Finite Group Databasebeta

← C31×#22443 #21479202

Subgroups — C31×#22443 #21479202

Order 7936.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 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×#440C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2341C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1972C211yesmaximal, characteristic, complemented
7C31×#1970C211yesmaximal, characteristic, complemented
8C31×#1880C211yesmaximal, characteristic, complemented
9C31×#1880C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, 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×Q8×C31C2211yescharacteristic, complemented
27C2×C4×Q8×C31C2211yescharacteristic, complemented
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C22×C22⋊C4×C31—21no—
31C31×#440—24no—
32C4×SD16×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×#390—21no—
47C31×#390—21no—
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic, complemented
51C31×#390C2211yescharacteristic, complemented
52C31×#386—21no—
53C31×#386—21no—
54C31×#380—21no—
55C31×#380C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#379—21no—
58C4×C22⋊C4×C31—21no—
59C4×C22⋊C4×C31C2211yescharacteristic
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×C414yes—
80C22×D4×C31C2311yescharacteristic
81C22×D4×C31C2311yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C23×C4×C31—21no—
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31C2311yescharacteristic
87C31×AGL(1,ℤ/8)—232no—
88C2×SD16×C31—22no—
89C2×SD16×C31—22no—
90C2×SD16×C31C2×C414yes—
91C2×SD16×C31C2×C414yescomplemented
92C2×SD16×C31D414yes—
93C2×SD16×C31D414yes—
94C2×D8×C31—22no—
95C2×D8×C31—22no—
96C2×D8×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31C2×C414yes—
99C2×D8×C31C2×C414yescomplemented
100C2×M16×C31—22no—
101C2×M16×C31—22no—
102C2×M16×C31C2×C414yescomplemented
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C4×Q8×C31—22no—
108C4×Q8×C31—22no—
109C4×Q8×C31—41no—
110C4×Q8×C31—41no—
111C4×D4×C31—22no—
112C4×D4×C31—22no—
113C4×D4×C31—41no—
114C4×D4×C31—41no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
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—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—44no—
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C42×C31—21no—
137C2×C42×C31—21no—
138C2×C42×C31C2311yescharacteristic
139C2×C42×C31C2311yescharacteristic
140C31×#107—22no—
141C31×#106—22no—
142C31×#103—22no—
143C31×#103—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—41no—
147C31×#102—41no—
148C31×#102—41no—
149C31×#102—41no—
150C31×C22⋊C8—22no—
151C31×#97—22no—
152C4×C8×C31—22no—
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×C31C22×C412yes—
176C2×Q8×C31C2×D412yes—
177C2×Q8×C31C2×D412yes—
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—21no—
193C2×D4×C31—21no—
194C2×D4×C31—44no—
195C2×D4×C31—44no—
196C2×D4×C31—44no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31C22×C412yes—
202C2×D4×C31C22×C412yes—
203C2×D4×C31C22×C412yes—
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—81no—
223C22×C4×C31—81no—
224C22×C4×C31C22×C412yes—
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31#4112yes—
231C22×C4×C31C2411yescharacteristic
232SD16×C31—28no—
233SD16×C31C22⋊C4116yescomplemented
234D8×C31—28no—
235D8×C31—28no—
236M16×C31—28no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31C22×C412yes—
246C2×C8×C31C22×C412yes—
247C2×C8×C31C2×D412yes—
248C2×C8×C31C2×D412yes—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—42no—
258C4⋊C4×C31—42no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—41no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—42no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—81no—
269C22⋊C4×C31—81no—
270C22⋊C4×C31—81no—
271C22⋊C4×C31—81no—
272C22⋊C4×C31—81no—
273C42×C31—21no—
274C42×C31—21no—
275C42×C31—21no—
276C42×C31—21no—
277C42×C31—42no—
278C42×C31—42no—
279#22443C3111yesmaximal, characteristic, direct product factor, Sylow
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—48no—
292C23×C31—48no—
293C23×C31—41no—
294C23×C31—41no—
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—22no—
319Q8×C31C2×C22⋊C414yescomplemented
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—48no—
328D4×C31—48no—
329D4×C31—41no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—41no—
333D4×C31C2×C22⋊C414yes—
334C2×C4×C31—22no—
335C2×C4×C31—21no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
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—21no—
353C2×C4×C31—21no—
354C2×C4×C31—48no—
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×C31C4×D412yes—
370C2×C4×C31AGL(1,ℤ/8)12yescomplemented
371C2×C4×C31C23×C411yescharacteristic
372C2×C4×C31C22×D411yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C2×#4111yescharacteristic
375C2×C4×C31H(5,𝔽2)11yescharacteristic
376C2×C4×C31H(5,𝔽2)11yescharacteristic
377C8×C31—22no—
378C8×C31—41no—
379C8×C31—41no—
380C8×C31C2×C22⋊C414yescomplemented
381C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
382C2×#440C2×C3111yescharacteristic, complemented
383C2×C4×SD16C2×C3111yescharacteristic, complemented
384#2341C2×C3111yescharacteristic, complemented
385D4×C22⋊C4C2×C3111yescharacteristic, complemented
386#1972C2×C3111yescharacteristic, complemented
387#1970C2×C3111yescharacteristic, complemented
388#1880C2×C3111yescharacteristic, complemented
389#1880C2×C3111yescharacteristic, complemented
390#1879C2×C3111yescharacteristic, complemented
391#1879C2×C3111yescharacteristic, complemented
392#1809C2×C3111yescharacteristic, complemented
393#1788C2×C3111yescharacteristic, complemented
394#1786C2×C3111yescharacteristic, complemented
395#1753C2×C3111yescharacteristic, complemented
396C22×C31—22no—
397C22×C31—24no—
398C22×C31—22no—
399C22×C31—22no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—816no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31C2×C4×D411yescharacteristic
426C22×C31D4211yescharacteristic
427C22×C31D4211yescharacteristic
428C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C31#57511yescharacteristic
430C22×C31#57611yescharacteristic
431C22×C31#57711yescharacteristic
432C4×C31—22no—
433C4×C31—24no—
434C4×C31—22no—
435C4×C31—41no—
436C4×C31—41no—
437C4×C31—41no—
438C4×C31—81no—
439C4×C31—81no—
440C4×C31—81no—
441C4×C31—81no—
442C4×C31C22×C22⋊C411yescharacteristic
443C4×C31#51811yescharacteristic
444C4×C31#54611yescharacteristic
445C4×C31#54611yescharacteristic
446C22×#41C22×C3111yescharacteristic
447C23×D4C22×C3111yescharacteristic
448C2×AGL(1,ℤ/8)—24no—
449C2×AGL(1,ℤ/8)—24no—
450C2×AGL(1,ℤ/8)C4×C3118yescomplemented
451C22×SD16C22×C3111yescharacteristic
452C22×SD16C22×C3111yescharacteristic
453C22×D8C22×C3111yescharacteristic
454C22×D8C22×C3111yescharacteristic
455C22×M16C22×C3111yescharacteristic
456C2×C4×Q8C22×C3111yescharacteristic, complemented
457C2×C4×Q8C22×C3111yescharacteristic, complemented
458C2×C4×D4C22×C3111yescharacteristic
459C2×C4×D4C22×C3111yescharacteristic
460C22×C22⋊C4—21no—
461#440—24no—
462C4×SD16—24no—
463C2×#107C22×C3111yescharacteristic, complemented
464C2×#106C22×C3111yescharacteristic, complemented
465C2×#103C22×C3111yescharacteristic, complemented
466C2×#103C22×C3111yescharacteristic, complemented
467C2×#102C22×C3111yescharacteristic
468C2×#102C22×C3111yescharacteristic
469C2×#102C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×#102C22×C3111yescharacteristic, complemented
472C2×#102C22×C3111yescharacteristic, complemented
473C2×C22⋊C8C22×C3111yescharacteristic
474C2×#97C22×C3111yescharacteristic, complemented
475C2×C4×C8C22×C3111yescharacteristic, complemented
476#390—21no—
477#390—21no—
478#390C22×C3111yescharacteristic
479#390C22×C3111yescharacteristic
480#390C22×C3111yescharacteristic, complemented
481#390C22×C3111yescharacteristic, complemented
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C3111yescharacteristic
486#380C22×C3111yescharacteristic
487#379—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4C22×C3111yescharacteristic
490#340C22×C3111yescharacteristic, complemented
491#340C22×C3111yescharacteristic, complemented
492#336C22×C3111yescharacteristic, complemented
493#336C22×C3111yescharacteristic, complemented
494C2×C31—42no—
495C2×C31—44no—
496C2×C31—82no—
497C2×C31—82no—
498C2×C31D4×C22⋊C411yescharacteristic
499C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
500C2×C31#294611yescharacteristic
501C2×C31#326511yescharacteristic
502C2×C31#326811yescharacteristic
503C2×C31#327411yescharacteristic
504C2×C31#327511yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41C2×C4×C3114yescomplemented
512C22×Q8C23×C3111yescharacteristic
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×C4×C3114yes—
521C22×D4C23×C3111yescharacteristic
522C22×D4C23×C3111yescharacteristic
523C22×D4C23×C3111yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C23×C3111yescharacteristic
528AGL(1,ℤ/8)—232no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16C2×C4×C3114yes—
532C2×SD16C2×C4×C3114yescomplemented
533C2×SD16D4×C3114yes—
534C2×SD16D4×C3114yes—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8C2×C4×C3114yes—
540C2×D8C2×C4×C3114yescomplemented
541C2×M16—22no—
542C2×M16—22no—
543C2×M16C2×C4×C3114yescomplemented
544C22×C8C23×C3111yescharacteristic
545C22×C8C23×C3111yescharacteristic
546C22×C8C23×C3111yescharacteristic
547C22×C8C23×C3111yescharacteristic
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—41no—
555C4×D4—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4C23×C3111yescharacteristic
559C2×C4⋊C4C23×C3111yescharacteristic
560C2×C4⋊C4C23×C3111yescharacteristic
561C2×C4⋊C4C23×C3111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
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×C42—21no—
578C2×C42—21no—
579C2×C42C23×C3111yescharacteristic
580C2×C42C23×C3111yescharacteristic
581#107—22no—
582#106—22no—
583#103—22no—
584#103—22no—
585#102—22no—
586#102—22no—
587#102—41no—
588#102—41no—
589#102—41no—
590#102—41no—
591C22⋊C8—22no—
592#97—22no—
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95D4×C3111yescharacteristic
597#95D4×C3111yescharacteristic
598C31#2244311yescharacteristic, direct product factor, Sylow
599C24—21no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24C2×D4×C3111yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C22×C4×C3112yes—
618C2×Q8C2×D4×C3112yes—
619C2×Q8C2×D4×C3112yes—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
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—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—81no—
666C22×C4C22×C4×C3112yes—
667C22×C4C2×D4×C3111yescharacteristic
668C22×C4C2×D4×C3111yescharacteristic
669C22×C4C2×D4×C3111yescharacteristic
670C22×C4C2×D4×C3111yescharacteristic
671C22×C4C2×D4×C3111yescharacteristic
672C22×C4#41×C3112yes—
673C22×C4C24×C3111yescharacteristic
674SD16—28no—
675SD16C22⋊C4×C31116yescomplemented
676D8—28no—
677D8—28no—
678M16—28no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8C22×C4×C3112yes—
688C2×C8C22×C4×C3112yes—
689C2×C8C2×D4×C3112yes—
690C2×C8C2×D4×C3112yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—48no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
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—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23C4×D4×C3112yes—
756C23C22×D4×C3111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×C22⋊C4×C3114yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C3114yes—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
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—84no—
809C2×C4—84no—
810C2×C4C4×D4×C3112yes—
811C2×C4C31×AGL(1,ℤ/8)12yescomplemented
812C2×C4C23×C4×C3111yescharacteristic
813C2×C4C22×D4×C3111yescharacteristic
814C2×C4C22×D4×C3111yescharacteristic
815C2×C4C2×#41×C3111yescharacteristic
816C2×C4C31×H(5,𝔽2)11yescharacteristic
817C2×C4C31×H(5,𝔽2)11yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8C2×C22⋊C4×C3114yescomplemented
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22C2×C4×D4×C3111yescharacteristic
852C22D42×C3111yescharacteristic
853C22D42×C3111yescharacteristic
854C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
855C22C31×#57511yescharacteristic
856C22C31×#57611yescharacteristic
857C22C31×#57711yescharacteristic
858C4—22no—
859C4—24no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4C22×C22⋊C4×C3111yescharacteristic
869C4C31×#51811yescharacteristic
870C4C31×#54611yescharacteristic
871C4C31×#54611yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—82no—
876C2D4×C22⋊C4×C3111yescharacteristic
877C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
878C2C31×#294611yescharacteristic
879C2C31×#326511yescharacteristic
880C2C31×#326811yescharacteristic
881C2C31×#327411yescharacteristic
882C2C31×#327511yescharacteristic
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×#440C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2341C2semidirect
5. D4×C22⋊C4×C31C2semidirect
6. C31×#1972C2semidirect
7. C31×#1970C2semidirect
8. C31×#1880C2semidirect
9. C31×#1880C2semidirect
10. C31×#1879C2semidirect
11. C31×#1879C2semidirect
12. C31×#1809C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C31×#1753C2semidirect
20. C2×C31×AGL(1,ℤ/8)C4semidirect
26. C2×C4×Q8×C31C22semidirect
27. C2×C4×Q8×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
50. C31×#390C22semidirect
51. C31×#390C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#336C22semidirect
63. C31×#336C22semidirect
70. C2×#41×C31C2×C4semidirect
91. C2×SD16×C31C2×C4semidirect
99. C2×D8×C31C2×C4semidirect
102. C2×M16×C31C2×C4semidirect
233. SD16×C31C22⋊C4semidirect
279. #22443C31direct (N × H)
319. Q8×C31C2×C22⋊C4semidirect
370. C2×C4×C31AGL(1,ℤ/8)semidirect
380. C8×C31C2×C22⋊C4semidirect
382. C2×#440C2×C31semidirect
383. C2×C4×SD16C2×C31semidirect
384. #2341C2×C31semidirect
385. D4×C22⋊C4C2×C31semidirect
386. #1972C2×C31semidirect
387. #1970C2×C31semidirect
388. #1880C2×C31semidirect
389. #1880C2×C31semidirect
390. #1879C2×C31semidirect
391. #1879C2×C31semidirect
392. #1809C2×C31semidirect
393. #1788C2×C31semidirect
394. #1786C2×C31semidirect
395. #1753C2×C31semidirect
450. C2×AGL(1,ℤ/8)C4×C31semidirect
456. C2×C4×Q8C22×C31semidirect
457. C2×C4×Q8C22×C31semidirect
463. C2×#107C22×C31semidirect
464. C2×#106C22×C31semidirect
465. C2×#103C22×C31semidirect
466. C2×#103C22×C31semidirect
471. C2×#102C22×C31semidirect
472. C2×#102C22×C31semidirect
474. C2×#97C22×C31semidirect
475. C2×C4×C8C22×C31semidirect
480. #390C22×C31semidirect
481. #390C22×C31semidirect
490. #340C22×C31semidirect
491. #340C22×C31semidirect
492. #336C22×C31semidirect
493. #336C22×C31semidirect
511. C2×#41C2×C4×C31semidirect
532. C2×SD16C2×C4×C31semidirect
540. C2×D8C2×C4×C31semidirect
543. C2×M16C2×C4×C31semidirect
598. C31#22443direct (N × H)
675. SD16C22⋊C4×C31semidirect
760. Q8C2×C22⋊C4×C31semidirect
811. C2×C4C31×AGL(1,ℤ/8)semidirect
821. 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×#4402
C2×C4×SD16×C312
C31×#23412
D4×C22⋊C4×C312
C31×#19722
C31×#19702
C31×#18802
C31×#18792
C31×#18092
C31×#17882
C31×#17862
C31×#17532
#2244331