Finite Group Databasebeta

← C31×#26392 #21483151

Subgroups — C31×#26392 #21483151

Order 7936.

962 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#476C211yesmaximal, characteristic, complemented
2C2×C31×#442C211yesmaximal, characteristic
3C31×#2452C211yesmaximal, characteristic, complemented
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2084C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2058C211yesmaximal, characteristic, complemented
9C31×#1943C211yesmaximal, characteristic, complemented
10C31×#1917C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic
12C31×#1879C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×C22⋊Q8—21no—
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31—21no—
24C31×#476—24no—
25C31×#442—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#97C2211yescharacteristic
39C31×#396—21no—
40C31×#393—21no—
41C31×#390C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#385—21no—
48C31×#385—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic
51C31×#380—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×D4×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C2×D8×C31—22no—
69C2×D8×C31—22no—
70C2×D8×C31Q814yescomplemented
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C31×C4⋊Q8—22no—
76C31×C4⋊Q8—41no—
77C31×C22⋊Q8—44no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—41no—
84C4×D4×C31—41no—
85C4×D4×C31—41no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—44no—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C42×C31C2311yescharacteristic
111C2×C42×C31C2311yescharacteristic
112C2×C42×C31C2311yescharacteristic
113C31×#107—22no—
114C31×#106—22no—
115C31×#106—22no—
116C31×#106—22no—
117C31×#106—41no—
118C31×C4⋊C8—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—41no—
124C31×#102D414yes—
125C31×#97—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95D411yescharacteristic
131C31×#95D411yescharacteristic
132C24×C31—21no—
133C24×C31—21no—
134C2×Q8×C31—42no—
135C2×Q8×C31—42no—
136C2×Q8×C31—81no—
137C2×D4×C31—21no—
138C2×D4×C31—21no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31C2×D412yes—
146C2×D4×C31C2×Q812yes—
147C2×D4×C31C2×Q812yes—
148C2×D4×C31#4112yes—
149C22×C4×C31—24no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—42no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31—42no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31—81no—
165C22×C4×C31—81no—
166C22×C4×C31—81no—
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2411yescharacteristic
174D8×C31—28no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31C2×D412yes—
186C2×C8×C31C2×Q812yes—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—81no—
206C4⋊C4×C31C2×D412yes—
207C4⋊C4×C31#4112yes—
208C22⋊C4×C31—24no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—81no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222#26392C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31C22×D411yescharacteristic
238Q8×C31—84no—
239D4×C31—22no—
240D4×C31—22no—
241D4×C31—22no—
242D4×C31—22no—
243D4×C31—22no—
244D4×C31—41no—
245D4×C31—41no—
246D4×C31C22⋊Q814yescomplemented
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—48no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—84no—
283C2×C4×C31—84no—
284C2×C4×C31—84no—
285C2×C4×C31AGL(1,ℤ/8)12yes—
286C2×C4×C31AGL(1,ℤ/8)12yes—
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C22×Q811yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31H(5,𝔽2)11yescharacteristic
292C2×C4×C312−1+411yescharacteristic
293C8×C31—22no—
294C8×C31—22no—
295C8×C31—41no—
296C8×C31—41no—
297C2×#476C2×C3111yescharacteristic, complemented
298C2×#442C2×C3111yescharacteristic
299#2452C2×C3111yescharacteristic, complemented
300D4×C4⋊C4C2×C3111yescharacteristic, complemented
301#2094C2×C3111yescharacteristic, complemented
302#2084C2×C3111yescharacteristic, complemented
303#2067C2×C3111yescharacteristic, complemented
304#2058C2×C3111yescharacteristic, complemented
305#1943C2×C3111yescharacteristic, complemented
306#1917C2×C3111yescharacteristic, complemented
307#1879C2×C3111yescharacteristic
308#1879C2×C3111yescharacteristic
309#1864C2×C3111yescharacteristic, complemented
310#1864C2×C3111yescharacteristic, complemented
311#1862C2×C3111yescharacteristic, complemented
312C22×C31—24no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—42no—
316C22×C31—42no—
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31#52511yescharacteristic
327C22×C31D4211yescharacteristic
328C22×C31D4×Q811yescharacteristic
329C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C31#57711yescharacteristic
332C22×C31#57711yescharacteristic
333C4×C31—22no—
334C4×C31—22no—
335C4×C31—42no—
336C4×C31—41no—
337C4×C31—41no—
338C4×C31—41no—
339C4×C31—41no—
340C4×C31—42no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31—81no—
344C4×C31—81no—
345C4×C31C2×C22⋊Q811yescharacteristic
346C4×C31#53911yescharacteristic
347C4×C31#54711yescharacteristic
348C4×C31#55411yescharacteristic
349C22×D8C22×C3111yescharacteristic
350C2×C4⋊Q8C22×C3111yescharacteristic
351C2×C22⋊Q8—21no—
352C2×C4×D4C22×C3111yescharacteristic
353C2×C4×D4C22×C3111yescharacteristic
354C2×C4×D4C22×C3111yescharacteristic
355C2×C4×D4C22×C3111yescharacteristic
356C22×C4⋊C4—21no—
357#476—24no—
358#442—24no—
359C2×#107C22×C3111yescharacteristic
360C2×#106C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×#106C22×C3111yescharacteristic
363C2×#106C22×C3111yescharacteristic
364C2×C4⋊C8C22×C3111yescharacteristic
365C2×#102C22×C3111yescharacteristic
366C2×#102C22×C3111yescharacteristic
367C2×#102C22×C3111yescharacteristic
368C2×#102C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#97C22×C3111yescharacteristic
372#396—21no—
373#393—21no—
374#390C22×C3111yescharacteristic
375#390C22×C3111yescharacteristic
376#389C22×C3111yescharacteristic
377#389C22×C3111yescharacteristic
378#389C22×C3111yescharacteristic
379#389C22×C3111yescharacteristic
380#385—21no—
381#385—21no—
382#385—21no—
383#384C22×C3111yescharacteristic
384#380—21no—
385C4×C4⋊C4C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#336C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392#336C22×C3111yescharacteristic
393#336C22×C3111yescharacteristic
394C2×C31—44no—
395C2×C31—82no—
396C2×C31#244911yescharacteristic
397C2×C31#310911yescharacteristic
398C2×C31#312511yescharacteristic
399C2×C31#326511yescharacteristic
400C2×C31#327211yescharacteristic
401C2×C31#338411yescharacteristic
402C2×C31#338411yescharacteristic
403C22×Q8—21no—
404C22×D4C23×C3111yescharacteristic
405C22×D4C23×C3111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—21no—
410C2×D8—22no—
411C2×D8—22no—
412C2×D8Q8×C3114yescomplemented
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415C22×C8C23×C3111yescharacteristic
416C22×C8C23×C3111yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—41no—
419C22⋊Q8—44no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—41no—
426C4×D4—41no—
427C4×D4—41no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4D4×C3111yescharacteristic
437C2×C4⋊C4D4×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C4⋊C4C23×C3111yescharacteristic
440C2×C4⋊C4C23×C3111yescharacteristic
441C2×C4⋊C4C23×C3111yescharacteristic
442C2×C4⋊C4C23×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C42C23×C3111yescharacteristic
453C2×C42C23×C3111yescharacteristic
454C2×C42C23×C3111yescharacteristic
455#107—22no—
456#106—22no—
457#106—22no—
458#106—22no—
459#106—41no—
460C4⋊C8—22no—
461#102—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—41no—
466#102D4×C3114yes—
467#97—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C3111yescharacteristic
473#95D4×C3111yescharacteristic
474C31#2639211yescharacteristic, direct product factor, Sylow
475C24—21no—
476C24—21no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—81no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×D4×C3112yes—
489C2×D4C2×Q8×C3112yes—
490C2×D4C2×Q8×C3112yes—
491C2×D4#41×C3112yes—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C2×D4×C3111yescharacteristic
514C22×C4C2×D4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C24×C3111yescharacteristic
517D8—28no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×D4×C3112yes—
529C2×C8C2×Q8×C3112yes—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4C2×D4×C3112yes—
550C4⋊C4#41×C3112yes—
551C22⋊C4—24no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×D4×C3111yescharacteristic
580Q8—84no—
581D4—22no—
582D4—22no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4C31×C22⋊Q814yescomplemented
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—48no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4—84no—
627C2×C4C31×AGL(1,ℤ/8)12yes—
628C2×C4C31×AGL(1,ℤ/8)12yes—
629C2×C4C22×D4×C3111yescharacteristic
630C2×C4C22×Q8×C3111yescharacteristic
631C2×C4C2×#41×C3111yescharacteristic
632C2×C4C2×#41×C3111yescharacteristic
633C2×C4C31×H(5,𝔽2)11yescharacteristic
634C2×C4C31×2−1+411yescharacteristic
635C8—22no—
636C8—22no—
637C8—41no—
638C8—41no—
639C22—24no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C31×#52511yescharacteristic
654C22D42×C3111yescharacteristic
655C22D4×Q8×C3111yescharacteristic
656C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
657C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
658C22C31×#57711yescharacteristic
659C22C31×#57711yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C2×C31×C22⋊Q811yescharacteristic
673C4C31×#53911yescharacteristic
674C4C31×#54711yescharacteristic
675C4C31×#55411yescharacteristic
676C2—44no—
677C2—82no—
678C2C31×#244911yescharacteristic
679C2C31×#310911yescharacteristic
680C2C31×#312511yescharacteristic
681C2C31×#326511yescharacteristic
682C2C31×#327211yescharacteristic
683C2C31×#338411yescharacteristic
684C2C31×#338411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#476C2semidirect
3. C31×#2452C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2084C2semidirect
7. C31×#2067C2semidirect
8. C31×#2058C2semidirect
9. C31×#1943C2semidirect
10. C31×#1917C2semidirect
13. C31×#1864C2semidirect
14. C31×#1864C2semidirect
15. C31×#1862C2semidirect
70. C2×D8×C31Q8semidirect
222. #26392C31direct (N × H)
246. D4×C31C22⋊Q8semidirect
297. C2×#476C2×C31semidirect
299. #2452C2×C31semidirect
300. D4×C4⋊C4C2×C31semidirect
301. #2094C2×C31semidirect
302. #2084C2×C31semidirect
303. #2067C2×C31semidirect
304. #2058C2×C31semidirect
305. #1943C2×C31semidirect
306. #1917C2×C31semidirect
309. #1864C2×C31semidirect
310. #1864C2×C31semidirect
311. #1862C2×C31semidirect
412. C2×D8Q8×C31semidirect
474. C31#26392direct (N × H)
588. D4C31×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4762
C2×C31×#4422
C31×#24522
D4×C4⋊C4×C312
C31×#20942
C31×#20842
C31×#20672
C31×#20582
C31×#19432
C31×#19172
C31×#18792
C31×#18642
C31×#18622
#2639231