Finite Group Databasebeta

← C31×#13970 #21470729

Subgroups — C31×#13970 #21470729

Order 7936.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#390C211yesmaximal, characteristic, complemented
4C2×C31×#386C212yesmaximal, complemented
5C2×C31×#380C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C31×C4⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2212yes—
16C2×C31×#121—24no—
17C2×C31×#121—24no—
18C2×C31×#121C418yescomplemented
19C2×C4×D4×C31—24no—
20C2×C4×D4×C31—24no—
21C2×C4×D4×C31—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C42×C31C2211yescharacteristic
33C22×C42×C31C2211yescharacteristic
34C31×#390—24no—
35C31×#386—28no—
36C31×#380—24no—
37C4×C22⋊C4×C31—24no—
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2212yes—
44C2×C31×#95C2212yes—
45C25×C31C2312yes—
46C25×C31C2311yescharacteristic
47C22×D4×C31—24no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—22no—
55C22×D4×C31—42no—
56C22×D4×C31—42no—
57C22×D4×C31C2×C414yes—
58C22×D4×C31C2×C418yescomplemented
59C22×D4×C31D414yes—
60C22×D4×C31D414yes—
61C23×C4×C31—24no—
62C23×C4×C31—24no—
63C23×C4×C31—24no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—24no—
71C23×C4×C31—24no—
72C23×C4×C31—42no—
73C23×C4×C31—42no—
74C23×C4×C31C2×C414yescomplemented
75C23×C4×C31C2312yes—
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2312yes—
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C31×#121—232no—
85C4×D4×C31—232no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31C2×C414yescomplemented
94C2×C4⋊C4×C31D414yescomplemented
95C2×C22⋊C4×C31—24no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—24no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31—42no—
114C2×C22⋊C4×C31C2×C418yescomplemented
115C2×C22⋊C4×C31D414yescomplemented
116C2×C42×C31—22no—
117C2×C42×C31—22no—
118C2×C42×C31—22no—
119C2×C42×C31—22no—
120C2×C42×C31—22no—
121C2×C42×C31D414yescomplemented
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—24no—
125C31×#95—24no—
126C31×#95—24no—
127C31×#95—42no—
128C31×#95—42no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—22no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—21no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—22no—
152C24×C31—21no—
153C24×C31C22×C414yes—
154C24×C31C22×C412yes—
155C24×C31C2×D414yes—
156C24×C31C2×D414yes—
157C24×C31C2×D412yes—
158C24×C31#4112yes—
159C24×C31C2411yescharacteristic
160C2×D4×C31—216no—
161C2×D4×C31—216no—
162C2×D4×C31—28no—
163C2×D4×C31—28no—
164C2×D4×C31—28no—
165C2×D4×C31—28no—
166C2×D4×C31—28no—
167C2×D4×C31—28no—
168C2×D4×C31—48no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31C22⋊C4116yescomplemented
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—216no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—22no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—22no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
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—22no—
204C22×C4×C31—22no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—28no—
216C22×C4×C31—28no—
217C22×C4×C31—28no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—48no—
226C22×C4×C31—48no—
227C22×C4×C31—48no—
228C22×C4×C31—48no—
229C22×C4×C31—48no—
230C22×C4×C31—44no—
231C22×C4×C31—44no—
232C22×C4×C31—44no—
233C22×C4×C31—48no—
234C22×C4×C31—44no—
235C22×C4×C31C22×C412yes—
236C22×C4×C31C22×C414yes—
237C22×C4×C31C22×C412yes—
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D414yes—
241C22×C4×C31C2×D412yes—
242C22×C4×C31C2×D412yes—
243C22×C4×C31C2×D412yes—
244C22×C4×C31C2×D412yes—
245C22×C4×C31C2×D412yes—
246C22×C4×C31C2×D412yes—
247C22×C4×C31#4112yes—
248C22×C4×C31#4112yes—
249C22×C4×C31#4112yes—
250C22×C4×C31#4112yes—
251C4⋊C4×C31—28no—
252C4⋊C4×C31—28no—
253C4⋊C4×C31—44no—
254C22⋊C4×C31—28no—
255C22⋊C4×C31—216no—
256C22⋊C4×C31—216no—
257C22⋊C4×C31—28no—
258C22⋊C4×C31—48no—
259C22⋊C4×C31—48no—
260C22⋊C4×C31—48no—
261C42×C31—28no—
262C42×C31—44no—
263#13970C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—24no—
274C23×C31—24no—
275C23×C31—22no—
276C23×C31—24no—
277C23×C31—22no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—24no—
286C23×C31—24no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—24no—
290C23×C31—24no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—24no—
296C23×C31—24no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—41no—
301C23×C31—42no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—42no—
312C23×C31—41no—
313C23×C31—42no—
314C23×C31—41no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—41no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31—41no—
329C23×C31—42no—
330C23×C31—41no—
331C23×C31—42no—
332C23×C31C2×C22⋊C418yes—
333C23×C31C4×D414yescomplemented
334C23×C31C23×C411yescharacteristic
335C23×C31C22×D411yescharacteristic
336C23×C31C22×D411yescharacteristic
337C23×C31C22×D411yescharacteristic
338C23×C31C22×D411yescharacteristic
339C23×C31C22×D411yescharacteristic
340C23×C31C2×#4111yescharacteristic
341C23×C31C2×#4111yescharacteristic
342C23×C31C2×#4111yescharacteristic
343C23×C31C2×#4111yescharacteristic
344C23×C31C2×#4111yescharacteristic
345C23×C31H(5,𝔽2)11yescharacteristic
346C23×C31H(5,𝔽2)11yescharacteristic
347C23×C31H(5,𝔽2)11yescharacteristic
348C23×C312−1+411yescharacteristic
349D4×C31—232no—
350D4×C31—432no—
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—24no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—24no—
362C2×C4×C31—24no—
363C2×C4×C31—22no—
364C2×C4×C31—24no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—24no—
371C2×C4×C31—22no—
372C2×C4×C31—24no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—432no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—42no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—42no—
385C2×C4×C31—41no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—42no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—416no—
401C2×C4×C31—42no—
402C2×C4×C31—42no—
403C2×C4×C31—42no—
404C2×C4×C31—42no—
405C2×C4×C31—42no—
406C2×C4×C31—42no—
407C2×C4×C31—42no—
408C2×C4×C31C2×C22⋊C414yes—
409C2×C4×C31C4×D414yes—
410C2×C4×C31C4×D414yes—
411C2×C4×C31#12014yes—
412C2×C4×C31#12114yes—
413C2×C4×C31#12114yes—
414C2×C4×C31#12114yescomplemented
415C2×C4×C31#12314yes—
416C22×#121C2×C3111yescharacteristic
417C22×C4×D4C2×C3111yescharacteristic, complemented
418C2×#390C2×C3111yescharacteristic, complemented
419C2×#386C2×C3112yescomplemented
420C2×#380C2×C3111yescharacteristic, complemented
421C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
422#1440C2×C3112yescomplemented
423#1438C2×C3112yescomplemented
424C4⋊#95C2×C3111yescharacteristic, complemented
425C4⋊#95C2×C3111yescharacteristic, complemented
426C22⋊#95C2×C3112yescomplemented
427C22×C31—24no—
428C22×C31—28no—
429C22×C31—28no—
430C22×C31—24no—
431C22×C31—28no—
432C22×C31—24no—
433C22×C31—42no—
434C22×C31—44no—
435C22×C31—42no—
436C22×C31—44no—
437C22×C31—42no—
438C22×C31—44no—
439C22×C31—44no—
440C22×C31—42no—
441C22×C31—44no—
442C22×C31—42no—
443C22×C31—44no—
444C22×C31—42no—
445C22×C31—44no—
446C22×C31—42no—
447C22×C31—44no—
448C22×C31—42no—
449C22×C31—44no—
450C22×C31—42no—
451C22×C31—44no—
452C22×C31—42no—
453C22×C31—42no—
454C22×C31—44no—
455C22×C31—42no—
456C22×C31—44no—
457C22×C31C22×C22⋊C411yescharacteristic
458C22×C31C2×C4×D411yescharacteristic
459C22×C31C2×C4×D411yescharacteristic
460C22×C31C2×C4×D411yescharacteristic
461C22×C31C4×#4111yescharacteristic
462C22×C31#51811yescharacteristic
463C22×C31#52011yescharacteristic
464C22×C31C2×#12011yescharacteristic
465C22×C31C2×#12111yescharacteristic
466C22×C31C2×#12111yescharacteristic
467C22×C31C2×#12111yescharacteristic
468C22×C31C2×#12311yescharacteristic
469C22×C31#52511yescharacteristic
470C22×C31#52911yescharacteristic
471C22×C31#53211yescharacteristic
472C22×C31#53511yescharacteristic
473C22×C31#53711yescharacteristic
474C22×C31#54011yescharacteristic
475C22×C31#54211yescharacteristic
476C22×C31D4211yescharacteristic
477C22×C31D4211yescharacteristic
478C22×C31D4211yescharacteristic
479C22×C31#54611yescharacteristic
480C22×C31#54611yescharacteristic
481C22×C31#54611yescharacteristic
482C22×C31#54611yescharacteristic
483C22×C31#54611yescharacteristic
484C22×C31#54711yescharacteristic
485C22×C31#54711yescharacteristic
486C22×C31#54711yescharacteristic
487C22×C31#54811yescharacteristic
488C22×C31#55011yescharacteristic
489C22×C31#55311yescharacteristic
490C22×C31#55311yescharacteristic
491C22×C31#55511yescharacteristic
492C4×C31—24no—
493C4×C31—44no—
494C4×C31—42no—
495C4×C31—44no—
496C4×C31—42no—
497C4×C31—42no—
498C4×C31—42no—
499C4×C31—82no—
500C4×C31#38618yescomplemented
501C23×D4C22×C3112yes—
502C23×D4C22×C3111yescharacteristic
503C24×C4C22×C3111yescharacteristic
504C24×C4C22×C3112yes—
505C2×#121—24no—
506C2×#121—24no—
507C2×#121C4×C3118yescomplemented
508C2×C4×D4—24no—
509C2×C4×D4—24no—
510C2×C4×D4—24no—
511C22×C4⋊C4C22×C3111yescharacteristic
512C22×C4⋊C4C22×C3111yescharacteristic
513C22×C4⋊C4C22×C3111yescharacteristic
514C22×C22⋊C4C22×C3112yes—
515C22×C22⋊C4C22×C3111yescharacteristic
516C22×C22⋊C4C22×C3112yes—
517C22×C22⋊C4C22×C3112yes—
518C22×C22⋊C4C22×C3112yes—
519C22×C22⋊C4C22×C3112yes—
520C22×C22⋊C4C22×C3111yescharacteristic
521C22×C42C22×C3111yescharacteristic
522C22×C42C22×C3111yescharacteristic
523#390—24no—
524#386—28no—
525#380—24no—
526C4×C22⋊C4—24no—
527C2×#95C22×C3111yescharacteristic
528C2×#95C22×C3112yes—
529C2×#95C22×C3112yes—
530C2×#95C22×C3112yes—
531C2×#95C22×C3111yescharacteristic
532C2×#95C22×C3112yes—
533C2×#95C22×C3112yes—
534C2×C31—44no—
535C2×C31—48no—
536C2×C31C2×#38611yescharacteristic
537C2×C31C4×#12111yescharacteristic
538C2×C31#232411yescharacteristic
539C2×C31D4×C22⋊C411yescharacteristic
540C2×C31#233911yescharacteristic
541C2×C31#236111yescharacteristic
542C2×C31#236311yescharacteristic
543C2×C31#240711yescharacteristic
544C2×C31#240811yescharacteristic
545C2×C31#242011yescharacteristic
546C2×C31#242211yescharacteristic
547C2×C31#242711yescharacteristic
548C2×C31#242811yescharacteristic
549C2×C31#253511yescharacteristic
550C2×C31#253711yescharacteristic
551C25C23×C3112yes—
552C25C23×C3111yescharacteristic
553C22×D4—24no—
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4C2×C4×C3114yes—
564C22×D4C2×C4×C3118yescomplemented
565C22×D4D4×C3114yes—
566C22×D4D4×C3114yes—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—24no—
577C23×C4—24no—
578C23×C4—42no—
579C23×C4—42no—
580C23×C4C2×C4×C3114yescomplemented
581C23×C4C23×C3112yes—
582C23×C4C23×C3111yescharacteristic
583C23×C4C23×C3112yes—
584C23×C4C23×C3111yescharacteristic
585C23×C4C23×C3111yescharacteristic
586C23×C4C23×C3112yes—
587C23×C4C23×C3111yescharacteristic
588C23×C4C23×C3111yescharacteristic
589C23×C4C23×C3111yescharacteristic
590#121—232no—
591C4×D4—232no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4C2×C4×C3114yescomplemented
600C2×C4⋊C4D4×C3114yescomplemented
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4C2×C4×C3118yescomplemented
621C2×C22⋊C4D4×C3114yescomplemented
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42D4×C3114yescomplemented
628#95—22no—
629#95—22no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—42no—
634#95—42no—
635C31#1397011yescharacteristic, direct product factor, Sylow
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—21no—
660C24C22×C4×C3114yes—
661C24C22×C4×C3112yes—
662C24C2×D4×C3114yes—
663C24C2×D4×C3114yes—
664C24C2×D4×C3112yes—
665C24#41×C3112yes—
666C24C24×C3111yescharacteristic
667C2×D4—216no—
668C2×D4—216no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4C22⋊C4×C31116yescomplemented
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—216no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—48no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—48no—
741C22×C4—44no—
742C22×C4C22×C4×C3112yes—
743C22×C4C22×C4×C3114yes—
744C22×C4C22×C4×C3112yes—
745C22×C4C2×D4×C3112yes—
746C22×C4C2×D4×C3112yes—
747C22×C4C2×D4×C3114yes—
748C22×C4C2×D4×C3112yes—
749C22×C4C2×D4×C3112yes—
750C22×C4C2×D4×C3112yes—
751C22×C4C2×D4×C3112yes—
752C22×C4C2×D4×C3112yes—
753C22×C4C2×D4×C3112yes—
754C22×C4#41×C3112yes—
755C22×C4#41×C3112yes—
756C22×C4#41×C3112yes—
757C22×C4#41×C3112yes—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—44no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—28no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C42—28no—
769C42—44no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—22no—
778C23—22no—
779C23—24no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—22no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—24no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—22no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—41no—
807C23—42no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—41no—
816C23—41no—
817C23—42no—
818C23—41no—
819C23—42no—
820C23—41no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—42no—
830C23—42no—
831C23—41no—
832C23—42no—
833C23—42no—
834C23—41no—
835C23—42no—
836C23—41no—
837C23—42no—
838C23C2×C22⋊C4×C3118yes—
839C23C4×D4×C3114yescomplemented
840C23C23×C4×C3111yescharacteristic
841C23C22×D4×C3111yescharacteristic
842C23C22×D4×C3111yescharacteristic
843C23C22×D4×C3111yescharacteristic
844C23C22×D4×C3111yescharacteristic
845C23C22×D4×C3111yescharacteristic
846C23C2×#41×C3111yescharacteristic
847C23C2×#41×C3111yescharacteristic
848C23C2×#41×C3111yescharacteristic
849C23C2×#41×C3111yescharacteristic
850C23C2×#41×C3111yescharacteristic
851C23C31×H(5,𝔽2)11yescharacteristic
852C23C31×H(5,𝔽2)11yescharacteristic
853C23C31×H(5,𝔽2)11yescharacteristic
854C23C31×2−1+411yescharacteristic
855D4—232no—
856D4—432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—432no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—42no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—416no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4C2×C22⋊C4×C3114yes—
915C2×C4C4×D4×C3114yes—
916C2×C4C4×D4×C3114yes—
917C2×C4C31×#12014yes—
918C2×C4C31×#12114yes—
919C2×C4C31×#12114yes—
920C2×C4C31×#12114yescomplemented
921C2×C4C31×#12314yes—
922C22—24no—
923C22—28no—
924C22—28no—
925C22—24no—
926C22—28no—
927C22—24no—
928C22—42no—
929C22—44no—
930C22—42no—
931C22—44no—
932C22—42no—
933C22—44no—
934C22—44no—
935C22—42no—
936C22—44no—
937C22—42no—
938C22—44no—
939C22—42no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—42no—
946C22—44no—
947C22—42no—
948C22—42no—
949C22—44no—
950C22—42no—
951C22—44no—
952C22C22×C22⋊C4×C3111yescharacteristic
953C22C2×C4×D4×C3111yescharacteristic
954C22C2×C4×D4×C3111yescharacteristic
955C22C2×C4×D4×C3111yescharacteristic
956C22C4×#41×C3111yescharacteristic
957C22C31×#51811yescharacteristic
958C22C31×#52011yescharacteristic
959C22C2×C31×#12011yescharacteristic
960C22C2×C31×#12111yescharacteristic
961C22C2×C31×#12111yescharacteristic
962C22C2×C31×#12111yescharacteristic
963C22C2×C31×#12311yescharacteristic
964C22C31×#52511yescharacteristic
965C22C31×#52911yescharacteristic
966C22C31×#53211yescharacteristic
967C22C31×#53511yescharacteristic
968C22C31×#53711yescharacteristic
969C22C31×#54011yescharacteristic
970C22C31×#54211yescharacteristic
971C22D42×C3111yescharacteristic
972C22D42×C3111yescharacteristic
973C22D42×C3111yescharacteristic
974C22C31×#54611yescharacteristic
975C22C31×#54611yescharacteristic
976C22C31×#54611yescharacteristic
977C22C31×#54611yescharacteristic
978C22C31×#54611yescharacteristic
979C22C31×#54711yescharacteristic
980C22C31×#54711yescharacteristic
981C22C31×#54711yescharacteristic
982C22C31×#54811yescharacteristic
983C22C31×#55011yescharacteristic
984C22C31×#55311yescharacteristic
985C22C31×#55311yescharacteristic
986C22C31×#55511yescharacteristic
987C4—24no—
988C4—44no—
989C4—42no—
990C4—44no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—82no—
995C4C31×#38618yescomplemented
996C2—44no—
997C2—48no—
998C2C2×C31×#38611yescharacteristic
999C2C4×C31×#12111yescharacteristic
1000C2C31×#232411yescharacteristic
1001C2D4×C22⋊C4×C3111yescharacteristic
1002C2C31×#233911yescharacteristic
1003C2C31×#236111yescharacteristic
1004C2C31×#236311yescharacteristic
1005C2C31×#240711yescharacteristic
1006C2C31×#240811yescharacteristic
1007C2C31×#242011yescharacteristic
1008C2C31×#242211yescharacteristic
1009C2C31×#242711yescharacteristic
1010C2C31×#242811yescharacteristic
1011C2C31×#253511yescharacteristic
1012C2C31×#253711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C31C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#380C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1440C2semidirect
8. C31×#1438C2semidirect
9. C31×C4⋊#95C2semidirect
10. C31×C4⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
18. C2×C31×#121C4semidirect
58. C22×D4×C31C2×C4semidirect
74. C23×C4×C31C2×C4semidirect
93. C2×C4⋊C4×C31C2×C4semidirect
94. C2×C4⋊C4×C31D4semidirect
114. C2×C22⋊C4×C31C2×C4semidirect
115. C2×C22⋊C4×C31D4semidirect
121. C2×C42×C31D4semidirect
173. C2×D4×C31C22⋊C4semidirect
263. #13970C31direct (N × H)
333. C23×C31C4×D4semidirect
414. C2×C4×C31#121semidirect
417. C22×C4×D4C2×C31semidirect
418. C2×#390C2×C31semidirect
419. C2×#386C2×C31semidirect
420. C2×#380C2×C31semidirect
421. C2×C4×C22⋊C4C2×C31semidirect
422. #1440C2×C31semidirect
423. #1438C2×C31semidirect
424. C4⋊#95C2×C31semidirect
425. C4⋊#95C2×C31semidirect
426. C22⋊#95C2×C31semidirect
500. C4×C31#386semidirect
507. C2×#121C4×C31semidirect
564. C22×D4C2×C4×C31semidirect
580. C23×C4C2×C4×C31semidirect
599. C2×C4⋊C4C2×C4×C31semidirect
600. C2×C4⋊C4D4×C31semidirect
620. C2×C22⋊C4C2×C4×C31semidirect
621. C2×C22⋊C4D4×C31semidirect
627. C2×C42D4×C31semidirect
635. C31#13970direct (N × H)
680. C2×D4C22⋊C4×C31semidirect
839. C23C4×D4×C31semidirect
920. C2×C4C31×#121semidirect
995. C4C31×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C4×D4×C312
C2×C31×#3902
C2×C31×#3862
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14402
C31×#14382
C31×C4⋊#952
C31×C22⋊#952
#1397031