Finite Group Databasebeta

← C31×#15302 #21472061

Subgroups — C31×#15302 #21472061

Order 7936.

1930 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#396C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic
3C2×C31×#394C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic, complemented
5C2×C31×#388C211yesmaximal, characteristic, complemented
6C2×C31×#386C211yesmaximal, characteristic
7C2×C31×#385C211yesmaximal, characteristic, complemented
8C2×C31×#380C211yesmaximal, characteristic, complemented
9C31×#1442C211yesmaximal, characteristic, complemented
10C31×#1441C211yesmaximal, characteristic, complemented
11C31×#1441C211yesmaximal, characteristic, complemented
12C31×#1440C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1439C211yesmaximal, characteristic, complemented
15C31×#1437C211yesmaximal, 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×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊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
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C42×C31C2211yescharacteristic
37C31×#396—24no—
38C31×#394—24no—
39C31×#394—24no—
40C31×#389—24no—
41C31×#388—24no—
42C31×#386—24no—
43C31×#385—24no—
44C31×#380—24no—
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
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—41no—
67C22×D4×C31—41no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—22no—
72C23×C4×C31—22no—
73C23×C4×C31—41no—
74C23×C4×C31—41no—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31—41no—
105C2×C4⋊C4×C31—41no—
106C2×C4⋊C4×C31—41no—
107C2×C4⋊C4×C31—41no—
108C2×C4⋊C4×C31D414yescomplemented
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
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—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31D414yes—
141C2×C22⋊C4×C31D414yes—
142C2×C42×C31—22no—
143C2×C42×C31—22no—
144C2×C42×C31—41no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—41no—
157C31×#95—41no—
158C31×#95D414yes—
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×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31C2×D412yes—
186C24×C31C2×D412yes—
187C24×C31#4112yes—
188C24×C31#4112yes—
189C24×C31C2411yescharacteristic
190C2×D4×C31—28no—
191C2×D4×C31—44no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—44no—
195C2×D4×C31—44no—
196C2×D4×C31—44no—
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—28no—
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—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—44no—
277C22×C4×C31—44no—
278C22×C4×C31—44no—
279C22×C4×C31—44no—
280C22×C4×C31—44no—
281C22×C4×C31—44no—
282C22×C4×C31C2×D412yes—
283C22×C4×C31C2×D412yes—
284C22×C4×C31C2×D412yes—
285C22×C4×C31C2×D412yes—
286C22×C4×C31C2×D412yes—
287C22×C4×C31C2×D412yes—
288C22×C4×C31C2×D412yes—
289C22×C4×C31C2×D412yes—
290C22×C4×C31C2×D412yes—
291C22×C4×C31C2×D412yes—
292C22×C4×C31#4112yes—
293C22×C4×C31#4112yes—
294C22×C4×C31#4112yes—
295C4⋊C4×C31—28no—
296C4⋊C4×C31—44no—
297C4⋊C4×C31—44no—
298C4⋊C4×C31—44no—
299C4⋊C4×C31—44no—
300C4⋊C4×C31—44no—
301C4⋊C4×C31—44no—
302C22⋊C4×C31—28no—
303C22⋊C4×C31—28no—
304C22⋊C4×C31—44no—
305C22⋊C4×C31—44no—
306C22⋊C4×C31—44no—
307C22⋊C4×C31—44no—
308C22⋊C4×C31—44no—
309C22⋊C4×C31—44no—
310C22⋊C4×C31—44no—
311C22⋊C4×C31—44no—
312C22⋊C4×C31—44no—
313C42×C31—44no—
314#15302C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
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×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31#12114yes—
385C23×C31C22×D411yescharacteristic
386C23×C31C22×D411yescharacteristic
387C23×C31C22×D411yescharacteristic
388C23×C31C22×D411yescharacteristic
389C23×C31C2×#4111yescharacteristic
390C23×C31C2×#4111yescharacteristic
391C23×C31C2×#4111yescharacteristic
392C23×C31C2×#4111yescharacteristic
393C23×C31C2×#4111yescharacteristic
394C23×C31H(5,𝔽2)11yescharacteristic
395C23×C31H(5,𝔽2)11yescharacteristic
396C23×C31H(5,𝔽2)11yescharacteristic
397C23×C312−1+411yescharacteristic
398C23×C312−1+411yescharacteristic
399C23×C312−1+411yescharacteristic
400D4×C31—416no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—416no—
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×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31#12114yes—
492C2×C4×C31#12114yes—
493C2×#396C2×C3111yescharacteristic, complemented
494C2×#394C2×C3111yescharacteristic
495C2×#394C2×C3111yescharacteristic
496C2×#389C2×C3111yescharacteristic, complemented
497C2×#388C2×C3111yescharacteristic, complemented
498C2×#386C2×C3111yescharacteristic
499C2×#385C2×C3111yescharacteristic, complemented
500C2×#380C2×C3111yescharacteristic, complemented
501#1442C2×C3111yescharacteristic, complemented
502#1441C2×C3111yescharacteristic, complemented
503#1441C2×C3111yescharacteristic, complemented
504#1440C2×C3111yescharacteristic, complemented
505#1439C2×C3111yescharacteristic, complemented
506#1439C2×C3111yescharacteristic, complemented
507#1437C2×C3111yescharacteristic, complemented
508C22×C31—24no—
509C22×C31—24no—
510C22×C31—24no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—42no—
515C22×C31—42no—
516C22×C31—42no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—42no—
523C22×C31—42no—
524C22×C31—42no—
525C22×C31—42no—
526C22×C31—42no—
527C22×C31—42no—
528C22×C31—42no—
529C22×C31—42no—
530C22×C31—81no—
531C22×C31—81no—
532C22×C31—81no—
533C22×C31—81no—
534C22×C31—81no—
535C22×C31—81no—
536C22×C31—81no—
537C22×C31—81no—
538C22×C31C2×#12111yescharacteristic
539C22×C31C2×#12111yescharacteristic
540C22×C31C2×#12111yescharacteristic
541C22×C31#52511yescharacteristic
542C22×C31#52511yescharacteristic
543C22×C31#52911yescharacteristic
544C22×C31#53611yescharacteristic
545C22×C31#53611yescharacteristic
546C22×C31#53711yescharacteristic
547C22×C31#53711yescharacteristic
548C22×C31#53811yescharacteristic
549C22×C31#53811yescharacteristic
550C22×C31#53911yescharacteristic
551C22×C31#54211yescharacteristic
552C22×C31#54211yescharacteristic
553C22×C31D4211yescharacteristic
554C22×C31D4211yescharacteristic
555C22×C31D4211yescharacteristic
556C22×C31#54611yescharacteristic
557C22×C31#54611yescharacteristic
558C22×C31#54611yescharacteristic
559C22×C31#54611yescharacteristic
560C22×C31#54711yescharacteristic
561C22×C31#54711yescharacteristic
562C22×C31#54711yescharacteristic
563C22×C31#54811yescharacteristic
564C22×C31#54811yescharacteristic
565C22×C31#54811yescharacteristic
566C22×C31#55211yescharacteristic
567C22×C31#55211yescharacteristic
568C22×C31#55211yescharacteristic
569C22×C31#55311yescharacteristic
570C22×C31#55311yescharacteristic
571C22×C31#56211yescharacteristic
572C22×C31#56311yescharacteristic
573C4×C31—24no—
574C4×C31—24no—
575C4×C31—42no—
576C4×C31—42no—
577C4×C31—42no—
578C4×C31—42no—
579C4×C31—42no—
580C4×C31—42no—
581C4×C31—42no—
582C4×C31—81no—
583C4×C31—81no—
584C4×C31—81no—
585C4×C31—81no—
586C23×D4C22×C3111yescharacteristic
587C24×C4C22×C3111yescharacteristic
588C22×C4⋊C4C22×C3111yescharacteristic
589C22×C4⋊C4C22×C3111yescharacteristic
590C22×C4⋊C4C22×C3111yescharacteristic
591C22×C4⋊C4C22×C3111yescharacteristic
592C22×C4⋊C4C22×C3111yescharacteristic
593C22×C4⋊C4C22×C3111yescharacteristic
594C22×C4⋊C4C22×C3111yescharacteristic
595C22×C22⋊C4C22×C3111yescharacteristic
596C22×C22⋊C4C22×C3111yescharacteristic
597C22×C22⋊C4C22×C3111yescharacteristic
598C22×C22⋊C4C22×C3111yescharacteristic
599C22×C22⋊C4C22×C3111yescharacteristic
600C22×C22⋊C4C22×C3111yescharacteristic
601C22×C22⋊C4C22×C3111yescharacteristic
602C22×C22⋊C4C22×C3111yescharacteristic
603C22×C22⋊C4C22×C3111yescharacteristic
604C22×C22⋊C4C22×C3111yescharacteristic
605C22×C22⋊C4C22×C3111yescharacteristic
606C22×C42C22×C3111yescharacteristic
607#396—24no—
608#394—24no—
609#394—24no—
610#389—24no—
611#388—24no—
612#386—24no—
613#385—24no—
614#380—24no—
615C2×#95C22×C3111yescharacteristic
616C2×#95C22×C3111yescharacteristic
617C2×#95C22×C3111yescharacteristic
618C2×#95C22×C3111yescharacteristic
619C2×#95C22×C3111yescharacteristic
620C2×#95C22×C3111yescharacteristic
621C2×#95C22×C3111yescharacteristic
622C2×#95C22×C3111yescharacteristic
623C2×#95C22×C3111yescharacteristic
624C2×#95C22×C3111yescharacteristic
625C2×#95C22×C3111yescharacteristic
626C2×#95C22×C3111yescharacteristic
627C2×#95C22×C3111yescharacteristic
628C2×#95C22×C3111yescharacteristic
629C2×C31—44no—
630C2×C31—82no—
631C2×C31#241311yescharacteristic
632C2×C31#241611yescharacteristic
633C2×C31#241611yescharacteristic
634C2×C31#242411yescharacteristic
635C2×C31#242411yescharacteristic
636C2×C31#242711yescharacteristic
637C2×C31#246011yescharacteristic
638C2×C31#247011yescharacteristic
639C2×C31#253611yescharacteristic
640C2×C31#267211yescharacteristic
641C2×C31#267411yescharacteristic
642C2×C31#268111yescharacteristic
643C2×C31#269511yescharacteristic
644C2×C31#270211yescharacteristic
645C2×C31#277911yescharacteristic
646C25C23×C3111yescharacteristic
647C25C23×C3111yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—41no—
654C22×D4—41no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4C23×C3111yescharacteristic
663C23×C4C23×C3111yescharacteristic
664C23×C4C23×C3111yescharacteristic
665C23×C4C23×C3111yescharacteristic
666C23×C4C23×C3111yescharacteristic
667C23×C4C23×C3111yescharacteristic
668C23×C4C23×C3111yescharacteristic
669C23×C4C23×C3111yescharacteristic
670C23×C4C23×C3111yescharacteristic
671C23×C4C23×C3111yescharacteristic
672C23×C4C23×C3111yescharacteristic
673C23×C4C23×C3111yescharacteristic
674C23×C4C23×C3111yescharacteristic
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4D4×C3114yescomplemented
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4D4×C3114yes—
728C2×C22⋊C4D4×C3114yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—41no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95D4×C3114yes—
746C31#1530211yescharacteristic, direct product factor, Sylow
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C2×D4×C3112yes—
774C24C2×D4×C3112yes—
775C24#41×C3112yes—
776C24#41×C3112yes—
777C24C24×C3111yescharacteristic
778C2×D4—28no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
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—28no—
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—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4C2×D4×C3112yes—
871C22×C4C2×D4×C3112yes—
872C22×C4C2×D4×C3112yes—
873C22×C4C2×D4×C3112yes—
874C22×C4C2×D4×C3112yes—
875C22×C4C2×D4×C3112yes—
876C22×C4C2×D4×C3112yes—
877C22×C4C2×D4×C3112yes—
878C22×C4C2×D4×C3112yes—
879C22×C4C2×D4×C3112yes—
880C22×C4#41×C3112yes—
881C22×C4#41×C3112yes—
882C22×C4#41×C3112yes—
883C4⋊C4—28no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C31×#12114yes—
972C23C22×D4×C3111yescharacteristic
973C23C22×D4×C3111yescharacteristic
974C23C22×D4×C3111yescharacteristic
975C23C22×D4×C3111yescharacteristic
976C23C2×#41×C3111yescharacteristic
977C23C2×#41×C3111yescharacteristic
978C23C2×#41×C3111yescharacteristic
979C23C2×#41×C3111yescharacteristic
980C23C2×#41×C3111yescharacteristic
981C23C31×H(5,𝔽2)11yescharacteristic
982C23C31×H(5,𝔽2)11yescharacteristic
983C23C31×H(5,𝔽2)11yescharacteristic
984C23C31×2−1+411yescharacteristic
985C23C31×2−1+411yescharacteristic
986C23C31×2−1+411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—416no—
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—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4C31×#12114yes—
1079C2×C4C31×#12114yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×C31×#12111yescharacteristic
1111C22C2×C31×#12111yescharacteristic
1112C22C2×C31×#12111yescharacteristic
1113C22C31×#52511yescharacteristic
1114C22C31×#52511yescharacteristic
1115C22C31×#52911yescharacteristic
1116C22C31×#53611yescharacteristic
1117C22C31×#53611yescharacteristic
1118C22C31×#53711yescharacteristic
1119C22C31×#53711yescharacteristic
1120C22C31×#53811yescharacteristic
1121C22C31×#53811yescharacteristic
1122C22C31×#53911yescharacteristic
1123C22C31×#54211yescharacteristic
1124C22C31×#54211yescharacteristic
1125C22D42×C3111yescharacteristic
1126C22D42×C3111yescharacteristic
1127C22D42×C3111yescharacteristic
1128C22C31×#54611yescharacteristic
1129C22C31×#54611yescharacteristic
1130C22C31×#54611yescharacteristic
1131C22C31×#54611yescharacteristic
1132C22C31×#54711yescharacteristic
1133C22C31×#54711yescharacteristic
1134C22C31×#54711yescharacteristic
1135C22C31×#54811yescharacteristic
1136C22C31×#54811yescharacteristic
1137C22C31×#54811yescharacteristic
1138C22C31×#55211yescharacteristic
1139C22C31×#55211yescharacteristic
1140C22C31×#55211yescharacteristic
1141C22C31×#55311yescharacteristic
1142C22C31×#55311yescharacteristic
1143C22C31×#56211yescharacteristic
1144C22C31×#56311yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C31×#241311yescharacteristic
1161C2C31×#241611yescharacteristic
1162C2C31×#241611yescharacteristic
1163C2C31×#242411yescharacteristic
1164C2C31×#242411yescharacteristic
1165C2C31×#242711yescharacteristic
1166C2C31×#246011yescharacteristic
1167C2C31×#247011yescharacteristic
1168C2C31×#253611yescharacteristic
1169C2C31×#267211yescharacteristic
1170C2C31×#267411yescharacteristic
1171C2C31×#268111yescharacteristic
1172C2C31×#269511yescharacteristic
1173C2C31×#270211yescharacteristic
1174C2C31×#277911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#396C2semidirect
4. C2×C31×#389C2semidirect
5. C2×C31×#388C2semidirect
7. C2×C31×#385C2semidirect
8. C2×C31×#380C2semidirect
9. C31×#1442C2semidirect
10. C31×#1441C2semidirect
11. C31×#1441C2semidirect
12. C31×#1440C2semidirect
13. C31×#1439C2semidirect
14. C31×#1439C2semidirect
15. C31×#1437C2semidirect
108. C2×C4⋊C4×C31D4semidirect
314. #15302C31direct (N × H)
493. C2×#396C2×C31semidirect
496. C2×#389C2×C31semidirect
497. C2×#388C2×C31semidirect
499. C2×#385C2×C31semidirect
500. C2×#380C2×C31semidirect
501. #1442C2×C31semidirect
502. #1441C2×C31semidirect
503. #1441C2×C31semidirect
504. #1440C2×C31semidirect
505. #1439C2×C31semidirect
506. #1439C2×C31semidirect
507. #1437C2×C31semidirect
695. C2×C4⋊C4D4×C31semidirect
746. C31#15302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3962
C2×C31×#3942
C2×C31×#3892
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14372
#1530231