Finite Group Databasebeta

← C4×C31×#388 #21470522

Subgroups — C4×C31×#388 #21470522

Order 7936.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C212yesmaximal
2C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
6C2×C43×C31C211yesmaximal, characteristic, complemented
7C31×#1437C212yesmaximal
8C31×#1436C212yesmaximal, complemented
9C31×#1434C212yesmaximal, complemented
10C4×C31×#95C211yesmaximal, characteristic, complemented
11C4×C31×#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C31×#388C4116yesdirect product factor
27C4×C4⋊C4×C31—24no—
28C4×C22⋊C4×C31—24no—
29C4×C22⋊C4×C31—24no—
30C4×C22⋊C4×C31C418yescomplemented
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C43×C31—24no—
41C25×C31C2311yescharacteristic
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31—22no—
46C23×C4×C31—22no—
47C23×C4×C31—22no—
48C23×C4×C31C2×C414yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31C2×C418yescomplemented
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31C2×C414yes—
68C2×C22⋊C4×C31C2×C418yes—
69C2×C22⋊C4×C31C2×C418yes—
70C2×C22⋊C4×C31C2×C414yes—
71C2×C22⋊C4×C31C2×C418yes—
72C2×C42×C31—24no—
73C2×C42×C31—22no—
74C2×C42×C31—24no—
75C2×C42×C31—22no—
76C2×C42×C31—22no—
77C2×C42×C31—24no—
78C2×C42×C31—24no—
79C2×C42×C31—22no—
80C2×C42×C31—22no—
81C2×C42×C31—24no—
82C2×C42×C31—22no—
83C2×C42×C31—22no—
84C2×C42×C31—22no—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31—22no—
89C2×C42×C31—22no—
90C2×C42×C31—22no—
91C2×C42×C31C2×C414yes—
92C2×C42×C31C2×C414yes—
93C2×C42×C31C2×C418yescomplemented
94C2×C42×C31D414yes—
95C2×C42×C31D414yes—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—24no—
101C31×#95C2×C414yes—
102C31×#95C2×C414yes—
103C31×#95C2×C418yescomplemented
104C31×#95C2×C418yescomplemented
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31C22×C414yes—
115C24×C31C22×C412yes—
116C24×C31C2411yescharacteristic
117C22×C4×C31—21no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—28no—
157C22×C4×C31—28no—
158C22×C4×C31—28no—
159C22×C4×C31—44no—
160C22×C4×C31—44no—
161C22×C4×C31—44no—
162C22×C4×C31—44no—
163C22×C4×C31C22×C412yes—
164C22×C4×C31C22×C412yes—
165C22×C4×C31C22×C414yes—
166C22×C4×C31C22×C414yes—
167C22×C4×C31C22×C412yes—
168C22×C4×C31C22×C412yes—
169C22×C4×C31C22×C414yes—
170C22×C4×C31C22×C414yes—
171C22×C4×C31C22×C412yes—
172C22×C4×C31C22×C414yes—
173C22×C4×C31C22×C414yes—
174C22×C4×C31C22×C412yes—
175C22×C4×C31C2×D414yes—
176C22×C4×C31C2×D414yes—
177C22×C4×C31C2×D412yes—
178C22×C4×C31C2×D412yes—
179C22×C4×C31#4114yes—
180C22×C4×C31#4114yes—
181C22×C4×C31#4114yes—
182C22×C4×C31#4112yes—
183C22×C4×C31#4112yes—
184C22×C4×C31#4112yes—
185C22×C4×C31#4112yes—
186C4⋊C4×C31—216no—
187C22⋊C4×C31—28no—
188C22⋊C4×C31—216no—
189C22⋊C4×C31—216no—
190C22⋊C4×C31C42116yescomplemented
191C42×C31—216no—
192C42×C31—28no—
193C42×C31—28no—
194C42×C31—216no—
195C42×C31—28no—
196C42×C31—28no—
197C42×C31—44no—
198C42×C31—44no—
199C4×#388C3111yesmaximal, characteristic, direct product factor, Sylow
200C23×C31—22no—
201C23×C31—22no—
202C23×C31—24no—
203C23×C31—24no—
204C23×C31—22no—
205C23×C31—22no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—41no—
213C23×C31—41no—
214C23×C31—42no—
215C23×C31—41no—
216C23×C31—41no—
217C23×C31—42no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—42no—
221C23×C31—42no—
222C23×C31C2×C4214yes—
223C23×C31C23×C411yescharacteristic
224C23×C31C23×C412yes—
225C23×C31C22×D411yescharacteristic
226C23×C31C22×D411yescharacteristic
227C23×C31C2×#4111yescharacteristic
228C23×C31C2×#4111yescharacteristic
229C23×C31C2×#4112yes—
230C23×C31C2×#4111yescharacteristic
231C23×C31C2×#4112yes—
232C23×C31C2×#4111yescharacteristic
233C23×C31C2×#4112yes—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—24no—
237C2×C4×C31—22no—
238C2×C4×C31—24no—
239C2×C4×C31—24no—
240C2×C4×C31—24no—
241C2×C4×C31—24no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—24no—
250C2×C4×C31—24no—
251C2×C4×C31—24no—
252C2×C4×C31—24no—
253C2×C4×C31—24no—
254C2×C4×C31—24no—
255C2×C4×C31—24no—
256C2×C4×C31—24no—
257C2×C4×C31—24no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—24no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—24no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—42no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—416no—
285C2×C4×C31C2×C4214yes—
286C2×C4×C31C2×C4214yes—
287C2×C4×C31#11714yes—
288C2×C4×C31#11714yes—
289C2×C4×C31C4×D418yes—
290C2×C4×C31C4×D418yes—
291C2×C4×C31C4×D414yes—
292C2×C4×C31C4×D414yes—
293C2×C4×C31#12114yes—
294C2×C4×C31#12314yes—
295C2×C4×C31#12414yes—
296C2×C4×C31#12614yes—
297C2×#388C2×C3112yes—
298C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
299C2×C4×C22⋊C4C2×C3111yescharacteristic
300C2×C4×C22⋊C4C2×C3111yescharacteristic
301C2×C4×C22⋊C4C2×C3111yescharacteristic
302C2×C43C2×C3111yescharacteristic, complemented
303#1437C2×C3112yes—
304#1436C2×C3112yescomplemented
305#1434C2×C3112yescomplemented
306C4×#95C2×C3111yescharacteristic, complemented
307C4×#95C2×C3111yescharacteristic, complemented
308C22×C31—24no—
309C22×C31—24no—
310C22×C31—24no—
311C22×C31—44no—
312C22×C31—42no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—42no—
316C22×C31—44no—
317C22×C31—44no—
318C22×C31—44no—
319C22×C31C22×C4211yescharacteristic
320C22×C31C2×#11711yescharacteristic
321C22×C31C2×#11711yescharacteristic
322C22×C31C2×C4×D411yescharacteristic
323C22×C31C2×C4×D411yescharacteristic
324C22×C31C2×C4×D412yes—
325C22×C31C2×C4×D412yes—
326C22×C31C4×#4112yes—
327C22×C31C4×#4112yes—
328C22×C31C4×#4112yes—
329C22×C31C4×#4112yes—
330C22×C31C4×#4111yescharacteristic
331C22×C31C4×#4111yescharacteristic
332C22×C31C2×#12111yescharacteristic
333C22×C31C2×#12311yescharacteristic
334C22×C31#52512yes—
335C22×C31C2×#12411yescharacteristic
336C22×C31C2×#12611yescharacteristic
337C22×C31#52912yes—
338C22×C31#52912yes—
339C22×C31#52912yes—
340C22×C31#52912yes—
341C22×C31#53212yes—
342C4×C31—24no—
343C4×C31—24no—
344C4×C31—24no—
345C4×C31—28no—
346C4×C31—28no—
347C4×C31—42no—
348C4×C31—42no—
349C4×C31—44no—
350C4×C31—44no—
351C4×C31#38818yesdirect product factor
352C24×C4C22×C3111yescharacteristic
353C22×C4⋊C4C22×C3112yes—
354C22×C22⋊C4C22×C3111yescharacteristic
355C22×C22⋊C4C22×C3112yes—
356C22×C22⋊C4C22×C3112yes—
357C22×C22⋊C4C22×C3111yescharacteristic
358C22×C42C22×C3111yescharacteristic
359C22×C42C22×C3111yescharacteristic
360C22×C42C22×C3112yes—
361C22×C42C22×C3111yescharacteristic
362C22×C42C22×C3111yescharacteristic
363C22×C42C22×C3112yes—
364C22×C42C22×C3111yescharacteristic
365C22×C42C22×C3111yescharacteristic
366#388C4×C31116yesdirect product factor
367C4×C4⋊C4—24no—
368C4×C22⋊C4—24no—
369C4×C22⋊C4—24no—
370C4×C22⋊C4C4×C3118yescomplemented
371C2×#95C22×C3112yes—
372C2×#95C22×C3112yes—
373C2×#95C22×C3112yes—
374C2×#95C22×C3112yes—
375C2×#95C22×C3112yes—
376C2×#95C22×C3111yescharacteristic
377C2×#95C22×C3111yescharacteristic
378C2×#95C22×C3112yes—
379C2×#95C22×C3112yes—
380C43—24no—
381C2×C31—44no—
382C2×C31C4×#11711yescharacteristic
383C2×C31C42×D411yescharacteristic
384C2×C31C42×D411yescharacteristic
385C2×C31C2×#38811yescharacteristic
386C2×C31#229011yescharacteristic
387C2×C31#229311yescharacteristic
388C2×C31#229811yescharacteristic
389C2×C31C4×#12112yes—
390C2×C31C4×#12312yes—
391C2×C31C4×#12412yes—
392C2×C31C4×#12612yes—
393C25C23×C3111yescharacteristic
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4C2×C4×C3114yes—
401C23×C4C23×C3112yes—
402C23×C4C23×C3111yescharacteristic
403C23×C4C23×C3112yes—
404C23×C4C23×C3111yescharacteristic
405C23×C4C23×C3111yescharacteristic
406C23×C4C23×C3111yescharacteristic
407C23×C4C23×C3112yes—
408C23×C4C23×C3112yes—
409C23×C4C23×C3111yescharacteristic
410C23×C4C23×C3111yescharacteristic
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4C2×C4×C3118yescomplemented
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4C2×C4×C3114yes—
420C2×C22⋊C4C2×C4×C3118yes—
421C2×C22⋊C4C2×C4×C3118yes—
422C2×C22⋊C4C2×C4×C3114yes—
423C2×C22⋊C4C2×C4×C3118yes—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—24no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42C2×C4×C3114yes—
444C2×C42C2×C4×C3114yes—
445C2×C42C2×C4×C3118yescomplemented
446C2×C42D4×C3114yes—
447C2×C42D4×C3114yes—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95C2×C4×C3114yes—
454#95C2×C4×C3114yes—
455#95C2×C4×C3118yescomplemented
456#95C2×C4×C3118yescomplemented
457C31C4×#38811yescharacteristic, direct product factor, Sylow
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24C22×C4×C3114yes—
468C24C22×C4×C3112yes—
469C24C24×C3111yescharacteristic
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4C22×C4×C3112yes—
517C22×C4C22×C4×C3112yes—
518C22×C4C22×C4×C3114yes—
519C22×C4C22×C4×C3114yes—
520C22×C4C22×C4×C3112yes—
521C22×C4C22×C4×C3112yes—
522C22×C4C22×C4×C3114yes—
523C22×C4C22×C4×C3114yes—
524C22×C4C22×C4×C3112yes—
525C22×C4C22×C4×C3114yes—
526C22×C4C22×C4×C3114yes—
527C22×C4C22×C4×C3112yes—
528C22×C4C2×D4×C3114yes—
529C22×C4C2×D4×C3114yes—
530C22×C4C2×D4×C3112yes—
531C22×C4C2×D4×C3112yes—
532C22×C4#41×C3114yes—
533C22×C4#41×C3114yes—
534C22×C4#41×C3114yes—
535C22×C4#41×C3112yes—
536C22×C4#41×C3112yes—
537C22×C4#41×C3112yes—
538C22×C4#41×C3112yes—
539C4⋊C4—216no—
540C22⋊C4—28no—
541C22⋊C4—216no—
542C22⋊C4—216no—
543C22⋊C4C42×C31116yescomplemented
544C42—216no—
545C42—28no—
546C42—28no—
547C42—216no—
548C42—28no—
549C42—28no—
550C42—44no—
551C42—44no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—24no—
556C23—22no—
557C23—22no—
558C23—24no—
559C23—24no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23C2×C42×C3114yes—
575C23C23×C4×C3111yescharacteristic
576C23C23×C4×C3112yes—
577C23C22×D4×C3111yescharacteristic
578C23C22×D4×C3111yescharacteristic
579C23C2×#41×C3111yescharacteristic
580C23C2×#41×C3111yescharacteristic
581C23C2×#41×C3112yes—
582C23C2×#41×C3111yescharacteristic
583C23C2×#41×C3112yes—
584C23C2×#41×C3111yescharacteristic
585C23C2×#41×C3112yes—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—416no—
637C2×C4C2×C42×C3114yes—
638C2×C4C2×C42×C3114yes—
639C2×C4C31×#11714yes—
640C2×C4C31×#11714yes—
641C2×C4C4×D4×C3118yes—
642C2×C4C4×D4×C3118yes—
643C2×C4C4×D4×C3114yes—
644C2×C4C4×D4×C3114yes—
645C2×C4C31×#12114yes—
646C2×C4C31×#12314yes—
647C2×C4C31×#12414yes—
648C2×C4C31×#12614yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22C22×C42×C3111yescharacteristic
661C22C2×C31×#11711yescharacteristic
662C22C2×C31×#11711yescharacteristic
663C22C2×C4×D4×C3111yescharacteristic
664C22C2×C4×D4×C3111yescharacteristic
665C22C2×C4×D4×C3112yes—
666C22C2×C4×D4×C3112yes—
667C22C4×#41×C3112yes—
668C22C4×#41×C3112yes—
669C22C4×#41×C3111yescharacteristic
670C22C4×#41×C3111yescharacteristic
671C22C4×#41×C3112yes—
672C22C4×#41×C3112yes—
673C22C2×C31×#12111yescharacteristic
674C22C2×C31×#12311yescharacteristic
675C22C31×#52512yes—
676C22C2×C31×#12411yescharacteristic
677C22C2×C31×#12611yescharacteristic
678C22C31×#52912yes—
679C22C31×#52912yes—
680C22C31×#52912yes—
681C22C31×#52912yes—
682C22C31×#53212yes—
683C4—24no—
684C4—24no—
685C4—24no—
686C4—28no—
687C4—28no—
688C4—42no—
689C4—42no—
690C4—44no—
691C4—44no—
692C4C31×#38818yesdirect product factor
693C2—44no—
694C2C4×C31×#11711yescharacteristic
695C2C42×D4×C3111yescharacteristic
696C2C42×D4×C3111yescharacteristic
697C2C2×C31×#38811yescharacteristic
698C2C31×#229011yescharacteristic
699C2C31×#229311yescharacteristic
700C2C31×#229811yescharacteristic
701C2C4×C31×#12112yes—
702C2C4×C31×#12312yes—
703C2C4×C31×#12412yes—
704C2C4×C31×#12612yes—
subgroupG/H
centerC23×C4×C31C23
commutatorC22C22×C42×C31
Frattini, cosocleC24C24×C31
socleC24×C31C24
prime radicalC25×C31C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊C4×C31C2semidirect
6. C2×C43×C31C2semidirect
8. C31×#1436C2semidirect
9. C31×#1434C2semidirect
10. C4×C31×#95C2semidirect
11. C4×C31×#95C2semidirect
26. C31×#388C4direct (N × H)
30. C4×C22⋊C4×C31C4semidirect
61. C2×C4⋊C4×C31C2×C4semidirect
93. C2×C42×C31C2×C4semidirect
103. C31×#95C2×C4semidirect
104. C31×#95C2×C4semidirect
190. C22⋊C4×C31C42semidirect
199. C4×#388C31direct (N × H)
298. C2×C4×C4⋊C4C2×C31semidirect
302. C2×C43C2×C31semidirect
304. #1436C2×C31semidirect
305. #1434C2×C31semidirect
306. C4×#95C2×C31semidirect
307. C4×#95C2×C31semidirect
351. C4×C31#388direct (N × H)
366. #388C4×C31direct (N × H)
370. C4×C22⋊C4C4×C31semidirect
413. C2×C4⋊C4C2×C4×C31semidirect
445. C2×C42C2×C4×C31semidirect
455. #95C2×C4×C31semidirect
456. #95C2×C4×C31semidirect
457. C31C4×#388direct (N × H)
543. C22⋊C4C42×C31semidirect
692. C4C31×#388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C2×C43×C312
C31×#14372
C31×#14362
C31×#14342
C4×C31×#952
C4×#38831