Finite Group Databasebeta

← C31×#22442 #21479201

Subgroups — C31×#22442 #21479201

Order 7936.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic, complemented
4C31×#2339C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1973C211yesmaximal, characteristic, complemented
7C31×#1968C211yesmaximal, characteristic, complemented
8C31×#1879C211yesmaximal, characteristic, complemented
9C31×#1879C211yesmaximal, characteristic, complemented
10C31×#1877C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1809C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)—24no—
19C2×C31×AGL(1,ℤ/8)—24no—
20C2×C31×AGL(1,ℤ/8)C418yescomplemented
21C22×SD16×C31C2211yescharacteristic
22C22×SD16×C31C2211yescharacteristic
23C22×D8×C31C2211yescharacteristic
24C22×D8×C31C2211yescharacteristic
25C22×M16×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic, complemented
29C2×C4×D4×C31C2211yescharacteristic, complemented
30C22×C22⋊C4×C31—21no—
31C31×#442—24no—
32C4×D8×C31—24no—
33C2×C31×#107C2211yescharacteristic, complemented
34C2×C31×#106C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×#97C2211yescharacteristic, complemented
45C2×C4×C8×C31C2211yescharacteristic, complemented
46C31×#391C2211yescharacteristic, complemented
47C31×#391C2211yescharacteristic, complemented
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#386—21no—
51C31×#386—21no—
52C31×#386—21no—
53C31×#386—21no—
54C31×#381—21no—
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#379—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C2×C31×#95—21no—
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C25×C31—21no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31C2×C414yescomplemented
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—22no—
77C22×D4×C31—41no—
78C22×D4×C31—41no—
79C22×D4×C31C2×C414yescomplemented
80C22×D4×C31C2311yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C23×C4×C31—21no—
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C31×AGL(1,ℤ/8)—232no—
90C2×SD16×C31—22no—
91C2×SD16×C31—22no—
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31C2×C414yescomplemented
95C2×SD16×C31C2×C414yescomplemented
96C2×D8×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31C2×C414yes—
99C2×D8×C31C2×C414yescomplemented
100C2×D8×C31D414yes—
101C2×D8×C31D414yes—
102C2×M16×C31—22no—
103C2×M16×C31—22no—
104C2×M16×C31C2×C414yescomplemented
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C4×D4×C31—41no—
114C4×D4×C31—41no—
115C4×D4×C31—41no—
116C4×D4×C31—41no—
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—44no—
132C2×C22⋊C4×C31D411yescharacteristic
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C42×C31C2311yescharacteristic
135C2×C42×C31C2311yescharacteristic
136C31×#107—22no—
137C31×#106—22no—
138C31×#103—41no—
139C31×#103—41no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—41no—
145C31×#102—41no—
146C31×C22⋊C8—22no—
147C31×#97—22no—
148C4×C8×C31—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C31×#95—21no—
155C31×#95D411yescharacteristic
156C31×#95D411yescharacteristic
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—24no—
161C24×C31—42no—
162C24×C31—42no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—81no—
166C24×C31—81no—
167C24×C31C2×D411yescharacteristic
168#41×C31—28no—
169#41×C31—44no—
170#41×C31—44no—
171#41×C31—44no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31C22×C412yes—
178C2×D4×C31—28no—
179C2×D4×C31—24no—
180C2×D4×C31—24no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—44no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31C22×C412yes—
200C2×D4×C31C22×C412yes—
201C2×D4×C31C22×C412yes—
202C2×D4×C31C2×D412yes—
203C2×D4×C31C2×D412yes—
204C2×D4×C31C2×D412yes—
205C2×D4×C31C2×D412yes—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—24no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—42no—
217C22×C4×C31—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—81no—
227C22×C4×C31—81no—
228C22×C4×C31—81no—
229C22×C4×C31—81no—
230C22×C4×C31C22×C412yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31#4112yes—
237C22×C4×C31C2411yescharacteristic
238SD16×C31—28no—
239SD16×C31—28no—
240D8×C31—28no—
241D8×C31C22⋊C4116yescomplemented
242M16×C31—28no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31C22×C412yes—
252C2×C8×C31C22×C412yes—
253C2×C8×C31C2×D412yes—
254C2×C8×C31C2×D412yes—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C22⋊C4×C31—22no—
264C22⋊C4×C31—41no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—81no—
273C22⋊C4×C31—81no—
274C22⋊C4×C31—81no—
275C42×C31—21no—
276C42×C31—21no—
277C42×C31—21no—
278C42×C31—21no—
279#22442C3111yesmaximal, characteristic, direct product factor, Sylow
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—22no—
293C23×C31—48no—
294C23×C31—48no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—84no—
310C23×C31—84no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31C4×D412yes—
315C23×C31C22×D411yescharacteristic
316Q8×C31—22no—
317Q8×C31—22no—
318Q8×C31—41no—
319Q8×C31—41no—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—22no—
328D4×C31—48no—
329D4×C31—48no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31C2×C22⋊C414yes—
333D4×C31C2×C22⋊C414yescomplemented
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—48no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—84no—
368C2×C4×C31—84no—
369C2×C4×C31—84no—
370C2×C4×C31—84no—
371C2×C4×C31C4×D412yes—
372C2×C4×C31AGL(1,ℤ/8)12yescomplemented
373C2×C4×C31C23×C411yescharacteristic
374C2×C4×C31C22×D411yescharacteristic
375C2×C4×C31C22×D411yescharacteristic
376C2×C4×C31C2×#4111yescharacteristic
377C2×C4×C31H(5,𝔽2)11yescharacteristic
378C2×C4×C31H(5,𝔽2)11yescharacteristic
379C8×C31—22no—
380C8×C31—41no—
381C8×C31—41no—
382C8×C31C2×C22⋊C414yescomplemented
383C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
384C2×#442C2×C3111yescharacteristic, complemented
385C2×C4×D8C2×C3111yescharacteristic, complemented
386#2339C2×C3111yescharacteristic, complemented
387D4×C22⋊C4C2×C3111yescharacteristic, complemented
388#1973C2×C3111yescharacteristic, complemented
389#1968C2×C3111yescharacteristic, complemented
390#1879C2×C3111yescharacteristic, complemented
391#1879C2×C3111yescharacteristic, complemented
392#1877C2×C3111yescharacteristic, complemented
393#1877C2×C3111yescharacteristic, complemented
394#1809C2×C3111yescharacteristic, complemented
395#1788C2×C3111yescharacteristic, complemented
396#1786C2×C3111yescharacteristic, complemented
397#1753C2×C3111yescharacteristic, complemented
398C22×C31—22no—
399C22×C31—24no—
400C22×C31—24no—
401C22×C31—22no—
402C22×C31—22no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—41no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—41no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—816no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31C2×C4×D411yescharacteristic
428C22×C31D4211yescharacteristic
429C22×C31D4211yescharacteristic
430C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C31#57511yescharacteristic
432C22×C31#57611yescharacteristic
433C22×C31#57711yescharacteristic
434C4×C31—22no—
435C4×C31—22no—
436C4×C31—42no—
437C4×C31—41no—
438C4×C31—41no—
439C4×C31—41no—
440C4×C31—81no—
441C4×C31—81no—
442C4×C31—81no—
443C4×C31—81no—
444C4×C31C22×C22⋊C411yescharacteristic
445C4×C31#51811yescharacteristic
446C4×C31#54611yescharacteristic
447C4×C31#54611yescharacteristic
448C22×#41C22×C3111yescharacteristic
449C23×D4C22×C3111yescharacteristic
450C2×AGL(1,ℤ/8)—24no—
451C2×AGL(1,ℤ/8)—24no—
452C2×AGL(1,ℤ/8)C4×C3118yescomplemented
453C22×SD16C22×C3111yescharacteristic
454C22×SD16C22×C3111yescharacteristic
455C22×D8C22×C3111yescharacteristic
456C22×D8C22×C3111yescharacteristic
457C22×M16C22×C3111yescharacteristic
458C2×C4×D4C22×C3111yescharacteristic
459C2×C4×D4C22×C3111yescharacteristic
460C2×C4×D4C22×C3111yescharacteristic, complemented
461C2×C4×D4C22×C3111yescharacteristic, complemented
462C22×C22⋊C4—21no—
463#442—24no—
464C4×D8—24no—
465C2×#107C22×C3111yescharacteristic, complemented
466C2×#106C22×C3111yescharacteristic, complemented
467C2×#103C22×C3111yescharacteristic, complemented
468C2×#103C22×C3111yescharacteristic, complemented
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×#102C22×C3111yescharacteristic
472C2×#102C22×C3111yescharacteristic
473C2×#102C22×C3111yescharacteristic, complemented
474C2×#102C22×C3111yescharacteristic, complemented
475C2×C22⋊C8C22×C3111yescharacteristic
476C2×#97C22×C3111yescharacteristic, complemented
477C2×C4×C8C22×C3111yescharacteristic, complemented
478#391C22×C3111yescharacteristic, complemented
479#391C22×C3111yescharacteristic, complemented
480#390C22×C3111yescharacteristic
481#390C22×C3111yescharacteristic
482#386—21no—
483#386—21no—
484#386—21no—
485#386—21no—
486#381—21no—
487#380C22×C3111yescharacteristic
488#380C22×C3111yescharacteristic
489#379—21no—
490C4×C22⋊C4C22×C3111yescharacteristic
491C2×#95—21no—
492#340C22×C3111yescharacteristic, complemented
493#340C22×C3111yescharacteristic, complemented
494#336C22×C3111yescharacteristic, complemented
495#336C22×C3111yescharacteristic, complemented
496C2×C31—42no—
497C2×C31—44no—
498C2×C31—44no—
499C2×C31—82no—
500C2×C31D4×C22⋊C411yescharacteristic
501C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
502C2×C31#294611yescharacteristic
503C2×C31#326411yescharacteristic
504C2×C31#326711yescharacteristic
505C2×C31#327211yescharacteristic
506C2×C31#327311yescharacteristic
507C25—21no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41C2×C4×C3114yescomplemented
514C22×Q8C23×C3111yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×C4×C3114yescomplemented
523C22×D4C23×C3111yescharacteristic
524C22×D4C23×C3111yescharacteristic
525C22×D4C23×C3111yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C3111yescharacteristic
532AGL(1,ℤ/8)—232no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16C2×C4×C3114yescomplemented
538C2×SD16C2×C4×C3114yescomplemented
539C2×D8—22no—
540C2×D8—22no—
541C2×D8C2×C4×C3114yes—
542C2×D8C2×C4×C3114yescomplemented
543C2×D8D4×C3114yes—
544C2×D8D4×C3114yes—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16C2×C4×C3114yescomplemented
548C22×C8C23×C3111yescharacteristic
549C22×C8C23×C3111yescharacteristic
550C22×C8C23×C3111yescharacteristic
551C22×C8C23×C3111yescharacteristic
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—41no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C2×C4⋊C4C23×C3111yescharacteristic
561C2×C4⋊C4C23×C3111yescharacteristic
562C2×C4⋊C4C23×C3111yescharacteristic
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—44no—
575C2×C22⋊C4D4×C3111yescharacteristic
576C2×C22⋊C4D4×C3111yescharacteristic
577C2×C42C23×C3111yescharacteristic
578C2×C42C23×C3111yescharacteristic
579#107—22no—
580#106—22no—
581#103—41no—
582#103—41no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—41no—
588#102—41no—
589C22⋊C8—22no—
590#97—22no—
591C4×C8—22no—
592#95—21no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95D4×C3111yescharacteristic
599#95D4×C3111yescharacteristic
600C31#2244211yescharacteristic, direct product factor, Sylow
601C24—21no—
602C24—21no—
603C24—21no—
604C24—24no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—81no—
610C24—81no—
611C24C2×D4×C3111yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C22×C4×C3112yes—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C3112yes—
644C2×D4C22×C4×C3112yes—
645C2×D4C22×C4×C3112yes—
646C2×D4C2×D4×C3112yes—
647C2×D4C2×D4×C3112yes—
648C2×D4C2×D4×C3112yes—
649C2×D4C2×D4×C3112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4—81no—
674C22×C4C22×C4×C3112yes—
675C22×C4C2×D4×C3111yescharacteristic
676C22×C4C2×D4×C3111yescharacteristic
677C22×C4C2×D4×C3111yescharacteristic
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4#41×C3112yes—
681C22×C4C24×C3111yescharacteristic
682SD16—28no—
683SD16—28no—
684D8—28no—
685D8C22⋊C4×C31116yescomplemented
686M16—28no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8C22×C4×C3112yes—
696C2×C8C22×C4×C3112yes—
697C2×C8C2×D4×C3112yes—
698C2×C8C2×D4×C3112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—81no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23C4×D4×C3112yes—
758C23C22×D4×C3111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊C4×C3114yes—
776D4C2×C22⋊C4×C3114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4C4×D4×C3112yes—
815C2×C4C31×AGL(1,ℤ/8)12yescomplemented
816C2×C4C23×C4×C3111yescharacteristic
817C2×C4C22×D4×C3111yescharacteristic
818C2×C4C22×D4×C3111yescharacteristic
819C2×C4C2×#41×C3111yescharacteristic
820C2×C4C31×H(5,𝔽2)11yescharacteristic
821C2×C4C31×H(5,𝔽2)11yescharacteristic
822C8—22no—
823C8—41no—
824C8—41no—
825C8C2×C22⋊C4×C3114yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×C4×D4×C3111yescharacteristic
856C22D42×C3111yescharacteristic
857C22D42×C3111yescharacteristic
858C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
859C22C31×#57511yescharacteristic
860C22C31×#57611yescharacteristic
861C22C31×#57711yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4C22×C22⋊C4×C3111yescharacteristic
873C4C31×#51811yescharacteristic
874C4C31×#54611yescharacteristic
875C4C31×#54611yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊C4×C3111yescharacteristic
881C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
882C2C31×#294611yescharacteristic
883C2C31×#326411yescharacteristic
884C2C31×#326711yescharacteristic
885C2C31×#327211yescharacteristic
886C2C31×#327311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
LCSG ▷ C2×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. C2×C4×D8×C31C2semidirect
4. C31×#2339C2semidirect
5. D4×C22⋊C4×C31C2semidirect
6. C31×#1973C2semidirect
7. C31×#1968C2semidirect
8. C31×#1879C2semidirect
9. C31×#1879C2semidirect
10. C31×#1877C2semidirect
11. C31×#1877C2semidirect
12. C31×#1809C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C31×#1753C2semidirect
20. C2×C31×AGL(1,ℤ/8)C4semidirect
28. C2×C4×D4×C31C22semidirect
29. C2×C4×D4×C31C22semidirect
33. C2×C31×#107C22semidirect
34. C2×C31×#106C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
44. C2×C31×#97C22semidirect
45. C2×C4×C8×C31C22semidirect
46. C31×#391C22semidirect
47. C31×#391C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#336C22semidirect
63. C31×#336C22semidirect
70. C2×#41×C31C2×C4semidirect
79. C22×D4×C31C2×C4semidirect
94. C2×SD16×C31C2×C4semidirect
95. C2×SD16×C31C2×C4semidirect
99. C2×D8×C31C2×C4semidirect
104. C2×M16×C31C2×C4semidirect
241. D8×C31C22⋊C4semidirect
279. #22442C31direct (N × H)
333. D4×C31C2×C22⋊C4semidirect
372. C2×C4×C31AGL(1,ℤ/8)semidirect
382. C8×C31C2×C22⋊C4semidirect
384. C2×#442C2×C31semidirect
385. C2×C4×D8C2×C31semidirect
386. #2339C2×C31semidirect
387. D4×C22⋊C4C2×C31semidirect
388. #1973C2×C31semidirect
389. #1968C2×C31semidirect
390. #1879C2×C31semidirect
391. #1879C2×C31semidirect
392. #1877C2×C31semidirect
393. #1877C2×C31semidirect
394. #1809C2×C31semidirect
395. #1788C2×C31semidirect
396. #1786C2×C31semidirect
397. #1753C2×C31semidirect
452. C2×AGL(1,ℤ/8)C4×C31semidirect
460. C2×C4×D4C22×C31semidirect
461. C2×C4×D4C22×C31semidirect
465. C2×#107C22×C31semidirect
466. C2×#106C22×C31semidirect
467. C2×#103C22×C31semidirect
468. C2×#103C22×C31semidirect
473. C2×#102C22×C31semidirect
474. C2×#102C22×C31semidirect
476. C2×#97C22×C31semidirect
477. C2×C4×C8C22×C31semidirect
478. #391C22×C31semidirect
479. #391C22×C31semidirect
492. #340C22×C31semidirect
493. #340C22×C31semidirect
494. #336C22×C31semidirect
495. #336C22×C31semidirect
513. C2×#41C2×C4×C31semidirect
522. C22×D4C2×C4×C31semidirect
537. C2×SD16C2×C4×C31semidirect
538. C2×SD16C2×C4×C31semidirect
542. C2×D8C2×C4×C31semidirect
547. C2×M16C2×C4×C31semidirect
600. C31#22442direct (N × H)
685. D8C22⋊C4×C31semidirect
776. D4C2×C22⋊C4×C31semidirect
815. C2×C4C31×AGL(1,ℤ/8)semidirect
825. C8C2×C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#4422
C2×C4×D8×C312
C31×#23392
D4×C22⋊C4×C312
C31×#19732
C31×#19682
C31×#18792
C31×#18772
C31×#18092
C31×#17882
C31×#17862
C31×#17532
#2244231