Finite Group Databasebeta

← C31×#25098 #21481857

Subgroups — C31×#25098 #21481857

Order 7936.

1088 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#470C211yesmaximal, characteristic, complemented
2C2×C31×#462C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic
4C2×C31×#417C211yesmaximal, characteristic
5C31×#2432C211yesmaximal, characteristic
6C31×#2360C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2056C211yesmaximal, characteristic, complemented
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1927C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1872C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C31×#470—24no—
28C31×#462—24no—
29C31×#452—24no—
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C31×#417—24no—
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389—21no—
51C31×#389C2211yescharacteristic
52C31×#387—21no—
53C31×#385—21no—
54C31×#385—21no—
55C31×#385—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C2×Q16×C31—22no—
78C2×Q16×C31—22no—
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31—41no—
82C2×Q16×C31—41no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—41no—
86C2×M16×C31—22no—
87C2×M16×C31—22no—
88C2×M16×C31—41no—
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C31×C4⋊Q8—22no—
94C31×C4⋊Q8—41no—
95C31×#124—22no—
96C31×#124—41no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8D414yes—
101C4×Q8×C31—22no—
102C4×Q8×C31—41no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—41no—
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C22⋊C4×C31D411yescharacteristic
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31C2311yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#106—22no—
129C31×C4⋊C8—22no—
130C31×C4⋊C8—41no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#103D414yes—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152#41×C31—28no—
153#41×C31—44no—
154#41×C31—44no—
155#41×C31—44no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31C2×D412yes—
173C2×Q8×C31C2×D412yes—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
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—21no—
193C22×C4×C31—21no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31—81no—
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31#4112yes—
207C22×C4×C31C2411yescharacteristic
208Q16×C31—44no—
209Q16×C31—44no—
210SD16×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×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31C2×D412yes—
224C4⋊C4×C31—24no—
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—42no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—42no—
236C4⋊C4×C31—81no—
237C4⋊C4×C31C2×D412yes—
238C4⋊C4×C31C2×D412yes—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—41no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—42no—
252C42×C31—81no—
253#25098C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31#12112yes—
268C23×C31C22×D411yescharacteristic
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—22no—
272Q8×C31—22no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31—41no—
281D4×C31—22no—
282D4×C31—22no—
283D4×C31—48no—
284D4×C31—41no—
285D4×C31—41no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—21no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—48no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—84no—
326C2×C4×C31#12112yes—
327C2×C4×C31#13712yes—
328C2×C4×C31C22×D411yescharacteristic
329C2×C4×C31C22×D411yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31H(5,𝔽2)11yescharacteristic
333C2×C4×C31H(5,𝔽2)11yescharacteristic
334C8×C31—22no—
335C8×C31—41no—
336C8×C31—41no—
337C8×C31—41no—
338C2×#470C2×C3111yescharacteristic, complemented
339C2×#462C2×C3111yescharacteristic, complemented
340C2×#452C2×C3111yescharacteristic
341C2×#417C2×C3111yescharacteristic
342#2432C2×C3111yescharacteristic
343#2360C2×C3111yescharacteristic, complemented
344#2065C2×C3111yescharacteristic, complemented
345#2056C2×C3111yescharacteristic, complemented
346#2043C2×C3111yescharacteristic, complemented
347#2015C2×C3111yescharacteristic, complemented
348#1983C2×C3111yescharacteristic, complemented
349#1927C2×C3111yescharacteristic, complemented
350#1880C2×C3111yescharacteristic, complemented
351#1872C2×C3111yescharacteristic, complemented
352#1851C2×C3111yescharacteristic, complemented
353C22×C31—22no—
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—41no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31C2×#12111yescharacteristic
368C22×C31D4211yescharacteristic
369C22×C31#54611yescharacteristic
370C22×C31C2×#13711yescharacteristic
371C22×C31#57511yescharacteristic
372C22×C31#57711yescharacteristic
373C22×C31#57811yescharacteristic
374C4×C31—22no—
375C4×C31—22no—
376C4×C31—41no—
377C4×C31—42no—
378C4×C31—42no—
379C4×C31—41no—
380C4×C31—42no—
381C4×C31—42no—
382C4×C31—41no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31#52511yescharacteristic
387C4×C31#53811yescharacteristic
388C4×C31D4211yescharacteristic
389C4×C31#54611yescharacteristic
390C22×#41C22×C3111yescharacteristic
391C22×Q16C22×C3111yescharacteristic
392C22×Q16C22×C3111yescharacteristic
393C22×SD16C22×C3111yescharacteristic
394C22×M16C22×C3111yescharacteristic
395C2×C4⋊Q8C22×C3111yescharacteristic
396C2×#124C22×C3111yescharacteristic
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×C22⋊Q8C22×C3111yescharacteristic
399C2×C4×Q8C22×C3111yescharacteristic
400C22×C4⋊C4C22×C3111yescharacteristic
401#470—24no—
402#462—24no—
403#452—24no—
404C2×#106C22×C3111yescharacteristic
405C2×C4⋊C8C22×C3111yescharacteristic
406C2×C4⋊C8C22×C3111yescharacteristic
407#417—24no—
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#103C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×#102C22×C3111yescharacteristic
417C2×#102C22×C3111yescharacteristic
418C2×C22⋊C8C22×C3111yescharacteristic
419#394—21no—
420#394—21no—
421#391C22×C3111yescharacteristic
422#391C22×C3111yescharacteristic
423#390C22×C3111yescharacteristic
424#389—21no—
425#389C22×C3111yescharacteristic
426#387—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430C4×C4⋊C4C22×C3111yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic
434#340C22×C3111yescharacteristic
435#336C22×C3111yescharacteristic
436#336C22×C3111yescharacteristic
437C2×C31—42no—
438C2×C31—82no—
439C2×C31#242411yescharacteristic
440C2×C31#303711yescharacteristic
441C2×C31#304611yescharacteristic
442C2×C31#327011yescharacteristic
443C2×C31#327511yescharacteristic
444C2×C31#331511yescharacteristic
445C2×C31#333111yescharacteristic
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C22×Q8C23×C3111yescharacteristic
453C22×Q8C23×C3111yescharacteristic
454C22×Q8C23×C3111yescharacteristic
455C22×D4—21no—
456C22×D4C23×C3111yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4C23×C3111yescharacteristic
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16—22no—
464C2×Q16—41no—
465C2×Q16—41no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×M16—22no—
470C2×M16—22no—
471C2×M16—41no—
472C22×C8C23×C3111yescharacteristic
473C22×C8C23×C3111yescharacteristic
474C22×C8C23×C3111yescharacteristic
475C22×C8C23×C3111yescharacteristic
476C4⋊Q8—22no—
477C4⋊Q8—41no—
478#124—22no—
479#124—41no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8D4×C3114yes—
484C4×Q8—22no—
485C4×Q8—41no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C4⋊C4C23×C3111yescharacteristic
498C2×C4⋊C4C23×C3111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C3111yescharacteristic
506C2×C22⋊C4D4×C3111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C23×C3111yescharacteristic
510C2×C42C23×C3111yescharacteristic
511#106—22no—
512C4⋊C8—22no—
513C4⋊C8—41no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—41no—
520#103D4×C3114yes—
521#102—22no—
522#102—22no—
523#102—22no—
524C22⋊C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C3111yescharacteristic
532#95D4×C3111yescharacteristic
533C31#2509811yescharacteristic, direct product factor, Sylow
534C24—21no—
535C24C2×D4×C3111yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C2×D4×C3112yes—
557C2×Q8C2×D4×C3112yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4#41×C3112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3112yes—
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4#41×C3112yes—
591C22×C4C24×C3111yescharacteristic
592Q16—44no—
593Q16—44no—
594SD16—44no—
595M16—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8C2×D4×C3112yes—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—81no—
621C4⋊C4C2×D4×C3112yes—
622C4⋊C4C2×D4×C3112yes—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—81no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C31×#12112yes—
651C23C22×D4×C3111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—84no—
709C2×C4C31×#12112yes—
710C2×C4C31×#13712yes—
711C2×C4C22×D4×C3111yescharacteristic
712C2×C4C22×D4×C3111yescharacteristic
713C2×C4C2×#41×C3111yescharacteristic
714C2×C4C2×#41×C3111yescharacteristic
715C2×C4C31×H(5,𝔽2)11yescharacteristic
716C2×C4C31×H(5,𝔽2)11yescharacteristic
717C8—22no—
718C8—41no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C2×C31×#12111yescharacteristic
736C22D42×C3111yescharacteristic
737C22C31×#54611yescharacteristic
738C22C2×C31×#13711yescharacteristic
739C22C31×#57511yescharacteristic
740C22C31×#57711yescharacteristic
741C22C31×#57811yescharacteristic
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4C31×#52511yescharacteristic
755C4C31×#53811yescharacteristic
756C4D42×C3111yescharacteristic
757C4C31×#54611yescharacteristic
758C2—42no—
759C2—82no—
760C2C31×#242411yescharacteristic
761C2C31×#303711yescharacteristic
762C2C31×#304611yescharacteristic
763C2C31×#327011yescharacteristic
764C2C31×#327511yescharacteristic
765C2C31×#331511yescharacteristic
766C2C31×#333111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×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
1. C2×C31×#470C2semidirect
2. C2×C31×#462C2semidirect
6. C31×#2360C2semidirect
7. C31×#2065C2semidirect
8. C31×#2056C2semidirect
9. C31×#2043C2semidirect
10. C31×#2015C2semidirect
11. C31×#1983C2semidirect
12. C31×#1927C2semidirect
13. C31×#1880C2semidirect
14. C31×#1872C2semidirect
15. C31×#1851C2semidirect
253. #25098C31direct (N × H)
338. C2×#470C2×C31semidirect
339. C2×#462C2×C31semidirect
343. #2360C2×C31semidirect
344. #2065C2×C31semidirect
345. #2056C2×C31semidirect
346. #2043C2×C31semidirect
347. #2015C2×C31semidirect
348. #1983C2×C31semidirect
349. #1927C2×C31semidirect
350. #1880C2×C31semidirect
351. #1872C2×C31semidirect
352. #1851C2×C31semidirect
533. C31#25098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4702
C2×C31×#4622
C2×C31×#4522
C2×C31×#4172
C31×#24322
C31×#23602
C31×#20652
C31×#20562
C31×#20432
C31×#20152
C31×#19832
C31×#19272
C31×#18802
C31×#18722
C31×#18512
#2509831