Finite Group Databasebeta

← C31×#22880 #21479639

Subgroups — C31×#22880 #21479639

Order 7936.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#447C211yesmaximal, characteristic
2C2×C4×D8×C31C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C31×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1972C211yesmaximal, characteristic, complemented
7C31×#1934C211yesmaximal, characteristic, complemented
8C31×#1925C211yesmaximal, characteristic, complemented
9C31×#1895C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1864C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1762C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic, complemented
24C2×C31×#117C2211yescharacteristic
25C22×C22⋊C4×C31—21no—
26C31×#447C418yescomplemented
27C4×D8×C31—24no—
28C2×C31×#107C2211yescharacteristic, complemented
29C2×C31×#106C2211yescharacteristic, complemented
30C31×#418—24no—
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic, complemented
38C2×C31×#102C2211yescharacteristic, complemented
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic, complemented
41C2×C4×C8×C31C2211yescharacteristic, complemented
42C31×#390—21no—
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic, complemented
46C31×#389C2211yescharacteristic, complemented
47C31×#388—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#386—21no—
51C31×#380C2211yescharacteristic
52C31×#379—21no—
53C4×C4⋊C4×C31C2211yescharacteristic, complemented
54C4×C22⋊C4×C31—21no—
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C25×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2×C414yescomplemented
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—41no—
81C2×D8×C31—41no—
82C2×D8×C31C2×C414yes—
83C2×D8×C31C2×C414yescomplemented
84C2×M16×C31—22no—
85C2×M16×C31—22no—
86C2×M16×C31—41no—
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C31×#121—22no—
92C31×#121C2×C414yescomplemented
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—41no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C31×#117—22no—
100C31×#117—41no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—44no—
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C42×C31—21no—
123C2×C42×C31—21no—
124C2×C42×C31C2311yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C31×#107—22no—
127C31×#106—41no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—41no—
133C31×#102C2×C414yescomplemented
134C31×#102C2×C414yescomplemented
135C31×#102D414yescomplemented
136C31×C22⋊C8C2×C414yescomplemented
137C31×#97—41no—
138C4×C8×C31—22no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—24no—
148C24×C31—42no—
149C24×C31—42no—
150C24×C31—42no—
151C24×C31—42no—
152C24×C31—81no—
153C24×C31—81no—
154C24×C31C2×D411yescharacteristic
155C2×D4×C31—28no—
156C2×D4×C31—24no—
157C2×D4×C31—24no—
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—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
173C2×D4×C31—44no—
174C2×D4×C31—42no—
175C2×D4×C31—42no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31C22×C412yes—
179C2×D4×C31C22×C412yes—
180C2×D4×C31C22×C412yes—
181C2×D4×C31C2×D412yes—
182C2×D4×C31#4112yes—
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—21no—
191C22×C4×C31—21no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—81no—
199C22×C4×C31—81no—
200C22×C4×C31—81no—
201C22×C4×C31C22×C412yes—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31#4112yes—
208C22×C4×C31C2411yescharacteristic
209D8×C31—28no—
210D8×C31—44no—
211M16×C31—44no—
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×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31C22×C412yes—
222C2×C8×C31C22×C412yes—
223C2×C8×C31C2×D412yes—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—81no—
233C4⋊C4×C31C22×C412yes—
234C4⋊C4×C31C2×D412yes—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—41no—
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—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—81no—
247C22⋊C4×C31—81no—
248C22⋊C4×C31—81no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—21no—
252C42×C31—21no—
253C42×C31—42no—
254C42×C31—81no—
255#22880C3111yesmaximal, characteristic, direct product factor, Sylow
256C23×C31—22no—
257C23×C31—21no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—48no—
268C23×C31—48no—
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—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—84no—
286C23×C31—84no—
287C23×C31—84no—
288C23×C31—84no—
289C23×C31—84no—
290C23×C31C4×D412yes—
291C23×C31C22×D411yescharacteristic
292D4×C31—22no—
293D4×C31—22no—
294D4×C31—22no—
295D4×C31—22no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—22no—
299D4×C31—48no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—84no—
305D4×C31C4×D414yes—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
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—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—84no—
339C2×C4×C31—84no—
340C2×C4×C31—84no—
341C2×C4×C31C4×D412yes—
342C2×C4×C31AGL(1,ℤ/8)12yes—
343C2×C4×C31C23×C411yescharacteristic
344C2×C4×C31C22×D411yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C2×C4×C31C2×#4111yescharacteristic
347C2×C4×C31H(5,𝔽2)11yescharacteristic
348C2×C4×C31H(5,𝔽2)11yescharacteristic
349C8×C31—22no—
350C8×C31—22no—
351C8×C31—22no—
352C8×C31—41no—
353C2×#447C2×C3111yescharacteristic
354C2×C4×D8C2×C3111yescharacteristic, complemented
355C2×#418C2×C3111yescharacteristic, complemented
356#2363C2×C3111yescharacteristic, complemented
357D4×C22⋊C4C2×C3111yescharacteristic, complemented
358#1972C2×C3111yescharacteristic, complemented
359#1934C2×C3111yescharacteristic, complemented
360#1925C2×C3111yescharacteristic, complemented
361#1895C2×C3111yescharacteristic, complemented
362#1879C2×C3111yescharacteristic, complemented
363#1879C2×C3111yescharacteristic, complemented
364#1864C2×C3111yescharacteristic, complemented
365#1854C2×C3111yescharacteristic, complemented
366#1762C2×C3111yescharacteristic, complemented
367#1753C2×C3111yescharacteristic, complemented
368C22×C31—22no—
369C22×C31—24no—
370C22×C31—22no—
371C22×C31—22no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—41no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—816no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31C2×C4×D411yescharacteristic
398C22×C31D4211yescharacteristic
399C22×C31#54611yescharacteristic
400C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C31#57511yescharacteristic
402C22×C31#57611yescharacteristic
403C22×C31#57611yescharacteristic
404C4×C31—22no—
405C4×C31—22no—
406C4×C31—42no—
407C4×C31—42no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—41no—
411C4×C31—81no—
412C4×C31—81no—
413C4×C31—81no—
414C4×C31C2×C4×D411yescharacteristic
415C4×C31#51811yescharacteristic
416C4×C31#54611yescharacteristic
417C4×C31#55111yescharacteristic
418C23×D4C22×C3111yescharacteristic
419C22×D8C22×C3111yescharacteristic
420C22×D8C22×C3111yescharacteristic
421C22×M16C22×C3111yescharacteristic
422C2×#121C22×C3111yescharacteristic
423C2×C4×D4C22×C3111yescharacteristic
424C2×C4×D4C22×C3111yescharacteristic
425C2×C4×D4C22×C3111yescharacteristic, complemented
426C2×#117C22×C3111yescharacteristic
427C22×C22⋊C4—21no—
428#447C4×C3118yescomplemented
429C4×D8—24no—
430C2×#107C22×C3111yescharacteristic, complemented
431C2×#106C22×C3111yescharacteristic, complemented
432#418—24no—
433C2×#102C22×C3111yescharacteristic
434C2×#102C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic, complemented
440C2×#102C22×C3111yescharacteristic, complemented
441C2×C22⋊C8C22×C3111yescharacteristic
442C2×#97C22×C3111yescharacteristic, complemented
443C2×C4×C8C22×C3111yescharacteristic, complemented
444#390—21no—
445#390C22×C3111yescharacteristic
446#390C22×C3111yescharacteristic
447#390C22×C3111yescharacteristic, complemented
448#389C22×C3111yescharacteristic, complemented
449#388—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#380C22×C3111yescharacteristic
454#379—21no—
455C4×C4⋊C4C22×C3111yescharacteristic, complemented
456C4×C22⋊C4—21no—
457C4×C22⋊C4C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic, complemented
459#340C22×C3111yescharacteristic, complemented
460#340C22×C3111yescharacteristic, complemented
461#340C22×C3111yescharacteristic, complemented
462#336C22×C3111yescharacteristic, complemented
463#336C22×C3111yescharacteristic, complemented
464C2×C31—42no—
465C2×C31—44no—
466C2×C31—82no—
467C2×C31—82no—
468C2×C31#235811yescharacteristic
469C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
470C2×C31#294811yescharacteristic
471C2×C31#326411yescharacteristic
472C2×C31#326811yescharacteristic
473C2×C31#332211yescharacteristic
474C2×C31#332511yescharacteristic
475C25—21no—
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4C2×C4×C3114yescomplemented
484C22×D4C23×C3111yescharacteristic
485C22×D4C23×C3111yescharacteristic
486C22×D4C23×C3111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C23×C3111yescharacteristic
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×D8—41no—
495C2×D8C2×C4×C3114yes—
496C2×D8C2×C4×C3114yescomplemented
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8C23×C3111yescharacteristic
501C22×C8C23×C3111yescharacteristic
502C22×C8C23×C3111yescharacteristic
503C22×C8C23×C3111yescharacteristic
504#121—22no—
505#121C2×C4×C3114yescomplemented
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—41no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4C23×C3111yescharacteristic
516C2×C4⋊C4C23×C3111yescharacteristic
517C2×C4⋊C4C23×C3111yescharacteristic
518C2×C4⋊C4C23×C3111yescharacteristic
519C2×C4⋊C4C23×C3111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—44no—
533C2×C22⋊C4D4×C3111yescharacteristic
534C2×C22⋊C4D4×C3111yescharacteristic
535C2×C42—21no—
536C2×C42—21no—
537C2×C42C23×C3111yescharacteristic
538C2×C42C23×C3111yescharacteristic
539#107—22no—
540#106—41no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102C2×C4×C3114yescomplemented
547#102C2×C4×C3114yescomplemented
548#102D4×C3114yescomplemented
549C22⋊C8C2×C4×C3114yescomplemented
550#97—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95D4×C3111yescharacteristic
556#95D4×C3111yescharacteristic
557C31#2288011yescharacteristic, direct product factor, Sylow
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C3111yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C3112yes—
593C2×D4C22×C4×C3112yes—
594C2×D4C22×C4×C3112yes—
595C2×D4C2×D4×C3112yes—
596C2×D4#41×C3112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C3112yes—
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C2×D4×C3111yescharacteristic
621C22×C4#41×C3112yes—
622C22×C4C24×C3111yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C3112yes—
636C2×C8C22×C4×C3112yes—
637C2×C8C2×D4×C3112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C3112yes—
648C4⋊C4C2×D4×C3112yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C3112yes—
704C23C22×D4×C3111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C3114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C3112yes—
755C2×C4C31×AGL(1,ℤ/8)12yes—
756C2×C4C23×C4×C3111yescharacteristic
757C2×C4C22×D4×C3111yescharacteristic
758C2×C4C2×#41×C3111yescharacteristic
759C2×C4C2×#41×C3111yescharacteristic
760C2×C4C31×H(5,𝔽2)11yescharacteristic
761C2×C4C31×H(5,𝔽2)11yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C3111yescharacteristic
796C22D42×C3111yescharacteristic
797C22C31×#54611yescharacteristic
798C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
799C22C31×#57511yescharacteristic
800C22C31×#57611yescharacteristic
801C22C31×#57611yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C3111yescharacteristic
813C4C31×#51811yescharacteristic
814C4C31×#54611yescharacteristic
815C4C31×#55111yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C31×#235811yescharacteristic
821C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
822C2C31×#294811yescharacteristic
823C2C31×#326411yescharacteristic
824C2C31×#326811yescharacteristic
825C2C31×#332211yescharacteristic
826C2C31×#332511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
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×C4×D8×C31C2semidirect
3. C2×C31×#418C2semidirect
4. C31×#2363C2semidirect
5. D4×C22⋊C4×C31C2semidirect
6. C31×#1972C2semidirect
7. C31×#1934C2semidirect
8. C31×#1925C2semidirect
9. C31×#1895C2semidirect
10. C31×#1879C2semidirect
11. C31×#1879C2semidirect
12. C31×#1864C2semidirect
13. C31×#1854C2semidirect
14. C31×#1762C2semidirect
15. C31×#1753C2semidirect
23. C2×C4×D4×C31C22semidirect
26. C31×#447C4semidirect
28. C2×C31×#107C22semidirect
29. C2×C31×#106C22semidirect
37. C2×C31×#102C22semidirect
38. C2×C31×#102C22semidirect
40. C2×C31×#97C22semidirect
41. C2×C4×C8×C31C22semidirect
45. C31×#390C22semidirect
46. C31×#389C22semidirect
53. C4×C4⋊C4×C31C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#336C22semidirect
61. C31×#336C22semidirect
70. C22×D4×C31C2×C4semidirect
83. C2×D8×C31C2×C4semidirect
92. C31×#121C2×C4semidirect
133. C31×#102C2×C4semidirect
134. C31×#102C2×C4semidirect
135. C31×#102D4semidirect
136. C31×C22⋊C8C2×C4semidirect
255. #22880C31direct (N × H)
354. C2×C4×D8C2×C31semidirect
355. C2×#418C2×C31semidirect
356. #2363C2×C31semidirect
357. D4×C22⋊C4C2×C31semidirect
358. #1972C2×C31semidirect
359. #1934C2×C31semidirect
360. #1925C2×C31semidirect
361. #1895C2×C31semidirect
362. #1879C2×C31semidirect
363. #1879C2×C31semidirect
364. #1864C2×C31semidirect
365. #1854C2×C31semidirect
366. #1762C2×C31semidirect
367. #1753C2×C31semidirect
425. C2×C4×D4C22×C31semidirect
428. #447C4×C31semidirect
430. C2×#107C22×C31semidirect
431. C2×#106C22×C31semidirect
439. C2×#102C22×C31semidirect
440. C2×#102C22×C31semidirect
442. C2×#97C22×C31semidirect
443. C2×C4×C8C22×C31semidirect
447. #390C22×C31semidirect
448. #389C22×C31semidirect
455. C4×C4⋊C4C22×C31semidirect
458. #340C22×C31semidirect
459. #340C22×C31semidirect
460. #340C22×C31semidirect
461. #340C22×C31semidirect
462. #336C22×C31semidirect
463. #336C22×C31semidirect
483. C22×D4C2×C4×C31semidirect
496. C2×D8C2×C4×C31semidirect
505. #121C2×C4×C31semidirect
546. #102C2×C4×C31semidirect
547. #102C2×C4×C31semidirect
548. #102D4×C31semidirect
549. C22⋊C8C2×C4×C31semidirect
557. C31#22880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C2×C4×D8×C312
C2×C31×#4182
C31×#23632
D4×C22⋊C4×C312
C31×#19722
C31×#19342
C31×#19252
C31×#18952
C31×#18792
C31×#18642
C31×#18542
C31×#17622
C31×#17532
#2288031