Finite Group Databasebeta

← C31×#16266 #21473025

Subgroups — C31×#16266 #21473025

Order 7936.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C31×#1445C211yesmaximal, characteristic, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic, complemented
15C31×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊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
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C31×#394—24no—
38C31×#394—24no—
39C31×#392—24no—
40C31×#386—24no—
41C31×#386—24no—
42C31×#385—24no—
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
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C25×C31C2311yescharacteristic
58C25×C31C2311yescharacteristic
59C25×C31C2311yescharacteristic
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—22no—
69C22×D4×C31—22no—
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×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31D414yes—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—22no—
84C23×C4×C31—41no—
85C23×C4×C31—41no—
86C23×C4×C31—41no—
87C23×C4×C31—41no—
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
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—41no—
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—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×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31—41no—
147C2×C22⋊C4×C31—41no—
148C2×C22⋊C4×C31—41no—
149C2×C22⋊C4×C31—41no—
150C2×C22⋊C4×C31D414yescomplemented
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—22no—
158C31×#95—22no—
159C31×#95—22no—
160C31×#95—22no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95—41no—
164C31×#95—41no—
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×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31C2×D412yes—
206C24×C31C2×D412yes—
207C24×C31C2×D412yes—
208C24×C31#4112yes—
209C24×C31#4112yes—
210C24×C31C2411yescharacteristic
211C2×D4×C31—28no—
212C2×D4×C31—28no—
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—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—44no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C2×D4×C31—44no—
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—21no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—21no—
308C22×C4×C31—44no—
309C22×C4×C31—44no—
310C22×C4×C31—44no—
311C22×C4×C31—44no—
312C22×C4×C31—44no—
313C22×C4×C31—44no—
314C22×C4×C31—44no—
315C22×C4×C31C2×D412yes—
316C22×C4×C31C2×D412yes—
317C22×C4×C31C2×D412yes—
318C22×C4×C31C2×D412yes—
319C22×C4×C31C2×D412yes—
320C22×C4×C31C2×D412yes—
321C22×C4×C31#4112yes—
322C22×C4×C31#4112yes—
323C4⋊C4×C31—44no—
324C4⋊C4×C31—44no—
325C4⋊C4×C31—44no—
326C22⋊C4×C31—28no—
327C22⋊C4×C31—44no—
328C22⋊C4×C31—44no—
329C22⋊C4×C31—44no—
330C22⋊C4×C31—44no—
331C22⋊C4×C31—44no—
332C22⋊C4×C31—44no—
333C22⋊C4×C31—44no—
334C22⋊C4×C31—44no—
335C22⋊C4×C31—44no—
336C22⋊C4×C31—44no—
337C22⋊C4×C31—44no—
338C22⋊C4×C31—44no—
339C22⋊C4×C31—44no—
340#16266C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
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—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31#12314yes—
446C23×C31C22×D411yescharacteristic
447C23×C31C22×D411yescharacteristic
448C23×C31C22×D411yescharacteristic
449C23×C31C2×#4111yescharacteristic
450C23×C31C2×#4111yescharacteristic
451C23×C31C2×#4111yescharacteristic
452C23×C31C2×#4111yescharacteristic
453C23×C31H(5,𝔽2)11yescharacteristic
454C23×C31H(5,𝔽2)11yescharacteristic
455C23×C31H(5,𝔽2)11yescharacteristic
456C23×C31H(5,𝔽2)11yescharacteristic
457C23×C31H(5,𝔽2)11yescharacteristic
458C23×C31H(5,𝔽2)11yescharacteristic
459C23×C31H(5,𝔽2)11yescharacteristic
460C23×C312−1+411yescharacteristic
461D4×C31—416no—
462D4×C31—416no—
463D4×C31—416no—
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—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—416no—
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×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×#394C2×C3111yescharacteristic, complemented
550C2×#394C2×C3111yescharacteristic, complemented
551C2×#392C2×C3111yescharacteristic
552C2×#386C2×C3111yescharacteristic, complemented
553C2×#386C2×C3111yescharacteristic, complemented
554C2×#385C2×C3111yescharacteristic, complemented
555#1445C2×C3111yescharacteristic, complemented
556#1442C2×C3111yescharacteristic, complemented
557#1440C2×C3111yescharacteristic, complemented
558#1440C2×C3111yescharacteristic, complemented
559#1439C2×C3111yescharacteristic, complemented
560#1439C2×C3111yescharacteristic, complemented
561#1439C2×C3111yescharacteristic, complemented
562#1438C2×C3111yescharacteristic, complemented
563#1438C2×C3111yescharacteristic, complemented
564C22×C31—24no—
565C22×C31—24no—
566C22×C31—24no—
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—42no—
586C22×C31—42no—
587C22×C31—42no—
588C22×C31—42no—
589C22×C31—42no—
590C22×C31—42no—
591C22×C31—42no—
592C22×C31—42no—
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×C31—81no—
602C22×C31—81no—
603C22×C31—81no—
604C22×C31—81no—
605C22×C31—81no—
606C22×C31—81no—
607C22×C31—81no—
608C22×C31—81no—
609C22×C31C2×#12311yescharacteristic
610C22×C31#52511yescharacteristic
611C22×C31#52511yescharacteristic
612C22×C31#53411yescharacteristic
613C22×C31#53411yescharacteristic
614C22×C31#53411yescharacteristic
615C22×C31#53411yescharacteristic
616C22×C31#53511yescharacteristic
617C22×C31#53711yescharacteristic
618C22×C31#53811yescharacteristic
619C22×C31#53811yescharacteristic
620C22×C31#53811yescharacteristic
621C22×C31#53811yescharacteristic
622C22×C31#53811yescharacteristic
623C22×C31#53911yescharacteristic
624C22×C31#54011yescharacteristic
625C22×C31#54011yescharacteristic
626C22×C31#54011yescharacteristic
627C22×C31#54211yescharacteristic
628C22×C31D4211yescharacteristic
629C22×C31D4211yescharacteristic
630C22×C31D4211yescharacteristic
631C22×C31#54611yescharacteristic
632C22×C31#54611yescharacteristic
633C22×C31#54611yescharacteristic
634C22×C31#54711yescharacteristic
635C22×C31#54811yescharacteristic
636C22×C31#55011yescharacteristic
637C22×C31#55111yescharacteristic
638C22×C31#55311yescharacteristic
639C22×C31#55311yescharacteristic
640C22×C31#56011yescharacteristic
641C22×C31H(3,𝔽4)11yescharacteristic
642C22×C31#56211yescharacteristic
643C22×C31#56211yescharacteristic
644C4×C31—42no—
645C4×C31—42no—
646C4×C31—42no—
647C4×C31—42no—
648C4×C31—42no—
649C4×C31—42no—
650C4×C31—42no—
651C4×C31—42no—
652C4×C31—81no—
653C4×C31—81no—
654C4×C31—81no—
655C4×C31—81no—
656C23×D4C22×C3111yescharacteristic
657C23×D4C22×C3111yescharacteristic
658C23×D4C22×C3111yescharacteristic
659C24×C4C22×C3111yescharacteristic
660C22×C4⋊C4C22×C3111yescharacteristic
661C22×C4⋊C4C22×C3111yescharacteristic
662C22×C4⋊C4C22×C3111yescharacteristic
663C22×C22⋊C4C22×C3111yescharacteristic
664C22×C22⋊C4C22×C3111yescharacteristic
665C22×C22⋊C4C22×C3111yescharacteristic
666C22×C22⋊C4C22×C3111yescharacteristic
667C22×C22⋊C4C22×C3111yescharacteristic
668C22×C22⋊C4C22×C3111yescharacteristic
669C22×C22⋊C4C22×C3111yescharacteristic
670C22×C22⋊C4C22×C3111yescharacteristic
671C22×C22⋊C4C22×C3111yescharacteristic
672C22×C22⋊C4C22×C3111yescharacteristic
673C22×C22⋊C4C22×C3111yescharacteristic
674C22×C22⋊C4C22×C3111yescharacteristic
675C22×C22⋊C4C22×C3111yescharacteristic
676C22×C22⋊C4C22×C3111yescharacteristic
677#394—24no—
678#394—24no—
679#392—24no—
680#386—24no—
681#386—24no—
682#385—24no—
683C2×#95C22×C3111yescharacteristic
684C2×#95C22×C3111yescharacteristic
685C2×#95C22×C3111yescharacteristic
686C2×#95C22×C3111yescharacteristic
687C2×#95C22×C3111yescharacteristic
688C2×#95C22×C3111yescharacteristic
689C2×#95C22×C3111yescharacteristic
690C2×#95C22×C3111yescharacteristic
691C2×#95C22×C3111yescharacteristic
692C2×#95C22×C3111yescharacteristic
693C2×#95C22×C3111yescharacteristic
694C2×#95C22×C3111yescharacteristic
695C2×#95C22×C3111yescharacteristic
696C2×#95C22×C3111yescharacteristic
697C2×C31—44no—
698C2×C31—82no—
699C2×C31—82no—
700C2×C31#241811yescharacteristic
701C2×C31#244311yescharacteristic
702C2×C31#245611yescharacteristic
703C2×C31#262211yescharacteristic
704C2×C31#263011yescharacteristic
705C2×C31#263511yescharacteristic
706C2×C31#267111yescharacteristic
707C2×C31#267311yescharacteristic
708C2×C31#267611yescharacteristic
709C2×C31#267911yescharacteristic
710C2×C31#268811yescharacteristic
711C2×C31#270111yescharacteristic
712C2×C31#273011yescharacteristic
713C2×C31#275311yescharacteristic
714C2×C31#282411yescharacteristic
715C25C23×C3111yescharacteristic
716C25C23×C3111yescharacteristic
717C25C23×C3111yescharacteristic
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4D4×C3114yes—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4C23×C3111yescharacteristic
747C23×C4C23×C3111yescharacteristic
748C23×C4C23×C3111yescharacteristic
749C23×C4C23×C3111yescharacteristic
750C23×C4C23×C3111yescharacteristic
751C23×C4C23×C3111yescharacteristic
752C23×C4C23×C3111yescharacteristic
753C23×C4C23×C3111yescharacteristic
754C23×C4C23×C3111yescharacteristic
755C23×C4C23×C3111yescharacteristic
756C23×C4C23×C3111yescharacteristic
757C23×C4C23×C3111yescharacteristic
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—41no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4D4×C3114yescomplemented
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4D4×C3114yescomplemented
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823C31#1626611yescharacteristic, direct product factor, Sylow
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—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C3112yes—
865C24C2×D4×C3112yes—
866C24C2×D4×C3112yes—
867C24#41×C3112yes—
868C24#41×C3112yes—
869C24C24×C3111yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
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—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—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C3112yes—
975C22×C4C2×D4×C3112yes—
976C22×C4C2×D4×C3112yes—
977C22×C4C2×D4×C3112yes—
978C22×C4C2×D4×C3112yes—
979C22×C4C2×D4×C3112yes—
980C22×C4#41×C3112yes—
981C22×C4#41×C3112yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—28no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
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—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
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—
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—
1103C23C31×#12314yes—
1104C23C22×D4×C3111yescharacteristic
1105C23C22×D4×C3111yescharacteristic
1106C23C22×D4×C3111yescharacteristic
1107C23C2×#41×C3111yescharacteristic
1108C23C2×#41×C3111yescharacteristic
1109C23C2×#41×C3111yescharacteristic
1110C23C2×#41×C3111yescharacteristic
1111C23C31×H(5,𝔽2)11yescharacteristic
1112C23C31×H(5,𝔽2)11yescharacteristic
1113C23C31×H(5,𝔽2)11yescharacteristic
1114C23C31×H(5,𝔽2)11yescharacteristic
1115C23C31×H(5,𝔽2)11yescharacteristic
1116C23C31×H(5,𝔽2)11yescharacteristic
1117C23C31×H(5,𝔽2)11yescharacteristic
1118C23C31×2−1+411yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—416no—
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—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×C31×#12311yescharacteristic
1253C22C31×#52511yescharacteristic
1254C22C31×#52511yescharacteristic
1255C22C31×#53411yescharacteristic
1256C22C31×#53411yescharacteristic
1257C22C31×#53411yescharacteristic
1258C22C31×#53411yescharacteristic
1259C22C31×#53511yescharacteristic
1260C22C31×#53711yescharacteristic
1261C22C31×#53811yescharacteristic
1262C22C31×#53811yescharacteristic
1263C22C31×#53811yescharacteristic
1264C22C31×#53811yescharacteristic
1265C22C31×#53811yescharacteristic
1266C22C31×#53911yescharacteristic
1267C22C31×#54011yescharacteristic
1268C22C31×#54011yescharacteristic
1269C22C31×#54011yescharacteristic
1270C22C31×#54211yescharacteristic
1271C22D42×C3111yescharacteristic
1272C22D42×C3111yescharacteristic
1273C22D42×C3111yescharacteristic
1274C22C31×#54611yescharacteristic
1275C22C31×#54611yescharacteristic
1276C22C31×#54611yescharacteristic
1277C22C31×#54711yescharacteristic
1278C22C31×#54811yescharacteristic
1279C22C31×#55011yescharacteristic
1280C22C31×#55111yescharacteristic
1281C22C31×#55311yescharacteristic
1282C22C31×#55311yescharacteristic
1283C22C31×#56011yescharacteristic
1284C22C31×H(3,𝔽4)11yescharacteristic
1285C22C31×#56211yescharacteristic
1286C22C31×#56211yescharacteristic
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C31×#241811yescharacteristic
1303C2C31×#244311yescharacteristic
1304C2C31×#245611yescharacteristic
1305C2C31×#262211yescharacteristic
1306C2C31×#263011yescharacteristic
1307C2C31×#263511yescharacteristic
1308C2C31×#267111yescharacteristic
1309C2C31×#267311yescharacteristic
1310C2C31×#267611yescharacteristic
1311C2C31×#267911yescharacteristic
1312C2C31×#268811yescharacteristic
1313C2C31×#270111yescharacteristic
1314C2C31×#273011yescharacteristic
1315C2C31×#275311yescharacteristic
1316C2C31×#282411yescharacteristic
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
2. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C31×#1445C2semidirect
8. C31×#1442C2semidirect
9. C31×#1440C2semidirect
10. C31×#1440C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1439C2semidirect
14. C31×#1438C2semidirect
15. C31×#1438C2semidirect
108. C2×C4⋊C4×C31D4semidirect
150. C2×C22⋊C4×C31D4semidirect
340. #16266C31direct (N × H)
549. C2×#394C2×C31semidirect
550. C2×#394C2×C31semidirect
552. C2×#386C2×C31semidirect
553. C2×#386C2×C31semidirect
554. C2×#385C2×C31semidirect
555. #1445C2×C31semidirect
556. #1442C2×C31semidirect
557. #1440C2×C31semidirect
558. #1440C2×C31semidirect
559. #1439C2×C31semidirect
560. #1439C2×C31semidirect
561. #1439C2×C31semidirect
562. #1438C2×C31semidirect
563. #1438C2×C31semidirect
766. C2×C4⋊C4D4×C31semidirect
808. C2×C22⋊C4D4×C31semidirect
823. C31#16266direct (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
C2×C31×#3852
C31×#14452
C31×#14422
C31×#14402
C31×#14392
C31×#14382
#1626631