Finite Group Databasebeta

← C2×C31×#2424 #21491409

Subgroups — C2×C31×#2424 #21491409

Order 7936.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C22×C31×#120C211yesmaximal, characteristic, complemented
4C22×C31×#120C211yesmaximal, characteristic, complemented
5C22×C4×D4×C31C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2424C2116yesmaximal, direct product factor
8C2×C31×#396C211yesmaximal, characteristic, complemented
9C2×C31×#394C211yesmaximal, characteristic, complemented
10C2×C31×#394C211yesmaximal, characteristic, complemented
11C2×C31×#392C211yesmaximal, characteristic, complemented
12C2×C31×#390C211yesmaximal, characteristic, complemented
13C2×C31×#388C211yesmaximal, characteristic, complemented
14C2×C31×#386C211yesmaximal, characteristic, complemented
15C2×C31×#386C211yesmaximal, characteristic, complemented
16C2×C31×#385C211yesmaximal, characteristic, complemented
17C26×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C23×D4×C31C2211yescharacteristic
21C23×D4×C31C2211yescharacteristic
22C23×D4×C31C2211yescharacteristic
23C23×D4×C31C2211yescharacteristic
24C23×D4×C31C2211yescharacteristic, complemented
25C24×C4×C31C2211yescharacteristic
26C24×C4×C31C2211yescharacteristic
27C24×C4×C31C2211yescharacteristic, complemented
28C2×C31×#121—28no—
29C2×C31×#121—28no—
30C2×C31×#121C2218yescomplemented
31C2×C31×#121C2218yescomplemented
32C2×C31×#120—28no—
33C2×C31×#120—28no—
34C2×C31×#120C2218yescomplemented
35C2×C31×#120C2218yescomplemented
36C2×C4×D4×C31—28no—
37C2×C4×D4×C31C2218yescomplemented
38C22×C4⋊C4×C31C2211yescharacteristic, complemented
39C22×C4⋊C4×C31C2211yescharacteristic, complemented
40C22×C4⋊C4×C31C2211yescharacteristic, complemented
41C22×C4⋊C4×C31C2211yescharacteristic, complemented
42C22×C22⋊C4×C31—28no—
43C22×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C22⋊C4×C31C2211yescharacteristic
46C22×C22⋊C4×C31C2211yescharacteristic
47C22×C22⋊C4×C31C2211yescharacteristic
48C22×C22⋊C4×C31C2211yescharacteristic
49C22×C22⋊C4×C31C2211yescharacteristic
50C22×C22⋊C4×C31C2211yescharacteristic
51C22×C22⋊C4×C31C2211yescharacteristic
52C22×C22⋊C4×C31C2211yescharacteristic
53C22×C22⋊C4×C31C2218yescomplemented
54C22×C22⋊C4×C31C2211yescharacteristic, complemented
55C22×C22⋊C4×C31C2211yescharacteristic, complemented
56C22×C22⋊C4×C31C2211yescharacteristic, complemented
57C22×C22⋊C4×C31C2211yescharacteristic, complemented
58C22×C22⋊C4×C31C2211yescharacteristic, complemented
59C22×C42×C31C2211yescharacteristic, complemented
60C31×#396C2218yescomplemented
61C31×#394C2218yescomplemented
62C31×#394C2218yescomplemented
63C31×#392C2218yescomplemented
64C31×#390C2218yescomplemented
65C31×#388C2218yescomplemented
66C31×#386C2218yescomplemented
67C31×#386C2218yescomplemented
68C31×#385C2218yescomplemented
69C2×C31×#95C2211yescharacteristic, complemented
70C2×C31×#95C2211yescharacteristic, complemented
71C2×C31×#95C2211yescharacteristic, complemented
72C2×C31×#95C2211yescharacteristic, complemented
73C25×C31—24no—
74C25×C31—24no—
75C25×C31—24no—
76C25×C31—24no—
77C25×C31—24no—
78C25×C31—42no—
79C25×C31—42no—
80C25×C31C2311yescharacteristic
81C25×C31C2311yescharacteristic
82C25×C31C2311yescharacteristic
83C25×C31C2311yescharacteristic
84C25×C31C2314yes—
85C25×C31C2311yescharacteristic
86C22×D4×C31—24no—
87C22×D4×C31—24no—
88C22×D4×C31—24no—
89C22×D4×C31—24no—
90C22×D4×C31—24no—
91C22×D4×C31—24no—
92C22×D4×C31—24no—
93C22×D4×C31—24no—
94C22×D4×C31—24no—
95C22×D4×C31—24no—
96C22×D4×C31—24no—
97C22×D4×C31—24no—
98C22×D4×C31—24no—
99C22×D4×C31—24no—
100C22×D4×C31—24no—
101C22×D4×C31—42no—
102C22×D4×C31—42no—
103C22×D4×C31—42no—
104C22×D4×C31—42no—
105C22×D4×C31—42no—
106C22×D4×C31D418yescomplemented
107C22×D4×C31C2314yes—
108C22×D4×C31C2314yes—
109C22×D4×C31C2314yes—
110C22×D4×C31C2314yes—
111C22×D4×C31C2314yes—
112C22×D4×C31C2314yes—
113C22×D4×C31C2314yescomplemented
114C23×C4×C31—24no—
115C23×C4×C31—24no—
116C23×C4×C31—24no—
117C23×C4×C31—24no—
118C23×C4×C31—24no—
119C23×C4×C31—24no—
120C23×C4×C31—42no—
121C23×C4×C31—42no—
122C23×C4×C31—42no—
123C23×C4×C31C2311yescharacteristic
124C23×C4×C31C2311yescharacteristic
125C23×C4×C31C2311yescharacteristic
126C23×C4×C31C2311yescharacteristic
127C23×C4×C31C2311yescharacteristic
128C23×C4×C31C2314yes—
129C23×C4×C31C2314yes—
130C23×C4×C31C2311yescharacteristic
131C23×C4×C31C2311yescharacteristic
132C23×C4×C31C2311yescharacteristic
133C23×C4×C31C2311yescharacteristic
134C23×C4×C31C2311yescharacteristic
135C23×C4×C31C2314yescomplemented
136C31×#121—232no—
137C31×#121—232no—
138C31×#120—232no—
139C31×#120—232no—
140C4×D4×C31—232no—
141C2×C4⋊C4×C31—24no—
142C2×C4⋊C4×C31—24no—
143C2×C4⋊C4×C31—24no—
144C2×C4⋊C4×C31—42no—
145C2×C4⋊C4×C31C2314yescomplemented
146C2×C4⋊C4×C31C2314yescomplemented
147C2×C4⋊C4×C31C2314yescomplemented
148C2×C4⋊C4×C31C2314yescomplemented
149C2×C22⋊C4×C31—24no—
150C2×C22⋊C4×C31—24no—
151C2×C22⋊C4×C31—24no—
152C2×C22⋊C4×C31—24no—
153C2×C22⋊C4×C31—24no—
154C2×C22⋊C4×C31—24no—
155C2×C22⋊C4×C31—24no—
156C2×C22⋊C4×C31—24no—
157C2×C22⋊C4×C31—24no—
158C2×C22⋊C4×C31—24no—
159C2×C22⋊C4×C31—24no—
160C2×C22⋊C4×C31—24no—
161C2×C22⋊C4×C31—232no—
162C2×C22⋊C4×C31—42no—
163C2×C22⋊C4×C31D418yescomplemented
164C2×C22⋊C4×C31D418yescomplemented
165C2×C22⋊C4×C31C2314yes—
166C2×C22⋊C4×C31C2314yes—
167C2×C22⋊C4×C31C2314yes—
168C2×C22⋊C4×C31C2314yes—
169C2×C22⋊C4×C31C2314yes—
170C2×C22⋊C4×C31C2314yes—
171C2×C22⋊C4×C31C2314yes—
172C2×C22⋊C4×C31C2314yes—
173C2×C22⋊C4×C31C2314yes—
174C2×C22⋊C4×C31C2314yes—
175C2×C22⋊C4×C31C2314yescomplemented
176C2×C22⋊C4×C31C2314yescomplemented
177C2×C22⋊C4×C31C2314yescomplemented
178C2×C22⋊C4×C31C2314yescomplemented
179C2×C22⋊C4×C31C2314yescomplemented
180C2×C42×C31—24no—
181C2×C42×C31C2314yescomplemented
182C31×#95C2314yescomplemented
183C31×#95C2314yescomplemented
184C31×#95C2314yescomplemented
185C31×#95C2314yescomplemented
186C24×C31—22no—
187C24×C31—22no—
188C24×C31—22no—
189C24×C31—22no—
190C24×C31—232no—
191C24×C31—28no—
192C24×C31—22no—
193C24×C31—22no—
194C24×C31—22no—
195C24×C31—22no—
196C24×C31—22no—
197C24×C31—22no—
198C24×C31—22no—
199C24×C31—22no—
200C24×C31—22no—
201C24×C31—28no—
202C24×C31—28no—
203C24×C31—22no—
204C24×C31—22no—
205C24×C31—22no—
206C24×C31—22no—
207C24×C31—22no—
208C24×C31—22no—
209C24×C31—22no—
210C24×C31—22no—
211C24×C31—22no—
212C24×C31—22no—
213C24×C31—22no—
214C24×C31—28no—
215C24×C31—28no—
216C24×C31—22no—
217C24×C31—22no—
218C24×C31—22no—
219C24×C31—22no—
220C24×C31—22no—
221C24×C31—44no—
222C24×C31—44no—
223C24×C31—416no—
224C24×C31—416no—
225C24×C31—416no—
226C24×C31—416no—
227C24×C31—416no—
228C24×C31—416no—
229C24×C31C2×D414yes—
230C24×C31C2×D414yes—
231C24×C31C2×D414yes—
232C24×C31C2×D414yes—
233C24×C31#4114yes—
234C24×C31#4114yes—
235C24×C31C2412yes—
236C24×C31C2412yes—
237C24×C31C2412yes—
238C24×C31C2412yes—
239C24×C31C2412yes—
240C24×C31C2411yescharacteristic
241C2×D4×C31—232no—
242C2×D4×C31—28no—
243C2×D4×C31—28no—
244C2×D4×C31—28no—
245C2×D4×C31—28no—
246C2×D4×C31—28no—
247C2×D4×C31—28no—
248C2×D4×C31—28no—
249C2×D4×C31—28no—
250C2×D4×C31—28no—
251C2×D4×C31—28no—
252C2×D4×C31—28no—
253C2×D4×C31—28no—
254C2×D4×C31—28no—
255C2×D4×C31—28no—
256C2×D4×C31—28no—
257C2×D4×C31—44no—
258C2×D4×C31—44no—
259C2×D4×C31—44no—
260C2×D4×C31—44no—
261C2×D4×C31—44no—
262C2×D4×C31—416no—
263C2×D4×C31—416no—
264C2×D4×C31—416no—
265C2×D4×C31—416no—
266C2×D4×C31—416no—
267C2×D4×C31—416no—
268C2×D4×C31C2×D4116yescomplemented
269C22×C4×C31—22no—
270C22×C4×C31—22no—
271C22×C4×C31—22no—
272C22×C4×C31—22no—
273C22×C4×C31—22no—
274C22×C4×C31—22no—
275C22×C4×C31—22no—
276C22×C4×C31—22no—
277C22×C4×C31—22no—
278C22×C4×C31—22no—
279C22×C4×C31—22no—
280C22×C4×C31—22no—
281C22×C4×C31—22no—
282C22×C4×C31—22no—
283C22×C4×C31—22no—
284C22×C4×C31—22no—
285C22×C4×C31—22no—
286C22×C4×C31—22no—
287C22×C4×C31—22no—
288C22×C4×C31—28no—
289C22×C4×C31—28no—
290C22×C4×C31—22no—
291C22×C4×C31—22no—
292C22×C4×C31—22no—
293C22×C4×C31—22no—
294C22×C4×C31—22no—
295C22×C4×C31—22no—
296C22×C4×C31—28no—
297C22×C4×C31—28no—
298C22×C4×C31—28no—
299C22×C4×C31—28no—
300C22×C4×C31—44no—
301C22×C4×C31—44no—
302C22×C4×C31—44no—
303C22×C4×C31—416no—
304C22×C4×C31—416no—
305C22×C4×C31—416no—
306C22×C4×C31C2×D414yes—
307C22×C4×C31C2×D414yes—
308C22×C4×C31C2×D414yes—
309C22×C4×C31C2×D414yes—
310C22×C4×C31C2×D414yes—
311C22×C4×C31C2412yes—
312C22×C4×C31C2412yes—
313C22×C4×C31C2412yes—
314C22×C4×C31C2412yes—
315C22×C4×C31C2412yes—
316C22×C4×C31C2412yes—
317C22×C4×C31C2412yes—
318C22×C4×C31C2412yes—
319C22×C4×C31C2412yes—
320C22×C4×C31C2412yes—
321C4⋊C4×C31—28no—
322C4⋊C4×C31—28no—
323C4⋊C4×C31—28no—
324C4⋊C4×C31—44no—
325C22⋊C4×C31—28no—
326C22⋊C4×C31—28no—
327C22⋊C4×C31—28no—
328C22⋊C4×C31—28no—
329C22⋊C4×C31—28no—
330C22⋊C4×C31—28no—
331C22⋊C4×C31—28no—
332C22⋊C4×C31—28no—
333C22⋊C4×C31—28no—
334C22⋊C4×C31—28no—
335C22⋊C4×C31—28no—
336C22⋊C4×C31—28no—
337C22⋊C4×C31—44no—
338C22⋊C4×C31C2×D4116yescomplemented
339C22⋊C4×C31C2×D4116yescomplemented
340C42×C31—28no—
341C2×#2424C3111yesmaximal, characteristic, direct product factor, Sylow
342C23×C31—28no—
343C23×C31—28no—
344C23×C31—28no—
345C23×C31—28no—
346C23×C31—28no—
347C23×C31—28no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—232no—
353C23×C31—28no—
354C23×C31—28no—
355C23×C31—28no—
356C23×C31—28no—
357C23×C31—28no—
358C23×C31—28no—
359C23×C31—28no—
360C23×C31—28no—
361C23×C31—28no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
373C23×C31—22no—
374C23×C31—22no—
375C23×C31—22no—
376C23×C31—22no—
377C23×C31—22no—
378C23×C31—22no—
379C23×C31—22no—
380C23×C31—22no—
381C23×C31—22no—
382C23×C31—22no—
383C23×C31—22no—
384C23×C31—22no—
385C23×C31—22no—
386C23×C31—22no—
387C23×C31—416no—
388C23×C31—416no—
389C23×C31—416no—
390C23×C31—416no—
391C23×C31—4128no—
392C23×C31—416no—
393C23×C31—44no—
394C23×C31—44no—
395C23×C31—416no—
396C23×C31—44no—
397C23×C31—44no—
398C23×C31—44no—
399C23×C31—44no—
400C23×C31—44no—
401C23×C31—44no—
402C23×C31—44no—
403C23×C31—44no—
404C23×C31—44no—
405C23×C31—44no—
406C23×C31—44no—
407C23×C31—44no—
408C23×C31—44no—
409C23×C31—44no—
410C23×C31—44no—
411C23×C31—44no—
412C23×C31—44no—
413C23×C31#121116yescomplemented
414C23×C31C22×D414yes—
415C23×C31C22×D414yes—
416C23×C31C22×D414yes—
417C23×C31C22×D414yes—
418C23×C31C22×D412yes—
419C23×C31C22×D412yes—
420C23×C31C22×D412yes—
421C23×C31C2×#4114yes—
422C23×C31C2×#4114yes—
423C23×C31C2×#4112yes—
424C23×C31C2×#4112yes—
425C23×C31H(5,𝔽2)12yes—
426C23×C31H(5,𝔽2)12yes—
427C23×C31C2511yescharacteristic
428D4×C31—232no—
429D4×C31—416no—
430D4×C31—416no—
431D4×C31—416no—
432D4×C31—416no—
433D4×C31—416no—
434D4×C31—416no—
435C2×C4×C31—28no—
436C2×C4×C31—28no—
437C2×C4×C31—28no—
438C2×C4×C31—28no—
439C2×C4×C31—28no—
440C2×C4×C31—22no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—22no—
444C2×C4×C31—22no—
445C2×C4×C31—22no—
446C2×C4×C31—22no—
447C2×C4×C31—22no—
448C2×C4×C31—22no—
449C2×C4×C31—22no—
450C2×C4×C31—22no—
451C2×C4×C31—22no—
452C2×C4×C31—22no—
453C2×C4×C31—22no—
454C2×C4×C31—22no—
455C2×C4×C31—22no—
456C2×C4×C31—22no—
457C2×C4×C31—22no—
458C2×C4×C31—22no—
459C2×C4×C31—22no—
460C2×C4×C31—22no—
461C2×C4×C31—22no—
462C2×C4×C31—22no—
463C2×C4×C31—22no—
464C2×C4×C31—22no—
465C2×C4×C31—416no—
466C2×C4×C31—416no—
467C2×C4×C31—416no—
468C2×C4×C31—44no—
469C2×C4×C31—44no—
470C2×C4×C31—44no—
471C2×C4×C31—44no—
472C2×C4×C31—44no—
473C2×C4×C31C22×D414yes—
474C2×C4×C31C22×D414yes—
475C2×C4×C31C22×D414yes—
476C2×C4×C31C22×D414yes—
477C2×C4×C31C22×D414yes—
478C22×#121C2×C3111yescharacteristic, complemented
479C22×#121C2×C3111yescharacteristic, complemented
480C22×#120C2×C3111yescharacteristic, complemented
481C22×#120C2×C3111yescharacteristic, complemented
482C22×C4×D4C2×C3111yescharacteristic, complemented
483C23×C22⋊C4C2×C3111yescharacteristic, complemented
484#2424C2×C31116yesdirect product factor
485C2×#396C2×C3111yescharacteristic, complemented
486C2×#394C2×C3111yescharacteristic, complemented
487C2×#394C2×C3111yescharacteristic, complemented
488C2×#392C2×C3111yescharacteristic, complemented
489C2×#390C2×C3111yescharacteristic, complemented
490C2×#388C2×C3111yescharacteristic, complemented
491C2×#386C2×C3111yescharacteristic, complemented
492C2×#386C2×C3111yescharacteristic, complemented
493C2×#385C2×C3111yescharacteristic, complemented
494C22×C31—24no—
495C22×C31—232no—
496C22×C31—24no—
497C22×C31—24no—
498C22×C31—24no—
499C22×C31—24no—
500C22×C31—24no—
501C22×C31—24no—
502C22×C31—24no—
503C22×C31—24no—
504C22×C31—24no—
505C22×C31—24no—
506C22×C31—24no—
507C22×C31—24no—
508C22×C31—24no—
509C22×C31—24no—
510C22×C31—464no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—416no—
515C22×C31—416no—
516C22×C31—416no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—42no—
523C22×C31—42no—
524C22×C31—42no—
525C22×C31—42no—
526C22×C31—42no—
527C22×C31—42no—
528C22×C31—42no—
529C22×C31—42no—
530C22×C31—42no—
531C22×C31—42no—
532C22×C31—42no—
533C22×C31—88no—
534C22×C31C2×#12114yes—
535C22×C31C2×#12118yescomplemented
536C22×C31#52514yes—
537C22×C31#53814yes—
538C22×C31D4214yes—
539C22×C31D4214yes—
540C22×C31#54614yes—
541C22×C31#54614yes—
542C22×C31C23×D411yescharacteristic
543C22×C31C23×D411yescharacteristic
544C22×C31C23×D411yescharacteristic
545C22×C31C22×#4111yescharacteristic
546C22×C31C22×#4111yescharacteristic
547C22×C31C2×H(5,𝔽2)11yescharacteristic
548C22×C31C2×H(5,𝔽2)11yescharacteristic
549C4×C31—24no—
550C4×C31—24no—
551C4×C31—24no—
552C4×C31—24no—
553C4×C31—24no—
554C4×C31—42no—
555C4×C31—42no—
556C4×C31—42no—
557C4×C31—42no—
558C4×C31—42no—
559C26C22×C3111yescharacteristic
560C23×D4C22×C3111yescharacteristic
561C23×D4C22×C3111yescharacteristic
562C23×D4C22×C3111yescharacteristic
563C23×D4C22×C3111yescharacteristic
564C23×D4C22×C3111yescharacteristic
565C23×D4C22×C3111yescharacteristic
566C23×D4C22×C3111yescharacteristic, complemented
567C24×C4C22×C3111yescharacteristic
568C24×C4C22×C3111yescharacteristic
569C24×C4C22×C3111yescharacteristic, complemented
570C2×#121—28no—
571C2×#121—28no—
572C2×#121C22×C3118yescomplemented
573C2×#121C22×C3118yescomplemented
574C2×#120—28no—
575C2×#120—28no—
576C2×#120C22×C3118yescomplemented
577C2×#120C22×C3118yescomplemented
578C2×C4×D4—28no—
579C2×C4×D4C22×C3118yescomplemented
580C22×C4⋊C4C22×C3111yescharacteristic, complemented
581C22×C4⋊C4C22×C3111yescharacteristic, complemented
582C22×C4⋊C4C22×C3111yescharacteristic, complemented
583C22×C4⋊C4C22×C3111yescharacteristic, complemented
584C22×C22⋊C4—28no—
585C22×C22⋊C4C22×C3111yescharacteristic
586C22×C22⋊C4C22×C3111yescharacteristic
587C22×C22⋊C4C22×C3111yescharacteristic
588C22×C22⋊C4C22×C3111yescharacteristic
589C22×C22⋊C4C22×C3111yescharacteristic
590C22×C22⋊C4C22×C3111yescharacteristic
591C22×C22⋊C4C22×C3111yescharacteristic
592C22×C22⋊C4C22×C3111yescharacteristic
593C22×C22⋊C4C22×C3111yescharacteristic
594C22×C22⋊C4C22×C3111yescharacteristic
595C22×C22⋊C4C22×C3118yescomplemented
596C22×C22⋊C4C22×C3111yescharacteristic, complemented
597C22×C22⋊C4C22×C3111yescharacteristic, complemented
598C22×C22⋊C4C22×C3111yescharacteristic, complemented
599C22×C22⋊C4C22×C3111yescharacteristic, complemented
600C22×C22⋊C4C22×C3111yescharacteristic, complemented
601C22×C42C22×C3111yescharacteristic, complemented
602#396C22×C3118yescomplemented
603#394C22×C3118yescomplemented
604#394C22×C3118yescomplemented
605#392C22×C3118yescomplemented
606#390C22×C3118yescomplemented
607#388C22×C3118yescomplemented
608#386C22×C3118yescomplemented
609#386C22×C3118yescomplemented
610#385C22×C3118yescomplemented
611C2×#95C22×C3111yescharacteristic, complemented
612C2×#95C22×C3111yescharacteristic, complemented
613C2×#95C22×C3111yescharacteristic, complemented
614C2×#95C22×C3111yescharacteristic, complemented
615C2×C31—28no—
616C2×C31—44no—
617C2×C31—44no—
618C2×C31—44no—
619C2×C31—82no—
620C2×C31#242418yesdirect product factor
621C2×C31C22×#12111yescharacteristic
622C2×C31C2×#52511yescharacteristic
623C2×C31C2×#53811yescharacteristic
624C2×C31C2×D4211yescharacteristic
625C2×C31C2×D4211yescharacteristic
626C2×C31C2×#54611yescharacteristic
627C2×C31C2×#54611yescharacteristic
628C25—24no—
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—42no—
634C25—42no—
635C25C23×C3111yescharacteristic
636C25C23×C3111yescharacteristic
637C25C23×C3111yescharacteristic
638C25C23×C3111yescharacteristic
639C25C23×C3114yes—
640C25C23×C3111yescharacteristic
641C22×D4—24no—
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—42no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4D4×C3118yescomplemented
662C22×D4C23×C3114yes—
663C22×D4C23×C3114yes—
664C22×D4C23×C3114yes—
665C22×D4C23×C3114yes—
666C22×D4C23×C3114yes—
667C22×D4C23×C3114yes—
668C22×D4C23×C3114yescomplemented
669C23×C4—24no—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—42no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4C23×C3111yescharacteristic
679C23×C4C23×C3111yescharacteristic
680C23×C4C23×C3111yescharacteristic
681C23×C4C23×C3111yescharacteristic
682C23×C4C23×C3111yescharacteristic
683C23×C4C23×C3114yes—
684C23×C4C23×C3114yes—
685C23×C4C23×C3111yescharacteristic
686C23×C4C23×C3111yescharacteristic
687C23×C4C23×C3111yescharacteristic
688C23×C4C23×C3111yescharacteristic
689C23×C4C23×C3111yescharacteristic
690C23×C4C23×C3114yescomplemented
691#121—232no—
692#121—232no—
693#120—232no—
694#120—232no—
695C4×D4—232no—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—42no—
700C2×C4⋊C4C23×C3114yescomplemented
701C2×C4⋊C4C23×C3114yescomplemented
702C2×C4⋊C4C23×C3114yescomplemented
703C2×C4⋊C4C23×C3114yescomplemented
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—232no—
717C2×C22⋊C4—42no—
718C2×C22⋊C4D4×C3118yescomplemented
719C2×C22⋊C4D4×C3118yescomplemented
720C2×C22⋊C4C23×C3114yes—
721C2×C22⋊C4C23×C3114yes—
722C2×C22⋊C4C23×C3114yes—
723C2×C22⋊C4C23×C3114yes—
724C2×C22⋊C4C23×C3114yes—
725C2×C22⋊C4C23×C3114yes—
726C2×C22⋊C4C23×C3114yes—
727C2×C22⋊C4C23×C3114yes—
728C2×C22⋊C4C23×C3114yes—
729C2×C22⋊C4C23×C3114yes—
730C2×C22⋊C4C23×C3114yescomplemented
731C2×C22⋊C4C23×C3114yescomplemented
732C2×C22⋊C4C23×C3114yescomplemented
733C2×C22⋊C4C23×C3114yescomplemented
734C2×C22⋊C4C23×C3114yescomplemented
735C2×C42—24no—
736C2×C42C23×C3114yescomplemented
737#95C23×C3114yescomplemented
738#95C23×C3114yescomplemented
739#95C23×C3114yescomplemented
740#95C23×C3114yescomplemented
741C31C2×#242411yescharacteristic, direct product factor, Sylow
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C3114yes—
786C24C2×D4×C3114yes—
787C24C2×D4×C3114yes—
788C24C2×D4×C3114yes—
789C24#41×C3114yes—
790C24#41×C3114yes—
791C24C24×C3112yes—
792C24C24×C3112yes—
793C24C24×C3112yes—
794C24C24×C3112yes—
795C24C24×C3112yes—
796C24C24×C3111yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C31116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C3114yes—
863C22×C4C2×D4×C3114yes—
864C22×C4C2×D4×C3114yes—
865C22×C4C2×D4×C3114yes—
866C22×C4C2×D4×C3114yes—
867C22×C4C24×C3112yes—
868C22×C4C24×C3112yes—
869C22×C4C24×C3112yes—
870C22×C4C24×C3112yes—
871C22×C4C24×C3112yes—
872C22×C4C24×C3112yes—
873C22×C4C24×C3112yes—
874C22×C4C24×C3112yes—
875C22×C4C24×C3112yes—
876C22×C4C24×C3112yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C31116yescomplemented
895C22⋊C4C2×D4×C31116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23C31×#121116yescomplemented
969C23C22×D4×C3114yes—
970C23C22×D4×C3114yes—
971C23C22×D4×C3114yes—
972C23C22×D4×C3114yes—
973C23C22×D4×C3112yes—
974C23C22×D4×C3112yes—
975C23C22×D4×C3112yes—
976C23C2×#41×C3114yes—
977C23C2×#41×C3114yes—
978C23C2×#41×C3112yes—
979C23C2×#41×C3112yes—
980C23C31×H(5,𝔽2)12yes—
981C23C31×H(5,𝔽2)12yes—
982C23C25×C3111yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C3114yes—
1029C2×C4C22×D4×C3114yes—
1030C2×C4C22×D4×C3114yes—
1031C2×C4C22×D4×C3114yes—
1032C2×C4C22×D4×C3114yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—416no—
1054C22—416no—
1055C22—416no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×C31×#12114yes—
1074C22C2×C31×#12118yescomplemented
1075C22C31×#52514yes—
1076C22C31×#53814yes—
1077C22D42×C3114yes—
1078C22D42×C3114yes—
1079C22C31×#54614yes—
1080C22C31×#54614yes—
1081C22C23×D4×C3111yescharacteristic
1082C22C23×D4×C3111yescharacteristic
1083C22C23×D4×C3111yescharacteristic
1084C22C22×#41×C3111yescharacteristic
1085C22C22×#41×C3111yescharacteristic
1086C22C2×C31×H(5,𝔽2)11yescharacteristic
1087C22C2×C31×H(5,𝔽2)11yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C31×#242418yesdirect product factor
1104C2C22×C31×#12111yescharacteristic
1105C2C2×C31×#52511yescharacteristic
1106C2C2×C31×#53811yescharacteristic
1107C2C2×D42×C3111yescharacteristic
1108C2C2×D42×C3111yescharacteristic
1109C2C2×C31×#54611yescharacteristic
1110C2C2×C31×#54611yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C22×C31×#121C2semidirect
3. C22×C31×#120C2semidirect
4. C22×C31×#120C2semidirect
5. C22×C4×D4×C31C2semidirect
6. C23×C22⋊C4×C31C2semidirect
7. C31×#2424C2direct (N × H)
8. C2×C31×#396C2semidirect
9. C2×C31×#394C2semidirect
10. C2×C31×#394C2semidirect
11. C2×C31×#392C2semidirect
12. C2×C31×#390C2semidirect
13. C2×C31×#388C2semidirect
14. C2×C31×#386C2semidirect
15. C2×C31×#386C2semidirect
16. C2×C31×#385C2semidirect
24. C23×D4×C31C22semidirect
27. C24×C4×C31C22semidirect
30. C2×C31×#121C22semidirect
31. C2×C31×#121C22semidirect
34. C2×C31×#120C22semidirect
35. C2×C31×#120C22semidirect
37. C2×C4×D4×C31C22semidirect
38. C22×C4⋊C4×C31C22semidirect
39. C22×C4⋊C4×C31C22semidirect
40. C22×C4⋊C4×C31C22semidirect
41. C22×C4⋊C4×C31C22semidirect
53. C22×C22⋊C4×C31C22semidirect
54. C22×C22⋊C4×C31C22semidirect
55. C22×C22⋊C4×C31C22semidirect
56. C22×C22⋊C4×C31C22semidirect
57. C22×C22⋊C4×C31C22semidirect
58. C22×C22⋊C4×C31C22semidirect
59. C22×C42×C31C22semidirect
60. C31×#396C22semidirect
61. C31×#394C22semidirect
62. C31×#394C22semidirect
63. C31×#392C22semidirect
64. C31×#390C22semidirect
65. C31×#388C22semidirect
66. C31×#386C22semidirect
67. C31×#386C22semidirect
68. C31×#385C22semidirect
69. C2×C31×#95C22semidirect
70. C2×C31×#95C22semidirect
71. C2×C31×#95C22semidirect
72. C2×C31×#95C22semidirect
106. C22×D4×C31D4semidirect
113. C22×D4×C31C23semidirect
135. C23×C4×C31C23semidirect
145. C2×C4⋊C4×C31C23semidirect
146. C2×C4⋊C4×C31C23semidirect
147. C2×C4⋊C4×C31C23semidirect
148. C2×C4⋊C4×C31C23semidirect
163. C2×C22⋊C4×C31D4semidirect
164. C2×C22⋊C4×C31D4semidirect
175. C2×C22⋊C4×C31C23semidirect
176. C2×C22⋊C4×C31C23semidirect
177. C2×C22⋊C4×C31C23semidirect
178. C2×C22⋊C4×C31C23semidirect
179. C2×C22⋊C4×C31C23semidirect
181. C2×C42×C31C23semidirect
182. C31×#95C23semidirect
183. C31×#95C23semidirect
184. C31×#95C23semidirect
185. C31×#95C23semidirect
268. C2×D4×C31C2×D4semidirect
338. C22⋊C4×C31C2×D4semidirect
339. C22⋊C4×C31C2×D4semidirect
341. C2×#2424C31direct (N × H)
413. C23×C31#121semidirect
478. C22×#121C2×C31semidirect
479. C22×#121C2×C31semidirect
480. C22×#120C2×C31semidirect
481. C22×#120C2×C31semidirect
482. C22×C4×D4C2×C31semidirect
483. C23×C22⋊C4C2×C31semidirect
484. #2424C2×C31direct (N × H)
485. C2×#396C2×C31semidirect
486. C2×#394C2×C31semidirect
487. C2×#394C2×C31semidirect
488. C2×#392C2×C31semidirect
489. C2×#390C2×C31semidirect
490. C2×#388C2×C31semidirect
491. C2×#386C2×C31semidirect
492. C2×#386C2×C31semidirect
493. C2×#385C2×C31semidirect
535. C22×C31C2×#121semidirect
566. C23×D4C22×C31semidirect
569. C24×C4C22×C31semidirect
572. C2×#121C22×C31semidirect
573. C2×#121C22×C31semidirect
576. C2×#120C22×C31semidirect
577. C2×#120C22×C31semidirect
579. C2×C4×D4C22×C31semidirect
580. C22×C4⋊C4C22×C31semidirect
581. C22×C4⋊C4C22×C31semidirect
582. C22×C4⋊C4C22×C31semidirect
583. C22×C4⋊C4C22×C31semidirect
595. C22×C22⋊C4C22×C31semidirect
596. C22×C22⋊C4C22×C31semidirect
597. C22×C22⋊C4C22×C31semidirect
598. C22×C22⋊C4C22×C31semidirect
599. C22×C22⋊C4C22×C31semidirect
600. C22×C22⋊C4C22×C31semidirect
601. C22×C42C22×C31semidirect
602. #396C22×C31semidirect
603. #394C22×C31semidirect
604. #394C22×C31semidirect
605. #392C22×C31semidirect
606. #390C22×C31semidirect
607. #388C22×C31semidirect
608. #386C22×C31semidirect
609. #386C22×C31semidirect
610. #385C22×C31semidirect
611. C2×#95C22×C31semidirect
612. C2×#95C22×C31semidirect
613. C2×#95C22×C31semidirect
614. C2×#95C22×C31semidirect
620. C2×C31#2424direct (N × H)
661. C22×D4D4×C31semidirect
668. C22×D4C23×C31semidirect
690. C23×C4C23×C31semidirect
700. C2×C4⋊C4C23×C31semidirect
701. C2×C4⋊C4C23×C31semidirect
702. C2×C4⋊C4C23×C31semidirect
703. C2×C4⋊C4C23×C31semidirect
718. C2×C22⋊C4D4×C31semidirect
719. C2×C22⋊C4D4×C31semidirect
730. C2×C22⋊C4C23×C31semidirect
731. C2×C22⋊C4C23×C31semidirect
732. C2×C22⋊C4C23×C31semidirect
733. C2×C22⋊C4C23×C31semidirect
734. C2×C22⋊C4C23×C31semidirect
736. C2×C42C23×C31semidirect
737. #95C23×C31semidirect
738. #95C23×C31semidirect
739. #95C23×C31semidirect
740. #95C23×C31semidirect
741. C31C2×#2424direct (N × H)
824. C2×D4C2×D4×C31semidirect
894. C22⋊C4C2×D4×C31semidirect
895. C22⋊C4C2×D4×C31semidirect
968. C23C31×#121semidirect
1074. C22C2×C31×#121semidirect
1103. C2C31×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C31×#1202
C22×C4×D4×C312
C23×C22⋊C4×C312
C31×#24242
C2×C31×#3962
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×#242431