Finite Group Databasebeta

← C31×#25149 #21481908

Subgroups — C31×#25149 #21481908

Order 7936.

1086 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×#464C211yesmaximal, characteristic, complemented
2C2×C31×#451C211yesmaximal, characteristic, complemented
3C2×C31×#448C211yesmaximal, characteristic
4C2×C4×Q16×C31C211yesmaximal, characteristic, complemented
5C31×#2426C211yesmaximal, characteristic
6Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1878C211yesmaximal, characteristic, complemented
15C31×#1865C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C31×#464—24no—
28C31×#451—24no—
29C31×#448—24no—
30C4×Q16×C31—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×#106C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#396—21no—
46C31×#394—21no—
47C31×#391—21no—
48C31×#391—21no—
49C31×#391C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#390—21no—
52C31×#390C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#388—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—21no—
66C22×Q8×C31—22no—
67C22×Q8×C31—22no—
68C22×Q8×C31—41no—
69C22×Q8×C31—41no—
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
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×C31D414yescomplemented
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—22no—
88C2×SD16×C31—41no—
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C31×#124—22no—
94C31×#124—41no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—41no—
97C31×#121—22no—
98C31×#121—41no—
99C4×Q8×C31—22no—
100C4×Q8×C31—22no—
101C4×Q8×C31—22no—
102C4×Q8×C31—41no—
103C4×Q8×C31—41no—
104C4×Q8×C31—41no—
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×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C42×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31C2311yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×#106—41no—
130C31×C4⋊C8—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103D414yes—
137C31×#102—22no—
138C31×#102—41no—
139C31×C22⋊C8—22no—
140C31×C22⋊C8—22no—
141C4×C8×C31—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
152C2×Q8×C31—24no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
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—42no—
167C2×Q8×C31—42no—
168C2×Q8×C31—44no—
169C2×Q8×C31—44no—
170C2×Q8×C31—44no—
171C2×Q8×C31—44no—
172C2×Q8×C31C2×D412yes—
173C2×Q8×C31C2×D412yes—
174C2×Q8×C31C2×D412yes—
175C2×Q8×C31#4112yes—
176C2×Q8×C31#4112yes—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—81no—
186C22×C4×C31—21no—
187C22×C4×C31—24no—
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—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2411yescharacteristic
208Q16×C31—28no—
209Q16×C31—44no—
210SD16×C31—44no—
211SD16×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×C31C2×D412yes—
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—42no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—81no—
236C4⋊C4×C31C2×D412yes—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
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—81no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—42no—
251C42×C31—42no—
252C42×C31—42no—
253#25149C3111yesmaximal, 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—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31#13512yes—
268C23×C31C22×D411yescharacteristic
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—22no—
272Q8×C31—22no—
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—22no—
276Q8×C31—48no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31—41no—
281Q8×C31#12114yes—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—84no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
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—41no—
326C2×C4×C31—41no—
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—22no—
336C8×C31—41no—
337C8×C31—41no—
338C2×#464C2×C3111yescharacteristic, complemented
339C2×#451C2×C3111yescharacteristic, complemented
340C2×#448C2×C3111yescharacteristic
341C2×C4×Q16C2×C3111yescharacteristic, complemented
342#2426C2×C3111yescharacteristic
343Q8×C22⋊C4C2×C3111yescharacteristic, complemented
344#2068C2×C3111yescharacteristic, complemented
345#2035C2×C3111yescharacteristic, complemented
346#2033C2×C3111yescharacteristic
347#2015C2×C3111yescharacteristic, complemented
348#1968C2×C3111yescharacteristic, complemented
349#1923C2×C3111yescharacteristic, complemented
350#1880C2×C3111yescharacteristic, complemented
351#1878C2×C3111yescharacteristic, complemented
352#1865C2×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—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31#52511yescharacteristic
368C22×C31D4211yescharacteristic
369C22×C31D4211yescharacteristic
370C22×C31C2×#13511yescharacteristic
371C22×C31C2×#13711yescharacteristic
372C22×C31#57711yescharacteristic
373C22×C31#57811yescharacteristic
374C4×C31—24no—
375C4×C31—22no—
376C4×C31—41no—
377C4×C31—42no—
378C4×C31—42no—
379C4×C31—41no—
380C4×C31—41no—
381C4×C31—42no—
382C4×C31—41no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31C2×#12111yescharacteristic
387C4×C31#53811yescharacteristic
388C4×C31#54611yescharacteristic
389C4×C31#54611yescharacteristic
390C23×Q8C22×C3111yescharacteristic
391C22×Q16C22×C3111yescharacteristic
392C22×Q16C22×C3111yescharacteristic
393C22×SD16C22×C3111yescharacteristic
394C22×SD16C22×C3111yescharacteristic
395C2×#124C22×C3111yescharacteristic
396C2×C22⋊Q8C22×C3111yescharacteristic
397C2×#121C22×C3111yescharacteristic
398C2×C4×Q8C22×C3111yescharacteristic
399C2×C4×Q8C22×C3111yescharacteristic
400C2×C4×Q8C22×C3111yescharacteristic
401#464—24no—
402#451—24no—
403#448—24no—
404C4×Q16—24no—
405C2×#107C22×C3111yescharacteristic
406C2×#106C22×C3111yescharacteristic
407C2×C4⋊C8C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417C2×C22⋊C8C22×C3111yescharacteristic
418C2×C4×C8C22×C3111yescharacteristic
419#396—21no—
420#394—21no—
421#391—21no—
422#391—21no—
423#391C22×C3111yescharacteristic
424#391C22×C3111yescharacteristic
425#390—21no—
426#390C22×C3111yescharacteristic
427#389C22×C3111yescharacteristic
428#388—21no—
429#380—21no—
430#380C22×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—161no—
439C2×C31#242411yescharacteristic
440C2×C31#310811yescharacteristic
441C2×C31#312111yescharacteristic
442C2×C31#327011yescharacteristic
443C2×C31#327811yescharacteristic
444C2×C31#328211yescharacteristic
445C2×C31#328511yescharacteristic
446C22×Q8—22no—
447C22×Q8—22no—
448C22×Q8—21no—
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—41no—
452C22×Q8—41no—
453C22×Q8C23×C3111yescharacteristic
454C22×Q8C23×C3111yescharacteristic
455C22×Q8C23×C3111yescharacteristic
456C22×D4—21no—
457C22×D4C23×C3111yescharacteristic
458C23×C4—21no—
459C23×C4C23×C3111yescharacteristic
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16—22no—
464C2×Q16—41no—
465C2×Q16D4×C3114yescomplemented
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—41no—
472C22×C8C23×C3111yescharacteristic
473C22×C8C23×C3111yescharacteristic
474C22×C8C23×C3111yescharacteristic
475C22×C8C23×C3111yescharacteristic
476#124—22no—
477#124—41no—
478C22⋊Q8—22no—
479C22⋊Q8—41no—
480#121—22no—
481#121—41no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×Q8—41no—
486C4×Q8—41no—
487C4×Q8—41no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4C23×C3111yescharacteristic
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C3111yescharacteristic
505C2×C22⋊C4D4×C3111yescharacteristic
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C23×C3111yescharacteristic
510C2×C42C23×C3111yescharacteristic
511#107—22no—
512#106—41no—
513C4⋊C8—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103D4×C3114yes—
520#102—22no—
521#102—41no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C4×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#2514911yescharacteristic, direct product factor, Sylow
534C24—21no—
535C24C2×D4×C3111yescharacteristic
536C2×Q8—24no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
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—42no—
551C2×Q8—42no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8C2×D4×C3112yes—
557C2×Q8C2×D4×C3112yes—
558C2×Q8C2×D4×C3112yes—
559C2×Q8#41×C3112yes—
560C2×Q8#41×C3112yes—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C24×C3111yescharacteristic
592Q16—28no—
593Q16—44no—
594SD16—44no—
595SD16—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×C8C2×D4×C3112yes—
607C2×C8C2×D4×C3112yes—
608C4⋊C4—21no—
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—81no—
620C4⋊C4C2×D4×C3112yes—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—42no—
636C42—42no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C31×#13512yes—
651C23C22×D4×C3111yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—48no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8C31×#12114yes—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—84no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
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—41no—
709C2×C4—41no—
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—22no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22C31×#52511yescharacteristic
736C22D42×C3111yescharacteristic
737C22D42×C3111yescharacteristic
738C22C2×C31×#13511yescharacteristic
739C22C2×C31×#13711yescharacteristic
740C22C31×#57711yescharacteristic
741C22C31×#57811yescharacteristic
742C4—24no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4C2×C31×#12111yescharacteristic
755C4C31×#53811yescharacteristic
756C4C31×#54611yescharacteristic
757C4C31×#54611yescharacteristic
758C2—42no—
759C2—161no—
760C2C31×#242411yescharacteristic
761C2C31×#310811yescharacteristic
762C2C31×#312111yescharacteristic
763C2C31×#327011yescharacteristic
764C2C31×#327811yescharacteristic
765C2C31×#328211yescharacteristic
766C2C31×#328511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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×#464C2semidirect
2. C2×C31×#451C2semidirect
4. C2×C4×Q16×C31C2semidirect
6. Q8×C22⋊C4×C31C2semidirect
7. C31×#2068C2semidirect
8. C31×#2035C2semidirect
10. C31×#2015C2semidirect
11. C31×#1968C2semidirect
12. C31×#1923C2semidirect
13. C31×#1880C2semidirect
14. C31×#1878C2semidirect
15. C31×#1865C2semidirect
82. C2×Q16×C31D4semidirect
253. #25149C31direct (N × H)
338. C2×#464C2×C31semidirect
339. C2×#451C2×C31semidirect
341. C2×C4×Q16C2×C31semidirect
343. Q8×C22⋊C4C2×C31semidirect
344. #2068C2×C31semidirect
345. #2035C2×C31semidirect
347. #2015C2×C31semidirect
348. #1968C2×C31semidirect
349. #1923C2×C31semidirect
350. #1880C2×C31semidirect
351. #1878C2×C31semidirect
352. #1865C2×C31semidirect
465. C2×Q16D4×C31semidirect
533. C31#25149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4642
C2×C31×#4512
C2×C31×#4482
C2×C4×Q16×C312
C31×#24262
Q8×C22⋊C4×C312
C31×#20682
C31×#20352
C31×#20332
C31×#20152
C31×#19682
C31×#19232
C31×#18802
C31×#18782
C31×#18652
#2514931