Finite Group Databasebeta

← C31×#25101 #21481860

Subgroups — C31×#25101 #21481860

Order 7936.

1248 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2435C211yesmaximal, characteristic, complemented
6C31×#2363C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1925C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1873C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic, complemented
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic, complemented
26C2×C31×#117C2211yescharacteristic
27C31×#468—24no—
28C31×#463—24no—
29C31×#447—24no—
30C2×C31×#107C2211yescharacteristic, complemented
31C2×C31×C4⋊C8C2211yescharacteristic, complemented
32C2×C31×C4⋊C8C2211yescharacteristic, complemented
33C31×#418—24no—
34C2×C31×#103C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#390—21no—
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic, complemented
51C31×#389C2211yescharacteristic, complemented
52C31×#388—21no—
53C31×#386—21no—
54C31×#379—21no—
55C31×#379—21no—
56C4×C4⋊C4×C31C2211yescharacteristic, complemented
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—41no—
81C2×D8×C31—22no—
82C2×D8×C31—22no—
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—41no—
86C2×D8×C31—41no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
89C2×M16×C31—41no—
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×#124—22no—
95C31×#124—22no—
96C31×#124—41no—
97C31×#124—41no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×#121—22no—
101C31×#121D414yes—
102C4×D4×C31—22no—
103C4×D4×C31—41no—
104C31×#117—22no—
105C31×#117—41no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31C2311yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×C4⋊C8—22no—
134C31×C4⋊C8—41no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—41no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102D414yescomplemented
145C31×C22⋊C8—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—42no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—81no—
159C24×C31—81no—
160C24×C31C2×D411yescharacteristic
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×D4×C31—28no—
168C2×D4×C31—24no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—44no—
185C2×D4×C31—44no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—44no—
189C2×D4×C31—42no—
190C2×D4×C31—81no—
191C2×D4×C31—81no—
192C2×D4×C31C2×D412yes—
193C2×D4×C31C2×D412yes—
194C2×D4×C31#4112yes—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31—81no—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D412yes—
213C22×C4×C31#4112yes—
214C22×C4×C31C2411yescharacteristic
215SD16×C31—44no—
216D8×C31—44no—
217D8×C31—44no—
218M16×C31—44no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31C2×D412yes—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31—81no—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D412yes—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—41no—
243C22⋊C4×C31—41no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—81no—
253C22⋊C4×C31—81no—
254C22⋊C4×C31—81no—
255C22⋊C4×C31—81no—
256C22⋊C4×C31—81no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—21no—
261C42×C31—42no—
262C42×C31—81no—
263#25101C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—48no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—84no—
293C23×C31—84no—
294C23×C31—84no—
295C23×C31—84no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31#12112yes—
299C23×C31C22×D411yescharacteristic
300Q8×C31—41no—
301Q8×C31—41no—
302Q8×C31—41no—
303Q8×C31—41no—
304D4×C31—22no—
305D4×C31—22no—
306D4×C31—22no—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—22no—
310D4×C31—48no—
311D4×C31—41no—
312D4×C31—41no—
313D4×C31—41no—
314D4×C31—41no—
315D4×C31—41no—
316D4×C31—41no—
317D4×C31—84no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—84no—
352C2×C4×C31#12112yes—
353C2×C4×C31C22×D411yescharacteristic
354C2×C4×C31C22×D411yescharacteristic
355C2×C4×C31C2×#4111yescharacteristic
356C2×C4×C31C2×#4111yescharacteristic
357C2×C4×C31H(5,𝔽2)11yescharacteristic
358C2×C4×C31H(5,𝔽2)11yescharacteristic
359C8×C31—22no—
360C8×C31—41no—
361C8×C31—41no—
362C8×C31—41no—
363C2×#468C2×C3111yescharacteristic, complemented
364C2×#463C2×C3111yescharacteristic, complemented
365C2×#447C2×C3111yescharacteristic
366C2×#418C2×C3111yescharacteristic, complemented
367#2435C2×C3111yescharacteristic, complemented
368#2363C2×C3111yescharacteristic, complemented
369#2067C2×C3111yescharacteristic, complemented
370#2054C2×C3111yescharacteristic, complemented
371#2042C2×C3111yescharacteristic, complemented
372#2012C2×C3111yescharacteristic, complemented
373#1983C2×C3111yescharacteristic, complemented
374#1925C2×C3111yescharacteristic, complemented
375#1879C2×C3111yescharacteristic, complemented
376#1873C2×C3111yescharacteristic, complemented
377#1851C2×C3111yescharacteristic, complemented
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—22no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—42no—
394C22×C31—816no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31—81no—
406C22×C31—81no—
407C22×C31C2×#12111yescharacteristic
408C22×C31D4211yescharacteristic
409C22×C31#54611yescharacteristic
410C22×C31#57511yescharacteristic
411C22×C31#57511yescharacteristic
412C22×C31#57611yescharacteristic
413C22×C31#57611yescharacteristic
414C4×C31—22no—
415C4×C31—41no—
416C4×C31—41no—
417C4×C31—42no—
418C4×C31—42no—
419C4×C31—41no—
420C4×C31—41no—
421C4×C31—81no—
422C4×C31—81no—
423C4×C31—81no—
424C4×C31#52511yescharacteristic
425C4×C31#53811yescharacteristic
426C4×C31D4211yescharacteristic
427C4×C31#54611yescharacteristic
428C23×D4C22×C3111yescharacteristic
429C22×SD16C22×C3111yescharacteristic, complemented
430C22×D8C22×C3111yescharacteristic
431C22×D8C22×C3111yescharacteristic
432C22×M16C22×C3111yescharacteristic
433C2×#124C22×C3111yescharacteristic
434C2×#124C22×C3111yescharacteristic
435C2×C22⋊Q8C22×C3111yescharacteristic
436C2×#121C22×C3111yescharacteristic
437C2×C4×D4C22×C3111yescharacteristic, complemented
438C2×#117C22×C3111yescharacteristic
439#468—24no—
440#463—24no—
441#447—24no—
442C2×#107C22×C3111yescharacteristic, complemented
443C2×C4⋊C8C22×C3111yescharacteristic, complemented
444C2×C4⋊C8C22×C3111yescharacteristic, complemented
445#418—24no—
446C2×#103C22×C3111yescharacteristic, complemented
447C2×#103C22×C3111yescharacteristic, complemented
448C2×#103C22×C3111yescharacteristic, complemented
449C2×#102C22×C3111yescharacteristic
450C2×#102C22×C3111yescharacteristic
451C2×#102C22×C3111yescharacteristic
452C2×#102C22×C3111yescharacteristic
453C2×#102C22×C3111yescharacteristic
454C2×#102C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic, complemented
456C2×C22⋊C8C22×C3111yescharacteristic
457#394—21no—
458#394—21no—
459#390—21no—
460#390C22×C3111yescharacteristic
461#390C22×C3111yescharacteristic
462#390C22×C3111yescharacteristic, complemented
463#389C22×C3111yescharacteristic, complemented
464#388—21no—
465#386—21no—
466#379—21no—
467#379—21no—
468C4×C4⋊C4C22×C3111yescharacteristic, complemented
469C4×C22⋊C4—21no—
470C4×C22⋊C4C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic, complemented
472#340C22×C3111yescharacteristic, complemented
473#336C22×C3111yescharacteristic, complemented
474#336C22×C3111yescharacteristic, complemented
475C2×C31—42no—
476C2×C31—82no—
477C2×C31—82no—
478C2×C31—82no—
479C2×C31#242411yescharacteristic
480C2×C31#304011yescharacteristic
481C2×C31#304111yescharacteristic
482C2×C31#326811yescharacteristic
483C2×C31#327311yescharacteristic
484C2×C31#331911yescharacteristic
485C2×C31#332211yescharacteristic
486C25—21no—
487C22×Q8C23×C3111yescharacteristic
488C22×D4—22no—
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—22no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C23×C3111yescharacteristic
497C22×D4C23×C3111yescharacteristic
498C22×D4C23×C3111yescharacteristic
499C23×C4—21no—
500C23×C4C23×C3111yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—41no—
513C22×C8C23×C3111yescharacteristic
514C22×C8C23×C3111yescharacteristic
515C22×C8C23×C3111yescharacteristic
516C22×C8C23×C3111yescharacteristic
517#124—22no—
518#124—22no—
519#124—41no—
520#124—41no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523#121—22no—
524#121D4×C3114yes—
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4C23×C3111yescharacteristic
532C2×C4⋊C4C23×C3111yescharacteristic
533C2×C4⋊C4C23×C3111yescharacteristic
534C2×C4⋊C4C23×C3111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C3111yescharacteristic
550C2×C22⋊C4D4×C3111yescharacteristic
551C2×C42—21no—
552C2×C42—21no—
553C2×C42C23×C3111yescharacteristic
554C2×C42C23×C3111yescharacteristic
555#107—22no—
556C4⋊C8—22no—
557C4⋊C8—41no—
558#103—22no—
559#103—22no—
560#103—41no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102D4×C3114yescomplemented
568C22⋊C8—22no—
569#95—21no—
570#95—21no—
571#95D4×C3111yescharacteristic
572#95D4×C3111yescharacteristic
573C31#2510111yescharacteristic, direct product factor, Sylow
574C24—21no—
575C24—21no—
576C24—21no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×D4×C3111yescharacteristic
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×D4—28no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4C2×D4×C3112yes—
617C2×D4C2×D4×C3112yes—
618C2×D4#41×C3112yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4C2×D4×C3111yescharacteristic
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C2×D4×C3111yescharacteristic
634C22×C4C2×D4×C3111yescharacteristic
635C22×C4C2×D4×C3111yescharacteristic
636C22×C4C2×D4×C3112yes—
637C22×C4#41×C3112yes—
638C22×C4C24×C3111yescharacteristic
639SD16—44no—
640D8—44no—
641D8—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8C2×D4×C3112yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C3112yes—
664C4⋊C4C2×D4×C3112yes—
665C22⋊C4—24no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—42no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23C31×#12112yes—
722C23C22×D4×C3111yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—84no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4C31×#12112yes—
776C2×C4C22×D4×C3111yescharacteristic
777C2×C4C22×D4×C3111yescharacteristic
778C2×C4C2×#41×C3111yescharacteristic
779C2×C4C2×#41×C3111yescharacteristic
780C2×C4C31×H(5,𝔽2)11yescharacteristic
781C2×C4C31×H(5,𝔽2)11yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—816no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×C31×#12111yescharacteristic
816C22D42×C3111yescharacteristic
817C22C31×#54611yescharacteristic
818C22C31×#57511yescharacteristic
819C22C31×#57511yescharacteristic
820C22C31×#57611yescharacteristic
821C22C31×#57611yescharacteristic
822C4—22no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4C31×#52511yescharacteristic
833C4C31×#53811yescharacteristic
834C4D42×C3111yescharacteristic
835C4C31×#54611yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2C31×#242411yescharacteristic
841C2C31×#304011yescharacteristic
842C2C31×#304111yescharacteristic
843C2C31×#326811yescharacteristic
844C2C31×#327311yescharacteristic
845C2C31×#331911yescharacteristic
846C2C31×#332211yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#468C2semidirect
2. C2×C31×#463C2semidirect
4. C2×C31×#418C2semidirect
5. C31×#2435C2semidirect
6. C31×#2363C2semidirect
7. C31×#2067C2semidirect
8. C31×#2054C2semidirect
9. C31×#2042C2semidirect
10. C31×#2012C2semidirect
11. C31×#1983C2semidirect
12. C31×#1925C2semidirect
13. C31×#1879C2semidirect
14. C31×#1873C2semidirect
15. C31×#1851C2semidirect
17. C22×SD16×C31C22semidirect
25. C2×C4×D4×C31C22semidirect
30. C2×C31×#107C22semidirect
31. C2×C31×C4⋊C8C22semidirect
32. C2×C31×C4⋊C8C22semidirect
34. C2×C31×#103C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
43. C2×C31×#102C22semidirect
50. C31×#390C22semidirect
51. C31×#389C22semidirect
56. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
144. C31×#102D4semidirect
263. #25101C31direct (N × H)
363. C2×#468C2×C31semidirect
364. C2×#463C2×C31semidirect
366. C2×#418C2×C31semidirect
367. #2435C2×C31semidirect
368. #2363C2×C31semidirect
369. #2067C2×C31semidirect
370. #2054C2×C31semidirect
371. #2042C2×C31semidirect
372. #2012C2×C31semidirect
373. #1983C2×C31semidirect
374. #1925C2×C31semidirect
375. #1879C2×C31semidirect
376. #1873C2×C31semidirect
377. #1851C2×C31semidirect
429. C22×SD16C22×C31semidirect
437. C2×C4×D4C22×C31semidirect
442. C2×#107C22×C31semidirect
443. C2×C4⋊C8C22×C31semidirect
444. C2×C4⋊C8C22×C31semidirect
446. C2×#103C22×C31semidirect
447. C2×#103C22×C31semidirect
448. C2×#103C22×C31semidirect
455. C2×#102C22×C31semidirect
462. #390C22×C31semidirect
463. #389C22×C31semidirect
468. C4×C4⋊C4C22×C31semidirect
471. #340C22×C31semidirect
472. #340C22×C31semidirect
473. #336C22×C31semidirect
474. #336C22×C31semidirect
567. #102D4×C31semidirect
573. C31#25101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4632
C2×C31×#4472
C2×C31×#4182
C31×#24352
C31×#23632
C31×#20672
C31×#20542
C31×#20422
C31×#20122
C31×#19832
C31×#19252
C31×#18792
C31×#18732
C31×#18512
#2510131