Finite Group Databasebeta

← C31×#26897 #21483656

Subgroups — C31×#26897 #21483656

Order 7936.

944 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#476C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2451C211yesmaximal, characteristic, complemented
4C31×#2366C211yesmaximal, characteristic
5C31×#2055C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic
7C31×#2023C211yesmaximal, characteristic, complemented
8C31×#2014C211yesmaximal, characteristic
9C31×#1934C211yesmaximal, characteristic, complemented
10C31×#1927C211yesmaximal, characteristic, complemented
11C31×#1920C211yesmaximal, characteristic, complemented
12C31×#1916C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1864C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#127C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#476—24no—
25C4×SD16×C31—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C31×#398—21no—
39C31×#395—21no—
40C31×#391—21no—
41C31×#391C2211yescharacteristic
42C31×#391C2211yescharacteristic
43C31×#390—21no—
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#387—21no—
49C31×#386—21no—
50C31×#386—21no—
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31—22no—
73C2×SD16×C31—22no—
74C2×SD16×C31—41no—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×C4⋊Q8—22no—
80C31×C4⋊Q8—41no—
81C31×#127—22no—
82C31×#127—22no—
83C4×Q8×C31—22no—
84C4×Q8×C31—41no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—41no—
88C4×D4×C31—41no—
89C4×D4×C31—44no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C2×C42×C31C2311yescharacteristic
112C31×#106—22no—
113C31×#106D414yescomplemented
114C31×C4⋊C8—22no—
115C31×#103—22no—
116C31×#103—22no—
117C31×#102—22no—
118C31×#102—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—41no—
123C4×C8×C31—22no—
124C31×#95—21no—
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×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—42no—
141C2×Q8×C31—42no—
142C2×Q8×C31—81no—
143C2×Q8×C31#4112yes—
144C2×D4×C31—24no—
145C2×D4×C31—24no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—42no—
157C2×D4×C31—42no—
158C2×D4×C31—81no—
159C2×D4×C31—81no—
160C2×D4×C31#4112yes—
161C2×D4×C31#4112yes—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2411yescharacteristic
181SD16×C31—28no—
182SD16×C31—44no—
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—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31C2×D412yes—
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—21no—
203C4⋊C4×C31—41no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—81no—
207C4⋊C4×C31—81no—
208C4⋊C4×C31SD1614yescomplemented
209C4⋊C4×C31C2×D412yes—
210C4⋊C4×C31C2×D412yes—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—81no—
216C22⋊C4×C31—81no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—42no—
224C42×C31—42no—
225#26897C3111yesmaximal, characteristic, direct product factor, Sylow
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31C22×D411yescharacteristic
241Q8×C31—22no—
242Q8×C31—22no—
243Q8×C31—41no—
244Q8×C31—41no—
245Q8×C31—84no—
246D4×C31—22no—
247D4×C31—22no—
248D4×C31—22no—
249D4×C31—22no—
250D4×C31—48no—
251D4×C31—41no—
252D4×C31—41no—
253D4×C31—41no—
254D4×C31—41no—
255D4×C31—84no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
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—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—84no—
290C2×C4×C31—84no—
291C2×C4×C31C2×SD1612yes—
292C2×C4×C31C2×SD1612yes—
293C2×C4×C31C2×SD1612yes—
294C2×C4×C31C22×D411yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31C2×#4111yescharacteristic
297C2×C4×C31C2×#4111yescharacteristic
298C2×C4×C31H(5,𝔽2)11yescharacteristic
299C2×C4×C312−1+411yescharacteristic
300C8×C31—22no—
301C8×C31—41no—
302C8×C31—41no—
303C8×C31—41no—
304C2×#476C2×C3111yescharacteristic, complemented
305C2×C4×SD16C2×C3111yescharacteristic, complemented
306#2451C2×C3111yescharacteristic, complemented
307#2366C2×C3111yescharacteristic
308#2055C2×C3111yescharacteristic, complemented
309#2041C2×C3111yescharacteristic
310#2023C2×C3111yescharacteristic, complemented
311#2014C2×C3111yescharacteristic
312#1934C2×C3111yescharacteristic, complemented
313#1927C2×C3111yescharacteristic, complemented
314#1920C2×C3111yescharacteristic, complemented
315#1916C2×C3111yescharacteristic, complemented
316#1880C2×C3111yescharacteristic, complemented
317#1877C2×C3111yescharacteristic, complemented
318#1864C2×C3111yescharacteristic, complemented
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31—42no—
324C22×C31—42no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31—81no—
330C22×C31—81no—
331C22×C31—81no—
332C22×C31—81no—
333C22×C31#52511yescharacteristic
334C22×C31D4211yescharacteristic
335C22×C31#54811yescharacteristic
336C22×C31C22×SD1611yescharacteristic
337C22×C31#57511yescharacteristic
338C22×C31#57611yescharacteristic
339C22×C31#57711yescharacteristic
340C4×C31—22no—
341C4×C31—22no—
342C4×C31—22no—
343C4×C31—41no—
344C4×C31—42no—
345C4×C31—41no—
346C4×C31—41no—
347C4×C31—42no—
348C4×C31—42no—
349C4×C31—81no—
350C4×C31—81no—
351C4×C31—81no—
352C4×C31#52511yescharacteristic
353C4×C31#53911yescharacteristic
354C4×C31#54811yescharacteristic
355C4×C31#55111yescharacteristic
356C22×SD16C22×C3111yescharacteristic
357C22×SD16C22×C3111yescharacteristic
358C2×C4⋊Q8C22×C3111yescharacteristic
359C2×#127C22×C3111yescharacteristic
360C2×C4×Q8C22×C3111yescharacteristic
361C2×C4×D4—21no—
362C2×C4×D4C22×C3111yescharacteristic
363C2×C4×D4C22×C3111yescharacteristic
364#476—24no—
365C4×SD16—24no—
366C2×#106C22×C3111yescharacteristic
367C2×#106C22×C3111yescharacteristic
368C2×C4⋊C8C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#102C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×C4×C8C22×C3111yescharacteristic
378#398—21no—
379#395—21no—
380#391—21no—
381#391C22×C3111yescharacteristic
382#391C22×C3111yescharacteristic
383#390—21no—
384#390C22×C3111yescharacteristic
385#390C22×C3111yescharacteristic
386#389C22×C3111yescharacteristic
387#389C22×C3111yescharacteristic
388#387—21no—
389#386—21no—
390#386—21no—
391C4×C4⋊C4C22×C3111yescharacteristic
392C4×C4⋊C4C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#340C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#336C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399#336C22×C3111yescharacteristic
400#336C22×C3111yescharacteristic
401C2×C31—82no—
402C2×C31—82no—
403C2×C31#246311yescharacteristic
404C2×C31#310111yescharacteristic
405C2×C31#311811yescharacteristic
406C2×C31#326811yescharacteristic
407C2×C31D4×SD1611yescharacteristic
408C2×C31#336211yescharacteristic
409C2×C31#337111yescharacteristic
410C22×Q8—21no—
411C22×Q8C23×C3111yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C23×C3111yescharacteristic
415C22×D4C23×C3111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—41no—
424C22×C8C23×C3111yescharacteristic
425C22×C8C23×C3111yescharacteristic
426C22×C8C23×C3111yescharacteristic
427C22×C8C23×C3111yescharacteristic
428C4⋊Q8—22no—
429C4⋊Q8—41no—
430#127—22no—
431#127—22no—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—44no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4D4×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⋊C4—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460C2×C42C23×C3111yescharacteristic
461#106—22no—
462#106D4×C3114yescomplemented
463C4⋊C8—22no—
464#103—22no—
465#103—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—41no—
472C4×C8—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C3111yescharacteristic
481#95D4×C3111yescharacteristic
482C31#2689711yescharacteristic, direct product factor, Sylow
483C24—21no—
484C24—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—81no—
493C2×Q8#41×C3112yes—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4#41×C3112yes—
511C2×D4#41×C3112yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C2×D4×C3111yescharacteristic
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C24×C3111yescharacteristic
531SD16—28no—
532SD16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×D4×C3112yes—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—41no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4SD16×C3114yescomplemented
559C4⋊C4C2×D4×C3112yes—
560C4⋊C4C2×D4×C3112yes—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—42no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C22×D4×C3111yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—84no—
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
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—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4C2×SD16×C3112yes—
641C2×C4C2×SD16×C3112yes—
642C2×C4C2×SD16×C3112yes—
643C2×C4C22×D4×C3111yescharacteristic
644C2×C4C2×#41×C3111yescharacteristic
645C2×C4C2×#41×C3111yescharacteristic
646C2×C4C2×#41×C3111yescharacteristic
647C2×C4C31×H(5,𝔽2)11yescharacteristic
648C2×C4C31×2−1+411yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22C31×#52511yescharacteristic
668C22D42×C3111yescharacteristic
669C22C31×#54811yescharacteristic
670C22C22×SD16×C3111yescharacteristic
671C22C31×#57511yescharacteristic
672C22C31×#57611yescharacteristic
673C22C31×#57711yescharacteristic
674C4—22no—
675C4—22no—
676C4—22no—
677C4—41no—
678C4—42no—
679C4—41no—
680C4—41no—
681C4—42no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4C31×#52511yescharacteristic
687C4C31×#53911yescharacteristic
688C4C31×#54811yescharacteristic
689C4C31×#55111yescharacteristic
690C2—82no—
691C2—82no—
692C2C31×#246311yescharacteristic
693C2C31×#310111yescharacteristic
694C2C31×#311811yescharacteristic
695C2C31×#326811yescharacteristic
696C2D4×SD16×C3111yescharacteristic
697C2C31×#336211yescharacteristic
698C2C31×#337111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#476C2semidirect
2. C2×C4×SD16×C31C2semidirect
3. C31×#2451C2semidirect
5. C31×#2055C2semidirect
7. C31×#2023C2semidirect
9. C31×#1934C2semidirect
10. C31×#1927C2semidirect
11. C31×#1920C2semidirect
12. C31×#1916C2semidirect
13. C31×#1880C2semidirect
14. C31×#1877C2semidirect
15. C31×#1864C2semidirect
113. C31×#106D4semidirect
208. C4⋊C4×C31SD16semidirect
225. #26897C31direct (N × H)
304. C2×#476C2×C31semidirect
305. C2×C4×SD16C2×C31semidirect
306. #2451C2×C31semidirect
308. #2055C2×C31semidirect
310. #2023C2×C31semidirect
312. #1934C2×C31semidirect
313. #1927C2×C31semidirect
314. #1920C2×C31semidirect
315. #1916C2×C31semidirect
316. #1880C2×C31semidirect
317. #1877C2×C31semidirect
318. #1864C2×C31semidirect
462. #106D4×C31semidirect
482. C31#26897direct (N × H)
558. C4⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4762
C2×C4×SD16×C312
C31×#24512
C31×#23662
C31×#20552
C31×#20412
C31×#20232
C31×#20142
C31×#19342
C31×#19272
C31×#19202
C31×#19162
C31×#18802
C31×#18772
C31×#18642
#2689731