Finite Group Databasebeta

← C31×#22676 #21479435

Subgroups — C31×#22676 #21479435

Order 7936.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#442C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic
3C2×C4×D8×C31C211yesmaximal, characteristic
4C31×#2349C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1944C211yesmaximal, characteristic, complemented
7C31×#1941C211yesmaximal, characteristic, complemented
8C31×#1864C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic, complemented
10C31×#1862C211yesmaximal, characteristic, complemented
11C31×#1862C211yesmaximal, characteristic, complemented
12C31×#1847C211yesmaximal, characteristic, complemented
13C31×#1804C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C31×#1771C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C2×C4×D4×C31C2211yescharacteristic
18C2×C4×D4×C31C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31—21no—
24C31×#442—24no—
25C31×#442C418yescomplemented
26C4×D8×C31—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#389C2211yescharacteristic
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#385—21no—
47C31×#385—21no—
48C31×#385—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic
51C31×#382C2211yescharacteristic
52C31×#380—21no—
53C31×#380—21no—
54C4×C4⋊C4×C31C2211yescharacteristic
55C2×C31×#95—21no—
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C2×D8×C31C2×C414yes—
71C2×D8×C31D414yes—
72C2×D8×C31Q814yes—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C4×D4×C31—22no—
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—
86C4×D4×C31—41no—
87C4×D4×C31C2×C414yescomplemented
88C4×D4×C31C2×C414yescomplemented
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—44no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
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×C42×C31C2311yescharacteristic
111C2×C42×C31C2311yescharacteristic
112C2×C42×C31C2311yescharacteristic
113C31×#107—22no—
114C31×#107—41no—
115C31×#106—22no—
116C31×#106—41no—
117C31×#106C2×C414yescomplemented
118C31×C4⋊C8—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102C2×C414yescomplemented
124C31×#102C2×C414yescomplemented
125C31×#97—22no—
126C31×#97C2×C414yescomplemented
127C4×C8×C31—22no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95D411yescharacteristic
135C31×#95D411yescharacteristic
136C24×C31—21no—
137C24×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×C31C22×C412yes—
145C2×D4×C31C22×C412yes—
146C2×D4×C31C2×D412yes—
147C2×D4×C31C2×D412yes—
148C2×D4×C31C2×Q812yes—
149C2×D4×C31C2×Q812yes—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—24no—
153C22×C4×C31—24no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
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—42no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—81no—
169C22×C4×C31—81no—
170C22×C4×C31—81no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2411yescharacteristic
181D8×C31C4⋊C4116yescomplemented
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31C22×C412yes—
191C2×C8×C31C22×C412yes—
192C2×C8×C31C2×D412yes—
193C2×C8×C31C2×Q812yes—
194C4⋊C4×C31—22no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—41no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—81no—
210C4⋊C4×C31—81no—
211C4⋊C4×C31—81no—
212C4⋊C4×C31C22×C412yes—
213C4⋊C4×C31C22×C412yes—
214C22⋊C4×C31—24no—
215C22⋊C4×C31—24no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—42no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31C22×C412yes—
225C42×C31#4112yes—
226#22676C3111yesmaximal, characteristic, direct product factor, Sylow
227C23×C31—22no—
228C23×C31—22no—
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31C22×D411yescharacteristic
242D4×C31—22no—
243D4×C31—22no—
244D4×C31—22no—
245D4×C31—22no—
246D4×C31—22no—
247D4×C31—22no—
248D4×C31C2×C4⋊C414yes—
249D4×C31C2×C4⋊C414yescomplemented
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
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—21no—
266C2×C4×C31—21no—
267C2×C4×C31—48no—
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—41no—
283C2×C4×C31—41no—
284C2×C4×C31—84no—
285C2×C4×C31—84no—
286C2×C4×C31—84no—
287C2×C4×C31—84no—
288C2×C4×C31—84no—
289C2×C4×C31C4×D412yes—
290C2×C4×C31C4×D412yes—
291C2×C4×C31AGL(1,ℤ/8)12yes—
292C2×C4×C31C23×C411yescharacteristic
293C2×C4×C31C22×D411yescharacteristic
294C2×C4×C31C22×Q811yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31H(5,𝔽2)11yescharacteristic
297C2×C4×C312−1+411yescharacteristic
298C8×C31—22no—
299C8×C31—41no—
300C8×C31—41no—
301C8×C31C2×C4⋊C414yescomplemented
302C2×#442C2×C3111yescharacteristic
303C2×#442C2×C3111yescharacteristic
304C2×C4×D8C2×C3111yescharacteristic
305#2349C2×C3111yescharacteristic, complemented
306D4×C4⋊C4C2×C3111yescharacteristic, complemented
307#1944C2×C3111yescharacteristic, complemented
308#1941C2×C3111yescharacteristic, complemented
309#1864C2×C3111yescharacteristic, complemented
310#1864C2×C3111yescharacteristic, complemented
311#1862C2×C3111yescharacteristic, complemented
312#1862C2×C3111yescharacteristic, complemented
313#1847C2×C3111yescharacteristic, complemented
314#1804C2×C3111yescharacteristic, complemented
315#1802C2×C3111yescharacteristic, complemented
316#1771C2×C3111yescharacteristic, complemented
317C22×C31—24no—
318C22×C31—24no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—42no—
326C22×C31—42no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31C2×C4×D411yescharacteristic
332C22×C31D4211yescharacteristic
333C22×C31D4×Q811yescharacteristic
334C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C31#57511yescharacteristic
336C22×C31#57611yescharacteristic
337C22×C31#57711yescharacteristic
338C4×C31—22no—
339C4×C31—22no—
340C4×C31—22no—
341C4×C31—42no—
342C4×C31—42no—
343C4×C31—41no—
344C4×C31—41no—
345C4×C31—41no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31—81no—
349C4×C31—81no—
350C4×C31C22×C4⋊C411yescharacteristic
351C4×C31#52011yescharacteristic
352C4×C31#54711yescharacteristic
353C4×C31#55411yescharacteristic
354C22×D8C22×C3111yescharacteristic
355C2×C4×D4C22×C3111yescharacteristic
356C2×C4×D4C22×C3111yescharacteristic
357C2×C4×D4C22×C3111yescharacteristic
358C2×C4×D4C22×C3111yescharacteristic
359C2×C4×D4C22×C3111yescharacteristic
360C2×C4×D4C22×C3111yescharacteristic
361C22×C4⋊C4—21no—
362#442—24no—
363#442C4×C3118yescomplemented
364C4×D8—24no—
365C2×#107C22×C3111yescharacteristic
366C2×#107C22×C3111yescharacteristic
367C2×#106C22×C3111yescharacteristic
368C2×#106C22×C3111yescharacteristic
369C2×#106C22×C3111yescharacteristic
370C2×C4⋊C8C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#102C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×#97C22×C3111yescharacteristic
378C2×#97C22×C3111yescharacteristic
379C2×C4×C8C22×C3111yescharacteristic
380#389C22×C3111yescharacteristic
381#389C22×C3111yescharacteristic
382#389C22×C3111yescharacteristic
383#389C22×C3111yescharacteristic
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C22×C3111yescharacteristic
389#382C22×C3111yescharacteristic
390#380—21no—
391#380—21no—
392C4×C4⋊C4C22×C3111yescharacteristic
393C2×#95—21no—
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399#336C22×C3111yescharacteristic
400C2×C31—44no—
401C2×C31—44no—
402C2×C31D4×C4⋊C411yescharacteristic
403C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
404C2×C31#294611yescharacteristic
405C2×C31#326411yescharacteristic
406C2×C31#326711yescharacteristic
407C2×C31#338411yescharacteristic
408C2×C31#338911yescharacteristic
409C22×D4C23×C3111yescharacteristic
410C22×D4C23×C3111yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—21no—
417C2×D8C2×C4×C3114yes—
418C2×D8D4×C3114yes—
419C2×D8Q8×C3114yes—
420C22×C8C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—41no—
433C4×D4—41no—
434C4×D4C2×C4×C3114yescomplemented
435C4×D4C2×C4×C3114yescomplemented
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—44no—
443C2×C4⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C42C23×C3111yescharacteristic
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460#107—22no—
461#107—41no—
462#106—22no—
463#106—41no—
464#106C2×C4×C3114yescomplemented
465C4⋊C8—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102C2×C4×C3114yescomplemented
471#102C2×C4×C3114yescomplemented
472#97—22no—
473#97C2×C4×C3114yescomplemented
474C4×C8—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C3111yescharacteristic
482#95D4×C3111yescharacteristic
483C31#2267611yescharacteristic, direct product factor, Sylow
484C24—21no—
485C24—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4C22×C4×C3112yes—
493C2×D4C22×C4×C3112yes—
494C2×D4C2×D4×C3112yes—
495C2×D4C2×D4×C3112yes—
496C2×D4C2×Q8×C3112yes—
497C2×D4C2×Q8×C3112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C24×C3111yescharacteristic
529D8C4⋊C4×C31116yescomplemented
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8C22×C4×C3112yes—
539C2×C8C22×C4×C3112yes—
540C2×C8C2×D4×C3112yes—
541C2×C8C2×Q8×C3112yes—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—41no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4C22×C4×C3112yes—
561C4⋊C4C22×C4×C3112yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42C22×C4×C3112yes—
573C42#41×C3112yes—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×D4×C3111yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4C2×C4⋊C4×C3114yes—
596D4C2×C4⋊C4×C3114yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—48no—
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—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4C4×D4×C3112yes—
637C2×C4C4×D4×C3112yes—
638C2×C4C31×AGL(1,ℤ/8)12yes—
639C2×C4C23×C4×C3111yescharacteristic
640C2×C4C22×D4×C3111yescharacteristic
641C2×C4C22×Q8×C3111yescharacteristic
642C2×C4C2×#41×C3111yescharacteristic
643C2×C4C31×H(5,𝔽2)11yescharacteristic
644C2×C4C31×2−1+411yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8C2×C4⋊C4×C3114yescomplemented
649C22—24no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×C4×D4×C3111yescharacteristic
664C22D42×C3111yescharacteristic
665C22D4×Q8×C3111yescharacteristic
666C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
667C22C31×#57511yescharacteristic
668C22C31×#57611yescharacteristic
669C22C31×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C22×C4⋊C4×C3111yescharacteristic
683C4C31×#52011yescharacteristic
684C4C31×#54711yescharacteristic
685C4C31×#55411yescharacteristic
686C2—44no—
687C2—44no—
688C2D4×C4⋊C4×C3111yescharacteristic
689C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
690C2C31×#294611yescharacteristic
691C2C31×#326411yescharacteristic
692C2C31×#326711yescharacteristic
693C2C31×#338411yescharacteristic
694C2C31×#338911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C2×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
4. C31×#2349C2semidirect
5. D4×C4⋊C4×C31C2semidirect
6. C31×#1944C2semidirect
7. C31×#1941C2semidirect
8. C31×#1864C2semidirect
9. C31×#1864C2semidirect
10. C31×#1862C2semidirect
11. C31×#1862C2semidirect
12. C31×#1847C2semidirect
13. C31×#1804C2semidirect
14. C31×#1802C2semidirect
15. C31×#1771C2semidirect
25. C31×#442C4semidirect
87. C4×D4×C31C2×C4semidirect
88. C4×D4×C31C2×C4semidirect
117. C31×#106C2×C4semidirect
123. C31×#102C2×C4semidirect
124. C31×#102C2×C4semidirect
126. C31×#97C2×C4semidirect
181. D8×C31C4⋊C4semidirect
226. #22676C31direct (N × H)
249. D4×C31C2×C4⋊C4semidirect
301. C8×C31C2×C4⋊C4semidirect
305. #2349C2×C31semidirect
306. D4×C4⋊C4C2×C31semidirect
307. #1944C2×C31semidirect
308. #1941C2×C31semidirect
309. #1864C2×C31semidirect
310. #1864C2×C31semidirect
311. #1862C2×C31semidirect
312. #1862C2×C31semidirect
313. #1847C2×C31semidirect
314. #1804C2×C31semidirect
315. #1802C2×C31semidirect
316. #1771C2×C31semidirect
363. #442C4×C31semidirect
434. C4×D4C2×C4×C31semidirect
435. C4×D4C2×C4×C31semidirect
464. #106C2×C4×C31semidirect
470. #102C2×C4×C31semidirect
471. #102C2×C4×C31semidirect
473. #97C2×C4×C31semidirect
483. C31#22676direct (N × H)
529. D8C4⋊C4×C31semidirect
596. D4C2×C4⋊C4×C31semidirect
648. C8C2×C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4422
C2×C4×D8×C312
C31×#23492
D4×C4⋊C4×C312
C31×#19442
C31×#19412
C31×#18642
C31×#18622
C31×#18472
C31×#18042
C31×#18022
C31×#17712
#2267631