Finite Group Databasebeta

← C31×#14721 #21471480

Subgroups — C31×#14721 #21471480

Order 7936.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C31×#1444C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C2×C31×#123—24no—
22C2×C31×#123—24no—
23C2×C31×#123—24no—
24C2×C4×D4×C31—24no—
25C2×C4×D4×C31—24no—
26C2×C4×D4×C31—24no—
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C22⋊C4×C31C2211yescharacteristic
44C22×C42×C31C2211yescharacteristic
45C31×#394—24no—
46C31×#392—24no—
47C31×#386—24no—
48C31×#385—24no—
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C25×C31C2311yescharacteristic
62C25×C31C2311yescharacteristic
63C25×C31C2311yescharacteristic
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—22no—
80C22×D4×C31—41no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31D414yes—
85C23×C4×C31—22no—
86C23×C4×C31—22no—
87C23×C4×C31—22no—
88C23×C4×C31—22no—
89C23×C4×C31—22no—
90C23×C4×C31—22no—
91C23×C4×C31—22no—
92C23×C4×C31—22no—
93C23×C4×C31—22no—
94C23×C4×C31—41no—
95C23×C4×C31—41no—
96C23×C4×C31—41no—
97C23×C4×C31—41no—
98C23×C4×C31D414yescomplemented
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C23×C4×C31C2311yescharacteristic
105C23×C4×C31C2311yescharacteristic
106C23×C4×C31C2311yescharacteristic
107C23×C4×C31C2311yescharacteristic
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C23×C4×C31C2311yescharacteristic
111C31×#123—232no—
112C4×D4×C31—232no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—22no—
118C2×C4⋊C4×C31—22no—
119C2×C4⋊C4×C31—22no—
120C2×C4⋊C4×C31—22no—
121C2×C4⋊C4×C31—22no—
122C2×C4⋊C4×C31—22no—
123C2×C4⋊C4×C31—41no—
124C2×C4⋊C4×C31D414yescomplemented
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—22no—
139C2×C22⋊C4×C31—22no—
140C2×C22⋊C4×C31—22no—
141C2×C22⋊C4×C31—22no—
142C2×C22⋊C4×C31—22no—
143C2×C22⋊C4×C31—22no—
144C2×C22⋊C4×C31—22no—
145C2×C22⋊C4×C31—22no—
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—22no—
148C2×C22⋊C4×C31—22no—
149C2×C22⋊C4×C31—22no—
150C2×C22⋊C4×C31—22no—
151C2×C22⋊C4×C31—22no—
152C2×C22⋊C4×C31—22no—
153C2×C22⋊C4×C31—22no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31—22no—
156C2×C22⋊C4×C31—41no—
157C2×C22⋊C4×C31—41no—
158C2×C22⋊C4×C31—41no—
159C2×C22⋊C4×C31—41no—
160C2×C22⋊C4×C31—41no—
161C2×C22⋊C4×C31—41no—
162C2×C22⋊C4×C31D414yescomplemented
163C2×C22⋊C4×C31D414yescomplemented
164C2×C42×C31—22no—
165C2×C42×C31—22no—
166C2×C42×C31—22no—
167C31×#95—22no—
168C31×#95—22no—
169C31×#95—22no—
170C31×#95—22no—
171C31×#95—22no—
172C31×#95—22no—
173C31×#95—22no—
174C31×#95—22no—
175C31×#95—22no—
176C31×#95—41no—
177C31×#95—41no—
178C31×#95—41no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31—21no—
196C24×C31—21no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—21no—
206C24×C31—21no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31—21no—
210C24×C31—21no—
211C24×C31—21no—
212C24×C31—21no—
213C24×C31—21no—
214C24×C31—21no—
215C24×C31—21no—
216C24×C31—21no—
217C24×C31C2×D412yes—
218C24×C31C2×D412yes—
219C24×C31C2×D412yes—
220C24×C31C2×D412yes—
221C24×C31C2×D412yes—
222C24×C31#4112yes—
223C24×C31#4112yes—
224C24×C31C2411yescharacteristic
225C2×D4×C31—28no—
226C2×D4×C31—28no—
227C2×D4×C31—28no—
228C2×D4×C31—28no—
229C2×D4×C31—28no—
230C2×D4×C31—28no—
231C2×D4×C31—28no—
232C2×D4×C31—28no—
233C2×D4×C31—28no—
234C2×D4×C31—44no—
235C2×D4×C31—44no—
236C2×D4×C31—44no—
237C2×D4×C31—44no—
238C2×D4×C31—44no—
239C2×D4×C31—44no—
240C2×D4×C31—44no—
241C2×D4×C31—44no—
242C2×D4×C31—44no—
243C2×D4×C31—44no—
244C2×D4×C31—44no—
245C2×D4×C31—44no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—28no—
255C22×C4×C31—28no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—28no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—21no—
308C22×C4×C31—21no—
309C22×C4×C31—21no—
310C22×C4×C31—21no—
311C22×C4×C31—21no—
312C22×C4×C31—21no—
313C22×C4×C31—21no—
314C22×C4×C31—21no—
315C22×C4×C31—21no—
316C22×C4×C31—21no—
317C22×C4×C31—21no—
318C22×C4×C31—21no—
319C22×C4×C31—44no—
320C22×C4×C31—44no—
321C22×C4×C31—44no—
322C22×C4×C31—44no—
323C22×C4×C31—44no—
324C22×C4×C31—44no—
325C22×C4×C31—44no—
326C22×C4×C31—44no—
327C22×C4×C31—44no—
328C22×C4×C31—44no—
329C22×C4×C31—44no—
330C22×C4×C31C2×D412yes—
331C22×C4×C31C2×D412yes—
332C22×C4×C31C2×D412yes—
333C22×C4×C31C2×D412yes—
334C22×C4×C31C2×D412yes—
335C22×C4×C31C2×D412yes—
336C22×C4×C31C2×D412yes—
337C22×C4×C31C2×D412yes—
338C22×C4×C31C2×D412yes—
339C22×C4×C31C2×D412yes—
340C22×C4×C31#4112yes—
341C22×C4×C31#4112yes—
342C22×C4×C31#4112yes—
343C22×C4×C31#4112yes—
344C4⋊C4×C31—28no—
345C4⋊C4×C31—28no—
346C4⋊C4×C31—28no—
347C4⋊C4×C31—44no—
348C22⋊C4×C31—28no—
349C22⋊C4×C31—28no—
350C22⋊C4×C31—28no—
351C22⋊C4×C31—28no—
352C22⋊C4×C31—28no—
353C22⋊C4×C31—28no—
354C22⋊C4×C31—44no—
355C22⋊C4×C31—44no—
356C22⋊C4×C31—44no—
357C22⋊C4×C31—44no—
358C22⋊C4×C31—44no—
359C22⋊C4×C31—44no—
360C22⋊C4×C31—44no—
361C42×C31—28no—
362#14721C3111yesmaximal, characteristic, direct product factor, Sylow
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
373C23×C31—22no—
374C23×C31—22no—
375C23×C31—22no—
376C23×C31—22no—
377C23×C31—22no—
378C23×C31—22no—
379C23×C31—22no—
380C23×C31—22no—
381C23×C31—22no—
382C23×C31—22no—
383C23×C31—22no—
384C23×C31—22no—
385C23×C31—22no—
386C23×C31—22no—
387C23×C31—22no—
388C23×C31—22no—
389C23×C31—22no—
390C23×C31—22no—
391C23×C31—22no—
392C23×C31—22no—
393C23×C31—22no—
394C23×C31—22no—
395C23×C31—22no—
396C23×C31—22no—
397C23×C31—22no—
398C23×C31—22no—
399C23×C31—22no—
400C23×C31—22no—
401C23×C31—22no—
402C23×C31—22no—
403C23×C31—22no—
404C23×C31—22no—
405C23×C31—22no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—41no—
409C23×C31—41no—
410C23×C31—41no—
411C23×C31—41no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—41no—
416C23×C31—41no—
417C23×C31—41no—
418C23×C31—41no—
419C23×C31—41no—
420C23×C31—41no—
421C23×C31—41no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—41no—
425C23×C31—41no—
426C23×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31—41no—
446C23×C31—41no—
447C23×C31—41no—
448C23×C31—41no—
449C23×C31—41no—
450C23×C31—41no—
451C23×C31—41no—
452C23×C31—41no—
453C23×C31—41no—
454C23×C31—41no—
455C23×C31—41no—
456C23×C31—41no—
457C23×C31—41no—
458C23×C31—41no—
459C23×C31—41no—
460C23×C31—41no—
461C23×C31—41no—
462C23×C31—41no—
463C23×C31—41no—
464C23×C31—41no—
465C23×C31—41no—
466C23×C31#12014yes—
467C23×C31#12314yescomplemented
468C23×C31C22×D411yescharacteristic
469C23×C31C22×D411yescharacteristic
470C23×C31C22×D411yescharacteristic
471C23×C31C22×D411yescharacteristic
472C23×C31C22×D411yescharacteristic
473C23×C31C2×#4111yescharacteristic
474C23×C31C2×#4111yescharacteristic
475C23×C31C2×#4111yescharacteristic
476C23×C31C2×#4111yescharacteristic
477C23×C31C2×#4111yescharacteristic
478C23×C31C2×#4111yescharacteristic
479C23×C31H(5,𝔽2)11yescharacteristic
480C23×C31H(5,𝔽2)11yescharacteristic
481C23×C31H(5,𝔽2)11yescharacteristic
482C23×C312−1+411yescharacteristic
483D4×C31—232no—
484D4×C31—416no—
485D4×C31—416no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—22no—
491C2×C4×C31—22no—
492C2×C4×C31—22no—
493C2×C4×C31—22no—
494C2×C4×C31—22no—
495C2×C4×C31—22no—
496C2×C4×C31—22no—
497C2×C4×C31—22no—
498C2×C4×C31—22no—
499C2×C4×C31—22no—
500C2×C4×C31—22no—
501C2×C4×C31—22no—
502C2×C4×C31—22no—
503C2×C4×C31—22no—
504C2×C4×C31—22no—
505C2×C4×C31—22no—
506C2×C4×C31—22no—
507C2×C4×C31—22no—
508C2×C4×C31—22no—
509C2×C4×C31—22no—
510C2×C4×C31—22no—
511C2×C4×C31—22no—
512C2×C4×C31—22no—
513C2×C4×C31—22no—
514C2×C4×C31—22no—
515C2×C4×C31—22no—
516C2×C4×C31—22no—
517C2×C4×C31—22no—
518C2×C4×C31—22no—
519C2×C4×C31—22no—
520C2×C4×C31—22no—
521C2×C4×C31—22no—
522C2×C4×C31—416no—
523C2×C4×C31—416no—
524C2×C4×C31—41no—
525C2×C4×C31—41no—
526C2×C4×C31—41no—
527C2×C4×C31—41no—
528C2×C4×C31—41no—
529C2×C4×C31—41no—
530C2×C4×C31—41no—
531C2×C4×C31—41no—
532C2×C4×C31—41no—
533C2×C4×C31—41no—
534C2×C4×C31—41no—
535C2×C4×C31—41no—
536C2×C4×C31—41no—
537C2×C4×C31—41no—
538C2×C4×C31—41no—
539C2×C4×C31—41no—
540C2×C4×C31—41no—
541C2×C4×C31—41no—
542C2×C4×C31—41no—
543C2×C4×C31—41no—
544C2×C4×C31—41no—
545C2×C4×C31—41no—
546C2×C4×C31—41no—
547C2×C4×C31—41no—
548C2×C4×C31—41no—
549C2×C4×C31—41no—
550C2×C4×C31—41no—
551C2×C4×C31—41no—
552C2×C4×C31—41no—
553C2×C4×C31—41no—
554C2×C4×C31—41no—
555C2×C4×C31—41no—
556C2×C4×C31—41no—
557C2×C4×C31—41no—
558C2×C4×C31—41no—
559C2×C4×C31—41no—
560C2×C4×C31—41no—
561C2×C4×C31—41no—
562C2×C4×C31—41no—
563C2×C4×C31—41no—
564C2×C4×C31—41no—
565C2×C4×C31—41no—
566C2×C4×C31—41no—
567C2×C4×C31—41no—
568C2×C4×C31—41no—
569C2×C4×C31—41no—
570C2×C4×C31#12014yes—
571C2×C4×C31#12314yescomplemented
572C22×#123C2×C3111yescharacteristic, complemented
573C22×C4×D4C2×C3111yescharacteristic, complemented
574C2×#394C2×C3111yescharacteristic, complemented
575C2×#392C2×C3111yescharacteristic
576C2×#386C2×C3111yescharacteristic, complemented
577C2×#385C2×C3111yescharacteristic, complemented
578#1444C2×C3111yescharacteristic, complemented
579#1440C2×C3111yescharacteristic, complemented
580#1439C2×C3111yescharacteristic, complemented
581#1439C2×C3111yescharacteristic, complemented
582#1438C2×C3111yescharacteristic, complemented
583#1438C2×C3111yescharacteristic, complemented
584#1437C2×C3111yescharacteristic, complemented
585#1436C2×C3111yescharacteristic, complemented
586C22⋊#95C2×C3111yescharacteristic, complemented
587C22×C31—24no—
588C22×C31—24no—
589C22×C31—24no—
590C22×C31—24no—
591C22×C31—24no—
592C22×C31—24no—
593C22×C31—42no—
594C22×C31—42no—
595C22×C31—42no—
596C22×C31—42no—
597C22×C31—42no—
598C22×C31—42no—
599C22×C31—42no—
600C22×C31—42no—
601C22×C31—42no—
602C22×C31—42no—
603C22×C31—42no—
604C22×C31—42no—
605C22×C31—42no—
606C22×C31—42no—
607C22×C31—42no—
608C22×C31—42no—
609C22×C31—42no—
610C22×C31—42no—
611C22×C31—42no—
612C22×C31—42no—
613C22×C31—42no—
614C22×C31—42no—
615C22×C31—42no—
616C22×C31—42no—
617C22×C31—42no—
618C22×C31—42no—
619C22×C31—42no—
620C22×C31—42no—
621C22×C31—42no—
622C22×C31—42no—
623C22×C31—42no—
624C22×C31—81no—
625C22×C31—81no—
626C22×C31—81no—
627C22×C31—81no—
628C22×C31—81no—
629C22×C31—81no—
630C22×C31—81no—
631C22×C31—81no—
632C22×C31C2×#12011yescharacteristic
633C22×C31C2×#12011yescharacteristic
634C22×C31C2×#12311yescharacteristic
635C22×C31C2×#12311yescharacteristic
636C22×C31#52511yescharacteristic
637C22×C31#52511yescharacteristic
638C22×C31#52511yescharacteristic
639C22×C31#52511yescharacteristic
640C22×C31#52511yescharacteristic
641C22×C31#52511yescharacteristic
642C22×C31#53211yescharacteristic
643C22×C31#53211yescharacteristic
644C22×C31#53211yescharacteristic
645C22×C31#53411yescharacteristic
646C22×C31#53711yescharacteristic
647C22×C31#53811yescharacteristic
648C22×C31#53911yescharacteristic
649C22×C31#54011yescharacteristic
650C22×C31#54211yescharacteristic
651C22×C31D4211yescharacteristic
652C22×C31D4211yescharacteristic
653C22×C31D4211yescharacteristic
654C22×C31D4211yescharacteristic
655C22×C31#54611yescharacteristic
656C22×C31#54611yescharacteristic
657C22×C31#54611yescharacteristic
658C22×C31#54711yescharacteristic
659C22×C31#54711yescharacteristic
660C22×C31#54711yescharacteristic
661C22×C31#54811yescharacteristic
662C22×C31#55011yescharacteristic
663C22×C31#55111yescharacteristic
664C22×C31#55311yescharacteristic
665C22×C31#55311yescharacteristic
666C22×C31#55911yescharacteristic
667C4×C31—24no—
668C4×C31—24no—
669C4×C31—42no—
670C4×C31—42no—
671C4×C31—42no—
672C4×C31—42no—
673C4×C31—42no—
674C4×C31—42no—
675C4×C31—42no—
676C4×C31—42no—
677C4×C31—81no—
678C4×C31—81no—
679C23×D4C22×C3111yescharacteristic
680C23×D4C22×C3111yescharacteristic
681C23×D4C22×C3111yescharacteristic
682C24×C4C22×C3111yescharacteristic
683C24×C4C22×C3111yescharacteristic
684C2×#123—24no—
685C2×#123—24no—
686C2×#123—24no—
687C2×C4×D4—24no—
688C2×C4×D4—24no—
689C2×C4×D4—24no—
690C22×C4⋊C4C22×C3111yescharacteristic
691C22×C4⋊C4C22×C3111yescharacteristic
692C22×C4⋊C4C22×C3111yescharacteristic
693C22×C4⋊C4C22×C3111yescharacteristic
694C22×C22⋊C4C22×C3111yescharacteristic
695C22×C22⋊C4C22×C3111yescharacteristic
696C22×C22⋊C4C22×C3111yescharacteristic
697C22×C22⋊C4C22×C3111yescharacteristic
698C22×C22⋊C4C22×C3111yescharacteristic
699C22×C22⋊C4C22×C3111yescharacteristic
700C22×C22⋊C4C22×C3111yescharacteristic
701C22×C22⋊C4C22×C3111yescharacteristic
702C22×C22⋊C4C22×C3111yescharacteristic
703C22×C22⋊C4C22×C3111yescharacteristic
704C22×C22⋊C4C22×C3111yescharacteristic
705C22×C22⋊C4C22×C3111yescharacteristic
706C22×C22⋊C4C22×C3111yescharacteristic
707C22×C42C22×C3111yescharacteristic
708#394—24no—
709#392—24no—
710#386—24no—
711#385—24no—
712C2×#95C22×C3111yescharacteristic
713C2×#95C22×C3111yescharacteristic
714C2×#95C22×C3111yescharacteristic
715C2×#95C22×C3111yescharacteristic
716C2×#95C22×C3111yescharacteristic
717C2×#95C22×C3111yescharacteristic
718C2×#95C22×C3111yescharacteristic
719C2×#95C22×C3111yescharacteristic
720C2×#95C22×C3111yescharacteristic
721C2×#95C22×C3111yescharacteristic
722C2×#95C22×C3111yescharacteristic
723C2×#95C22×C3111yescharacteristic
724C2×C31—44no—
725C2×C31—44no—
726C2×C31—82no—
727C2×C31#238811yescharacteristic
728C2×C31#240311yescharacteristic
729C2×C31#240711yescharacteristic
730C2×C31#241811yescharacteristic
731C2×C31#242211yescharacteristic
732C2×C31#243011yescharacteristic
733C2×C31#244311yescharacteristic
734C2×C31#244511yescharacteristic
735C2×C31#245511yescharacteristic
736C2×C31#245611yescharacteristic
737C2×C31#246111yescharacteristic
738C2×C31#246411yescharacteristic
739C2×C31#260211yescharacteristic
740C2×C31#263011yescharacteristic
741C2×C31#284911yescharacteristic
742C25C23×C3111yescharacteristic
743C25C23×C3111yescharacteristic
744C25C23×C3111yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—41no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4D4×C3114yes—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4D4×C3114yescomplemented
780C23×C4C23×C3111yescharacteristic
781C23×C4C23×C3111yescharacteristic
782C23×C4C23×C3111yescharacteristic
783C23×C4C23×C3111yescharacteristic
784C23×C4C23×C3111yescharacteristic
785C23×C4C23×C3111yescharacteristic
786C23×C4C23×C3111yescharacteristic
787C23×C4C23×C3111yescharacteristic
788C23×C4C23×C3111yescharacteristic
789C23×C4C23×C3111yescharacteristic
790C23×C4C23×C3111yescharacteristic
791C23×C4C23×C3111yescharacteristic
792#123—232no—
793C4×D4—232no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4—22no—
801C2×C4⋊C4—22no—
802C2×C4⋊C4—22no—
803C2×C4⋊C4—22no—
804C2×C4⋊C4—41no—
805C2×C4⋊C4D4×C3114yescomplemented
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4—41no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4D4×C3114yescomplemented
844C2×C22⋊C4D4×C3114yescomplemented
845C2×C42—22no—
846C2×C42—22no—
847C2×C42—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—41no—
858#95—41no—
859#95—41no—
860C31#1472111yescharacteristic, direct product factor, Sylow
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24C2×D4×C3112yes—
900C24C2×D4×C3112yes—
901C24C2×D4×C3112yes—
902C24C2×D4×C3112yes—
903C24C2×D4×C3112yes—
904C24#41×C3112yes—
905C24#41×C3112yes—
906C24C24×C3111yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—28no—
937C22×C4—28no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—28no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4C2×D4×C3112yes—
1013C22×C4C2×D4×C3112yes—
1014C22×C4C2×D4×C3112yes—
1015C22×C4C2×D4×C3112yes—
1016C22×C4C2×D4×C3112yes—
1017C22×C4C2×D4×C3112yes—
1018C22×C4C2×D4×C3112yes—
1019C22×C4C2×D4×C3112yes—
1020C22×C4C2×D4×C3112yes—
1021C22×C4C2×D4×C3112yes—
1022C22×C4#41×C3112yes—
1023C22×C4#41×C3112yes—
1024C22×C4#41×C3112yes—
1025C22×C4#41×C3112yes—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—44no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C42—28no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23C31×#12014yes—
1148C23C31×#12314yescomplemented
1149C23C22×D4×C3111yescharacteristic
1150C23C22×D4×C3111yescharacteristic
1151C23C22×D4×C3111yescharacteristic
1152C23C22×D4×C3111yescharacteristic
1153C23C22×D4×C3111yescharacteristic
1154C23C2×#41×C3111yescharacteristic
1155C23C2×#41×C3111yescharacteristic
1156C23C2×#41×C3111yescharacteristic
1157C23C2×#41×C3111yescharacteristic
1158C23C2×#41×C3111yescharacteristic
1159C23C2×#41×C3111yescharacteristic
1160C23C31×H(5,𝔽2)11yescharacteristic
1161C23C31×H(5,𝔽2)11yescharacteristic
1162C23C31×H(5,𝔽2)11yescharacteristic
1163C23C31×2−1+411yescharacteristic
1164D4—232no—
1165D4—416no—
1166D4—416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—416no—
1204C2×C4—416no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4C31×#12014yes—
1252C2×C4C31×#12314yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22C2×C31×#12011yescharacteristic
1299C22C2×C31×#12011yescharacteristic
1300C22C2×C31×#12311yescharacteristic
1301C22C2×C31×#12311yescharacteristic
1302C22C31×#52511yescharacteristic
1303C22C31×#52511yescharacteristic
1304C22C31×#52511yescharacteristic
1305C22C31×#52511yescharacteristic
1306C22C31×#52511yescharacteristic
1307C22C31×#52511yescharacteristic
1308C22C31×#53211yescharacteristic
1309C22C31×#53211yescharacteristic
1310C22C31×#53211yescharacteristic
1311C22C31×#53411yescharacteristic
1312C22C31×#53711yescharacteristic
1313C22C31×#53811yescharacteristic
1314C22C31×#53911yescharacteristic
1315C22C31×#54011yescharacteristic
1316C22C31×#54211yescharacteristic
1317C22D42×C3111yescharacteristic
1318C22D42×C3111yescharacteristic
1319C22D42×C3111yescharacteristic
1320C22D42×C3111yescharacteristic
1321C22C31×#54611yescharacteristic
1322C22C31×#54611yescharacteristic
1323C22C31×#54611yescharacteristic
1324C22C31×#54711yescharacteristic
1325C22C31×#54711yescharacteristic
1326C22C31×#54711yescharacteristic
1327C22C31×#54811yescharacteristic
1328C22C31×#55011yescharacteristic
1329C22C31×#55111yescharacteristic
1330C22C31×#55311yescharacteristic
1331C22C31×#55311yescharacteristic
1332C22C31×#55911yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2C31×#238811yescharacteristic
1349C2C31×#240311yescharacteristic
1350C2C31×#240711yescharacteristic
1351C2C31×#241811yescharacteristic
1352C2C31×#242211yescharacteristic
1353C2C31×#243011yescharacteristic
1354C2C31×#244311yescharacteristic
1355C2C31×#244511yescharacteristic
1356C2C31×#245511yescharacteristic
1357C2C31×#245611yescharacteristic
1358C2C31×#246111yescharacteristic
1359C2C31×#246411yescharacteristic
1360C2C31×#260211yescharacteristic
1361C2C31×#263011yescharacteristic
1362C2C31×#284911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#123C2semidirect
2. C22×C4×D4×C31C2semidirect
3. C2×C31×#394C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C31×#1444C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1437C2semidirect
14. C31×#1436C2semidirect
15. C31×C22⋊#95C2semidirect
98. C23×C4×C31D4semidirect
124. C2×C4⋊C4×C31D4semidirect
162. C2×C22⋊C4×C31D4semidirect
163. C2×C22⋊C4×C31D4semidirect
362. #14721C31direct (N × H)
467. C23×C31#123semidirect
571. C2×C4×C31#123semidirect
572. C22×#123C2×C31semidirect
573. C22×C4×D4C2×C31semidirect
574. C2×#394C2×C31semidirect
576. C2×#386C2×C31semidirect
577. C2×#385C2×C31semidirect
578. #1444C2×C31semidirect
579. #1440C2×C31semidirect
580. #1439C2×C31semidirect
581. #1439C2×C31semidirect
582. #1438C2×C31semidirect
583. #1438C2×C31semidirect
584. #1437C2×C31semidirect
585. #1436C2×C31semidirect
586. C22⋊#95C2×C31semidirect
779. C23×C4D4×C31semidirect
805. C2×C4⋊C4D4×C31semidirect
843. C2×C22⋊C4D4×C31semidirect
844. C2×C22⋊C4D4×C31semidirect
860. C31#14721direct (N × H)
1148. C23C31×#123semidirect
1252. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C4×D4×C312
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C2×C31×#3852
C31×#14442
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14362
C31×C22⋊#952
#1472131