Finite Group Databasebeta

← C31×#24913 #21481672

Subgroups — C31×#24913 #21481672

Order 7936.

1226 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#447C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C31×#2422C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2054C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#1936C211yesmaximal, characteristic, complemented
10C31×#1924C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic, complemented
24C22×C22⋊C4×C31—21no—
25C31×#447—24no—
26C31×#442—24no—
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#106C2211yescharacteristic, complemented
29C2×C31×C4⋊C8C2211yescharacteristic, complemented
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic, complemented
37C2×C31×#102C2211yescharacteristic, complemented
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic, complemented
41C31×#397—21no—
42C31×#394—21no—
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic, complemented
46C31×#389C2211yescharacteristic, complemented
47C31×#386—21no—
48C31×#386—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic, complemented
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31—41no—
82C2×D8×C31D414yes—
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C31×#123—44no—
88C31×#121—22no—
89C31×#121—41no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—41no—
94C4×D4×C31—41no—
95C4×D4×C31—41no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—44no—
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#106—22no—
122C31×#106—41no—
123C31×C4⋊C8—41no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—41no—
131C31×#102—41no—
132C31×C22⋊C8—22no—
133C31×C22⋊C8—41no—
134C31×#97—22no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95D411yescharacteristic
139C31×#95D411yescharacteristic
140C24×C31—21no—
141C24×C31—24no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—42no—
147C24×C31—42no—
148C24×C31—81no—
149C24×C31—81no—
150C24×C31C2×D411yescharacteristic
151C2×D4×C31—24no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31—44no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—81no—
174C2×D4×C31C2×D412yes—
175C2×D4×C31C2×D412yes—
176C2×D4×C31#4112yes—
177C2×D4×C31#4112yes—
178C2×D4×C31#4112yes—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—81no—
197C22×C4×C31—81no—
198C22×C4×C31—81no—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2411yescharacteristic
205D8×C31—28no—
206D8×C31—44no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31C2×D412yes—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—81no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—81no—
245C22⋊C4×C31—81no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—21no—
250#24913C3111yesmaximal, characteristic, direct product factor, Sylow
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—21no—
255C23×C31—22no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—48no—
263C23×C31—48no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—84no—
281C23×C31—84no—
282C23×C31—84no—
283C23×C31—84no—
284C23×C31—84no—
285C23×C31AGL(1,ℤ/8)12yes—
286C23×C31C22×D411yescharacteristic
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—22no—
292D4×C31—22no—
293D4×C31—22no—
294D4×C31—48no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—41no—
299D4×C31—84no—
300D4×C31#12314yescomplemented
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—84no—
335C2×C4×C31—84no—
336C2×C4×C31—84no—
337C2×C4×C31AGL(1,ℤ/8)12yes—
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C2×#4111yescharacteristic
340C2×C4×C31C2×#4111yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31H(5,𝔽2)11yescharacteristic
343C2×C4×C31H(5,𝔽2)11yescharacteristic
344C8×C31—22no—
345C8×C31—41no—
346C8×C31—41no—
347C8×C31—41no—
348C2×#447C2×C3111yescharacteristic
349C2×#442C2×C3111yescharacteristic, complemented
350#2422C2×C3111yescharacteristic, complemented
351D4×C22⋊C4C2×C3111yescharacteristic, complemented
352#2094C2×C3111yescharacteristic, complemented
353#2077C2×C3111yescharacteristic, complemented
354#2054C2×C3111yescharacteristic, complemented
355#2034C2×C3111yescharacteristic, complemented
356#1936C2×C3111yescharacteristic, complemented
357#1924C2×C3111yescharacteristic, complemented
358#1879C2×C3111yescharacteristic, complemented
359#1879C2×C3111yescharacteristic, complemented
360#1864C2×C3111yescharacteristic, complemented
361#1802C2×C3111yescharacteristic, complemented
362#1786C2×C3111yescharacteristic, complemented
363C22×C31—22no—
364C22×C31—24no—
365C22×C31—22no—
366C22×C31—22no—
367C22×C31—42no—
368C22×C31—41no—
369C22×C31—42no—
370C22×C31—41no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—41no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—816no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31#52511yescharacteristic
393C22×C31D4211yescharacteristic
394C22×C31#54611yescharacteristic
395C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C31#57611yescharacteristic
398C22×C31#57711yescharacteristic
399C4×C31—22no—
400C4×C31—41no—
401C4×C31—41no—
402C4×C31—41no—
403C4×C31—41no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31—81no—
407C4×C31—81no—
408C4×C31—81no—
409C4×C31C2×#12311yescharacteristic
410C4×C31#53811yescharacteristic
411C4×C31#54611yescharacteristic
412C4×C31#55111yescharacteristic
413C23×D4C22×C3111yescharacteristic
414C22×D8C22×C3111yescharacteristic
415C22×D8C22×C3111yescharacteristic
416C2×#123—21no—
417C2×#121C22×C3111yescharacteristic
418C2×C4×D4C22×C3111yescharacteristic
419C2×C4×D4C22×C3111yescharacteristic
420C2×C4×D4C22×C3111yescharacteristic, complemented
421C22×C22⋊C4—21no—
422#447—24no—
423#442—24no—
424C2×#106C22×C3111yescharacteristic, complemented
425C2×#106C22×C3111yescharacteristic, complemented
426C2×C4⋊C8C22×C3111yescharacteristic, complemented
427C2×#102C22×C3111yescharacteristic
428C2×#102C22×C3111yescharacteristic
429C2×#102C22×C3111yescharacteristic
430C2×#102C22×C3111yescharacteristic
431C2×#102C22×C3111yescharacteristic
432C2×#102C22×C3111yescharacteristic
433C2×#102C22×C3111yescharacteristic, complemented
434C2×#102C22×C3111yescharacteristic, complemented
435C2×C22⋊C8C22×C3111yescharacteristic
436C2×C22⋊C8C22×C3111yescharacteristic
437C2×#97C22×C3111yescharacteristic, complemented
438#397—21no—
439#394—21no—
440#390C22×C3111yescharacteristic
441#390C22×C3111yescharacteristic
442#390C22×C3111yescharacteristic, complemented
443#389C22×C3111yescharacteristic, complemented
444#386—21no—
445#386—21no—
446#385—21no—
447#384C22×C3111yescharacteristic, complemented
448#380C22×C3111yescharacteristic
449#380C22×C3111yescharacteristic
450#379—21no—
451C4×C22⋊C4C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic, complemented
453#340C22×C3111yescharacteristic, complemented
454#340C22×C3111yescharacteristic, complemented
455#340C22×C3111yescharacteristic, complemented
456#336C22×C3111yescharacteristic, complemented
457#336C22×C3111yescharacteristic, complemented
458C2×C31—42no—
459C2×C31—44no—
460C2×C31—82no—
461C2×C31—82no—
462C2×C31#241811yescharacteristic
463C2×C31#310911yescharacteristic
464C2×C31#311811yescharacteristic
465C2×C31#326411yescharacteristic
466C2×C31#327211yescharacteristic
467C2×C31#330611yescharacteristic
468C2×C31#331811yescharacteristic
469C25—21no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—41no—
477C22×D4—41no—
478C22×D4C23×C3111yescharacteristic
479C22×D4C23×C3111yescharacteristic
480C22×D4C23×C3111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C3111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×D8D4×C3114yes—
491C22×C8C23×C3111yescharacteristic
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495#123—44no—
496#121—22no—
497#121—41no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—41no—
503C4×D4—41no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4C23×C3111yescharacteristic
508C2×C4⋊C4C23×C3111yescharacteristic
509C2×C4⋊C4C23×C3111yescharacteristic
510C2×C4⋊C4C23×C3111yescharacteristic
511C2×C4⋊C4C23×C3111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4D4×C3111yescharacteristic
526C2×C22⋊C4D4×C3111yescharacteristic
527C2×C42C23×C3111yescharacteristic
528C2×C42C23×C3111yescharacteristic
529#106—22no—
530#106—41no—
531C4⋊C8—41no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—41no—
539#102—41no—
540C22⋊C8—22no—
541C22⋊C8—41no—
542#97—22no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95D4×C3111yescharacteristic
547#95D4×C3111yescharacteristic
548C31#2491311yescharacteristic, direct product factor, Sylow
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C3111yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C3112yes—
584C2×D4C2×D4×C3112yes—
585C2×D4#41×C3112yes—
586C2×D4#41×C3112yes—
587C2×D4#41×C3112yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C24×C3111yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C3112yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23C31×AGL(1,ℤ/8)12yes—
694C23C22×D4×C3111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4C31×#12314yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4C31×AGL(1,ℤ/8)12yes—
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C2×#41×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C2×#41×C3111yescharacteristic
750C2×C4C31×H(5,𝔽2)11yescharacteristic
751C2×C4C31×H(5,𝔽2)11yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C31×#52511yescharacteristic
786C22D42×C3111yescharacteristic
787C22C31×#54611yescharacteristic
788C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
789C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
790C22C31×#57611yescharacteristic
791C22C31×#57711yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×C31×#12311yescharacteristic
803C4C31×#53811yescharacteristic
804C4C31×#54611yescharacteristic
805C4C31×#55111yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2C31×#241811yescharacteristic
811C2C31×#310911yescharacteristic
812C2C31×#311811yescharacteristic
813C2C31×#326411yescharacteristic
814C2C31×#327211yescharacteristic
815C2C31×#330611yescharacteristic
816C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#442C2semidirect
3. C31×#2422C2semidirect
4. D4×C22⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2077C2semidirect
7. C31×#2054C2semidirect
8. C31×#2034C2semidirect
9. C31×#1936C2semidirect
10. C31×#1924C2semidirect
11. C31×#1879C2semidirect
12. C31×#1879C2semidirect
13. C31×#1864C2semidirect
14. C31×#1802C2semidirect
15. C31×#1786C2semidirect
23. C2×C4×D4×C31C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×#106C22semidirect
29. C2×C31×C4⋊C8C22semidirect
36. C2×C31×#102C22semidirect
37. C2×C31×#102C22semidirect
40. C2×C31×#97C22semidirect
45. C31×#390C22semidirect
46. C31×#389C22semidirect
50. C31×#384C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
250. #24913C31direct (N × H)
300. D4×C31#123semidirect
349. C2×#442C2×C31semidirect
350. #2422C2×C31semidirect
351. D4×C22⋊C4C2×C31semidirect
352. #2094C2×C31semidirect
353. #2077C2×C31semidirect
354. #2054C2×C31semidirect
355. #2034C2×C31semidirect
356. #1936C2×C31semidirect
357. #1924C2×C31semidirect
358. #1879C2×C31semidirect
359. #1879C2×C31semidirect
360. #1864C2×C31semidirect
361. #1802C2×C31semidirect
362. #1786C2×C31semidirect
420. C2×C4×D4C22×C31semidirect
424. C2×#106C22×C31semidirect
425. C2×#106C22×C31semidirect
426. C2×C4⋊C8C22×C31semidirect
433. C2×#102C22×C31semidirect
434. C2×#102C22×C31semidirect
437. C2×#97C22×C31semidirect
442. #390C22×C31semidirect
443. #389C22×C31semidirect
447. #384C22×C31semidirect
452. #340C22×C31semidirect
453. #340C22×C31semidirect
454. #340C22×C31semidirect
455. #340C22×C31semidirect
456. #336C22×C31semidirect
457. #336C22×C31semidirect
548. C31#24913direct (N × H)
708. D4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C2×C31×#4422
C31×#24222
D4×C22⋊C4×C312
C31×#20942
C31×#20772
C31×#20542
C31×#20342
C31×#19362
C31×#19242
C31×#18792
C31×#18642
C31×#18022
C31×#17862
#2491331