Finite Group Databasebeta

← C31×#24427 #21481186

Subgroups — C31×#24427 #21481186

Order 7936.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic
2C2×C31×#465C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic, complemented
4C2×C31×#452C211yesmaximal, characteristic, complemented
5C2×C31×#416C211yesmaximal, characteristic, complemented
6C31×#2415C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2014C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1865C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C31×#550—24no—
23C31×#550—24no—
24C2×C31×#127—21no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×#121—21no—
29C2×C31×#121—21no—
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C2×C4×D4×C31—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic
36C31×#465—24no—
37C31×#452—24no—
38C31×#452—24no—
39C2×C31×#106C2211yescharacteristic
40C31×#416—24no—
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×#102C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#397—21no—
55C31×#394—21no—
56C31×#391C2211yescharacteristic
57C31×#389—21no—
58C31×#389C2211yescharacteristic
59C31×#388—21no—
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
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—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31D414yes—
77C22×Q8×C31C2311yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31D411yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C2×Q16×C31—22no—
93C2×Q16×C31—22no—
94C2×Q16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—41no—
99C2×SD16×C31—41no—
100C2×SD16×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×#127—28no—
109C31×#127—22no—
110C31×#127—22no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—41no—
115C31×#121—28no—
116C31×#121—28no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121D414yes—
121C4×Q8×C31—22no—
122C4×Q8×C31—22no—
123C4×D4×C31—28no—
124C4×D4×C31—22no—
125C4×D4×C31—22no—
126C31×#117—22no—
127C31×#117—41no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31D411yescharacteristic
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×C31D411yescharacteristic
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C42×C31—21no—
146C2×C42×C31—21no—
147C2×C42×C31C2311yescharacteristic
148C31×#106—22no—
149C31×#103—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103D414yescomplemented
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—41no—
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—41no—
162C31×#95—21no—
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170#41×C31—28no—
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—21no—
179C2×Q8×C31—21no—
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×C31C2×D412yes—
188C2×Q8×C31C2×D412yes—
189C2×Q8×C31#4112yes—
190C2×D4×C31—24no—
191C2×D4×C31—24no—
192C2×D4×C31—22no—
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—24no—
196C2×D4×C31—24no—
197C2×D4×C31—22no—
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—41no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—81no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31—81no—
219C2×D4×C31—81no—
220C2×D4×C31—81no—
221C2×D4×C31C2×D412yes—
222C2×D4×C31C2×D412yes—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—24no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—24no—
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—42no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31—42no—
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2×D412yes—
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2411yescharacteristic
252Q16×C31—44no—
253SD16×C31—44no—
254SD16×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—21no—
266C2×C8×C31—44no—
267C2×C8×C31C2×D412yes—
268C4⋊C4×C31—24no—
269C4⋊C4×C31—22no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—42no—
277C4⋊C4×C31—42no—
278C4⋊C4×C31—42no—
279C4⋊C4×C31C2×D412yes—
280C4⋊C4×C31C2×D412yes—
281C22⋊C4×C31—24no—
282C22⋊C4×C31—22no—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—22no—
285C22⋊C4×C31—42no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—42no—
288C22⋊C4×C31—42no—
289C42×C31—24no—
290C42×C31—21no—
291C42×C31—21no—
292C42×C31—42no—
293#24427C3111yesmaximal, characteristic, direct product factor, Sylow
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31#12012yes—
322C23×C31C22×D411yescharacteristic
323Q8×C31—22no—
324Q8×C31—22no—
325Q8×C31—22no—
326Q8×C31—41no—
327Q8×C31—41no—
328Q8×C31—41no—
329Q8×C31—41no—
330Q8×C31#12114yes—
331D4×C31—22no—
332D4×C31—22no—
333D4×C31—22no—
334D4×C31—22no—
335D4×C31—44no—
336D4×C31—48no—
337D4×C31—48no—
338D4×C31—48no—
339D4×C31—41no—
340D4×C31—41no—
341D4×C31—41no—
342D4×C31—41no—
343D4×C31—84no—
344D4×C31—84no—
345D4×C31—84no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—21no—
349C2×C4×C31—22no—
350C2×C4×C31—21no—
351C2×C4×C31—22no—
352C2×C4×C31—21no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—21no—
358C2×C4×C31—22no—
359C2×C4×C31—21no—
360C2×C4×C31—22no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—48no—
366C2×C4×C31—48no—
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#12012yes—
385C2×C4×C31#13512yes—
386C2×C4×C31C22×D411yescharacteristic
387C2×C4×C31C22×D411yescharacteristic
388C2×C4×C31C22×D411yescharacteristic
389C2×C4×C31C2×#4111yescharacteristic
390C2×C4×C31H(5,𝔽2)11yescharacteristic
391C2×C4×C31H(5,𝔽2)11yescharacteristic
392C8×C31—22no—
393C8×C31—41no—
394C8×C31—41no—
395C8×C31—41no—
396C2×#550C2×C3111yescharacteristic
397C2×#465C2×C3111yescharacteristic, complemented
398C2×#452C2×C3111yescharacteristic, complemented
399C2×#452C2×C3111yescharacteristic, complemented
400C2×#416C2×C3111yescharacteristic, complemented
401#2415C2×C3111yescharacteristic, complemented
402#2041C2×C3111yescharacteristic, complemented
403#2034C2×C3111yescharacteristic, complemented
404#2014C2×C3111yescharacteristic, complemented
405#2000C2×C3111yescharacteristic, complemented
406#1878C2×C3111yescharacteristic, complemented
407#1875C2×C3111yescharacteristic, complemented
408#1869C2×C3111yescharacteristic, complemented
409#1865C2×C3111yescharacteristic, complemented
410#1788C2×C3111yescharacteristic, complemented
411C22×C31—22no—
412C22×C31—22no—
413C22×C31—22no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—41no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—41no—
421C22×C31—41no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—41no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—81no—
439C22×C31C2×#12011yescharacteristic
440C22×C31D4211yescharacteristic
441C22×C31#54611yescharacteristic
442C22×C31C2×#13511yescharacteristic
443C22×C31#57511yescharacteristic
444C22×C31#57711yescharacteristic
445C22×C31#57711yescharacteristic
446C4×C31—22no—
447C4×C31—24no—
448C4×C31—22no—
449C4×C31—41no—
450C4×C31—41no—
451C4×C31—42no—
452C4×C31—42no—
453C4×C31—81no—
454C4×C31—81no—
455C4×C31—81no—
456C4×C31C2×#12111yescharacteristic
457C4×C31#53411yescharacteristic
458C4×C31D4211yescharacteristic
459C4×C31#54611yescharacteristic
460C22×#41C22×C3111yescharacteristic
461C22×#41C22×C3111yescharacteristic
462C22×Q16C22×C3111yescharacteristic
463C22×SD16C22×C3111yescharacteristic
464C22×SD16C22×C3111yescharacteristic
465C23×C8C22×C3111yescharacteristic
466#550—24no—
467#550—24no—
468C2×#127—21no—
469C2×#127C22×C3111yescharacteristic
470C2×C22⋊Q8C22×C3111yescharacteristic
471C2×C22⋊Q8C22×C3111yescharacteristic
472C2×#121—21no—
473C2×#121—21no—
474C2×#121C22×C3111yescharacteristic
475C2×#121C22×C3111yescharacteristic
476C2×C4×Q8C22×C3111yescharacteristic
477C2×C4×D4—21no—
478C2×C4×D4C22×C3111yescharacteristic
479C2×#117C22×C3111yescharacteristic
480#465—24no—
481#452—24no—
482#452—24no—
483C2×#106C22×C3111yescharacteristic
484#416—24no—
485C2×#103C22×C3111yescharacteristic
486C2×#103C22×C3111yescharacteristic
487C2×#103C22×C3111yescharacteristic
488C2×#103C22×C3111yescharacteristic
489C2×#102C22×C3111yescharacteristic
490C2×#102C22×C3111yescharacteristic
491C2×#102C22×C3111yescharacteristic
492C2×#102C22×C3111yescharacteristic
493C2×#102C22×C3111yescharacteristic
494C2×#102C22×C3111yescharacteristic
495C2×C22⋊C8C22×C3111yescharacteristic
496C2×C22⋊C8C22×C3111yescharacteristic
497C2×C22⋊C8C22×C3111yescharacteristic
498#397—21no—
499#394—21no—
500#391C22×C3111yescharacteristic
501#389—21no—
502#389C22×C3111yescharacteristic
503#388—21no—
504#380C22×C3111yescharacteristic
505#340C22×C3111yescharacteristic
506#340C22×C3111yescharacteristic
507#336C22×C3111yescharacteristic
508#336C22×C3111yescharacteristic
509C2×C31—42no—
510C2×C31—81no—
511C2×C31—82no—
512C2×C31—82no—
513C2×C31#241011yescharacteristic
514C2×C31#300211yescharacteristic
515C2×C31#300911yescharacteristic
516C2×C31#327111yescharacteristic
517C2×C31#328411yescharacteristic
518C2×C31#330411yescharacteristic
519C2×C31#331711yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C3114yes—
532C22×Q8C23×C3111yescharacteristic
533C22×Q8C23×C3111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C3111yescharacteristic
541C22×D4C23×C3111yescharacteristic
542C22×D4C23×C3111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3111yescharacteristic
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8C23×C3111yescharacteristic
560C22×C8C23×C3111yescharacteristic
561C22×C8C23×C3111yescharacteristic
562C22×C8C23×C3111yescharacteristic
563#127—28no—
564#127—22no—
565#127—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570#121—28no—
571#121—28no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121D4×C3114yes—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—28no—
579C4×D4—22no—
580C4×D4—22no—
581#117—22no—
582#117—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C3111yescharacteristic
588C2×C4⋊C4C23×C3111yescharacteristic
589C2×C4⋊C4C23×C3111yescharacteristic
590C2×C4⋊C4C23×C3111yescharacteristic
591C2×C4⋊C4C23×C3111yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4D4×C3111yescharacteristic
599C2×C22⋊C4D4×C3111yescharacteristic
600C2×C42—21no—
601C2×C42—21no—
602C2×C42C23×C3111yescharacteristic
603#106—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103D4×C3114yescomplemented
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—41no—
614C22⋊C8—22no—
615C22⋊C8—22no—
616C22⋊C8—41no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621C31#2442711yescharacteristic, direct product factor, Sylow
622C24—21no—
623C24—21no—
624C24C2×D4×C3111yescharacteristic
625C24C2×D4×C3111yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C3112yes—
644C2×Q8C2×D4×C3112yes—
645C2×Q8#41×C3112yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C3112yes—
678C2×D4C2×D4×C3112yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
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—42no—
700C22×C4—42no—
701C22×C4C2×D4×C3111yescharacteristic
702C22×C4C2×D4×C3111yescharacteristic
703C22×C4C2×D4×C3111yescharacteristic
704C22×C4C2×D4×C3112yes—
705C22×C4C2×D4×C3112yes—
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C24×C3111yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711C2×C8—21no—
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—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C3112yes—
736C4⋊C4C2×D4×C3112yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23C31×#12012yes—
777C23C22×D4×C3111yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8C31×#12114yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
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×C4C31×#12012yes—
840C2×C4C31×#13512yes—
841C2×C4C22×D4×C3111yescharacteristic
842C2×C4C22×D4×C3111yescharacteristic
843C2×C4C22×D4×C3111yescharacteristic
844C2×C4C2×#41×C3111yescharacteristic
845C2×C4C31×H(5,𝔽2)11yescharacteristic
846C2×C4C31×H(5,𝔽2)11yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×C31×#12011yescharacteristic
880C22D42×C3111yescharacteristic
881C22C31×#54611yescharacteristic
882C22C2×C31×#13511yescharacteristic
883C22C31×#57511yescharacteristic
884C22C31×#57711yescharacteristic
885C22C31×#57711yescharacteristic
886C4—22no—
887C4—24no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×C31×#12111yescharacteristic
897C4C31×#53411yescharacteristic
898C4D42×C3111yescharacteristic
899C4C31×#54611yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2C31×#241011yescharacteristic
905C2C31×#300211yescharacteristic
906C2C31×#300911yescharacteristic
907C2C31×#327111yescharacteristic
908C2C31×#328411yescharacteristic
909C2C31×#330411yescharacteristic
910C2C31×#331711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#465C2semidirect
3. C2×C31×#452C2semidirect
4. C2×C31×#452C2semidirect
5. C2×C31×#416C2semidirect
6. C31×#2415C2semidirect
7. C31×#2041C2semidirect
8. C31×#2034C2semidirect
9. C31×#2014C2semidirect
10. C31×#2000C2semidirect
11. C31×#1878C2semidirect
12. C31×#1875C2semidirect
13. C31×#1869C2semidirect
14. C31×#1865C2semidirect
15. C31×#1788C2semidirect
152. C31×#103D4semidirect
293. #24427C31direct (N × H)
397. C2×#465C2×C31semidirect
398. C2×#452C2×C31semidirect
399. C2×#452C2×C31semidirect
400. C2×#416C2×C31semidirect
401. #2415C2×C31semidirect
402. #2041C2×C31semidirect
403. #2034C2×C31semidirect
404. #2014C2×C31semidirect
405. #2000C2×C31semidirect
406. #1878C2×C31semidirect
407. #1875C2×C31semidirect
408. #1869C2×C31semidirect
409. #1865C2×C31semidirect
410. #1788C2×C31semidirect
607. #103D4×C31semidirect
621. C31#24427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5502
C2×C31×#4652
C2×C31×#4522
C2×C31×#4162
C31×#24152
C31×#20412
C31×#20342
C31×#20142
C31×#20002
C31×#18782
C31×#18752
C31×#18692
C31×#18652
C31×#17882
#2442731