Finite Group Databasebeta

← C31×#24393 #21481152

Subgroups — C31×#24393 #21481152

Order 7936.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#537C211yesmaximal, characteristic
2C2×C31×#468C211yesmaximal, characteristic, complemented
3C2×C31×#467C211yesmaximal, characteristic, complemented
4C2×C31×#452C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic, complemented
6C31×#2616C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2001C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1872C211yesmaximal, characteristic, complemented
14C31×#1852C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C31×#537—24no—
23C31×#537—24no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×C22⋊Q8C2211yescharacteristic
30C2×C31×#121—21no—
31C2×C31×#121—21no—
32C2×C31×#121—21no—
33C2×C31×#121C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C31×#468—24no—
37C31×#467—24no—
38C31×#452—24no—
39C2×C31×#107C2211yescharacteristic
40C2×C31×#107C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#103C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C31×#408—24no—
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#395—21no—
55C31×#394—21no—
56C31×#394—21no—
57C31×#394—21no—
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C31×#340C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31—41no—
77C22×Q8×C31D411yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31D411yescharacteristic
84C22×D4×C31D411yescharacteristic
85C22×D4×C31D411yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C2×Q16×C31—22no—
93C2×Q16×C31—22no—
94C2×Q16×C31—41no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—41no—
98C2×M16×C31—22no—
99C2×M16×C31—22no—
100C2×M16×C31—41no—
101C22×C8×C31—22no—
102C22×C8×C31—22no—
103C22×C8×C31—41no—
104C22×C8×C31C2311yescharacteristic
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C31×C22⋊Q8—28no—
109C31×C22⋊Q8—22no—
110C31×C22⋊Q8—22no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8—22no—
116C31×C22⋊Q8—41no—
117C31×C22⋊Q8—41no—
118C31×C22⋊Q8D414yes—
119C31×#121—28no—
120C31×#121—28no—
121C31×#121—28no—
122C31×#121—22no—
123C31×#121—22no—
124C31×#121—22no—
125C31×#121D414yes—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—22no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31—21no—
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
149C31×#107—22no—
150C31×#107—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—22no—
155C31×#103—41no—
156C31×#102—22no—
157C31×#102—22no—
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—21no—
167C24×C31C2×D411yescharacteristic
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175#41×C31—44no—
176#41×C31—44no—
177#41×C31—44no—
178C2×Q8×C31—22no—
179C2×Q8×C31—22no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—41no—
192C2×Q8×C31C2×D412yes—
193C2×D4×C31—24no—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—24no—
199C2×D4×C31—24no—
200C2×D4×C31—22no—
201C2×D4×C31—22no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—41no—
208C2×D4×C31—41no—
209C2×D4×C31—41no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—81no—
213C2×D4×C31—81no—
214C2×D4×C31—81no—
215C2×D4×C31—81no—
216C2×D4×C31C2×D412yes—
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—24no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—24no—
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—42no—
241C22×C4×C31—42no—
242C22×C4×C31—81no—
243C22×C4×C31—81no—
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D412yes—
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D412yes—
250C22×C4×C31#4112yes—
251C22×C4×C31C2411yescharacteristic
252Q16×C31—44no—
253SD16×C31—44no—
254M16×C31—44no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—44no—
266C2×C8×C31C2×D412yes—
267C2×C8×C31C2×D412yes—
268C4⋊C4×C31—24no—
269C4⋊C4×C31—24no—
270C4⋊C4×C31—24no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—42no—
280C4⋊C4×C31—42no—
281C4⋊C4×C31—42no—
282C4⋊C4×C31C2×D412yes—
283C4⋊C4×C31C2×D412yes—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—24no—
286C22⋊C4×C31—24no—
287C22⋊C4×C31—24no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—42no—
290C22⋊C4×C31—42no—
291C22⋊C4×C31—81no—
292C22⋊C4×C31—81no—
293C22⋊C4×C31—81no—
294#24393C3111yesmaximal, characteristic, direct product factor, Sylow
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—22no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—21no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31#12012yes—
322C23×C31#12112yes—
323C23×C31C22×D411yescharacteristic
324Q8×C31—22no—
325Q8×C31—22no—
326Q8×C31—44no—
327Q8×C31—41no—
328Q8×C31—41no—
329Q8×C31—41no—
330Q8×C31—41no—
331Q8×C31—41no—
332Q8×C31—41no—
333D4×C31—22no—
334D4×C31—22no—
335D4×C31—44no—
336D4×C31—44no—
337D4×C31—44no—
338D4×C31—48no—
339D4×C31—41no—
340D4×C31—41no—
341D4×C31—84no—
342D4×C31—84no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—48no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—84no—
385C2×C4×C31#12012yes—
386C2×C4×C31#12112yes—
387C2×C4×C31C22×D411yescharacteristic
388C2×C4×C31C22×D411yescharacteristic
389C2×C4×C31C22×D411yescharacteristic
390C2×C4×C31C2×#4111yescharacteristic
391C2×C4×C31H(5,𝔽2)11yescharacteristic
392C2×C4×C31H(5,𝔽2)11yescharacteristic
393C8×C31—22no—
394C8×C31—22no—
395C8×C31—41no—
396C8×C31—41no—
397C2×#537C2×C3111yescharacteristic
398C2×#468C2×C3111yescharacteristic, complemented
399C2×#467C2×C3111yescharacteristic, complemented
400C2×#452C2×C3111yescharacteristic, complemented
401C2×#408C2×C3111yescharacteristic, complemented
402#2616C2×C3111yescharacteristic, complemented
403#2036C2×C3111yescharacteristic, complemented
404#2033C2×C3111yescharacteristic, complemented
405#2001C2×C3111yescharacteristic, complemented
406#2000C2×C3111yescharacteristic, complemented
407#1894C2×C3111yescharacteristic, complemented
408#1893C2×C3111yescharacteristic, complemented
409#1872C2×C3111yescharacteristic, complemented
410#1852C2×C3111yescharacteristic, complemented
411#1788C2×C3111yescharacteristic, complemented
412C22×C31—22no—
413C22×C31—22no—
414C22×C31—22no—
415C22×C31—22no—
416C22×C31—22no—
417C22×C31—22no—
418C22×C31—41no—
419C22×C31—41no—
420C22×C31—41no—
421C22×C31—41no—
422C22×C31—41no—
423C22×C31—41no—
424C22×C31—41no—
425C22×C31—41no—
426C22×C31—42no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—42no—
432C22×C31—41no—
433C22×C31—42no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—81no—
439C22×C31—81no—
440C22×C31C2×#12011yescharacteristic
441C22×C31C2×#12111yescharacteristic
442C22×C31#53411yescharacteristic
443C22×C31#57611yescharacteristic
444C22×C31#57711yescharacteristic
445C22×C31#57811yescharacteristic
446C22×C31#57811yescharacteristic
447C4×C31—22no—
448C4×C31—22no—
449C4×C31—41no—
450C4×C31—42no—
451C4×C31—42no—
452C4×C31—42no—
453C4×C31—81no—
454C4×C31—81no—
455C4×C31—81no—
456C4×C31—81no—
457C4×C31D4211yescharacteristic
458C4×C31D4211yescharacteristic
459C4×C31#54611yescharacteristic
460C4×C31#54611yescharacteristic
461C22×#41C22×C3111yescharacteristic
462C22×#41C22×C3111yescharacteristic
463C22×Q16C22×C3111yescharacteristic
464C22×SD16C22×C3111yescharacteristic
465C22×M16C22×C3111yescharacteristic
466C23×C8C22×C3111yescharacteristic
467#537—24no—
468#537—24no—
469C2×C22⋊Q8—21no—
470C2×C22⋊Q8C22×C3111yescharacteristic
471C2×C22⋊Q8C22×C3111yescharacteristic
472C2×C22⋊Q8C22×C3111yescharacteristic
473C2×C22⋊Q8C22×C3111yescharacteristic
474C2×C22⋊Q8C22×C3111yescharacteristic
475C2×#121—21no—
476C2×#121—21no—
477C2×#121—21no—
478C2×#121C22×C3111yescharacteristic
479C2×#121C22×C3111yescharacteristic
480C22×C4⋊C4C22×C3111yescharacteristic
481#468—24no—
482#467—24no—
483#452—24no—
484C2×#107C22×C3111yescharacteristic
485C2×#107C22×C3111yescharacteristic
486C2×#103C22×C3111yescharacteristic
487C2×#103C22×C3111yescharacteristic
488C2×#103C22×C3111yescharacteristic
489C2×#103C22×C3111yescharacteristic
490C2×#103C22×C3111yescharacteristic
491C2×#102C22×C3111yescharacteristic
492C2×#102C22×C3111yescharacteristic
493C2×#102C22×C3111yescharacteristic
494#408—24no—
495C2×C22⋊C8C22×C3111yescharacteristic
496C2×C22⋊C8C22×C3111yescharacteristic
497C2×C22⋊C8C22×C3111yescharacteristic
498C2×C22⋊C8C22×C3111yescharacteristic
499#395—21no—
500#394—21no—
501#394—21no—
502#394—21no—
503#380C22×C3111yescharacteristic
504#380C22×C3111yescharacteristic
505#380C22×C3111yescharacteristic
506#340C22×C3111yescharacteristic
507#340C22×C3111yescharacteristic
508#340C22×C3111yescharacteristic
509#340C22×C3111yescharacteristic
510C2×C31—42no—
511C2×C31—42no—
512C2×C31—81no—
513C2×C31—82no—
514C2×C31#241011yescharacteristic
515C2×C31#301111yescharacteristic
516C2×C31#301211yescharacteristic
517C2×C31#306111yescharacteristic
518C2×C31#306311yescharacteristic
519C2×C31#320111yescharacteristic
520C2×C31#320311yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C22×Q8D4×C3111yescharacteristic
534C22×Q8C23×C3111yescharacteristic
535C22×Q8C23×C3111yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C3111yescharacteristic
540C22×D4D4×C3111yescharacteristic
541C22×D4D4×C3111yescharacteristic
542C22×D4C23×C3111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3111yescharacteristic
547C23×C4C23×C3111yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×M16—22no—
555C2×M16—22no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C3111yescharacteristic
561C22×C8C23×C3111yescharacteristic
562C22×C8C23×C3111yescharacteristic
563C22×C8C23×C3111yescharacteristic
564C22⋊Q8—28no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8D4×C3114yes—
575#121—28no—
576#121—28no—
577#121—28no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121D4×C3114yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C4⋊C4C23×C3111yescharacteristic
593C2×C4⋊C4C23×C3111yescharacteristic
594C2×C4⋊C4C23×C3111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605#107—22no—
606#107—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8D4×C3114yescomplemented
619#95—21no—
620#95—21no—
621#95—21no—
622C31#2439311yescharacteristic, direct product factor, Sylow
623C24—21no—
624C24C2×D4×C3111yescharacteristic
625C24C2×D4×C3111yescharacteristic
626C24C2×D4×C3111yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C3112yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C3112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C3111yescharacteristic
702C22×C4C2×D4×C3111yescharacteristic
703C22×C4C2×D4×C3112yes—
704C22×C4C2×D4×C3112yes—
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3112yes—
707C22×C4#41×C3112yes—
708C22×C4C24×C3111yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C3112yes—
724C2×C8C2×D4×C3112yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C3112yes—
740C4⋊C4C2×D4×C3112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23C31×#12012yes—
778C23C31×#12112yes—
779C23C22×D4×C3111yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4C31×#12012yes—
842C2×C4C31×#12112yes—
843C2×C4C22×D4×C3111yescharacteristic
844C2×C4C22×D4×C3111yescharacteristic
845C2×C4C22×D4×C3111yescharacteristic
846C2×C4C2×#41×C3111yescharacteristic
847C2×C4C31×H(5,𝔽2)11yescharacteristic
848C2×C4C31×H(5,𝔽2)11yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×C31×#12011yescharacteristic
882C22C2×C31×#12111yescharacteristic
883C22C31×#53411yescharacteristic
884C22C31×#57611yescharacteristic
885C22C31×#57711yescharacteristic
886C22C31×#57811yescharacteristic
887C22C31×#57811yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C3111yescharacteristic
899C4D42×C3111yescharacteristic
900C4C31×#54611yescharacteristic
901C4C31×#54611yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C31×#241011yescharacteristic
907C2C31×#301111yescharacteristic
908C2C31×#301211yescharacteristic
909C2C31×#306111yescharacteristic
910C2C31×#306311yescharacteristic
911C2C31×#320111yescharacteristic
912C2C31×#320311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#537C2
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
2. C2×C31×#468C2semidirect
3. C2×C31×#467C2semidirect
4. C2×C31×#452C2semidirect
5. C2×C31×#408C2semidirect
6. C31×#2616C2semidirect
7. C31×#2036C2semidirect
8. C31×#2033C2semidirect
9. C31×#2001C2semidirect
10. C31×#2000C2semidirect
11. C31×#1894C2semidirect
12. C31×#1893C2semidirect
13. C31×#1872C2semidirect
14. C31×#1852C2semidirect
15. C31×#1788C2semidirect
162. C31×C22⋊C8D4semidirect
294. #24393C31direct (N × H)
398. C2×#468C2×C31semidirect
399. C2×#467C2×C31semidirect
400. C2×#452C2×C31semidirect
401. C2×#408C2×C31semidirect
402. #2616C2×C31semidirect
403. #2036C2×C31semidirect
404. #2033C2×C31semidirect
405. #2001C2×C31semidirect
406. #2000C2×C31semidirect
407. #1894C2×C31semidirect
408. #1893C2×C31semidirect
409. #1872C2×C31semidirect
410. #1852C2×C31semidirect
411. #1788C2×C31semidirect
618. C22⋊C8D4×C31semidirect
622. C31#24393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C2×C31×#4682
C2×C31×#4672
C2×C31×#4522
C2×C31×#4082
C31×#26162
C31×#20362
C31×#20332
C31×#20012
C31×#20002
C31×#18942
C31×#18932
C31×#18722
C31×#18522
C31×#17882
#2439331