Finite Group Databasebeta

← C31×#14622 #21471381

Subgroups — C31×#14622 #21471381

Order 7936.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#385C211yesmaximal, characteristic, complemented
4C31×#1445C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C31×#394C418yescomplemented
34C31×#386—24no—
35C31×#385—24no—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—41no—
59C22×D4×C31—41no—
60C22×D4×C31—41no—
61C22×D4×C31—41no—
62C22×D4×C31C2×C414yes—
63C23×C4×C31—41no—
64C23×C4×C31—41no—
65C23×C4×C31—41no—
66C23×C4×C31—41no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31D414yes—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31—41no—
89C2×C4⋊C4×C31—41no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31C2×C414yescomplemented
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—41no—
103C2×C22⋊C4×C31—41no—
104C2×C22⋊C4×C31—41no—
105C2×C22⋊C4×C31—41no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31—41no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—41no—
112C2×C22⋊C4×C31—41no—
113C2×C22⋊C4×C31—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31C2×C414yes—
125C2×C22⋊C4×C31C2×C414yes—
126C2×C22⋊C4×C31C2×C414yescomplemented
127C2×C22⋊C4×C31C2×C414yescomplemented
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95—41no—
139C31×#95—41no—
140C31×#95—41no—
141C31×#95—41no—
142C31×#95—41no—
143C31×#95—41no—
144C31×#95—41no—
145C31×#95C2×C414yescomplemented
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31C22×C412yes—
173C24×C31C22×C412yes—
174C24×C31C2×D412yes—
175C24×C31#4112yes—
176C24×C31C2411yescharacteristic
177C2×D4×C31—28no—
178C2×D4×C31—44no—
179C2×D4×C31—44no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
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—21no—
255C22×C4×C31—21no—
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—44no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31—44no—
275C22×C4×C31C22×C412yes—
276C22×C4×C31C22×C412yes—
277C22×C4×C31C22×C412yes—
278C22×C4×C31C22×C412yes—
279C22×C4×C31C22×C412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C4⋊C4×C31—44no—
283C4⋊C4×C31—44no—
284C4⋊C4×C31—44no—
285C4⋊C4×C31—44no—
286C22⋊C4×C31—28no—
287C22⋊C4×C31—44no—
288C22⋊C4×C31—44no—
289C22⋊C4×C31—44no—
290C22⋊C4×C31—44no—
291C22⋊C4×C31—44no—
292C22⋊C4×C31—44no—
293C22⋊C4×C31—44no—
294C22⋊C4×C31—44no—
295C22⋊C4×C31—44no—
296C22⋊C4×C31—44no—
297#14622C3111yesmaximal, characteristic, direct product factor, Sylow
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31C4×D414yes—
368C23×C31C23×C411yescharacteristic
369C23×C31C22×D411yescharacteristic
370C23×C31C2×#4111yescharacteristic
371C23×C31H(5,𝔽2)11yescharacteristic
372C23×C31H(5,𝔽2)11yescharacteristic
373C23×C31H(5,𝔽2)11yescharacteristic
374C23×C31H(5,𝔽2)11yescharacteristic
375C23×C31H(5,𝔽2)11yescharacteristic
376C23×C31H(5,𝔽2)11yescharacteristic
377C23×C31H(5,𝔽2)11yescharacteristic
378C23×C31H(5,𝔽2)11yescharacteristic
379C23×C31H(5,𝔽2)11yescharacteristic
380C23×C312−1+411yescharacteristic
381C23×C312−1+411yescharacteristic
382C23×C312−1+411yescharacteristic
383D4×C31—416no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—416no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×#394C2×C3111yescharacteristic
477C2×#386C2×C3111yescharacteristic
478C2×#385C2×C3111yescharacteristic, complemented
479#1445C2×C3111yescharacteristic, complemented
480#1442C2×C3111yescharacteristic, complemented
481#1442C2×C3111yescharacteristic, complemented
482#1441C2×C3111yescharacteristic, complemented
483#1440C2×C3111yescharacteristic, complemented
484#1440C2×C3111yescharacteristic, complemented
485#1439C2×C3111yescharacteristic, complemented
486#1439C2×C3111yescharacteristic, complemented
487#1439C2×C3111yescharacteristic, complemented
488#1439C2×C3111yescharacteristic, complemented
489#1438C2×C3111yescharacteristic
490C22⋊#95C2×C3111yescharacteristic, complemented
491C22×C31—24no—
492C22×C31—24no—
493C22×C31—24no—
494C22×C31—42no—
495C22×C31—42no—
496C22×C31—42no—
497C22×C31—42no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—42no—
502C22×C31—42no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—42no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—81no—
514C22×C31—81no—
515C22×C31—81no—
516C22×C31—81no—
517C22×C31—81no—
518C22×C31—81no—
519C22×C31—81no—
520C22×C31—81no—
521C22×C31C2×C4×D411yescharacteristic
522C22×C31#51811yescharacteristic
523C22×C31#51811yescharacteristic
524C22×C31#51811yescharacteristic
525C22×C31#52011yescharacteristic
526C22×C31#52011yescharacteristic
527C22×C31#52011yescharacteristic
528C22×C31#53411yescharacteristic
529C22×C31#53411yescharacteristic
530C22×C31#53411yescharacteristic
531C22×C31#53511yescharacteristic
532C22×C31#53611yescharacteristic
533C22×C31#53711yescharacteristic
534C22×C31#53811yescharacteristic
535C22×C31#53811yescharacteristic
536C22×C31#53811yescharacteristic
537C22×C31#53911yescharacteristic
538C22×C31#53911yescharacteristic
539C22×C31#53911yescharacteristic
540C22×C31#56011yescharacteristic
541C22×C31#56011yescharacteristic
542C22×C31#56011yescharacteristic
543C22×C31#56011yescharacteristic
544C22×C31#56011yescharacteristic
545C22×C31H(3,𝔽4)11yescharacteristic
546C22×C31#56211yescharacteristic
547C22×C31#56211yescharacteristic
548C22×C31#56211yescharacteristic
549C22×C31#56211yescharacteristic
550C22×C31#56211yescharacteristic
551C22×C31#56211yescharacteristic
552C22×C31#56211yescharacteristic
553C22×C31#56211yescharacteristic
554C22×C31#56311yescharacteristic
555C22×C31#56311yescharacteristic
556C4×C31—42no—
557C4×C31—42no—
558C4×C31—42no—
559C4×C31—42no—
560C4×C31—42no—
561C4×C31—42no—
562C4×C31—42no—
563C4×C31—81no—
564C4×C31—81no—
565C4×C31—81no—
566C4×C31—81no—
567C4×C31—81no—
568C4×C31—81no—
569C23×D4C22×C3111yescharacteristic
570C24×C4C22×C3111yescharacteristic
571C22×C4⋊C4C22×C3111yescharacteristic
572C22×C4⋊C4C22×C3111yescharacteristic
573C22×C4⋊C4C22×C3111yescharacteristic
574C22×C4⋊C4C22×C3111yescharacteristic
575C22×C22⋊C4C22×C3111yescharacteristic
576C22×C22⋊C4C22×C3111yescharacteristic
577C22×C22⋊C4C22×C3111yescharacteristic
578C22×C22⋊C4C22×C3111yescharacteristic
579C22×C22⋊C4C22×C3111yescharacteristic
580C22×C22⋊C4C22×C3111yescharacteristic
581C22×C22⋊C4C22×C3111yescharacteristic
582C22×C22⋊C4C22×C3111yescharacteristic
583C22×C22⋊C4C22×C3111yescharacteristic
584C22×C22⋊C4C22×C3111yescharacteristic
585C22×C22⋊C4C22×C3111yescharacteristic
586#394C4×C3118yescomplemented
587#386—24no—
588#385—24no—
589C2×#95C22×C3111yescharacteristic
590C2×#95C22×C3111yescharacteristic
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×#95C22×C3111yescharacteristic
595C2×#95C22×C3111yescharacteristic
596C2×#95C22×C3111yescharacteristic
597C2×#95C22×C3111yescharacteristic
598C2×#95C22×C3111yescharacteristic
599C2×#95C22×C3111yescharacteristic
600C2×#95C22×C3111yescharacteristic
601C2×#95C22×C3111yescharacteristic
602C2×#95C22×C3111yescharacteristic
603C2×#95C22×C3111yescharacteristic
604C2×#95C22×C3111yescharacteristic
605C2×#95C22×C3111yescharacteristic
606C2×#95C22×C3111yescharacteristic
607C2×C31—44no—
608C2×C31—82no—
609C2×C31#232111yescharacteristic
610C2×C31#232211yescharacteristic
611C2×C31#232511yescharacteristic
612C2×C31#237611yescharacteristic
613C2×C31#237711yescharacteristic
614C2×C31#237711yescharacteristic
615C2×C31#237911yescharacteristic
616C2×C31#281211yescharacteristic
617C2×C31#281311yescharacteristic
618C2×C31#281411yescharacteristic
619C2×C31#281611yescharacteristic
620C2×C31#282411yescharacteristic
621C2×C31#282611yescharacteristic
622C2×C31#282711yescharacteristic
623C2×C31#282711yescharacteristic
624C25C23×C3111yescharacteristic
625C25C23×C3111yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4C2×C4×C3114yes—
633C23×C4—41no—
634C23×C4—41no—
635C23×C4—41no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—41no—
639C23×C4D4×C3114yes—
640C23×C4C23×C3111yescharacteristic
641C23×C4C23×C3111yescharacteristic
642C23×C4C23×C3111yescharacteristic
643C23×C4C23×C3111yescharacteristic
644C23×C4C23×C3111yescharacteristic
645C23×C4C23×C3111yescharacteristic
646C23×C4C23×C3111yescharacteristic
647C23×C4C23×C3111yescharacteristic
648C23×C4C23×C3111yescharacteristic
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651C23×C4C23×C3111yescharacteristic
652C23×C4C23×C3111yescharacteristic
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4C2×C4×C3114yescomplemented
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4C2×C4×C3114yes—
695C2×C22⋊C4C2×C4×C3114yes—
696C2×C22⋊C4C2×C4×C3114yescomplemented
697C2×C22⋊C4C2×C4×C3114yescomplemented
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95C2×C4×C3114yescomplemented
716C31#1462211yescharacteristic, direct product factor, Sylow
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24C22×C4×C3112yes—
744C24C22×C4×C3112yes—
745C24C2×D4×C3112yes—
746C24#41×C3112yes—
747C24C24×C3111yescharacteristic
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4C22×C4×C3112yes—
847C22×C4C22×C4×C3112yes—
848C22×C4C22×C4×C3112yes—
849C22×C4C22×C4×C3112yes—
850C22×C4C22×C4×C3112yes—
851C22×C4C2×D4×C3112yes—
852C22×C4C2×D4×C3112yes—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C22⋊C4—28no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23C4×D4×C3114yes—
938C23C23×C4×C3111yescharacteristic
939C23C22×D4×C3111yescharacteristic
940C23C2×#41×C3111yescharacteristic
941C23C31×H(5,𝔽2)11yescharacteristic
942C23C31×H(5,𝔽2)11yescharacteristic
943C23C31×H(5,𝔽2)11yescharacteristic
944C23C31×H(5,𝔽2)11yescharacteristic
945C23C31×H(5,𝔽2)11yescharacteristic
946C23C31×H(5,𝔽2)11yescharacteristic
947C23C31×H(5,𝔽2)11yescharacteristic
948C23C31×H(5,𝔽2)11yescharacteristic
949C23C31×H(5,𝔽2)11yescharacteristic
950C23C31×2−1+411yescharacteristic
951C23C31×2−1+411yescharacteristic
952C23C31×2−1+411yescharacteristic
953D4—416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—416no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22C2×C4×D4×C3111yescharacteristic
1077C22C31×#51811yescharacteristic
1078C22C31×#51811yescharacteristic
1079C22C31×#51811yescharacteristic
1080C22C31×#52011yescharacteristic
1081C22C31×#52011yescharacteristic
1082C22C31×#52011yescharacteristic
1083C22C31×#53411yescharacteristic
1084C22C31×#53411yescharacteristic
1085C22C31×#53411yescharacteristic
1086C22C31×#53511yescharacteristic
1087C22C31×#53611yescharacteristic
1088C22C31×#53711yescharacteristic
1089C22C31×#53811yescharacteristic
1090C22C31×#53811yescharacteristic
1091C22C31×#53811yescharacteristic
1092C22C31×#53911yescharacteristic
1093C22C31×#53911yescharacteristic
1094C22C31×#53911yescharacteristic
1095C22C31×#56011yescharacteristic
1096C22C31×#56011yescharacteristic
1097C22C31×#56011yescharacteristic
1098C22C31×#56011yescharacteristic
1099C22C31×#56011yescharacteristic
1100C22C31×H(3,𝔽4)11yescharacteristic
1101C22C31×#56211yescharacteristic
1102C22C31×#56211yescharacteristic
1103C22C31×#56211yescharacteristic
1104C22C31×#56211yescharacteristic
1105C22C31×#56211yescharacteristic
1106C22C31×#56211yescharacteristic
1107C22C31×#56211yescharacteristic
1108C22C31×#56211yescharacteristic
1109C22C31×#56311yescharacteristic
1110C22C31×#56311yescharacteristic
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C2—44no—
1125C2—82no—
1126C2C31×#232111yescharacteristic
1127C2C31×#232211yescharacteristic
1128C2C31×#232511yescharacteristic
1129C2C31×#237611yescharacteristic
1130C2C31×#237711yescharacteristic
1131C2C31×#237711yescharacteristic
1132C2C31×#237911yescharacteristic
1133C2C31×#281211yescharacteristic
1134C2C31×#281311yescharacteristic
1135C2C31×#281411yescharacteristic
1136C2C31×#281611yescharacteristic
1137C2C31×#282411yescharacteristic
1138C2C31×#282611yescharacteristic
1139C2C31×#282711yescharacteristic
1140C2C31×#282711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#385C2semidirect
4. C31×#1445C2semidirect
5. C31×#1442C2semidirect
6. C31×#1442C2semidirect
7. C31×#1441C2semidirect
8. C31×#1440C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1439C2semidirect
15. C31×C22⋊#95C2semidirect
33. C31×#394C4semidirect
94. C2×C4⋊C4×C31C2×C4semidirect
126. C2×C22⋊C4×C31C2×C4semidirect
127. C2×C22⋊C4×C31C2×C4semidirect
145. C31×#95C2×C4semidirect
297. #14622C31direct (N × H)
478. C2×#385C2×C31semidirect
479. #1445C2×C31semidirect
480. #1442C2×C31semidirect
481. #1442C2×C31semidirect
482. #1441C2×C31semidirect
483. #1440C2×C31semidirect
484. #1440C2×C31semidirect
485. #1439C2×C31semidirect
486. #1439C2×C31semidirect
487. #1439C2×C31semidirect
488. #1439C2×C31semidirect
490. C22⋊#95C2×C31semidirect
586. #394C4×C31semidirect
664. C2×C4⋊C4C2×C4×C31semidirect
696. C2×C22⋊C4C2×C4×C31semidirect
697. C2×C22⋊C4C2×C4×C31semidirect
715. #95C2×C4×C31semidirect
716. C31#14622direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3862
C2×C31×#3852
C31×#14452
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1462231