Finite Group Databasebeta

← C31×#13998 #21470757

Subgroups — C31×#13998 #21470757

Order 7936.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#390C212yesmaximal, complemented
4C2×C31×#390C211yesmaximal, characteristic, complemented
5C2×C31×#389C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal, complemented
10C31×#1438C212yesmaximal, complemented
11C31×#1437C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C24×C4×C31C2211yescharacteristic
15C2×C31×#121—24no—
16C2×C31×#121—24no—
17C2×C31×#121C418yescomplemented
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C42×C31C2211yescharacteristic
31C22×C42×C31C2212yes—
32C22×C42×C31C2211yescharacteristic
33C31×#390—24no—
34C31×#390—28no—
35C31×#390—24no—
36C31×#389—24no—
37C31×#380—24no—
38C4×C4⋊C4×C31—24no—
39C4×C22⋊C4×C31—24no—
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C2×C31×#95C2212yes—
44C2×C31×#95C2211yescharacteristic
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—22no—
56C22×D4×C31—22no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31C2×C414yes—
60C22×D4×C31C2×C418yes—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31C2×C414yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2312yes—
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C31×#121—232no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—24no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—24no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—42no—
86C2×C4⋊C4×C31C2×C414yes—
87C2×C4⋊C4×C31D414yes—
88C2×C4⋊C4×C31D414yes—
89C2×C4⋊C4×C31D414yescomplemented
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—24no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—42no—
108C2×C22⋊C4×C31—42no—
109C2×C22⋊C4×C31—42no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31C2×C418yes—
113C2×C22⋊C4×C31D414yescomplemented
114C2×C42×C31—22no—
115C2×C42×C31—22no—
116C2×C42×C31—22no—
117C2×C42×C31—24no—
118C2×C42×C31—22no—
119C2×C42×C31—24no—
120C2×C42×C31—22no—
121C2×C42×C31—42no—
122C2×C42×C31D414yescomplemented
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—24no—
126C31×#95—24no—
127C31×#95—24no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31C22×C414yes—
155C24×C31C22×C412yes—
156C24×C31C2×D412yes—
157C24×C31#4112yes—
158C24×C31C2411yescharacteristic
159C2×D4×C31—216no—
160C2×D4×C31—216no—
161C2×D4×C31—28no—
162C2×D4×C31—28no—
163C2×D4×C31—28no—
164C2×D4×C31—48no—
165C2×D4×C31—48no—
166C2×D4×C31—48no—
167C2×D4×C31—48no—
168C2×D4×C31—48no—
169C2×D4×C31—44no—
170C2×D4×C31—44no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
173C22×C4×C31—21no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—22no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—28no—
212C22×C4×C31—28no—
213C22×C4×C31—28no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—44no—
222C22×C4×C31—44no—
223C22×C4×C31—44no—
224C22×C4×C31—44no—
225C22×C4×C31C22×C412yes—
226C22×C4×C31C22×C414yes—
227C22×C4×C31C22×C412yes—
228C22×C4×C31C2×D412yes—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D414yes—
232C22×C4×C31C2×D414yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D412yes—
236C22×C4×C31C2×D412yes—
237C22×C4×C31C2×D412yes—
238C22×C4×C31C2×D412yes—
239C22×C4×C31#4112yes—
240C22×C4×C31#4112yes—
241C22×C4×C31#4112yes—
242C22×C4×C31#4112yes—
243C4⋊C4×C31—28no—
244C4⋊C4×C31—48no—
245C4⋊C4×C31—44no—
246C4⋊C4×C31C22⋊C4116yescomplemented
247C22⋊C4×C31—28no—
248C22⋊C4×C31—216no—
249C22⋊C4×C31—28no—
250C22⋊C4×C31—48no—
251C22⋊C4×C31—48no—
252C22⋊C4×C31—48no—
253C22⋊C4×C31—48no—
254C22⋊C4×C31—48no—
255C42×C31—28no—
256C42×C31—48no—
257C42×C31—44no—
258#13998C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—24no—
278C23×C31—24no—
279C23×C31—24no—
280C23×C31—24no—
281C23×C31—24no—
282C23×C31—24no—
283C23×C31—24no—
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—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—42no—
314C23×C31—42no—
315C23×C31—42no—
316C23×C31—42no—
317C23×C31—42no—
318C23×C31—42no—
319C23×C31—42no—
320C23×C31—42no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—42no—
324C23×C31—42no—
325C23×C31—42no—
326C23×C31—42no—
327C23×C31—42no—
328C23×C31C4×D414yes—
329C23×C31C23×C411yescharacteristic
330C23×C31C22×D411yescharacteristic
331C23×C31C22×D411yescharacteristic
332C23×C31C22×D411yescharacteristic
333C23×C31C22×D411yescharacteristic
334C23×C31C22×D411yescharacteristic
335C23×C31C2×#4111yescharacteristic
336C23×C31C2×#4111yescharacteristic
337C23×C31C2×#4111yescharacteristic
338C23×C31C2×#4111yescharacteristic
339C23×C31C2×#4111yescharacteristic
340C23×C31H(5,𝔽2)11yescharacteristic
341C23×C31H(5,𝔽2)11yescharacteristic
342C23×C31H(5,𝔽2)11yescharacteristic
343C23×C312−1+411yescharacteristic
344D4×C31—432no—
345D4×C31—416no—
346C2×C4×C31—24no—
347C2×C4×C31—24no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—24no—
352C2×C4×C31—24no—
353C2×C4×C31—24no—
354C2×C4×C31—24no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—24no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—24no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—24no—
372C2×C4×C31—22no—
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—42no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—42no—
383C2×C4×C31—42no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—42no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—416no—
394C2×C4×C31—42no—
395C2×C4×C31—42no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—42no—
400C2×C4×C31—42no—
401C2×C4×C31C2×C22⋊C418yes—
402C2×C4×C31C2×C22⋊C414yes—
403C2×C4×C31C4×D414yes—
404C2×C4×C31C4×D414yes—
405C2×C4×C31#12114yes—
406C2×C4×C31#12114yes—
407C2×C4×C31#12114yescomplemented
408C2×C4×C31#12414yes—
409C2×C4×C31#12714yes—
410C22×#121C2×C3111yescharacteristic
411C2×#390C2×C3111yescharacteristic, complemented
412C2×#390C2×C3112yescomplemented
413C2×#390C2×C3111yescharacteristic, complemented
414C2×#389C2×C3111yescharacteristic, complemented
415C2×#380C2×C3111yescharacteristic, complemented
416C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
417C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
418#1439C2×C3112yescomplemented
419#1438C2×C3112yescomplemented
420#1437C2×C3112yescomplemented
421C22×C31—24no—
422C22×C31—24no—
423C22×C31—24no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—42no—
433C22×C31—42no—
434C22×C31—42no—
435C22×C31—42no—
436C22×C31—44no—
437C22×C31—44no—
438C22×C31—44no—
439C22×C31—44no—
440C22×C31—44no—
441C22×C31—44no—
442C22×C31—44no—
443C22×C31—82no—
444C22×C31—82no—
445C22×C31—82no—
446C22×C31—82no—
447C22×C31—82no—
448C22×C31—82no—
449C22×C31—82no—
450C22×C31—82no—
451C22×C31C22×C22⋊C411yescharacteristic
452C22×C31C2×C4×D411yescharacteristic
453C22×C31C2×C4×D411yescharacteristic
454C22×C31C2×C4×D411yescharacteristic
455C22×C31C4×#4111yescharacteristic
456C22×C31#51811yescharacteristic
457C22×C31#52011yescharacteristic
458C22×C31C2×#12111yescharacteristic
459C22×C31C2×#12111yescharacteristic
460C22×C31C2×#12111yescharacteristic
461C22×C31#52511yescharacteristic
462C22×C31C2×#12411yescharacteristic
463C22×C31#52911yescharacteristic
464C22×C31C2×#12711yescharacteristic
465C22×C31#53211yescharacteristic
466C22×C31#53511yescharacteristic
467C22×C31#53711yescharacteristic
468C22×C31#54011yescharacteristic
469C22×C31#54211yescharacteristic
470C22×C31D4211yescharacteristic
471C22×C31D4211yescharacteristic
472C22×C31D4211yescharacteristic
473C22×C31#54611yescharacteristic
474C22×C31#54611yescharacteristic
475C22×C31#54611yescharacteristic
476C22×C31#54711yescharacteristic
477C22×C31#54811yescharacteristic
478C22×C31#54811yescharacteristic
479C22×C31#54811yescharacteristic
480C22×C31#55011yescharacteristic
481C22×C31#55011yescharacteristic
482C22×C31#55011yescharacteristic
483C22×C31#55311yescharacteristic
484C22×C31#55311yescharacteristic
485C22×C31#55511yescharacteristic
486C4×C31—28no—
487C4×C31—24no—
488C4×C31—42no—
489C4×C31—44no—
490C4×C31—42no—
491C4×C31—42no—
492C4×C31—42no—
493C4×C31—82no—
494C4×C31#39018yescomplemented
495C23×D4C22×C3111yescharacteristic
496C23×D4C22×C3112yes—
497C24×C4C22×C3111yescharacteristic
498C2×#121—24no—
499C2×#121—24no—
500C2×#121C4×C3118yescomplemented
501C22×C4⋊C4C22×C3111yescharacteristic
502C22×C4⋊C4C22×C3112yes—
503C22×C4⋊C4C22×C3111yescharacteristic
504C22×C4⋊C4C22×C3111yescharacteristic
505C22×C22⋊C4C22×C3112yes—
506C22×C22⋊C4C22×C3111yescharacteristic
507C22×C22⋊C4C22×C3112yes—
508C22×C22⋊C4C22×C3112yes—
509C22×C22⋊C4C22×C3112yes—
510C22×C22⋊C4C22×C3112yes—
511C22×C22⋊C4C22×C3111yescharacteristic
512C22×C22⋊C4C22×C3112yes—
513C22×C42C22×C3111yescharacteristic
514C22×C42C22×C3112yes—
515C22×C42C22×C3111yescharacteristic
516#390—24no—
517#390—28no—
518#390—24no—
519#389—24no—
520#380—24no—
521C4×C4⋊C4—24no—
522C4×C22⋊C4—24no—
523C2×#95C22×C3111yescharacteristic
524C2×#95C22×C3112yes—
525C2×#95C22×C3112yes—
526C2×#95C22×C3112yes—
527C2×#95C22×C3111yescharacteristic
528C2×C31—44no—
529C2×C31—84no—
530C2×C31C2×#39011yescharacteristic
531C2×C31C4×#12111yescharacteristic
532C2×C31#232411yescharacteristic
533C2×C31D4×C22⋊C411yescharacteristic
534C2×C31#234111yescharacteristic
535C2×C31#236111yescharacteristic
536C2×C31#236311yescharacteristic
537C2×C31#241411yescharacteristic
538C2×C31#241611yescharacteristic
539C2×C31#242611yescharacteristic
540C2×C31#242811yescharacteristic
541C2×C31#249011yescharacteristic
542C2×C31#249111yescharacteristic
543C2×C31#254011yescharacteristic
544C2×C31#254111yescharacteristic
545C25C23×C3112yes—
546C25C23×C3111yescharacteristic
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4C2×C4×C3114yes—
560C22×D4C2×C4×C3118yes—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4C2×C4×C3114yes—
568C23×C4C23×C3112yes—
569C23×C4C23×C3111yescharacteristic
570C23×C4C23×C3111yescharacteristic
571C23×C4C23×C3112yes—
572C23×C4C23×C3111yescharacteristic
573C23×C4C23×C3111yescharacteristic
574C23×C4C23×C3112yes—
575C23×C4C23×C3111yescharacteristic
576C23×C4C23×C3111yescharacteristic
577#121—232no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—42no—
586C2×C4⋊C4C2×C4×C3114yes—
587C2×C4⋊C4D4×C3114yes—
588C2×C4⋊C4D4×C3114yes—
589C2×C4⋊C4D4×C3114yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4C2×C4×C3118yes—
613C2×C22⋊C4D4×C3114yescomplemented
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—24no—
618C2×C42—22no—
619C2×C42—24no—
620C2×C42—22no—
621C2×C42—42no—
622C2×C42D4×C3114yescomplemented
623#95—22no—
624#95—22no—
625#95—24no—
626#95—24no—
627#95—24no—
628C31#1399811yescharacteristic, direct product factor, Sylow
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24C22×C4×C3114yes—
656C24C22×C4×C3112yes—
657C24C2×D4×C3112yes—
658C24#41×C3112yes—
659C24C24×C3111yescharacteristic
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4C22×C4×C3112yes—
727C22×C4C22×C4×C3114yes—
728C22×C4C22×C4×C3112yes—
729C22×C4C2×D4×C3112yes—
730C22×C4C2×D4×C3114yes—
731C22×C4C2×D4×C3112yes—
732C22×C4C2×D4×C3114yes—
733C22×C4C2×D4×C3114yes—
734C22×C4C2×D4×C3112yes—
735C22×C4C2×D4×C3112yes—
736C22×C4C2×D4×C3112yes—
737C22×C4C2×D4×C3112yes—
738C22×C4C2×D4×C3112yes—
739C22×C4C2×D4×C3112yes—
740C22×C4#41×C3112yes—
741C22×C4#41×C3112yes—
742C22×C4#41×C3112yes—
743C22×C4#41×C3112yes—
744C4⋊C4—28no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4C22⋊C4×C31116yescomplemented
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—28no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C42—48no—
758C42—44no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23C4×D4×C3114yes—
829C23C23×C4×C3111yescharacteristic
830C23C22×D4×C3111yescharacteristic
831C23C22×D4×C3111yescharacteristic
832C23C22×D4×C3111yescharacteristic
833C23C22×D4×C3111yescharacteristic
834C23C22×D4×C3111yescharacteristic
835C23C2×#41×C3111yescharacteristic
836C23C2×#41×C3111yescharacteristic
837C23C2×#41×C3111yescharacteristic
838C23C2×#41×C3111yescharacteristic
839C23C2×#41×C3111yescharacteristic
840C23C31×H(5,𝔽2)11yescharacteristic
841C23C31×H(5,𝔽2)11yescharacteristic
842C23C31×H(5,𝔽2)11yescharacteristic
843C23C31×2−1+411yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—416no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4C2×C22⋊C4×C3118yes—
902C2×C4C2×C22⋊C4×C3114yes—
903C2×C4C4×D4×C3114yes—
904C2×C4C4×D4×C3114yes—
905C2×C4C31×#12114yes—
906C2×C4C31×#12114yes—
907C2×C4C31×#12114yescomplemented
908C2×C4C31×#12414yes—
909C2×C4C31×#12714yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C22×C22⋊C4×C3111yescharacteristic
941C22C2×C4×D4×C3111yescharacteristic
942C22C2×C4×D4×C3111yescharacteristic
943C22C2×C4×D4×C3111yescharacteristic
944C22C4×#41×C3111yescharacteristic
945C22C31×#51811yescharacteristic
946C22C31×#52011yescharacteristic
947C22C2×C31×#12111yescharacteristic
948C22C2×C31×#12111yescharacteristic
949C22C2×C31×#12111yescharacteristic
950C22C31×#52511yescharacteristic
951C22C2×C31×#12411yescharacteristic
952C22C31×#52911yescharacteristic
953C22C2×C31×#12711yescharacteristic
954C22C31×#53211yescharacteristic
955C22C31×#53511yescharacteristic
956C22C31×#53711yescharacteristic
957C22C31×#54011yescharacteristic
958C22C31×#54211yescharacteristic
959C22D42×C3111yescharacteristic
960C22D42×C3111yescharacteristic
961C22D42×C3111yescharacteristic
962C22C31×#54611yescharacteristic
963C22C31×#54611yescharacteristic
964C22C31×#54611yescharacteristic
965C22C31×#54711yescharacteristic
966C22C31×#54811yescharacteristic
967C22C31×#54811yescharacteristic
968C22C31×#54811yescharacteristic
969C22C31×#55011yescharacteristic
970C22C31×#55011yescharacteristic
971C22C31×#55011yescharacteristic
972C22C31×#55311yescharacteristic
973C22C31×#55311yescharacteristic
974C22C31×#55511yescharacteristic
975C4—28no—
976C4—24no—
977C4—42no—
978C4—44no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—82no—
983C4C31×#39018yescomplemented
984C2—44no—
985C2—84no—
986C2C2×C31×#39011yescharacteristic
987C2C4×C31×#12111yescharacteristic
988C2C31×#232411yescharacteristic
989C2D4×C22⋊C4×C3111yescharacteristic
990C2C31×#234111yescharacteristic
991C2C31×#236111yescharacteristic
992C2C31×#236311yescharacteristic
993C2C31×#241411yescharacteristic
994C2C31×#241611yescharacteristic
995C2C31×#242611yescharacteristic
996C2C31×#242811yescharacteristic
997C2C31×#249011yescharacteristic
998C2C31×#249111yescharacteristic
999C2C31×#254011yescharacteristic
1000C2C31×#254111yescharacteristic
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. C2×C31×#390C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#390C2semidirect
5. C2×C31×#389C2semidirect
6. C2×C31×#380C2semidirect
7. C2×C4×C4⋊C4×C31C2semidirect
8. C2×C4×C22⋊C4×C31C2semidirect
9. C31×#1439C2semidirect
10. C31×#1438C2semidirect
11. C31×#1437C2semidirect
17. C2×C31×#121C4semidirect
89. C2×C4⋊C4×C31D4semidirect
113. C2×C22⋊C4×C31D4semidirect
122. C2×C42×C31D4semidirect
246. C4⋊C4×C31C22⋊C4semidirect
258. #13998C31direct (N × H)
407. C2×C4×C31#121semidirect
411. C2×#390C2×C31semidirect
412. C2×#390C2×C31semidirect
413. C2×#390C2×C31semidirect
414. C2×#389C2×C31semidirect
415. C2×#380C2×C31semidirect
416. C2×C4×C4⋊C4C2×C31semidirect
417. C2×C4×C22⋊C4C2×C31semidirect
418. #1439C2×C31semidirect
419. #1438C2×C31semidirect
420. #1437C2×C31semidirect
494. C4×C31#390semidirect
500. C2×#121C4×C31semidirect
589. C2×C4⋊C4D4×C31semidirect
613. C2×C22⋊C4D4×C31semidirect
622. C2×C42D4×C31semidirect
628. C31#13998direct (N × H)
747. C4⋊C4C22⋊C4×C31semidirect
907. C2×C4C31×#121semidirect
983. C4C31×#390semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3902
C2×C31×#3892
C2×C31×#3802
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C31×#14392
C31×#14382
C31×#14372
#1399831