Finite Group Databasebeta

← C31×#25202 #21481961

Subgroups — C31×#25202 #21481961

Order 7936.

942 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×#481C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic
3C31×#2502C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic
5C31×#2084C211yesmaximal, characteristic, complemented
6C31×#2071C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#1948C211yesmaximal, characteristic, complemented
10C31×#1927C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1872C211yesmaximal, characteristic, complemented
13C31×#1850C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C2×C31×#340C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#481—24no—
25C31×#465—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C31×#398—21no—
39C31×#398—21no—
40C31×#391C2211yescharacteristic
41C31×#391C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#389C2211yescharacteristic
44C31×#388—21no—
45C31×#386—21no—
46C31×#385—21no—
47C31×#385—21no—
48C31×#385—21no—
49C31×#384C2211yescharacteristic
50C31×#384C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31C2311yescharacteristic
68C2×SD16×C31—22no—
69C2×SD16×C31—22no—
70C2×SD16×C31—41no—
71C22×C8×C31—22no—
72C22×C8×C31—22no—
73C22×C8×C31—41no—
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8—22no—
80C31×#121—22no—
81C31×#121D414yes—
82C4×D4×C31—22no—
83C4×D4×C31—41no—
84C4×D4×C31—44no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—21no—
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—21no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31D411yescharacteristic
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C42×C31—21no—
111C2×C42×C31C2311yescharacteristic
112C2×C42×C31C2311yescharacteristic
113C31×#106—22no—
114C31×#106—22no—
115C31×#106—22no—
116C31×C4⋊C8—22no—
117C31×C4⋊C8—41no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—41no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×C22⋊C8—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95D411yescharacteristic
132C31×#95D411yescharacteristic
133C24×C31—21no—
134C24×C31C2×D411yescharacteristic
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—21no—
141C2×D4×C31—24no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—42no—
148C2×D4×C31—42no—
149C2×D4×C31C2×D412yes—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—42no—
162C22×C4×C31—42no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31—42no—
166C22×C4×C31—81no—
167C22×C4×C31—81no—
168C22×C4×C31—81no—
169C22×C4×C31—81no—
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D412yes—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31#4112yes—
177C22×C4×C31C2411yescharacteristic
178SD16×C31—44no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
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×C31—44no—
191C2×C8×C31#4112yes—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
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—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—81no—
207C4⋊C4×C31—81no—
208C4⋊C4×C31—81no—
209C4⋊C4×C31—81no—
210C4⋊C4×C31C2×D412yes—
211C4⋊C4×C31#4112yes—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—24no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—81no—
218C22⋊C4×C31SD1614yescomplemented
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—42no—
224#25202C3111yesmaximal, characteristic, direct product factor, Sylow
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—22no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31#12112yes—
237C23×C31C2×SD1612yes—
238C23×C31#13712yes—
239C23×C31C22×D411yescharacteristic
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—41no—
244D4×C31—22no—
245D4×C31—22no—
246D4×C31—48no—
247D4×C31—41no—
248D4×C31—41no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—41no—
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—41no—
285C2×C4×C31—41no—
286C2×C4×C31—84no—
287C2×C4×C31—84no—
288C2×C4×C31—84no—
289C2×C4×C31#12112yes—
290C2×C4×C31C2×SD1612yes—
291C2×C4×C31C2×SD1612yes—
292C2×C4×C31C22×D411yescharacteristic
293C2×C4×C31C2×#4111yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
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×C31—41no—
302C2×#481C2×C3111yescharacteristic
303C2×#465C2×C3111yescharacteristic
304#2502C2×C3111yescharacteristic, complemented
305#2361C2×C3111yescharacteristic
306#2084C2×C3111yescharacteristic, complemented
307#2071C2×C3111yescharacteristic, complemented
308#2066C2×C3111yescharacteristic, complemented
309#2055C2×C3111yescharacteristic, complemented
310#1948C2×C3111yescharacteristic, complemented
311#1927C2×C3111yescharacteristic, complemented
312#1877C2×C3111yescharacteristic, complemented
313#1872C2×C3111yescharacteristic, complemented
314#1850C2×C3111yescharacteristic, complemented
315#1802C2×C3111yescharacteristic, complemented
316C2×#340C2×C3111yescharacteristic, complemented
317C22×C31—22no—
318C22×C31—22no—
319C22×C31—22no—
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—22no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—42no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31—81no—
330C22×C31#46114yes—
331C22×C31C2×#12111yescharacteristic
332C22×C31#54611yescharacteristic
333C22×C31#54711yescharacteristic
334C22×C31C22×SD1611yescharacteristic
335C22×C31C2×#13711yescharacteristic
336C22×C31#57611yescharacteristic
337C22×C31#57711yescharacteristic
338C4×C31—22no—
339C4×C31—22no—
340C4×C31—22no—
341C4×C31—41no—
342C4×C31—42no—
343C4×C31—42no—
344C4×C31—41no—
345C4×C31—81no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31—81no—
349C4×C31—81no—
350C4×C31#52911yescharacteristic
351C4×C31#53911yescharacteristic
352C4×C31#54611yescharacteristic
353C4×C31#54711yescharacteristic
354C22×SD16C22×C3111yescharacteristic
355C23×C8C22×C3111yescharacteristic
356C2×C22⋊Q8C22×C3111yescharacteristic
357C2×#121C22×C3111yescharacteristic
358C2×C4×D4—21no—
359C2×C4×D4C22×C3111yescharacteristic
360C22×C4⋊C4C22×C3111yescharacteristic
361C22×C4⋊C4C22×C3111yescharacteristic
362#481—24no—
363#465—24no—
364C2×#106C22×C3111yescharacteristic
365C2×#106C22×C3111yescharacteristic
366C2×#106C22×C3111yescharacteristic
367C2×C4⋊C8C22×C3111yescharacteristic
368C2×C4⋊C8C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#103C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#102C22×C3111yescharacteristic
375C2×C22⋊C8C22×C3111yescharacteristic
376#398—21no—
377#398—21no—
378#391C22×C3111yescharacteristic
379#391C22×C3111yescharacteristic
380#390C22×C3111yescharacteristic
381#389C22×C3111yescharacteristic
382#388—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#384C22×C3111yescharacteristic
388#384C22×C3111yescharacteristic
389C4×C4⋊C4C22×C3111yescharacteristic
390C4×C22⋊C4C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#336C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399C2×C31—24no—
400C2×C31—82no—
401C2×C31#242511yescharacteristic
402C2×C31C2×#46111yescharacteristic
403C2×C31#304511yescharacteristic
404C2×C31#329511yescharacteristic
405C2×C31#331611yescharacteristic
406C2×C31#333511yescharacteristic
407C2×C31#334611yescharacteristic
408C22×Q8C23×C3111yescharacteristic
409C22×D4—21no—
410C22×D4C23×C3111yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—21no—
414C23×C4C23×C3111yescharacteristic
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—41no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427#121—22no—
428#121D4×C3114yes—
429C4×D4—22no—
430C4×D4—41no—
431C4×D4—44no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
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—21no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4D4×C3111yescharacteristic
456C2×C22⋊C4D4×C3111yescharacteristic
457C2×C42—21no—
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460#106—22no—
461#106—22no—
462#106—22no—
463C4⋊C8—22no—
464C4⋊C8—41no—
465#103—22no—
466#103—22no—
467#103—41no—
468#102—22no—
469#102—22no—
470#102—22no—
471C22⋊C8—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95D4×C3111yescharacteristic
479#95D4×C3111yescharacteristic
480C31#2520211yescharacteristic, direct product factor, Sylow
481C24—21no—
482C24C2×D4×C3111yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C2×D4×C3112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3112yes—
522C22×C4C2×D4×C3111yescharacteristic
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4#41×C3112yes—
525C22×C4C24×C3111yescharacteristic
526SD16—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
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×C8—44no—
539C2×C8#41×C3112yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4C2×D4×C3112yes—
559C4⋊C4#41×C3112yes—
560C22⋊C4—22no—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4SD16×C3114yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C31×#12112yes—
584C23C2×SD16×C3112yes—
585C23C31×#13712yes—
586C23C22×D4×C3111yescharacteristic
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
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—41no—
632C2×C4—41no—
633C2×C4—84no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4C31×#12112yes—
637C2×C4C2×SD16×C3112yes—
638C2×C4C2×SD16×C3112yes—
639C2×C4C22×D4×C3111yescharacteristic
640C2×C4C2×#41×C3111yescharacteristic
641C2×C4C2×#41×C3111yescharacteristic
642C2×C4C2×#41×C3111yescharacteristic
643C2×C4C31×H(5,𝔽2)11yescharacteristic
644C2×C4C31×2−1+411yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22C31×#46114yes—
663C22C2×C31×#12111yescharacteristic
664C22C31×#54611yescharacteristic
665C22C31×#54711yescharacteristic
666C22C22×SD16×C3111yescharacteristic
667C22C2×C31×#13711yescharacteristic
668C22C31×#57611yescharacteristic
669C22C31×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—42no—
675C4—42no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C31×#52911yescharacteristic
683C4C31×#53911yescharacteristic
684C4C31×#54611yescharacteristic
685C4C31×#54711yescharacteristic
686C2—24no—
687C2—82no—
688C2C31×#242511yescharacteristic
689C2C2×C31×#46111yescharacteristic
690C2C31×#304511yescharacteristic
691C2C31×#329511yescharacteristic
692C2C31×#331611yescharacteristic
693C2C31×#333511yescharacteristic
694C2C31×#334611yescharacteristic
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
3. C31×#2502C2semidirect
5. C31×#2084C2semidirect
6. C31×#2071C2semidirect
7. C31×#2066C2semidirect
8. C31×#2055C2semidirect
9. C31×#1948C2semidirect
10. C31×#1927C2semidirect
11. C31×#1877C2semidirect
12. C31×#1872C2semidirect
13. C31×#1850C2semidirect
14. C31×#1802C2semidirect
15. C2×C31×#340C2semidirect
218. C22⋊C4×C31SD16semidirect
224. #25202C31direct (N × H)
304. #2502C2×C31semidirect
306. #2084C2×C31semidirect
307. #2071C2×C31semidirect
308. #2066C2×C31semidirect
309. #2055C2×C31semidirect
310. #1948C2×C31semidirect
311. #1927C2×C31semidirect
312. #1877C2×C31semidirect
313. #1872C2×C31semidirect
314. #1850C2×C31semidirect
315. #1802C2×C31semidirect
316. C2×#340C2×C31semidirect
480. C31#25202direct (N × H)
566. C22⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4812
C2×C31×#4652
C31×#25022
C31×#23612
C31×#20842
C31×#20712
C31×#20662
C31×#20552
C31×#19482
C31×#19272
C31×#18772
C31×#18722
C31×#18502
C31×#18022
C2×C31×#3402
#2520231