Finite Group Databasebeta

← C31×#24741 #21481500

Subgroups — C31×#24741 #21481500

Order 7936.

926 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#464C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C2×C31×#441C211yesmaximal, characteristic, complemented
5C31×#2545C211yesmaximal, characteristic
6Q8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2065C211yesmaximal, characteristic
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2042C211yesmaximal, characteristic
11C31×#1959C211yesmaximal, characteristic
12C31×#1940C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic
14C31×#1878C211yesmaximal, characteristic, complemented
15C31×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#124C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C31×#464—24no—
27C31×#464—24no—
28C31×#462—24no—
29C31×#441—24no—
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
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×#97C2211yescharacteristic
45C31×#396—21no—
46C31×#396—21no—
47C31×#391C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389—21no—
50C31×#389—21no—
51C31×#389C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#388—21no—
54C31×#388—21no—
55C31×#384—21no—
56C31×#384C2211yescharacteristic
57C4×C4⋊C4×C31—21no—
58C4×C4⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—22no—
70C2×Q16×C31—22no—
71C2×Q16×C31—22no—
72C2×Q16×C31D414yes—
73C2×SD16×C31—22no—
74C2×SD16×C31—22no—
75C2×SD16×C31—22no—
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C31×C4⋊Q8—22no—
81C31×C4⋊Q8—41no—
82C31×#124—22no—
83C31×#124—22no—
84C31×#124—22no—
85C31×#124—41no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—41no—
92C4×Q8×C31—41no—
93C4×Q8×C31D414yes—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×#106—22no—
124C31×C4⋊C8—22no—
125C31×C4⋊C8—22no—
126C31×C4⋊C8—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—41no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—41no—
137C31×#97—22no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95D411yescharacteristic
143C31×#95D411yescharacteristic
144C24×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
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×C31C2×D412yes—
160C2×Q8×C31C2×D412yes—
161C2×Q8×C31C2×D412yes—
162C2×Q8×C31#4112yes—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2411yescharacteristic
183Q16×C31—28no—
184Q16×C31—44no—
185SD16×C31—44no—
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×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31C2×D412yes—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—41no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—81no—
215C4⋊C4×C31—81no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31C2×D412yes—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—42no—
224C42×C31—24no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—42no—
230C42×C31—42no—
231C42×C31—42no—
232C42×C31C2×D412yes—
233C42×C31#4112yes—
234#24741C3111yesmaximal, characteristic, direct product factor, Sylow
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31C22×D411yescharacteristic
243Q8×C31—22no—
244Q8×C31—22no—
245Q8×C31—22no—
246Q8×C31—22no—
247Q8×C31—22no—
248Q8×C31—41no—
249Q8×C31—41no—
250Q8×C31—41no—
251Q8×C31—41no—
252Q8×C31—41no—
253Q8×C31—41no—
254Q8×C31#12114yes—
255D4×C31—41no—
256D4×C31—41no—
257D4×C31—41no—
258D4×C31—41no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—22no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—22no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—21no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
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—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31#12112yes—
296C2×C4×C31#12112yes—
297C2×C4×C31#13712yes—
298C2×C4×C31C22×D411yescharacteristic
299C2×C4×C31C22×D411yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C31C2×#4111yescharacteristic
302C2×C4×C31H(5,𝔽2)11yescharacteristic
303C2×C4×C312−1+411yescharacteristic
304C8×C31—22no—
305C8×C31—41no—
306C8×C31—41no—
307C8×C31—41no—
308C2×#464C2×C3111yescharacteristic
309C2×#464C2×C3111yescharacteristic
310C2×#462C2×C3111yescharacteristic, complemented
311C2×#441C2×C3111yescharacteristic, complemented
312#2545C2×C3111yescharacteristic
313Q8×C4⋊C4C2×C3111yescharacteristic, complemented
314#2066C2×C3111yescharacteristic, complemented
315#2065C2×C3111yescharacteristic
316#2043C2×C3111yescharacteristic, complemented
317#2042C2×C3111yescharacteristic
318#1959C2×C3111yescharacteristic
319#1940C2×C3111yescharacteristic, complemented
320#1880C2×C3111yescharacteristic
321#1878C2×C3111yescharacteristic, complemented
322#1803C2×C3111yescharacteristic, complemented
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31—81no—
330C22×C31C2×#12111yescharacteristic
331C22×C31D4211yescharacteristic
332C22×C31#54811yescharacteristic
333C22×C31C2×#13711yescharacteristic
334C22×C31#57511yescharacteristic
335C22×C31#57711yescharacteristic
336C22×C31#57811yescharacteristic
337C4×C31—24no—
338C4×C31—22no—
339C4×C31—22no—
340C4×C31—22no—
341C4×C31—42no—
342C4×C31—41no—
343C4×C31—41no—
344C4×C31—41no—
345C4×C31—42no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31—81no—
349C4×C31—81no—
350C4×C31C2×#12111yescharacteristic
351C4×C31#53711yescharacteristic
352C4×C31#54711yescharacteristic
353C4×C31#55311yescharacteristic
354C22×Q16C22×C3111yescharacteristic
355C22×Q16C22×C3111yescharacteristic
356C22×SD16C22×C3111yescharacteristic
357C2×C4⋊Q8C22×C3111yescharacteristic
358C2×#124C22×C3111yescharacteristic
359C2×#124C22×C3111yescharacteristic
360C2×C4×Q8C22×C3111yescharacteristic
361C2×C4×Q8C22×C3111yescharacteristic
362C2×C4×Q8C22×C3111yescharacteristic
363C2×C4×Q8C22×C3111yescharacteristic
364#464—24no—
365#464—24no—
366#462—24no—
367#441—24no—
368C2×#106C22×C3111yescharacteristic
369C2×C4⋊C8C22×C3111yescharacteristic
370C2×C4⋊C8C22×C3111yescharacteristic
371C2×C4⋊C8C22×C3111yescharacteristic
372C2×#103C22×C3111yescharacteristic
373C2×#103C22×C3111yescharacteristic
374C2×#103C22×C3111yescharacteristic
375C2×#103C22×C3111yescharacteristic
376C2×#103C22×C3111yescharacteristic
377C2×#103C22×C3111yescharacteristic
378C2×#103C22×C3111yescharacteristic
379C2×#102C22×C3111yescharacteristic
380C2×#102C22×C3111yescharacteristic
381C2×#102C22×C3111yescharacteristic
382C2×#97C22×C3111yescharacteristic
383#396—21no—
384#396—21no—
385#391C22×C3111yescharacteristic
386#390C22×C3111yescharacteristic
387#389—21no—
388#389—21no—
389#389C22×C3111yescharacteristic
390#389C22×C3111yescharacteristic
391#388—21no—
392#388—21no—
393#384—21no—
394#384C22×C3111yescharacteristic
395C4×C4⋊C4—21no—
396C4×C4⋊C4C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#336C22×C3111yescharacteristic
400#336C22×C3111yescharacteristic
401C2×C31—161no—
402C2×C31#241611yescharacteristic
403C2×C31#303711yescharacteristic
404C2×C31#304611yescharacteristic
405C2×C31#327011yescharacteristic
406C2×C31#327111yescharacteristic
407C2×C31#336911yescharacteristic
408C2×C31#337711yescharacteristic
409C22×Q8C23×C3111yescharacteristic
410C22×Q8C23×C3111yescharacteristic
411C22×Q8C23×C3111yescharacteristic
412C22×D4C23×C3111yescharacteristic
413C2×Q16—22no—
414C2×Q16—22no—
415C2×Q16—22no—
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16D4×C3114yes—
419C2×SD16—22no—
420C2×SD16—22no—
421C2×SD16—22no—
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425C22×C8C23×C3111yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—41no—
428#124—22no—
429#124—22no—
430#124—22no—
431#124—41no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—41no—
438C4×Q8—41no—
439C4×Q8D4×C3114yes—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C3111yescharacteristic
451C2×C4⋊C4D4×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C4⋊C4C23×C3111yescharacteristic
454C2×C4⋊C4C23×C3111yescharacteristic
455C2×C4⋊C4C23×C3111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C3111yescharacteristic
467C2×C42C23×C3111yescharacteristic
468C2×C42C23×C3111yescharacteristic
469#106—22no—
470C4⋊C8—22no—
471C4⋊C8—22no—
472C4⋊C8—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—41no—
480#102—22no—
481#102—22no—
482#102—41no—
483#97—22no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95D4×C3111yescharacteristic
489#95D4×C3111yescharacteristic
490C31#2474111yescharacteristic, direct product factor, Sylow
491C24—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C2×D4×C3112yes—
507C2×Q8C2×D4×C3112yes—
508C2×Q8C2×D4×C3112yes—
509C2×Q8#41×C3112yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3111yescharacteristic
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C2×D4×C3111yescharacteristic
529C22×C4C24×C3111yescharacteristic
530Q16—28no—
531Q16—44no—
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—24no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—41no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4C2×D4×C3112yes—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C42—24no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42C2×D4×C3112yes—
580C42#41×C3112yes—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C22×D4×C3111yescharacteristic
589Q8—22no—
590Q8—22no—
591Q8—22no—
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8C31×#12114yes—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
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—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4C31×#12112yes—
642C2×C4C31×#12112yes—
643C2×C4C31×#13712yes—
644C2×C4C22×D4×C3111yescharacteristic
645C2×C4C22×D4×C3111yescharacteristic
646C2×C4C2×#41×C3111yescharacteristic
647C2×C4C2×#41×C3111yescharacteristic
648C2×C4C31×H(5,𝔽2)11yescharacteristic
649C2×C4C31×2−1+411yescharacteristic
650C8—22no—
651C8—41no—
652C8—41no—
653C8—41no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C31×#12111yescharacteristic
662C22D42×C3111yescharacteristic
663C22C31×#54811yescharacteristic
664C22C2×C31×#13711yescharacteristic
665C22C31×#57511yescharacteristic
666C22C31×#57711yescharacteristic
667C22C31×#57811yescharacteristic
668C4—24no—
669C4—22no—
670C4—22no—
671C4—22no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4C2×C31×#12111yescharacteristic
682C4C31×#53711yescharacteristic
683C4C31×#54711yescharacteristic
684C4C31×#55311yescharacteristic
685C2—161no—
686C2C31×#241611yescharacteristic
687C2C31×#303711yescharacteristic
688C2C31×#304611yescharacteristic
689C2C31×#327011yescharacteristic
690C2C31×#327111yescharacteristic
691C2C31×#336911yescharacteristic
692C2C31×#337711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
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
3. C2×C31×#462C2semidirect
4. C2×C31×#441C2semidirect
6. Q8×C4⋊C4×C31C2semidirect
7. C31×#2066C2semidirect
9. C31×#2043C2semidirect
12. C31×#1940C2semidirect
14. C31×#1878C2semidirect
15. C31×#1803C2semidirect
234. #24741C31direct (N × H)
310. C2×#462C2×C31semidirect
311. C2×#441C2×C31semidirect
313. Q8×C4⋊C4C2×C31semidirect
314. #2066C2×C31semidirect
316. #2043C2×C31semidirect
319. #1940C2×C31semidirect
321. #1878C2×C31semidirect
322. #1803C2×C31semidirect
490. C31#24741direct (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×#4622
C2×C31×#4412
C31×#25452
Q8×C4⋊C4×C312
C31×#20662
C31×#20652
C31×#20432
C31×#20422
C31×#19592
C31×#19402
C31×#18802
C31×#18782
C31×#18032
#2474131