Finite Group Databasebeta

← C31×#16268 #21473027

Subgroups — C31×#16268 #21473027

Order 7936.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic, complemented
2C2×C31×#392C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C31×#1445C211yesmaximal, characteristic, complemented
6C31×#1443C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊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
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C31×#394—24no—
36C31×#392—24no—
37C31×#386—24no—
38C31×#386—24no—
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
54C2×C31×#95C2211yescharacteristic
55C25×C31C2311yescharacteristic
56C25×C31C2311yescharacteristic
57C25×C31C2311yescharacteristic
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31D414yes—
79C23×C4×C31—22no—
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—41no—
83C23×C4×C31—41no—
84C23×C4×C31—41no—
85C23×C4×C31—41no—
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—41no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
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—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×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C22⋊C4×C31—41no—
129C2×C22⋊C4×C31—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
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×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31D414yescomplemented
143C31×#95—22no—
144C31×#95—22no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—41no—
151C31×#95—41no—
152C31×#95—41no—
153C31×#95—41no—
154C31×#95—41no—
155C31×#95—41no—
156C31×#95—41no—
157C31×#95—41no—
158C31×#95—41no—
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×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×C31C2×D412yes—
200C24×C31C2×D412yes—
201C24×C31C2×D412yes—
202C24×C31#4112yes—
203C24×C31#4112yes—
204C24×C31C2411yescharacteristic
205C2×D4×C31—28no—
206C2×D4×C31—28no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
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—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—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×C31C2×D412yes—
312C22×C4×C31C2×D412yes—
313C22×C4×C31C2×D412yes—
314C22×C4×C31#4112yes—
315C22×C4×C31#4112yes—
316C22×C4×C31#4112yes—
317C4⋊C4×C31—44no—
318C22⋊C4×C31—44no—
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×C31—44no—
331C22⋊C4×C31—44no—
332#16268C3111yesmaximal, characteristic, direct product factor, Sylow
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
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—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—41no—
401C23×C31—41no—
402C23×C31—41no—
403C23×C31—41no—
404C23×C31—41no—
405C23×C31—41no—
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#12314yes—
438C23×C31C22×D411yescharacteristic
439C23×C31C22×D411yescharacteristic
440C23×C31C2×#4111yescharacteristic
441C23×C31C2×#4111yescharacteristic
442C23×C31C2×#4111yescharacteristic
443C23×C31C2×#4111yescharacteristic
444C23×C31C2×#4111yescharacteristic
445C23×C31H(5,𝔽2)11yescharacteristic
446C23×C31H(5,𝔽2)11yescharacteristic
447C23×C31H(5,𝔽2)11yescharacteristic
448C23×C31H(5,𝔽2)11yescharacteristic
449C23×C31H(5,𝔽2)11yescharacteristic
450C23×C31H(5,𝔽2)11yescharacteristic
451C23×C31H(5,𝔽2)11yescharacteristic
452C23×C31H(5,𝔽2)11yescharacteristic
453D4×C31—416no—
454D4×C31—416no—
455D4×C31—416no—
456C2×C4×C31—22no—
457C2×C4×C31—22no—
458C2×C4×C31—22no—
459C2×C4×C31—22no—
460C2×C4×C31—22no—
461C2×C4×C31—22no—
462C2×C4×C31—22no—
463C2×C4×C31—22no—
464C2×C4×C31—22no—
465C2×C4×C31—22no—
466C2×C4×C31—22no—
467C2×C4×C31—22no—
468C2×C4×C31—22no—
469C2×C4×C31—22no—
470C2×C4×C31—22no—
471C2×C4×C31—22no—
472C2×C4×C31—22no—
473C2×C4×C31—22no—
474C2×C4×C31—416no—
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—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31—41no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—41no—
515C2×C4×C31—41no—
516C2×C4×C31—41no—
517C2×C4×C31—41no—
518C2×C4×C31—41no—
519C2×C4×C31—41no—
520C2×C4×C31—41no—
521C2×C4×C31—41no—
522C2×C4×C31—41no—
523C2×C4×C31—41no—
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×#394C2×C3111yescharacteristic, complemented
542C2×#392C2×C3111yescharacteristic
543C2×#386C2×C3111yescharacteristic, complemented
544C2×#386C2×C3111yescharacteristic, complemented
545#1445C2×C3111yescharacteristic, complemented
546#1443C2×C3111yescharacteristic, complemented
547#1440C2×C3111yescharacteristic, complemented
548#1440C2×C3111yescharacteristic, complemented
549#1440C2×C3111yescharacteristic, complemented
550#1440C2×C3111yescharacteristic, complemented
551#1439C2×C3111yescharacteristic, complemented
552#1438C2×C3111yescharacteristic, complemented
553#1438C2×C3111yescharacteristic, complemented
554#1438C2×C3111yescharacteristic, complemented
555C22⋊#95C2×C3111yescharacteristic, complemented
556C22×C31—24no—
557C22×C31—24no—
558C22×C31—24no—
559C22×C31—42no—
560C22×C31—42no—
561C22×C31—42no—
562C22×C31—42no—
563C22×C31—42no—
564C22×C31—42no—
565C22×C31—42no—
566C22×C31—42no—
567C22×C31—42no—
568C22×C31—42no—
569C22×C31—42no—
570C22×C31—42no—
571C22×C31—42no—
572C22×C31—42no—
573C22×C31—42no—
574C22×C31—42no—
575C22×C31—42no—
576C22×C31—42no—
577C22×C31—42no—
578C22×C31—42no—
579C22×C31—42no—
580C22×C31—42no—
581C22×C31—42no—
582C22×C31—42no—
583C22×C31—42no—
584C22×C31—42no—
585C22×C31—81no—
586C22×C31—81no—
587C22×C31—81no—
588C22×C31—81no—
589C22×C31—81no—
590C22×C31—81no—
591C22×C31—81no—
592C22×C31—81no—
593C22×C31—81no—
594C22×C31—81no—
595C22×C31—81no—
596C22×C31—81no—
597C22×C31—81no—
598C22×C31—81no—
599C22×C31—81no—
600C22×C31—81no—
601C22×C31C2×#12311yescharacteristic
602C22×C31#52511yescharacteristic
603C22×C31#52911yescharacteristic
604C22×C31#53411yescharacteristic
605C22×C31#53411yescharacteristic
606C22×C31#53411yescharacteristic
607C22×C31#53511yescharacteristic
608C22×C31#53811yescharacteristic
609C22×C31#53811yescharacteristic
610C22×C31#53811yescharacteristic
611C22×C31#53811yescharacteristic
612C22×C31#53811yescharacteristic
613C22×C31#53811yescharacteristic
614C22×C31#53811yescharacteristic
615C22×C31#53811yescharacteristic
616C22×C31#54011yescharacteristic
617C22×C31#54011yescharacteristic
618C22×C31#54011yescharacteristic
619C22×C31#54011yescharacteristic
620C22×C31D4211yescharacteristic
621C22×C31#54611yescharacteristic
622C22×C31#54611yescharacteristic
623C22×C31#54611yescharacteristic
624C22×C31#54611yescharacteristic
625C22×C31#54611yescharacteristic
626C22×C31#54611yescharacteristic
627C22×C31#55111yescharacteristic
628C22×C31#55311yescharacteristic
629C22×C31#55311yescharacteristic
630C22×C31#55511yescharacteristic
631C22×C31#55911yescharacteristic
632C22×C31#56011yescharacteristic
633C22×C31#56011yescharacteristic
634C22×C31#56011yescharacteristic
635C22×C31#56011yescharacteristic
636C4×C31—42no—
637C4×C31—42no—
638C4×C31—42no—
639C4×C31—42no—
640C4×C31—42no—
641C4×C31—42no—
642C4×C31—81no—
643C4×C31—81no—
644C4×C31—81no—
645C4×C31—81no—
646C4×C31—81no—
647C4×C31—81no—
648C23×D4C22×C3111yescharacteristic
649C23×D4C22×C3111yescharacteristic
650C23×D4C22×C3111yescharacteristic
651C24×C4C22×C3111yescharacteristic
652C22×C4⋊C4C22×C3111yescharacteristic
653C22×C22⋊C4C22×C3111yescharacteristic
654C22×C22⋊C4C22×C3111yescharacteristic
655C22×C22⋊C4C22×C3111yescharacteristic
656C22×C22⋊C4C22×C3111yescharacteristic
657C22×C22⋊C4C22×C3111yescharacteristic
658C22×C22⋊C4C22×C3111yescharacteristic
659C22×C22⋊C4C22×C3111yescharacteristic
660C22×C22⋊C4C22×C3111yescharacteristic
661C22×C22⋊C4C22×C3111yescharacteristic
662C22×C22⋊C4C22×C3111yescharacteristic
663C22×C22⋊C4C22×C3111yescharacteristic
664C22×C22⋊C4C22×C3111yescharacteristic
665C22×C22⋊C4C22×C3111yescharacteristic
666C22×C22⋊C4C22×C3111yescharacteristic
667#394—24no—
668#392—24no—
669#386—24no—
670#386—24no—
671C2×#95C22×C3111yescharacteristic
672C2×#95C22×C3111yescharacteristic
673C2×#95C22×C3111yescharacteristic
674C2×#95C22×C3111yescharacteristic
675C2×#95C22×C3111yescharacteristic
676C2×#95C22×C3111yescharacteristic
677C2×#95C22×C3111yescharacteristic
678C2×#95C22×C3111yescharacteristic
679C2×#95C22×C3111yescharacteristic
680C2×#95C22×C3111yescharacteristic
681C2×#95C22×C3111yescharacteristic
682C2×#95C22×C3111yescharacteristic
683C2×#95C22×C3111yescharacteristic
684C2×#95C22×C3111yescharacteristic
685C2×#95C22×C3111yescharacteristic
686C2×#95C22×C3111yescharacteristic
687C2×C31—44no—
688C2×C31—82no—
689C2×C31—82no—
690C2×C31#241811yescharacteristic
691C2×C31#244411yescharacteristic
692C2×C31#245911yescharacteristic
693C2×C31#262211yescharacteristic
694C2×C31#263511yescharacteristic
695C2×C31#264811yescharacteristic
696C2×C31#266811yescharacteristic
697C2×C31#267811yescharacteristic
698C2×C31#268811yescharacteristic
699C2×C31#269911yescharacteristic
700C2×C31#270311yescharacteristic
701C2×C31#270911yescharacteristic
702C2×C31#275611yescharacteristic
703C2×C31#279711yescharacteristic
704C2×C31#282511yescharacteristic
705C25C23×C3111yescharacteristic
706C25C23×C3111yescharacteristic
707C25C23×C3111yescharacteristic
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4D4×C3114yes—
729C23×C4—22no—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—41no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4C23×C3111yescharacteristic
737C23×C4C23×C3111yescharacteristic
738C23×C4C23×C3111yescharacteristic
739C23×C4C23×C3111yescharacteristic
740C23×C4C23×C3111yescharacteristic
741C23×C4C23×C3111yescharacteristic
742C23×C4C23×C3111yescharacteristic
743C23×C4C23×C3111yescharacteristic
744C23×C4C23×C3111yescharacteristic
745C23×C4C23×C3111yescharacteristic
746C23×C4C23×C3111yescharacteristic
747C23×C4C23×C3111yescharacteristic
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4D4×C3114yescomplemented
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809C31#1626811yescharacteristic, direct product factor, Sylow
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C3112yes—
851C24C2×D4×C3112yes—
852C24C2×D4×C3112yes—
853C24#41×C3112yes—
854C24#41×C3112yes—
855C24C24×C3111yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
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—21no—
937C22×C4—21no—
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—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C3112yes—
963C22×C4C2×D4×C3112yes—
964C22×C4C2×D4×C3112yes—
965C22×C4#41×C3112yes—
966C22×C4#41×C3112yes—
967C22×C4#41×C3112yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23C31×#12314yes—
1088C23C22×D4×C3111yescharacteristic
1089C23C22×D4×C3111yescharacteristic
1090C23C2×#41×C3111yescharacteristic
1091C23C2×#41×C3111yescharacteristic
1092C23C2×#41×C3111yescharacteristic
1093C23C2×#41×C3111yescharacteristic
1094C23C2×#41×C3111yescharacteristic
1095C23C31×H(5,𝔽2)11yescharacteristic
1096C23C31×H(5,𝔽2)11yescharacteristic
1097C23C31×H(5,𝔽2)11yescharacteristic
1098C23C31×H(5,𝔽2)11yescharacteristic
1099C23C31×H(5,𝔽2)11yescharacteristic
1100C23C31×H(5,𝔽2)11yescharacteristic
1101C23C31×H(5,𝔽2)11yescharacteristic
1102C23C31×H(5,𝔽2)11yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×C31×#12311yescharacteristic
1237C22C31×#52511yescharacteristic
1238C22C31×#52911yescharacteristic
1239C22C31×#53411yescharacteristic
1240C22C31×#53411yescharacteristic
1241C22C31×#53411yescharacteristic
1242C22C31×#53511yescharacteristic
1243C22C31×#53811yescharacteristic
1244C22C31×#53811yescharacteristic
1245C22C31×#53811yescharacteristic
1246C22C31×#53811yescharacteristic
1247C22C31×#53811yescharacteristic
1248C22C31×#53811yescharacteristic
1249C22C31×#53811yescharacteristic
1250C22C31×#53811yescharacteristic
1251C22C31×#54011yescharacteristic
1252C22C31×#54011yescharacteristic
1253C22C31×#54011yescharacteristic
1254C22C31×#54011yescharacteristic
1255C22D42×C3111yescharacteristic
1256C22C31×#54611yescharacteristic
1257C22C31×#54611yescharacteristic
1258C22C31×#54611yescharacteristic
1259C22C31×#54611yescharacteristic
1260C22C31×#54611yescharacteristic
1261C22C31×#54611yescharacteristic
1262C22C31×#55111yescharacteristic
1263C22C31×#55311yescharacteristic
1264C22C31×#55311yescharacteristic
1265C22C31×#55511yescharacteristic
1266C22C31×#55911yescharacteristic
1267C22C31×#56011yescharacteristic
1268C22C31×#56011yescharacteristic
1269C22C31×#56011yescharacteristic
1270C22C31×#56011yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C31×#241811yescharacteristic
1287C2C31×#244411yescharacteristic
1288C2C31×#245911yescharacteristic
1289C2C31×#262211yescharacteristic
1290C2C31×#263511yescharacteristic
1291C2C31×#264811yescharacteristic
1292C2C31×#266811yescharacteristic
1293C2C31×#267811yescharacteristic
1294C2C31×#268811yescharacteristic
1295C2C31×#269911yescharacteristic
1296C2C31×#270311yescharacteristic
1297C2C31×#270911yescharacteristic
1298C2C31×#275611yescharacteristic
1299C2C31×#279711yescharacteristic
1300C2C31×#282511yescharacteristic
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. C2×C31×#394C2semidirect
3. C2×C31×#386C2semidirect
4. C2×C31×#386C2semidirect
5. C31×#1445C2semidirect
6. C31×#1443C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1440C2semidirect
10. C31×#1440C2semidirect
11. C31×#1439C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×C22⋊#95C2semidirect
142. C2×C22⋊C4×C31D4semidirect
332. #16268C31direct (N × H)
541. C2×#394C2×C31semidirect
543. C2×#386C2×C31semidirect
544. C2×#386C2×C31semidirect
545. #1445C2×C31semidirect
546. #1443C2×C31semidirect
547. #1440C2×C31semidirect
548. #1440C2×C31semidirect
549. #1440C2×C31semidirect
550. #1440C2×C31semidirect
551. #1439C2×C31semidirect
552. #1438C2×C31semidirect
553. #1438C2×C31semidirect
554. #1438C2×C31semidirect
555. C22⋊#95C2×C31semidirect
792. C2×C22⋊C4D4×C31semidirect
809. C31#16268direct (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×#3922
C2×C31×#3862
C31×#14452
C31×#14432
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1626831