×C31—22no—
299C22×C4×C31—22no—
300C22×C4×C31—22no—
301C22×C4×C31—22no—
302C22×C4×C31—22no—
303C22×C4×C31—42no—
304C22×C4×C31—42no—
305C22×C4×C31—44no—
306C22×C4×C31—44no—
307C22×C4×C31C2×D411yescharacteristic
308C22×C4×C31C2×D411yescharacteristic
309C22×C4×C31C2×D411yescharacteristic
310C22×C4×C31C2×D411yescharacteristic
311C22×C4×C31C2×D411yescharacteristic
312C22×C4×C31C2×D411yescharacteristic
313C22×C4×C31C2×D411yescharacteristic
314C22×C4×C31C2×D411yescharacteristic
315C22×C4×C31C2×D411yescharacteristic
316C22×C4×C31C2×D411yescharacteristic
317C22×C4×C31C2×D411yescharacteristic
318C22×C4×C31C2×D411yescharacteristic
319C22×C4×C31C2×D411yescharacteristic
320C22×C4×C31C2×D411yescharacteristic
321C22×C4×C31C2×D411yescharacteristic
322C22×C4×C31C2411yescharacteristic
323C22×C4×C31C2411yescharacteristic
324C22×C4×C31C2411yescharacteristic
325Q16×C31—28no—
326SD16×C31—28no—
327SD16×C31—28no—
328D8×C31—28no—
329M16×C31—24no—
330M16×C31—24no—
331C2×C8×C31C2414yes—
332C2×C8×C31C2414yes—
333C4⋊C4×C31—22no—
334C4⋊C4×C31—22no—
335C4⋊C4×C31—22no—
336C4⋊C4×C31—22no—
337C4⋊C4×C31—21no—
338C4⋊C4×C31—21no—
339C4⋊C4×C31—21no—
340C4⋊C4×C31—21no—
341C4⋊C4×C31—21no—
342C4⋊C4×C31—21no—
343C4⋊C4×C31—22no—
344C4⋊C4×C31—22no—
345C4⋊C4×C31—22no—
346C4⋊C4×C31—22no—
347C4⋊C4×C31—22no—
348C4⋊C4×C31—22no—
349C4⋊C4×C31C2412yes—
350C4⋊C4×C31C2412yes—
351C4⋊C4×C31C2412yes—
352C4⋊C4×C31C2412yes—
353C22⋊C4×C31—22no—
354C22⋊C4×C31—22no—
355C22⋊C4×C31—22no—
356C22⋊C4×C31—22no—
357C22⋊C4×C31—22no—
358C22⋊C4×C31—22no—
359C22⋊C4×C31—22no—
360C22⋊C4×C31—22no—
361C22⋊C4×C31—22no—
362C22⋊C4×C31—22no—
363C22⋊C4×C31—22no—
364C22⋊C4×C31—22no—
365C22⋊C4×C31—22no—
366C22⋊C4×C31—22no—
367C22⋊C4×C31—22no—
368C42×C31—22no—
369C42×C31—22no—
370C42×C31—22no—
371C42×C31—22no—
372C42×C31—22no—
373C42×C31—22no—
374C42×C31—22no—
375C42×C31—22no—
376C42×C31—22no—
377C42×C31C2×D411yescharacteristic
378C42×C31C2×D411yescharacteristic
379C42×C31C2×D411yescharacteristic
380C42×C31C2×D411yescharacteristic
381C42×C31C2×D411yescharacteristic
382C42×C31C2×D411yescharacteristic
383C42×C31C2×D411yescharacteristic
384C42×C31C2×D411yescharacteristic
385C42×C31C2×D411yescharacteristic
386C42×C31C2×D411yescharacteristic
387C42×C31C2×D411yescharacteristic
388C42×C31C2×D411yescharacteristic
389C42×C31C2411yescharacteristic
390C42×C31C2411yescharacteristic
391C42×C31C2411yescharacteristic
392C42×C31C2411yescharacteristic
393#60559C3111yesmaximal, characteristic, direct product factor, Sylow
394C23×C31—22no—
395C23×C31—24no—
396C23×C31—22no—
397C23×C31—22no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—42no—
401C23×C31—42no—
402C23×C31C22×D411yescharacteristic
403C23×C31C22×D411yescharacteristic
404C23×C31C22×D411yescharacteristic
405Q8×C31—24no—
406Q8×C31—22no—
407Q8×C31—22no—
408Q8×C31—22no—
409Q8×C31—42no—
410Q8×C31—42no—
411Q8×C31C2×#4114yes—
412D4×C31—28no—
413D4×C31—28no—
414D4×C31—24no—
415D4×C31—22no—
416D4×C31—22no—
417D4×C31—22no—
418D4×C31—42no—
419D4×C31—44no—
420D4×C31—44no—
421D4×C31—44no—
422D4×C31—42no—
423D4×C31C2×#4114yes—
424C2×C4×C31—28no—
425C2×C4×C31—28no—
426C2×C4×C31—22no—
427C2×C4×C31—24no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—22no—
437C2×C4×C31—21no—
438C2×C4×C31—21no—
439C2×C4×C31—21no—
440C2×C4×C31—21no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—22no—
444C2×C4×C31—22no—
445C2×C4×C31—22no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—44no—
453C2×C4×C31—44no—
454C2×C4×C31—44no—
455C2×C4×C31—42no—
456C2×C4×C31—42no—
457C2×C4×C31—44no—
458C2×C4×C31—44no—
459C2×C4×C31—44no—
460C2×C4×C31—44no—
461C2×C4×C31C22×D411yescharacteristic
462C2×C4×C31C22×D411yescharacteristic
463C2×C4×C31C22×D411yescharacteristic
464C2×C4×C31C22×D411yescharacteristic
465C2×C4×C31C22×D411yescharacteristic
466C2×C4×C31C22×D411yescharacteristic
467C2×C4×C31C22×D411yescharacteristic
468C2×C4×C31C22×D411yescharacteristic
469C2×C4×C31C22×D411yescharacteristic
470C2×C4×C31C22×D411yescharacteristic
471C2×C4×C31C22×D411yescharacteristic
472C2×C4×C31C2×#4112yes—
473C2×C4×C31C2×#4112yes—
474C2×C4×C31C2511yescharacteristic
475C8×C31—24no—
476C8×C31—24no—
477#3444C2×C3111yescharacteristic, complemented
478C2×C4×#41C2×C3111yescharacteristic, complemented
479#3116C2×C3112yescomplemented
480#3115C2×C3112yescomplemented
481#3111C2×C3114yescomplemented
482#3107C2×C3112yescomplemented
483#3106C2×C3112yescomplemented
484#3102C2×C3114yescomplemented
485#3093C2×C3112yescomplemented
486#3078C2×C3111yescharacteristic, complemented
487#3077C2×C3111yescharacteristic, complemented
488#3037C2×C3111yescharacteristic, complemented
489#3036C2×C3111yescharacteristic, complemented
490#3005C2×C3112yescomplemented
491C4×#137C2×C3112yescomplemented
492C4×AGL(1,ℤ/8)C2×C3112yescomplemented
493#2920C2×C3111yescharacteristic, complemented
494C22×C31—21no—
495C22×C31—21no—
496C22×C31—21no—
497C22×C31—21no—
498C22×C31—24no—
499C22×C31—21no—
500C22×C31—21no—
501C22×C31—21no—
502C22×C31—21no—
503C22×C31—44no—
504C22×C31—48no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—42no—
510C22×C31#52512yes—
511C22×C31C23×D411yescharacteristic
512C4×C31—21no—
513C4×C31—21no—
514C4×C31—24no—
515C4×C31—21no—
516C4×C31—21no—
517C4×C31—21no—
518C4×C31—21no—
519C4×C31—21no—
520C4×C31—21no—
521C4×C31—42no—
522C4×C31—42no—
523C4×C31—42no—
524C4×C31—42no—
525C4×C31—42no—
526C4×C31#52512yes—
527C4×C31#57512yes—
528C4×C31#57512yes—
529C4×C31C22×#4111yescharacteristic
530C4×C31C22×#4111yescharacteristic
531C22×#41C22×C3111yescharacteristic
532C2×#137C22×C3112yes—
533C2×AGL(1,ℤ/8)C22×C3112yes—
534#533C22×C3111yescharacteristic
535#533C22×C3111yescharacteristic, complemented
536#533C22×C3111yescharacteristic, complemented
537#532C22×C3111yescharacteristic
538#532C22×C3111yescharacteristic, complemented
539#532C22×C3111yescharacteristic, complemented
540#529—21no—
541#529—21no—
542#529—21no—
543#529—21no—
544#529C22×C3112yescomplemented
545#529C22×C3112yescomplemented
546#525—21no—
547#525—21no—
548#525C22×C3112yes—
549C4×#41—21no—
550C4×#41—21no—
551C4×#41—21no—
552C4×#41—21no—
553C4×#41—21no—
554C4×#41—21no—
555C4×#41C22×C3112yes—
556C4×#41C22×C3112yes—
557C4×#41C22×C3112yes—
558C4×#41C22×C3112yes—
559C4×#41C22×C3112yes—
560C2×C4×Q8C22×C3111yescharacteristic
561C2×C4×Q8C22×C3111yescharacteristic
562C2×C4×D4—21no—
563C2×C4×D4—21no—
564C2×C4×D4C22×C3111yescharacteristic
565C2×C4×D4C22×C3111yescharacteristic
566C2×#117—21no—
567C2×#117C22×C3111yescharacteristic
568C22×C42—21no—
569C22×C42C22×C3111yescharacteristic
570#485C22×C3114yescomplemented
571#485C22×C3114yescomplemented
572#482C22×C3114yescomplemented
573#482C22×C3114yescomplemented
574#479C22×C3114yescomplemented
575#478C22×C3114yescomplemented
576#477C22×C3112yescomplemented
577#476C22×C3112yescomplemented
578#475C22×C3112yescomplemented
579#474C22×C3112yescomplemented
580#464C22×C3114yescomplemented
581#463C22×C3114yescomplemented
582#462C22×C3112yescomplemented
583#461C22×C3112yescomplemented
584#460C22×C3112yescomplemented
585#459C22×C3112yescomplemented
586#452C22×C3114yes—
587#452C22×C3114yes—
588#449C22×C3114yes—
589#449C22×C3114yes—
590#442C22×C3114yescomplemented
591#441C22×C3114yescomplemented
592#440C22×C3114yescomplemented
593#440C22×C3114yescomplemented
594C4×Q16C22×C3114yescomplemented
595C4×SD16C22×C3114yescomplemented
596C4×SD16C22×C3114yescomplemented
597C4×D8C22×C3114yescomplemented
598#432C22×C3112yescomplemented
599#432C22×C3112yescomplemented
600#431C22×C3112yescomplemented
601#431C22×C3112yescomplemented
602#428C22×C3112yes—
603#428C22×C3112yes—
604#423C22×C3111yescharacteristic
605#423C22×C3111yescharacteristic
606#419C22×C3112yes—
607#418C22×C3112yes—
608#417C22×C3112yes—
609#417C22×C3112yes—
610#407C22×C3112yes—
611C4×M16C22×C3112yes—
612C2×C31—22no—
613C2×C31—41no—
614C2×C31—41no—
615C2×C31—44no—
616C2×C31—82no—
617C2×C31C2×#52511yescharacteristic
618C2×C31C2×#57511yescharacteristic
619C2×C31C2×#57511yescharacteristic
620C2×#41—24no—
621C2×#41—24no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41C23×C3112yes—
627C2×#41C23×C3112yes—
628C2×#41C23×C3112yes—
629C22×Q8C23×C3111yescharacteristic
630C22×D4—21no—
631C22×D4C23×C3111yescharacteristic
632C23×C4—21no—
633C23×C4—21no—
634C23×C4—21no—
635C23×C4D4×C3111yescharacteristic
636C23×C4D4×C3111yescharacteristic
637C23×C4C23×C3111yescharacteristic
638#137—28no—
639AGL(1,ℤ/8)—28no—
640C2×Q16C23×C3114yes—
641C2×SD16C23×C3114yes—
642C2×SD16C23×C3114yes—
643C2×D8C23×C3114yes—
644C2×M16C23×C3112yes—
645C2×M16C23×C3112yes—
646C4⋊Q8C23×C3111yescharacteristic
647C4⋊Q8C23×C3111yescharacteristic
648C4⋊Q8C23×C3111yescharacteristic
649#127C23×C3111yescharacteristic
650#126—22no—
651#126—22no—
652#125—21no—
653#125—21no—
654#125C23×C3112yes—
655#124—21no—
656#124—21no—
657#124C23×C3112yes—
658#123—22no—
659#123—22no—
660#123—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8C23×C3112yes—
666C22⋊Q8C23×C3112yes—
667#121—21no—
668#121—21no—
669#121—21no—
670#121—21no—
671#121C23×C3112yes—
672#121C23×C3112yes—
673#120—22no—
674C4×Q8—21no—
675C4×Q8—21no—
676C4×Q8—21no—
677C4×Q8—21no—
678C4×Q8—21no—
679C4×Q8—21no—
680C4×Q8—21no—
681C4×Q8—21no—
682C4×Q8C23×C3112yes—
683C4×Q8C23×C3112yes—
684C4×Q8C23×C3112yes—
685C4×Q8C23×C3112yes—
686C4×Q8C23×C3112yes—
687C4×Q8C23×C3112yes—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707C4×D4—21no—
708C4×D4—21no—
709C4×D4—21no—
710C4×D4C23×C3112yes—
711C4×D4C23×C3112yes—
712C4×D4C23×C3112yes—
713C4×D4C23×C3112yes—
714C4×D4C23×C3112yes—
715C4×D4C23×C3112yes—
716#117—21no—
717#117—21no—
718#117—21no—
719#117—21no—
720#117—22no—
721#117—22no—
722#117—22no—
723#117—22no—
724#117—22no—
725#117—22no—
726#117—22no—
727#117C23×C3112yes—
728#117C23×C3112yes—
729#117C23×C3112yes—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—21no—
732C2×C4⋊C4C23×C3111yescharacteristic
733C2×C4⋊C4C23×C3111yescharacteristic
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—22no—
741C2×C42—22no—
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42D4×C3111yescharacteristic
746C2×C42D4×C3111yescharacteristic
747C2×C42D4×C3111yescharacteristic
748C2×C42D4×C3111yescharacteristic
749C2×C42D4×C3111yescharacteristic
750C2×C42D4×C3111yescharacteristic
751C2×C42C23×C3111yescharacteristic
752C2×C42C23×C3111yescharacteristic
753C2×C42C23×C3111yescharacteristic
754C2×C42C23×C3111yescharacteristic
755C2×C42C23×C3111yescharacteristic
756C2×C42C23×C3111yescharacteristic
757#107C23×C3114yes—
758#107C23×C3114yes—
759#106C23×C3114yes—
760#106C23×C3114yes—
761C4⋊C8C23×C3112yes—
762C4⋊C8C23×C3112yes—
763C4⋊C8C23×C3112yes—
764C4⋊C8C23×C3112yes—
765#103C23×C3114yes—
766#103C23×C3114yes—
767#103C23×C3114yes—
768#103C23×C3114yes—
769#102C23×C3114yes—
770#102C23×C3114yes—
771#102C23×C3114yes—
772#102C23×C3114yes—
773C22⋊C8C23×C3114yes—
774C22⋊C8C23×C3114yes—
775#97C23×C3114yes—
776C4×C8C23×C3114yes—
777C31#6055911yescharacteristic, direct product factor, Sylow
778C24—21no—
779C24C2×D4×C3111yescharacteristic
780#41—28no—
781#41—28no—
782#41—24no—
783#41—24no—
784#41—24no—
785#41—24no—
786#41—24no—
787#41—24no—
788#41—44no—
789#41—44no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—22no—
794C2×Q8#41×C3114yescomplemented
795C2×Q8C24×C3112yes—
796C2×Q8C24×C3112yes—
797C2×D4—28no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4#41×C3114yescomplemented
808C2×D4C24×C3112yes—
809C2×D4C24×C3112yes—
810C22×C4—28no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4C2×D4×C3111yescharacteristic
830C22×C4C2×D4×C3111yescharacteristic
831C22×C4C2×D4×C3111yescharacteristic
832C22×C4C2×D4×C3111yescharacteristic
833C22×C4C2×D4×C3111yescharacteristic
834C22×C4C2×D4×C3111yescharacteristic
835C22×C4C2×D4×C3111yescharacteristic
836C22×C4C2×D4×C3111yescharacteristic
837C22×C4C2×D4×C3111yescharacteristic
838C22×C4C2×D4×C3111yescharacteristic
839C22×C4C2×D4×C3111yescharacteristic
840C22×C4C2×D4×C3111yescharacteristic
841C22×C4C2×D4×C3111yescharacteristic
842C22×C4C2×D4×C3111yescharacteristic
843C22×C4C2×D4×C3111yescharacteristic
844C22×C4C24×C3111yescharacteristic
845C22×C4C24×C3111yescharacteristic
846C22×C4C24×C3111yescharacteristic
847Q16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851M16—24no—
852M16—24no—
853C2×C8C24×C3114yes—
854C2×C8C24×C3114yes—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4C24×C3112yes—
872C4⋊C4C24×C3112yes—
873C4⋊C4C24×C3112yes—
874C4⋊C4C24×C3112yes—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42C2×D4×C3111yescharacteristic
900C42C2×D4×C3111yescharacteristic
901C42C2×D4×C3111yescharacteristic
902C42C2×D4×C3111yescharacteristic
903C42C2×D4×C3111yescharacteristic
904C42C2×D4×C3111yescharacteristic
905C42C2×D4×C3111yescharacteristic
906C42C2×D4×C3111yescharacteristic
907C42C2×D4×C3111yescharacteristic
908C42C2×D4×C3111yescharacteristic
909C42C2×D4×C3111yescharacteristic
910C42C2×D4×C3111yescharacteristic
911C42C24×C3111yescharacteristic
912C42C24×C3111yescharacteristic
913C42C24×C3111yescharacteristic
914C42C24×C3111yescharacteristic
915C23—22no—
916C23—24no—
917C23—22no—
918C23—22no—
919C23—41no—
920C23—41no—
921C23—42no—
922C23—42no—
923C23C22×D4×C3111yescharacteristic
924C23C22×D4×C3111yescharacteristic
925C23C22×D4×C3111yescharacteristic
926Q8—24no—
927Q8—22no—
928Q8—22no—
929Q8—22no—
930Q8—42no—
931Q8—42no—
932Q8C2×#41×C3114yes—
933D4—28no—
934D4—28no—
935D4—24no—
936D4—22no—
937D4—22no—
938D4—22no—
939D4—42no—
940D4—44no—
941D4—44no—
942D4—44no—
943D4—42no—
944D4C2×#41×C3114yes—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4C22×D4×C3111yescharacteristic
983C2×C4C22×D4×C3111yescharacteristic
984C2×C4C22×D4×C3111yescharacteristic
985C2×C4C22×D4×C3111yescharacteristic
986C2×C4C22×D4×C3111yescharacteristic
987C2×C4C22×D4×C3111yescharacteristic
988C2×C4C22×D4×C3111yescharacteristic
989C2×C4C22×D4×C3111yescharacteristic
990C2×C4C22×D4×C3111yescharacteristic
991C2×C4C22×D4×C3111yescharacteristic
992C2×C4C22×D4×C3111yescharacteristic
993C2×C4C2×#41×C3112yes—
994C2×C4C2×#41×C3112yes—
995C2×C4C25×C3111yescharacteristic
996C8—24no—
997C8—24no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—24no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—44no—
1008C22—48no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22C31×#52512yes—
1015C22C23×D4×C3111yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—24no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—21no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4C31×#52512yes—
1031C4C31×#57512yes—
1032C4C31×#57512yes—
1033C4C22×#41×C3111yescharacteristic
1034C4C22×#41×C3111yescharacteristic
1035C2—22no—
1036C2—41no—
1037C2—41no—
1038C2—44no—
1039C2—82no—
1040C2C2×C31×#52511yescharacteristic
1041C2C2×C31×#57511yescharacteristic
1042C2C2×C31×#57511yescharacteristic
subgroupG/H
centerC2×C4×C31C22×D4
commutator, Frattini, cosocleC2×C4C25×C31
socleC22×C31C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3444C2semidirect
2. C2×C4×#41×C31C2semidirect
3. C31×#3116C2semidirect
4. C31×#3115C2semidirect
5. C31×#3111C2semidirect
6. C31×#3107C2semidirect
7. C31×#3106C2semidirect
8. C31×#3102C2semidirect
9. C31×#3093C2semidirect
10. C31×#3078C2semidirect
11. C31×#3077C2semidirect
12. C31×#3037C2semidirect
13. C31×#3036C2semidirect
14. C31×#3005C2semidirect
15. C4×C31×#137C2semidirect
16. C4×C31×AGL(1,ℤ/8)C2semidirect
17. C31×#2920C2semidirect
22. C31×#533C22semidirect
23. C31×#533C22semidirect
25. C31×#532C22semidirect
26. C31×#532C22semidirect
31. C31×#529C22semidirect
32. C31×#529C22semidirect
57. C31×#485C22semidirect
58. C31×#485C22semidirect
59. C31×#482C22semidirect
60. C31×#482C22semidirect
61. C31×#479C22semidirect
62. C31×#478C22semidirect
63. C31×#477C22semidirect
64. C31×#476C22semidirect
65. C31×#475C22semidirect
66. C31×#474C22semidirect
67. C31×#464C22semidirect
68. C31×#463C22semidirect
69. C31×#462C22semidirect
70. C31×#461C22semidirect
71. C31×#460C22semidirect
72. C31×#459C22semidirect
77. C31×#442C22semidirect
78. C31×#441C22semidirect
79. C31×#440C22semidirect
80. C31×#440C22semidirect
81. C4×Q16×C31C22semidirect
82. C4×SD16×C31C22semidirect
83. C4×SD16×C31C22semidirect
84. C4×D8×C31C22semidirect
85. C31×#432C22semidirect
86. C31×#432C22semidirect
87. C31×#431C22semidirect
88. C31×#431C22semidirect
272. C2×Q8×C31#41semidirect
285. C2×D4×C31#41semidirect
393. #60559C31direct (N × H)
477. #3444C2×C31semidirect
478. C2×C4×#41C2×C31semidirect
479. #3116C2×C31semidirect
480. #3115C2×C31semidirect
481. #3111C2×C31semidirect
482. #3107C2×C31semidirect
483. #3106C2×C31semidirect
484. #3102C2×C31semidirect
485. #3093C2×C31semidirect
486. #3078C2×C31semidirect
487. #3077C2×C31semidirect
488. #3037C2×C31semidirect
489. #3036C2×C31semidirect
490. #3005C2×C31semidirect
491. C4×#137C2×C31semidirect
492. C4×AGL(1,ℤ/8)C2×C31semidirect
493. #2920C2×C31semidirect
535. #533C22×C31semidirect
536. #533C22×C31semidirect
538. #532C22×C31semidirect
539. #532C22×C31semidirect
544. #529C22×C31semidirect
545. #529C22×C31semidirect
570. #485C22×C31semidirect
571. #485C22×C31semidirect
572. #482C22×C31semidirect
573. #482C22×C31semidirect
574. #479C22×C31semidirect
575. #478C22×C31semidirect
576. #477C22×C31semidirect
577. #476C22×C31semidirect
578. #475C22×C31semidirect
579. #474C22×C31semidirect
580. #464C22×C31semidirect
581. #463C22×C31semidirect
582. #462C22×C31semidirect
583. #461C22×C31semidirect
584. #460C22×C31semidirect
585. #459C22×C31semidirect
590. #442C22×C31semidirect
591. #441C22×C31semidirect
592. #440C22×C31semidirect
593. #440C22×C31semidirect
594. C4×Q16C22×C31semidirect
595. C4×SD16C22×C31semidirect
596. C4×SD16C22×C31semidirect
597. C4×D8C22×C31semidirect
598. #432C22×C31semidirect
599. #432C22×C31semidirect
600. #431C22×C31semidirect
601. #431C22×C31semidirect
777. C31#60559direct (N × H)
794. C2×Q8#41×C31semidirect
807. C2×D4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34442
C2×C4×#41×C312
C31×#31162
C31×#31152
C31×#31112
C31×#31072
C31×#31062
C31×#31022
C31×#30932
C31×#30782
C31×#30772
C31×#30372
C31×#30362
C31×#30052
C4×C31×#1372
C4×C31×AGL(1,ℤ/8)2
C31×#29202
#6055931