Finite Group Databasebeta

← C31×#11219 #21467978

Subgroups — C31×#11219 #21467978

Order 7936.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#107C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic
3C2×C31×#340C211yesmaximal, characteristic
4C2×C31×#340C211yesmaximal, characteristic
5C2×C31×#340C211yesmaximal, characteristic
6C2×C31×#336C211yesmaximal, characteristic
7C31×C4⋊#95C211yesmaximal, characteristic
8C23×C8×C31C2211yescharacteristic
9C23×C8×C31C2211yescharacteristic
10C22×C4⋊C4×C31—21no—
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C42×C31C2211yescharacteristic
16C2×C31×#107—22no—
17C2×C31×#107—22no—
18C2×C31×#107C414yescomplemented
19C31×#389—22no—
20C31×#389—22no—
21C2×C31×#95—21no—
22C2×C31×#95—21no—
23C2×C31×#95—21no—
24C31×#340—22no—
25C31×#340—22no—
26C31×#340—22no—
27C31×#336—22no—
28C23×C4×C31—21no—
29C23×C4×C31—21no—
30C23×C4×C31—21no—
31C23×C4×C31—21no—
32C23×C4×C31D411yescharacteristic
33C23×C4×C31D411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C22×C8×C31—21no—
42C22×C8×C31—21no—
43C22×C8×C31—21no—
44C22×C8×C31—21no—
45C22×C8×C31C2×C412yes—
46C22×C8×C31D412yes—
47C22×C8×C31Q812yes—
48C22×C8×C31Q812yes—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31—21no—
60C2×C4⋊C4×C31—21no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—21no—
66C2×C4⋊C4×C31—21no—
67C2×C4⋊C4×C31—21no—
68C2×C4⋊C4×C31—42no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31C2×C412yes—
71C2×C4⋊C4×C31C2×C412yes—
72C2×C4⋊C4×C31D412yes—
73C2×C4⋊C4×C31D412yes—
74C2×C4⋊C4×C31D412yes—
75C2×C4⋊C4×C31Q812yes—
76C2×C42×C31—21no—
77C2×C42×C31—21no—
78C2×C42×C31—21no—
79C2×C42×C31—21no—
80C2×C42×C31—21no—
81C2×C42×C31—21no—
82C31×#107—28no—
83C31×#95—24no—
84C31×#95—42no—
85C31×#95—42no—
86C24×C31C2×D411yescharacteristic
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—22no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31—41no—
109C22×C4×C31—41no—
110C22×C4×C31—41no—
111C22×C4×C31—41no—
112C22×C4×C31—41no—
113C22×C4×C31—41no—
114C22×C4×C31—41no—
115C22×C4×C31—41no—
116C22×C4×C31—41no—
117C22×C4×C31—41no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—41no—
121C22×C4×C31—41no—
122C22×C4×C31—41no—
123C22×C4×C31—41no—
124C22×C4×C31—41no—
125C22×C4×C31—41no—
126C22×C4×C31—41no—
127C22×C4×C31D812yes—
128C22×C4×C31Q1612yes—
129C22×C4×C31C22×C411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D411yescharacteristic
132C22×C4×C31C2×D411yescharacteristic
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×Q811yescharacteristic
135C22×C4×C31C2×Q811yescharacteristic
136C22×C4×C31C2×Q811yescharacteristic
137C22×C4×C31#4111yescharacteristic
138C22×C4×C31#4111yescharacteristic
139C22×C4×C31#4111yescharacteristic
140C22×C4×C31#4111yescharacteristic
141C22×C4×C31#4111yescharacteristic
142C22×C4×C31#4111yescharacteristic
143C2×C8×C31—22no—
144C2×C8×C31—22no—
145C2×C8×C31—22no—
146C2×C8×C31—22no—
147C2×C8×C31—22no—
148C2×C8×C31—22no—
149C2×C8×C31—22no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—41no—
153C2×C8×C31—41no—
154C2×C8×C31—41no—
155C2×C8×C31—41no—
156C2×C8×C31C4⋊C414yescomplemented
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—48no—
167C4⋊C4×C31—41no—
168C4⋊C4×C31—41no—
169C4⋊C4×C31—41no—
170C4⋊C4×C31—41no—
171C4⋊C4×C31—41no—
172C4⋊C4×C31—41no—
173C4⋊C4×C31C22⋊C414yes—
174C42×C31—41no—
175C42×C31—41no—
176C42×C31—41no—
177C42×C31—41no—
178#11219C3111yesmaximal, characteristic, direct product factor, Sylow
179C23×C31C4×D411yescharacteristic
180C23×C31#12011yescharacteristic
181C23×C31#12111yescharacteristic
182C23×C31#12111yescharacteristic
183C23×C31C22⋊Q811yescharacteristic
184C23×C31#12311yescharacteristic
185C23×C31C4⋊Q811yescharacteristic
186C23×C31C2×D811yescharacteristic
187C23×C31C2×Q1611yescharacteristic
188C23×C31#13511yescharacteristic
189C23×C31#13511yescharacteristic
190C23×C31AGL(1,ℤ/8)11yescharacteristic
191C23×C31AGL(1,ℤ/8)11yescharacteristic
192C23×C31#13711yescharacteristic
193C23×C31#13711yescharacteristic
194C2×C4×C31—24no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—41no—
207C2×C4×C31—42no—
208C2×C4×C31—41no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—41no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—81no—
225C2×C4×C31—81no—
226C2×C4×C31—81no—
227C2×C4×C31—81no—
228C2×C4×C31—81no—
229C2×C4×C31—81no—
230C2×C4×C31—81no—
231C2×C4×C31—81no—
232C2×C4×C31—81no—
233C2×C4×C31—81no—
234C2×C4×C31—81no—
235C2×C4×C31—81no—
236C2×C4×C31C2×C22⋊C411yescharacteristic
237C2×C4×C31C2×C4⋊C411yescharacteristic
238C2×C4×C31#11711yescharacteristic
239C2×C4×C31C4×D411yescharacteristic
240C2×C4×C31C4×Q811yescharacteristic
241C2×C4×C31C4×Q811yescharacteristic
242C2×C4×C31#12111yescharacteristic
243C2×C4×C31#12111yescharacteristic
244C2×C4×C31#12111yescharacteristic
245C2×C4×C31#12111yescharacteristic
246C2×C4×C31C22⋊Q811yescharacteristic
247C2×C4×C31C22⋊Q811yescharacteristic
248C2×C4×C31C22⋊Q811yescharacteristic
249C2×C4×C31C22⋊Q811yescharacteristic
250C2×C4×C31C22⋊Q811yescharacteristic
251C2×C4×C31C22⋊Q811yescharacteristic
252C2×C4×C31C22⋊Q811yescharacteristic
253C2×C4×C31#12311yescharacteristic
254C2×C4×C31#12311yescharacteristic
255C2×C4×C31#12411yescharacteristic
256C2×C4×C31#12511yescharacteristic
257C2×C4×C31#12511yescharacteristic
258C2×C4×C31#12511yescharacteristic
259C2×C4×C31#12511yescharacteristic
260C2×C4×C31#12611yescharacteristic
261C2×C4×C31#12611yescharacteristic
262C2×C4×C31C4⋊Q811yescharacteristic
263C2×C4×C31C4⋊Q811yescharacteristic
264C8×C31—24no—
265C8×C31—42no—
266C22×#107C2×C3111yescharacteristic
267C2×#389C2×C3111yescharacteristic
268C2×#340C2×C3111yescharacteristic
269C2×#340C2×C3111yescharacteristic
270C2×#340C2×C3111yescharacteristic
271C2×#336C2×C3111yescharacteristic
272C4⋊#95C2×C3111yescharacteristic
273C22×C31#38611yescharacteristic
274C22×C31#38711yescharacteristic
275C22×C31#38911yescharacteristic
276C22×C31#39411yescharacteristic
277C22×C31#39511yescharacteristic
278C22×C31#39611yescharacteristic
279C22×C31#39811yescharacteristic
280C22×C31C4×D811yescharacteristic
281C22×C31C4×Q1611yescharacteristic
282C22×C31#44111yescharacteristic
283C22×C31#44211yescharacteristic
284C22×C31#44711yescharacteristic
285C22×C31#44911yescharacteristic
286C22×C31#45111yescharacteristic
287C22×C31#45211yescharacteristic
288C22×C31#45911yescharacteristic
289C22×C31#46211yescharacteristic
290C22×C31#46311yescharacteristic
291C22×C31#46411yescharacteristic
292C22×C31#46611yescharacteristic
293C22×C31#46711yescharacteristic
294C22×C31#46811yescharacteristic
295C22×C31#46811yescharacteristic
296C22×C31#47411yescharacteristic
297C22×C31#47711yescharacteristic
298C22×C31#47811yescharacteristic
299C22×C31#47911yescharacteristic
300C22×C31#48011yescharacteristic
301C22×C31#48211yescharacteristic
302C22×C31#48411yescharacteristic
303C22×C31#48511yescharacteristic
304C22×C31#49911yescharacteristic
305C22×C31#50011yescharacteristic
306C22×C31#50111yescharacteristic
307C22×C31#50111yescharacteristic
308C4×C31—44no—
309C4×C31—42no—
310C4×C31—42no—
311C4×C31—82no—
312C4×C31—82no—
313C4×C31—82no—
314C4×C31#38011yescharacteristic
315C4×C31#38711yescharacteristic
316C4×C31#38911yescharacteristic
317C4×C31#39111yescharacteristic
318C4×C31#39611yescharacteristic
319C4×C31#39811yescharacteristic
320C4×C31#39811yescharacteristic
321C4×C31#40011yescharacteristic
322C23×C8C22×C3111yescharacteristic
323C23×C8C22×C3111yescharacteristic
324C22×C4⋊C4—21no—
325C22×C4⋊C4C22×C3111yescharacteristic
326C22×C4⋊C4C22×C3111yescharacteristic
327C22×C4⋊C4C22×C3111yescharacteristic
328C22×C4⋊C4C22×C3111yescharacteristic
329C22×C42C22×C3111yescharacteristic
330C2×#107—22no—
331C2×#107—22no—
332C2×#107C4×C3114yescomplemented
333#389—22no—
334#389—22no—
335C2×#95—21no—
336C2×#95—21no—
337C2×#95—21no—
338#340—22no—
339#340—22no—
340#340—22no—
341#336—22no—
342C2×C31#144111yescharacteristic
343C2×C31#187811yescharacteristic
344C2×C31#187911yescharacteristic
345C2×C31#191811yescharacteristic
346C2×C31#192111yescharacteristic
347C2×C31#194211yescharacteristic
348C2×C31#194311yescharacteristic
349C2×C31#203311yescharacteristic
350C2×C31#203611yescharacteristic
351C2×C31#205711yescharacteristic
352C2×C31#205911yescharacteristic
353C2×C31#206711yescharacteristic
354C2×C31#206811yescharacteristic
355C2×C31#208311yescharacteristic
356C2×C31#208511yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4D4×C3111yescharacteristic
362C23×C4D4×C3111yescharacteristic
363C23×C4C23×C3111yescharacteristic
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8C2×C4×C3112yes—
375C22×C8D4×C3112yes—
376C22×C8Q8×C3112yes—
377C22×C8Q8×C3112yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4C2×C4×C3112yes—
400C2×C4⋊C4C2×C4×C3112yes—
401C2×C4⋊C4D4×C3112yes—
402C2×C4⋊C4D4×C3112yes—
403C2×C4⋊C4D4×C3112yes—
404C2×C4⋊C4Q8×C3112yes—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411#107—28no—
412#95—24no—
413#95—42no—
414#95—42no—
415C31#1121911yescharacteristic, direct product factor, Sylow
416C24C2×D4×C3111yescharacteristic
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4D8×C3112yes—
458C22×C4Q16×C3112yes—
459C22×C4C22×C4×C3111yescharacteristic
460C22×C4C2×D4×C3111yescharacteristic
461C22×C4C2×D4×C3111yescharacteristic
462C22×C4C2×D4×C3111yescharacteristic
463C22×C4C2×D4×C3111yescharacteristic
464C22×C4C2×Q8×C3111yescharacteristic
465C22×C4C2×Q8×C3111yescharacteristic
466C22×C4C2×Q8×C3111yescharacteristic
467C22×C4#41×C3111yescharacteristic
468C22×C4#41×C3111yescharacteristic
469C22×C4#41×C3111yescharacteristic
470C22×C4#41×C3111yescharacteristic
471C22×C4#41×C3111yescharacteristic
472C22×C4#41×C3111yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C4⋊C4×C3114yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—48no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C22⋊C4×C3114yes—
504C42—41no—
505C42—41no—
506C42—41no—
507C42—41no—
508C23C4×D4×C3111yescharacteristic
509C23C31×#12011yescharacteristic
510C23C31×#12111yescharacteristic
511C23C31×#12111yescharacteristic
512C23C31×C22⋊Q811yescharacteristic
513C23C31×#12311yescharacteristic
514C23C31×C4⋊Q811yescharacteristic
515C23C2×D8×C3111yescharacteristic
516C23C2×Q16×C3111yescharacteristic
517C23C31×#13511yescharacteristic
518C23C31×#13511yescharacteristic
519C23C31×AGL(1,ℤ/8)11yescharacteristic
520C23C31×AGL(1,ℤ/8)11yescharacteristic
521C23C31×#13711yescharacteristic
522C23C31×#13711yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4C2×C22⋊C4×C3111yescharacteristic
566C2×C4C2×C4⋊C4×C3111yescharacteristic
567C2×C4C31×#11711yescharacteristic
568C2×C4C4×D4×C3111yescharacteristic
569C2×C4C4×Q8×C3111yescharacteristic
570C2×C4C4×Q8×C3111yescharacteristic
571C2×C4C31×#12111yescharacteristic
572C2×C4C31×#12111yescharacteristic
573C2×C4C31×#12111yescharacteristic
574C2×C4C31×#12111yescharacteristic
575C2×C4C31×C22⋊Q811yescharacteristic
576C2×C4C31×C22⋊Q811yescharacteristic
577C2×C4C31×C22⋊Q811yescharacteristic
578C2×C4C31×C22⋊Q811yescharacteristic
579C2×C4C31×C22⋊Q811yescharacteristic
580C2×C4C31×C22⋊Q811yescharacteristic
581C2×C4C31×C22⋊Q811yescharacteristic
582C2×C4C31×#12311yescharacteristic
583C2×C4C31×#12311yescharacteristic
584C2×C4C31×#12411yescharacteristic
585C2×C4C31×#12511yescharacteristic
586C2×C4C31×#12511yescharacteristic
587C2×C4C31×#12511yescharacteristic
588C2×C4C31×#12511yescharacteristic
589C2×C4C31×#12611yescharacteristic
590C2×C4C31×#12611yescharacteristic
591C2×C4C31×C4⋊Q811yescharacteristic
592C2×C4C31×C4⋊Q811yescharacteristic
593C8—24no—
594C8—42no—
595C22C31×#38611yescharacteristic
596C22C31×#38711yescharacteristic
597C22C31×#38911yescharacteristic
598C22C31×#39411yescharacteristic
599C22C31×#39511yescharacteristic
600C22C31×#39611yescharacteristic
601C22C31×#39811yescharacteristic
602C22C4×D8×C3111yescharacteristic
603C22C4×Q16×C3111yescharacteristic
604C22C31×#44111yescharacteristic
605C22C31×#44211yescharacteristic
606C22C31×#44711yescharacteristic
607C22C31×#44911yescharacteristic
608C22C31×#45111yescharacteristic
609C22C31×#45211yescharacteristic
610C22C31×#45911yescharacteristic
611C22C31×#46211yescharacteristic
612C22C31×#46311yescharacteristic
613C22C31×#46411yescharacteristic
614C22C31×#46611yescharacteristic
615C22C31×#46711yescharacteristic
616C22C31×#46811yescharacteristic
617C22C31×#46811yescharacteristic
618C22C31×#47411yescharacteristic
619C22C31×#47711yescharacteristic
620C22C31×#47811yescharacteristic
621C22C31×#47911yescharacteristic
622C22C31×#48011yescharacteristic
623C22C31×#48211yescharacteristic
624C22C31×#48411yescharacteristic
625C22C31×#48511yescharacteristic
626C22C31×#49911yescharacteristic
627C22C31×#50011yescharacteristic
628C22C31×#50111yescharacteristic
629C22C31×#50111yescharacteristic
630C4—44no—
631C4—42no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4—82no—
636C4C31×#38011yescharacteristic
637C4C31×#38711yescharacteristic
638C4C31×#38911yescharacteristic
639C4C31×#39111yescharacteristic
640C4C31×#39611yescharacteristic
641C4C31×#39811yescharacteristic
642C4C31×#39811yescharacteristic
643C4C31×#40011yescharacteristic
644C2C31×#144111yescharacteristic
645C2C31×#187811yescharacteristic
646C2C31×#187911yescharacteristic
647C2C31×#191811yescharacteristic
648C2C31×#192111yescharacteristic
649C2C31×#194211yescharacteristic
650C2C31×#194311yescharacteristic
651C2C31×#203311yescharacteristic
652C2C31×#203611yescharacteristic
653C2C31×#205711yescharacteristic
654C2C31×#205911yescharacteristic
655C2C31×#206711yescharacteristic
656C2C31×#206811yescharacteristic
657C2C31×#208311yescharacteristic
658C2C31×#208511yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
18. C2×C31×#107C4semidirect
156. C2×C8×C31C4⋊C4semidirect
178. #11219C31direct (N × H)
332. C2×#107C4×C31semidirect
415. C31#11219direct (N × H)
486. C2×C8C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1072
C2×C31×#3892
C2×C31×#3402
C2×C31×#3362
C31×C4⋊#952
#1121931