Finite Group Databasebeta

← C31×#24390 #21481149

Subgroups — C31×#24390 #21481149

Order 7936.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#535C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#466C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic, complemented
6C31×#2615C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1999C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1875C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic, complemented
21C23×C8×C31C2211yescharacteristic, complemented
22C31×#535—24no—
23C31×#535—24no—
24C2×C31×#127—21no—
25C2×C31×#124—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic, complemented
32C2×C31×#121C2211yescharacteristic, complemented
33C2×C31×#120—21no—
34C2×C31×#120—21no—
35C2×C31×#117C2211yescharacteristic
36C31×#469—24no—
37C31×#466—24no—
38C31×#447—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C2×C31×#106C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C31×#408—24no—
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#393—21no—
55C31×#392—21no—
56C31×#392—21no—
57C31×#392—21no—
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic, complemented
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31D411yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—22no—
84C22×D4×C31—22no—
85C22×D4×C31—41no—
86C22×D4×C31—41no—
87C22×D4×C31D411yescharacteristic
88C22×D4×C31D411yescharacteristic
89C22×D4×C31D411yescharacteristic
90C22×D4×C31C2311yescharacteristic
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C2×D8×C31—22no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C2×D8×C31—41no—
102C2×M16×C31—22no—
103C2×M16×C31—22no—
104C2×M16×C31—41no—
105C22×C8×C31—22no—
106C22×C8×C31—22no—
107C22×C8×C31—41no—
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C31×#127—28no—
113C31×#124—28no—
114C31×#121—22no—
115C31×#121—22no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121—22no—
124C31×#121—41no—
125C31×#121—41no—
126C31×#121D414yescomplemented
127C31×#121D414yescomplemented
128C31×#120—28no—
129C31×#120—28no—
130C31×#117—22no—
131C31×#117—22no—
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C42×C31—21no—
149C31×#107—22no—
150C31×#106—22no—
151C31×#102—22no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—41no—
158C31×#102—41no—
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8D414yescomplemented
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—24no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—81no—
173C24×C31—81no—
174C24×C31—81no—
175C24×C31—81no—
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D411yescharacteristic
178C24×C31C2×D411yescharacteristic
179#41×C31—44no—
180#41×C31—44no—
181#41×C31—44no—
182#41×C31—44no—
183C2×Q8×C31—22no—
184C2×Q8×C31—22no—
185C2×Q8×C31—41no—
186C2×D4×C31—24no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—24no—
192C2×D4×C31—24no—
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—41no—
218C2×D4×C31—41no—
219C2×D4×C31—41no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
222C2×D4×C31—42no—
223C2×D4×C31—42no—
224C2×D4×C31—42no—
225C2×D4×C31—81no—
226C2×D4×C31—81no—
227C2×D4×C31—81no—
228C2×D4×C31—81no—
229C2×D4×C31—81no—
230C2×D4×C31—81no—
231C2×D4×C31—81no—
232C2×D4×C31—81no—
233C2×D4×C31—81no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31—81no—
237C2×D4×C31—81no—
238C2×D4×C31—81no—
239C2×D4×C31C2×D412yes—
240C2×D4×C31C2×D412yes—
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×C31C2×D411yescharacteristic
261C22×C4×C31C2×D411yescharacteristic
262C22×C4×C31C2×D412yes—
263C22×C4×C31C2×D412yes—
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2×D412yes—
266C22×C4×C31#4112yes—
267C22×C4×C31C2411yescharacteristic
268D8×C31—44no—
269D8×C31—44no—
270M16×C31—44no—
271C2×C8×C31—21no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—21no—
276C2×C8×C31—21no—
277C2×C8×C31—21no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—44no—
282C2×C8×C31C2×D412yes—
283C2×C8×C31C2×D412yes—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31C2×D412yes—
293C4⋊C4×C31C2×D412yes—
294C22⋊C4×C31—24no—
295C22⋊C4×C31—24no—
296C22⋊C4×C31—24no—
297C22⋊C4×C31—24no—
298C22⋊C4×C31—24no—
299C22⋊C4×C31—42no—
300C22⋊C4×C31—42no—
301C22⋊C4×C31—42no—
302C22⋊C4×C31—81no—
303C22⋊C4×C31—81no—
304C22⋊C4×C31—81no—
305C42×C31—24no—
306#24390C3111yesmaximal, characteristic, direct product factor, Sylow
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—21no—
325C23×C31—21no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—48no—
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—84no—
349C23×C31—84no—
350C23×C31—84no—
351C23×C31—84no—
352C23×C31—84no—
353C23×C31—84no—
354C23×C31#12012yes—
355C23×C31#12112yes—
356C23×C31C22×D411yescharacteristic
357Q8×C31—44no—
358D4×C31—22no—
359D4×C31—22no—
360D4×C31—22no—
361D4×C31—22no—
362D4×C31—44no—
363D4×C31—44no—
364D4×C31—48no—
365D4×C31—44no—
366D4×C31—41no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—41no—
374D4×C31—84no—
375D4×C31—84no—
376D4×C31—84no—
377D4×C31—84no—
378D4×C31—84no—
379D4×C31—84no—
380D4×C31—84no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
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—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
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#12012yes—
416C2×C4×C31#12112yes—
417C2×C4×C31C22×D411yescharacteristic
418C2×C4×C31C22×D411yescharacteristic
419C2×C4×C31C22×D411yescharacteristic
420C2×C4×C31C2×#4111yescharacteristic
421C2×C4×C31H(5,𝔽2)11yescharacteristic
422C2×C4×C31H(5,𝔽2)11yescharacteristic
423C8×C31—22no—
424C8×C31—22no—
425C8×C31—41no—
426C8×C31—41no—
427C2×#535C2×C3111yescharacteristic, complemented
428C2×#469C2×C3111yescharacteristic, complemented
429C2×#466C2×C3111yescharacteristic, complemented
430C2×#447C2×C3111yescharacteristic, complemented
431C2×#408C2×C3111yescharacteristic, complemented
432#2615C2×C3111yescharacteristic, complemented
433#2034C2×C3111yescharacteristic, complemented
434#2033C2×C3111yescharacteristic, complemented
435#1999C2×C3111yescharacteristic, complemented
436#1999C2×C3111yescharacteristic, complemented
437#1895C2×C3111yescharacteristic, complemented
438#1893C2×C3111yescharacteristic, complemented
439#1875C2×C3111yescharacteristic, complemented
440#1854C2×C3111yescharacteristic, complemented
441#1786C2×C3111yescharacteristic, complemented
442C22×C31—22no—
443C22×C31—22no—
444C22×C31—22no—
445C22×C31—22no—
446C22×C31—22no—
447C22×C31—22no—
448C22×C31—41no—
449C22×C31—41no—
450C22×C31—41no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—41no—
457C22×C31—42no—
458C22×C31—42no—
459C22×C31—41no—
460C22×C31—41no—
461C22×C31—41no—
462C22×C31—42no—
463C22×C31—42no—
464C22×C31—41no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—41no—
468C22×C31—41no—
469C22×C31—816no—
470C22×C31—81no—
471C22×C31—81no—
472C22×C31—81no—
473C22×C31—81no—
474C22×C31—81no—
475C22×C31—81no—
476C22×C31—81no—
477C22×C31—81no—
478C22×C31—81no—
479C22×C31—81no—
480C22×C31—81no—
481C22×C31—81no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31C2×#12011yescharacteristic
486C22×C31C2×#12111yescharacteristic
487C22×C31#53411yescharacteristic
488C22×C31#57611yescharacteristic
489C22×C31#57611yescharacteristic
490C22×C31#57611yescharacteristic
491C22×C31#57711yescharacteristic
492C4×C31—22no—
493C4×C31—22no—
494C4×C31—41no—
495C4×C31—42no—
496C4×C31—42no—
497C4×C31—81no—
498C4×C31—81no—
499C4×C31—81no—
500C4×C31D4211yescharacteristic
501C4×C31D4211yescharacteristic
502C4×C31#54611yescharacteristic
503C4×C31#54611yescharacteristic
504C22×#41C22×C3111yescharacteristic
505C23×D4C22×C3111yescharacteristic
506C22×D8C22×C3111yescharacteristic
507C22×D8C22×C3111yescharacteristic
508C22×M16C22×C3111yescharacteristic, complemented
509C23×C8C22×C3111yescharacteristic, complemented
510#535—24no—
511#535—24no—
512C2×#127—21no—
513C2×#124—21no—
514C2×#121C22×C3111yescharacteristic
515C2×#121C22×C3111yescharacteristic
516C2×#121C22×C3111yescharacteristic
517C2×#121C22×C3111yescharacteristic
518C2×#121C22×C3111yescharacteristic
519C2×#121C22×C3111yescharacteristic, complemented
520C2×#121C22×C3111yescharacteristic, complemented
521C2×#120—21no—
522C2×#120—21no—
523C2×#117C22×C3111yescharacteristic
524#469—24no—
525#466—24no—
526#447—24no—
527C2×#107C22×C3111yescharacteristic, complemented
528C2×#106C22×C3111yescharacteristic, complemented
529C2×#102C22×C3111yescharacteristic
530C2×#102C22×C3111yescharacteristic
531C2×#102C22×C3111yescharacteristic
532C2×#102C22×C3111yescharacteristic
533C2×#102C22×C3111yescharacteristic
534C2×#102C22×C3111yescharacteristic
535C2×#102C22×C3111yescharacteristic, complemented
536C2×#102C22×C3111yescharacteristic, complemented
537#408—24no—
538C2×C22⋊C8C22×C3111yescharacteristic
539C2×C22⋊C8C22×C3111yescharacteristic
540C2×C22⋊C8C22×C3111yescharacteristic, complemented
541C2×C22⋊C8C22×C3111yescharacteristic, complemented
542#393—21no—
543#392—21no—
544#392—21no—
545#392—21no—
546#380C22×C3111yescharacteristic
547#380C22×C3111yescharacteristic, complemented
548#380C22×C3111yescharacteristic, complemented
549#340C22×C3111yescharacteristic, complemented
550#340C22×C3111yescharacteristic, complemented
551#340C22×C3111yescharacteristic, complemented
552#340C22×C3111yescharacteristic, complemented
553C2×C31—42no—
554C2×C31—42no—
555C2×C31—81no—
556C2×C31—82no—
557C2×C31—82no—
558C2×C31—161no—
559C2×C31#241011yescharacteristic
560C2×C31#300811yescharacteristic
561C2×C31#301211yescharacteristic
562C2×C31#305811yescharacteristic
563C2×C31#306211yescharacteristic
564C2×C31#319811yescharacteristic
565C2×C31#319911yescharacteristic
566C25—21no—
567C2×#41—22no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—41no—
572C2×#41—41no—
573C22×Q8D4×C3111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—22no—
585C22×D4—22no—
586C22×D4—41no—
587C22×D4—41no—
588C22×D4D4×C3111yescharacteristic
589C22×D4D4×C3111yescharacteristic
590C22×D4D4×C3111yescharacteristic
591C22×D4C23×C3111yescharacteristic
592C22×D4C23×C3111yescharacteristic
593C22×D4C23×C3111yescharacteristic
594C23×C4C23×C3111yescharacteristic
595C23×C4C23×C3111yescharacteristic
596C23×C4C23×C3111yescharacteristic
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—41no—
602C2×D8—41no—
603C2×M16—22no—
604C2×M16—22no—
605C2×M16—41no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8—41no—
609C22×C8C23×C3111yescharacteristic
610C22×C8C23×C3111yescharacteristic
611C22×C8C23×C3111yescharacteristic
612C22×C8C23×C3111yescharacteristic
613#127—28no—
614#124—28no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—41no—
626#121—41no—
627#121D4×C3114yescomplemented
628#121D4×C3114yescomplemented
629#120—28no—
630#120—28no—
631#117—22no—
632#117—22no—
633C2×C4⋊C4C23×C3111yescharacteristic
634C2×C4⋊C4C23×C3111yescharacteristic
635C2×C4⋊C4C23×C3111yescharacteristic
636C2×C4⋊C4C23×C3111yescharacteristic
637C2×C4⋊C4C23×C3111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C42—21no—
650#107—22no—
651#106—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—41no—
659#102—41no—
660C22⋊C8—22no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8D4×C3114yescomplemented
664#95—21no—
665#95—21no—
666#95—21no—
667C31#2439011yescharacteristic, direct product factor, Sylow
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C3111yescharacteristic
679C24C2×D4×C3111yescharacteristic
680C24C2×D4×C3111yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C3112yes—
742C2×D4C2×D4×C3112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C3111yescharacteristic
763C22×C4C2×D4×C3111yescharacteristic
764C22×C4C2×D4×C3112yes—
765C22×C4C2×D4×C3112yes—
766C22×C4C2×D4×C3111yescharacteristic
767C22×C4C2×D4×C3112yes—
768C22×C4#41×C3112yes—
769C22×C4C24×C3111yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C3112yes—
785C2×C8C2×D4×C3112yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C3112yes—
795C4⋊C4C2×D4×C3112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23C31×#12012yes—
856C23C31×#12112yes—
857C23C22×D4×C3111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4C31×#12012yes—
917C2×C4C31×#12112yes—
918C2×C4C22×D4×C3111yescharacteristic
919C2×C4C22×D4×C3111yescharacteristic
920C2×C4C22×D4×C3111yescharacteristic
921C2×C4C2×#41×C3111yescharacteristic
922C2×C4C31×H(5,𝔽2)11yescharacteristic
923C2×C4C31×H(5,𝔽2)11yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×C31×#12011yescharacteristic
972C22C2×C31×#12111yescharacteristic
973C22C31×#53411yescharacteristic
974C22C31×#57611yescharacteristic
975C22C31×#57611yescharacteristic
976C22C31×#57611yescharacteristic
977C22C31×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C3111yescharacteristic
987C4D42×C3111yescharacteristic
988C4C31×#54611yescharacteristic
989C4C31×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C31×#241011yescharacteristic
997C2C31×#300811yescharacteristic
998C2C31×#301211yescharacteristic
999C2C31×#305811yescharacteristic
1000C2C31×#306211yescharacteristic
1001C2C31×#319811yescharacteristic
1002C2C31×#319911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#535C2semidirect
2. C2×C31×#469C2semidirect
3. C2×C31×#466C2semidirect
4. C2×C31×#447C2semidirect
5. C2×C31×#408C2semidirect
6. C31×#2615C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1999C2semidirect
10. C31×#1999C2semidirect
11. C31×#1895C2semidirect
12. C31×#1893C2semidirect
13. C31×#1875C2semidirect
14. C31×#1854C2semidirect
15. C31×#1786C2semidirect
20. C22×M16×C31C22semidirect
21. C23×C8×C31C22semidirect
31. C2×C31×#121C22semidirect
32. C2×C31×#121C22semidirect
39. C2×C31×#107C22semidirect
40. C2×C31×#106C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
59. C31×#380C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
126. C31×#121D4semidirect
127. C31×#121D4semidirect
162. C31×C22⋊C8D4semidirect
306. #24390C31direct (N × H)
427. C2×#535C2×C31semidirect
428. C2×#469C2×C31semidirect
429. C2×#466C2×C31semidirect
430. C2×#447C2×C31semidirect
431. C2×#408C2×C31semidirect
432. #2615C2×C31semidirect
433. #2034C2×C31semidirect
434. #2033C2×C31semidirect
435. #1999C2×C31semidirect
436. #1999C2×C31semidirect
437. #1895C2×C31semidirect
438. #1893C2×C31semidirect
439. #1875C2×C31semidirect
440. #1854C2×C31semidirect
441. #1786C2×C31semidirect
508. C22×M16C22×C31semidirect
509. C23×C8C22×C31semidirect
519. C2×#121C22×C31semidirect
520. C2×#121C22×C31semidirect
527. C2×#107C22×C31semidirect
528. C2×#106C22×C31semidirect
535. C2×#102C22×C31semidirect
536. C2×#102C22×C31semidirect
540. C2×C22⋊C8C22×C31semidirect
541. C2×C22⋊C8C22×C31semidirect
547. #380C22×C31semidirect
548. #380C22×C31semidirect
549. #340C22×C31semidirect
550. #340C22×C31semidirect
551. #340C22×C31semidirect
552. #340C22×C31semidirect
627. #121D4×C31semidirect
628. #121D4×C31semidirect
663. C22⋊C8D4×C31semidirect
667. C31#24390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5352
C2×C31×#4692
C2×C31×#4662
C2×C31×#4472
C2×C31×#4082
C31×#26152
C31×#20342
C31×#20332
C31×#19992
C31×#18952
C31×#18932
C31×#18752
C31×#18542
C31×#17862
#2439031