Finite Group Databasebeta

← C2×C31×#2464 #21491434

Subgroups — C2×C31×#2464 #21491434

Order 7936.

4218 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C22×C31×#121C211yesmaximal, characteristic, complemented
4C22×C4×D4×C31C211yesmaximal, characteristic, complemented
5C31×#2464C2116yesmaximal, direct product factor
6C2×C31×#398C211yesmaximal, characteristic, complemented
7C2×C31×#394C211yesmaximal, characteristic, complemented
8C2×C31×#392C211yesmaximal, characteristic, complemented
9C2×C31×#392C211yesmaximal, characteristic, complemented
10C2×C31×#390C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic, complemented
12C2×C31×#388C211yesmaximal, characteristic, complemented
13C2×C31×#386C211yesmaximal, characteristic, complemented
14C2×C31×#386C211yesmaximal, characteristic, complemented
15C2×C31×#385C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C23×D4×C31C2211yescharacteristic
21C23×D4×C31C2211yescharacteristic
22C23×D4×C31C2211yescharacteristic
23C24×C4×C31C2211yescharacteristic
24C24×C4×C31C2211yescharacteristic
25C24×C4×C31C2211yescharacteristic
26C2×C31×#123—28no—
27C2×C31×#123C2218yescomplemented
28C2×C31×#121—28no—
29C2×C31×#121—28no—
30C2×C31×#121C2218yescomplemented
31C2×C31×#121C2218yescomplemented
32C2×C4×D4×C31—28no—
33C2×C4×D4×C31C2218yescomplemented
34C22×C4⋊C4×C31C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic
37C22×C4⋊C4×C31C2211yescharacteristic
38C22×C4⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
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×C42×C31C2211yescharacteristic
53C22×C42×C31C2211yescharacteristic
54C31×#398C2218yescomplemented
55C31×#394C2218yescomplemented
56C31×#392C2218yescomplemented
57C31×#392C2218yescomplemented
58C31×#390C2218yescomplemented
59C31×#388C2218yescomplemented
60C31×#388C2218yescomplemented
61C31×#386C2218yescomplemented
62C31×#386C2218yescomplemented
63C31×#385C2218yescomplemented
64C4×C22⋊C4×C31C2218yescomplemented
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2211yescharacteristic
69C2×C31×#95C2211yescharacteristic
70C2×C31×#95C2211yescharacteristic
71C25×C31C2311yescharacteristic
72C25×C31C2311yescharacteristic
73C25×C31C2311yescharacteristic
74C25×C31C2311yescharacteristic
75C22×D4×C31—24no—
76C22×D4×C31—24no—
77C22×D4×C31—24no—
78C22×D4×C31—24no—
79C22×D4×C31—24no—
80C22×D4×C31—24no—
81C22×D4×C31—24no—
82C22×D4×C31—24no—
83C22×D4×C31—24no—
84C22×D4×C31—24no—
85C22×D4×C31—24no—
86C22×D4×C31—24no—
87C22×D4×C31—24no—
88C22×D4×C31—42no—
89C22×D4×C31—42no—
90C22×D4×C31—42no—
91C22×D4×C31—42no—
92C22×D4×C31—42no—
93C22×D4×C31C2314yes—
94C22×D4×C31C2314yes—
95C22×D4×C31C2314yes—
96C22×D4×C31C2314yes—
97C22×D4×C31C2314yes—
98C22×D4×C31C2314yes—
99C23×C4×C31—24no—
100C23×C4×C31—24no—
101C23×C4×C31—24no—
102C23×C4×C31—24no—
103C23×C4×C31—24no—
104C23×C4×C31—24no—
105C23×C4×C31—42no—
106C23×C4×C31—42no—
107C23×C4×C31—42no—
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C23×C4×C31C2311yescharacteristic
111C23×C4×C31C2311yescharacteristic
112C23×C4×C31C2311yescharacteristic
113C23×C4×C31C2314yes—
114C23×C4×C31C2314yes—
115C23×C4×C31C2314yes—
116C23×C4×C31C2311yescharacteristic
117C23×C4×C31C2311yescharacteristic
118C23×C4×C31C2311yescharacteristic
119C23×C4×C31C2311yescharacteristic
120C23×C4×C31C2311yescharacteristic
121C23×C4×C31C2311yescharacteristic
122C31×#123—232no—
123C31×#121—232no—
124C31×#121—232no—
125C4×D4×C31—232no—
126C2×C4⋊C4×C31—24no—
127C2×C4⋊C4×C31—24no—
128C2×C4⋊C4×C31—24no—
129C2×C4⋊C4×C31—24no—
130C2×C4⋊C4×C31—24no—
131C2×C4⋊C4×C31C2314yes—
132C2×C4⋊C4×C31C2314yes—
133C2×C4⋊C4×C31C2314yes—
134C2×C4⋊C4×C31C2314yes—
135C2×C4⋊C4×C31C2314yes—
136C2×C22⋊C4×C31—24no—
137C2×C22⋊C4×C31—24no—
138C2×C22⋊C4×C31—24no—
139C2×C22⋊C4×C31—24no—
140C2×C22⋊C4×C31—24no—
141C2×C22⋊C4×C31—24no—
142C2×C22⋊C4×C31—24no—
143C2×C22⋊C4×C31—24no—
144C2×C22⋊C4×C31—42no—
145C2×C22⋊C4×C31—42no—
146C2×C22⋊C4×C31—42no—
147C2×C22⋊C4×C31D418yescomplemented
148C2×C22⋊C4×C31D418yescomplemented
149C2×C22⋊C4×C31C2314yes—
150C2×C22⋊C4×C31C2314yes—
151C2×C22⋊C4×C31C2314yes—
152C2×C22⋊C4×C31C2314yes—
153C2×C22⋊C4×C31C2314yes—
154C2×C22⋊C4×C31C2314yes—
155C2×C22⋊C4×C31C2314yes—
156C2×C22⋊C4×C31C2314yes—
157C2×C22⋊C4×C31C2314yes—
158C2×C22⋊C4×C31C2314yes—
159C2×C22⋊C4×C31C2314yes—
160C2×C22⋊C4×C31C2314yes—
161C2×C22⋊C4×C31C2314yes—
162C2×C42×C31—24no—
163C2×C42×C31—42no—
164C2×C42×C31C2314yes—
165C2×C42×C31C2314yes—
166C31×#95C2314yes—
167C31×#95C2314yes—
168C31×#95C2314yes—
169C31×#95C2314yes—
170C31×#95C2314yes—
171C31×#95C2314yes—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—22no—
177C24×C31—22no—
178C24×C31—22no—
179C24×C31—22no—
180C24×C31—22no—
181C24×C31—22no—
182C24×C31—22no—
183C24×C31—22no—
184C24×C31—22no—
185C24×C31—22no—
186C24×C31—22no—
187C24×C31—22no—
188C24×C31—22no—
189C24×C31—22no—
190C24×C31—22no—
191C24×C31—22no—
192C24×C31—22no—
193C24×C31—22no—
194C24×C31—22no—
195C24×C31—22no—
196C24×C31—22no—
197C24×C31C2×D414yes—
198C24×C31C2×D414yes—
199C24×C31#4114yes—
200C24×C31C2412yes—
201C24×C31C2412yes—
202C24×C31C2412yes—
203C24×C31C2412yes—
204C24×C31C2411yescharacteristic
205C2×D4×C31—232no—
206C2×D4×C31—28no—
207C2×D4×C31—28no—
208C2×D4×C31—28no—
209C2×D4×C31—28no—
210C2×D4×C31—28no—
211C2×D4×C31—28no—
212C2×D4×C31—28no—
213C2×D4×C31—28no—
214C2×D4×C31—28no—
215C2×D4×C31—28no—
216C2×D4×C31—28no—
217C2×D4×C31—28no—
218C2×D4×C31—28no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—416no—
225C2×D4×C31—416no—
226C2×D4×C31—416no—
227C2×D4×C31—416no—
228C2×D4×C31—416no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—22no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—22no—
245C22×C4×C31—22no—
246C22×C4×C31—22no—
247C22×C4×C31—28no—
248C22×C4×C31—22no—
249C22×C4×C31—22no—
250C22×C4×C31—22no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—22no—
257C22×C4×C31—28no—
258C22×C4×C31—28no—
259C22×C4×C31—28no—
260C22×C4×C31—28no—
261C22×C4×C31—28no—
262C22×C4×C31—44no—
263C22×C4×C31—44no—
264C22×C4×C31—44no—
265C22×C4×C31—416no—
266C22×C4×C31—416no—
267C22×C4×C31—416no—
268C22×C4×C31C2×D414yes—
269C22×C4×C31C2×D414yes—
270C22×C4×C31C2×D414yes—
271C22×C4×C31C2×D414yes—
272C22×C4×C31#4114yes—
273C22×C4×C31#4114yes—
274C22×C4×C31C2412yes—
275C22×C4×C31C2412yes—
276C22×C4×C31C2412yes—
277C22×C4×C31C2412yes—
278C22×C4×C31C2412yes—
279C22×C4×C31C2412yes—
280C22×C4×C31C2412yes—
281C22×C4×C31C2412yes—
282C22×C4×C31C2412yes—
283C22×C4×C31C2412yes—
284C22×C4×C31C2412yes—
285C4⋊C4×C31—28no—
286C4⋊C4×C31—28no—
287C4⋊C4×C31—28no—
288C4⋊C4×C31—28no—
289C4⋊C4×C31—28no—
290C22⋊C4×C31—28no—
291C22⋊C4×C31—28no—
292C22⋊C4×C31—28no—
293C22⋊C4×C31—28no—
294C22⋊C4×C31—28no—
295C22⋊C4×C31—28no—
296C22⋊C4×C31—28no—
297C22⋊C4×C31—28no—
298C22⋊C4×C31—44no—
299C22⋊C4×C31—44no—
300C22⋊C4×C31—44no—
301C22⋊C4×C31C2×D4116yescomplemented
302C22⋊C4×C31C2×D4116yescomplemented
303C42×C31—28no—
304C42×C31—44no—
305C2×#2464C3111yesmaximal, characteristic, direct product factor, Sylow
306C23×C31—28no—
307C23×C31—28no—
308C23×C31—28no—
309C23×C31—28no—
310C23×C31—28no—
311C23×C31—28no—
312C23×C31—28no—
313C23×C31—28no—
314C23×C31—28no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—44no—
341C23×C31—44no—
342C23×C31—44no—
343C23×C31—44no—
344C23×C31—44no—
345C23×C31—44no—
346C23×C31—44no—
347C23×C31—44no—
348C23×C31—44no—
349C23×C31—44no—
350C23×C31—44no—
351C23×C31—44no—
352C23×C31—44no—
353C23×C31—44no—
354C23×C31—44no—
355C23×C31—44no—
356C23×C31—44no—
357C23×C31—44no—
358C23×C31—44no—
359C23×C31C22×D414yes—
360C23×C31C22×D414yes—
361C23×C31C22×D412yes—
362C23×C31C22×D412yes—
363C23×C31C2×#4114yes—
364C23×C31C2×#4112yes—
365C23×C31C2×#4112yes—
366C23×C31C2×#4112yes—
367C23×C31H(5,𝔽2)12yes—
368C23×C31H(5,𝔽2)12yes—
369C23×C31C2511yescharacteristic
370D4×C31—232no—
371D4×C31—416no—
372D4×C31—416no—
373D4×C31—416no—
374D4×C31—416no—
375D4×C31—416no—
376C2×C4×C31—28no—
377C2×C4×C31—28no—
378C2×C4×C31—28no—
379C2×C4×C31—28no—
380C2×C4×C31—28no—
381C2×C4×C31—28no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—416no—
410C2×C4×C31—416no—
411C2×C4×C31—416no—
412C2×C4×C31—44no—
413C2×C4×C31—44no—
414C2×C4×C31—44no—
415C2×C4×C31—44no—
416C2×C4×C31—44no—
417C2×C4×C31C22×D414yes—
418C2×C4×C31C22×D414yes—
419C2×C4×C31C22×D414yes—
420C2×C4×C31C22×D414yes—
421C2×C4×C31C2×#4114yes—
422C2×C4×C31C2×#4114yes—
423C22×#123C2×C3111yescharacteristic, complemented
424C22×#121C2×C3111yescharacteristic, complemented
425C22×#121C2×C3111yescharacteristic, complemented
426C22×C4×D4C2×C3111yescharacteristic, complemented
427#2464C2×C31116yesdirect product factor
428C2×#398C2×C3111yescharacteristic, complemented
429C2×#394C2×C3111yescharacteristic, complemented
430C2×#392C2×C3111yescharacteristic, complemented
431C2×#392C2×C3111yescharacteristic, complemented
432C2×#390C2×C3111yescharacteristic, complemented
433C2×#388C2×C3111yescharacteristic, complemented
434C2×#388C2×C3111yescharacteristic, complemented
435C2×#386C2×C3111yescharacteristic, complemented
436C2×#386C2×C3111yescharacteristic, complemented
437C2×#385C2×C3111yescharacteristic, complemented
438C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
439C22×C31—24no—
440C22×C31—24no—
441C22×C31—24no—
442C22×C31—24no—
443C22×C31—24no—
444C22×C31—24no—
445C22×C31—24no—
446C22×C31—24no—
447C22×C31—24no—
448C22×C31—42no—
449C22×C31—42no—
450C22×C31—42no—
451C22×C31—42no—
452C22×C31—42no—
453C22×C31—42no—
454C22×C31—42no—
455C22×C31—42no—
456C22×C31—42no—
457C22×C31—42no—
458C22×C31—42no—
459C22×C31—42no—
460C22×C31—416no—
461C22×C31—416no—
462C22×C31—416no—
463C22×C31—42no—
464C22×C31—42no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—42no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—88no—
471C22×C31#52514yes—
472C22×C31#53214yes—
473C22×C31#54014yes—
474C22×C31D4214yes—
475C22×C31#54614yes—
476C22×C31#54614yes—
477C22×C31#55314yes—
478C22×C31C23×D411yescharacteristic
479C22×C31C23×D411yescharacteristic
480C22×C31C22×#4111yescharacteristic
481C22×C31C22×#4111yescharacteristic
482C22×C31C22×#4111yescharacteristic
483C22×C31C2×H(5,𝔽2)11yescharacteristic
484C22×C31C2×H(5,𝔽2)11yescharacteristic
485C4×C31—24no—
486C4×C31—24no—
487C4×C31—24no—
488C4×C31—24no—
489C4×C31—24no—
490C4×C31—24no—
491C4×C31—42no—
492C4×C31—42no—
493C4×C31—42no—
494C4×C31—42no—
495C4×C31—42no—
496C23×D4C22×C3111yescharacteristic
497C23×D4C22×C3111yescharacteristic
498C23×D4C22×C3111yescharacteristic
499C23×D4C22×C3111yescharacteristic
500C23×D4C22×C3111yescharacteristic
501C23×D4C22×C3111yescharacteristic
502C24×C4C22×C3111yescharacteristic
503C24×C4C22×C3111yescharacteristic
504C24×C4C22×C3111yescharacteristic
505C2×#123—28no—
506C2×#123C22×C3118yescomplemented
507C2×#121—28no—
508C2×#121—28no—
509C2×#121C22×C3118yescomplemented
510C2×#121C22×C3118yescomplemented
511C2×C4×D4—28no—
512C2×C4×D4C22×C3118yescomplemented
513C22×C4⋊C4C22×C3111yescharacteristic
514C22×C4⋊C4C22×C3111yescharacteristic
515C22×C4⋊C4C22×C3111yescharacteristic
516C22×C4⋊C4C22×C3111yescharacteristic
517C22×C4⋊C4C22×C3111yescharacteristic
518C22×C22⋊C4C22×C3111yescharacteristic
519C22×C22⋊C4C22×C3111yescharacteristic
520C22×C22⋊C4C22×C3111yescharacteristic
521C22×C22⋊C4C22×C3111yescharacteristic
522C22×C22⋊C4C22×C3111yescharacteristic
523C22×C22⋊C4C22×C3111yescharacteristic
524C22×C22⋊C4C22×C3111yescharacteristic
525C22×C22⋊C4C22×C3111yescharacteristic
526C22×C22⋊C4C22×C3111yescharacteristic
527C22×C22⋊C4C22×C3111yescharacteristic
528C22×C22⋊C4C22×C3111yescharacteristic
529C22×C22⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C42C22×C3111yescharacteristic
532C22×C42C22×C3111yescharacteristic
533#398C22×C3118yescomplemented
534#394C22×C3118yescomplemented
535#392C22×C3118yescomplemented
536#392C22×C3118yescomplemented
537#390C22×C3118yescomplemented
538#388C22×C3118yescomplemented
539#388C22×C3118yescomplemented
540#386C22×C3118yescomplemented
541#386C22×C3118yescomplemented
542#385C22×C3118yescomplemented
543C4×C22⋊C4C22×C3118yescomplemented
544C2×#95C22×C3111yescharacteristic
545C2×#95C22×C3111yescharacteristic
546C2×#95C22×C3111yescharacteristic
547C2×#95C22×C3111yescharacteristic
548C2×#95C22×C3111yescharacteristic
549C2×#95C22×C3111yescharacteristic
550C2×C31—44no—
551C2×C31—44no—
552C2×C31—44no—
553C2×C31—82no—
554C2×C31#246418yesdirect product factor
555C2×C31C2×#52511yescharacteristic
556C2×C31C2×#53211yescharacteristic
557C2×C31C2×#54011yescharacteristic
558C2×C31C2×D4211yescharacteristic
559C2×C31C2×#54611yescharacteristic
560C2×C31C2×#54611yescharacteristic
561C2×C31C2×#55311yescharacteristic
562C25C23×C3111yescharacteristic
563C25C23×C3111yescharacteristic
564C25C23×C3111yescharacteristic
565C25C23×C3111yescharacteristic
566C22×D4—24no—
567C22×D4—24no—
568C22×D4—24no—
569C22×D4—24no—
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—42no—
580C22×D4—42no—
581C22×D4—42no—
582C22×D4—42no—
583C22×D4—42no—
584C22×D4C23×C3114yes—
585C22×D4C23×C3114yes—
586C22×D4C23×C3114yes—
587C22×D4C23×C3114yes—
588C22×D4C23×C3114yes—
589C22×D4C23×C3114yes—
590C23×C4—24no—
591C23×C4—24no—
592C23×C4—24no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—24no—
596C23×C4—42no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4C23×C3111yescharacteristic
600C23×C4C23×C3111yescharacteristic
601C23×C4C23×C3111yescharacteristic
602C23×C4C23×C3111yescharacteristic
603C23×C4C23×C3111yescharacteristic
604C23×C4C23×C3114yes—
605C23×C4C23×C3114yes—
606C23×C4C23×C3114yes—
607C23×C4C23×C3111yescharacteristic
608C23×C4C23×C3111yescharacteristic
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611C23×C4C23×C3111yescharacteristic
612C23×C4C23×C3111yescharacteristic
613#123—232no—
614#121—232no—
615#121—232no—
616C4×D4—232no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4C23×C3114yes—
623C2×C4⋊C4C23×C3114yes—
624C2×C4⋊C4C23×C3114yes—
625C2×C4⋊C4C23×C3114yes—
626C2×C4⋊C4C23×C3114yes—
627C2×C22⋊C4—24no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—42no—
636C2×C22⋊C4—42no—
637C2×C22⋊C4—42no—
638C2×C22⋊C4D4×C3118yescomplemented
639C2×C22⋊C4D4×C3118yescomplemented
640C2×C22⋊C4C23×C3114yes—
641C2×C22⋊C4C23×C3114yes—
642C2×C22⋊C4C23×C3114yes—
643C2×C22⋊C4C23×C3114yes—
644C2×C22⋊C4C23×C3114yes—
645C2×C22⋊C4C23×C3114yes—
646C2×C22⋊C4C23×C3114yes—
647C2×C22⋊C4C23×C3114yes—
648C2×C22⋊C4C23×C3114yes—
649C2×C22⋊C4C23×C3114yes—
650C2×C22⋊C4C23×C3114yes—
651C2×C22⋊C4C23×C3114yes—
652C2×C22⋊C4C23×C3114yes—
653C2×C42—24no—
654C2×C42—42no—
655C2×C42C23×C3114yes—
656C2×C42C23×C3114yes—
657#95C23×C3114yes—
658#95C23×C3114yes—
659#95C23×C3114yes—
660#95C23×C3114yes—
661#95C23×C3114yes—
662#95C23×C3114yes—
663C31C2×#246411yescharacteristic, direct product factor, Sylow
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24C2×D4×C3114yes—
690C24C2×D4×C3114yes—
691C24#41×C3114yes—
692C24C24×C3112yes—
693C24C24×C3112yes—
694C24C24×C3112yes—
695C24C24×C3112yes—
696C24C24×C3111yescharacteristic
697C2×D4—232no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—416no—
717C2×D4—416no—
718C2×D4—416no—
719C2×D4—416no—
720C2×D4—416no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—416no—
758C22×C4—416no—
759C22×C4—416no—
760C22×C4C2×D4×C3114yes—
761C22×C4C2×D4×C3114yes—
762C22×C4C2×D4×C3114yes—
763C22×C4C2×D4×C3114yes—
764C22×C4#41×C3114yes—
765C22×C4#41×C3114yes—
766C22×C4C24×C3112yes—
767C22×C4C24×C3112yes—
768C22×C4C24×C3112yes—
769C22×C4C24×C3112yes—
770C22×C4C24×C3112yes—
771C22×C4C24×C3112yes—
772C22×C4C24×C3112yes—
773C22×C4C24×C3112yes—
774C22×C4C24×C3112yes—
775C22×C4C24×C3112yes—
776C22×C4C24×C3112yes—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4C2×D4×C31116yescomplemented
794C22⋊C4C2×D4×C31116yescomplemented
795C42—28no—
796C42—44no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—28no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23C22×D4×C3114yes—
851C23C22×D4×C3114yes—
852C23C22×D4×C3112yes—
853C23C22×D4×C3112yes—
854C23C2×#41×C3114yes—
855C23C2×#41×C3112yes—
856C23C2×#41×C3112yes—
857C23C2×#41×C3112yes—
858C23C31×H(5,𝔽2)12yes—
859C23C31×H(5,𝔽2)12yes—
860C23C25×C3111yescharacteristic
861D4—232no—
862D4—416no—
863D4—416no—
864D4—416no—
865D4—416no—
866D4—416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4C22×D4×C3114yes—
909C2×C4C22×D4×C3114yes—
910C2×C4C22×D4×C3114yes—
911C2×C4C22×D4×C3114yes—
912C2×C4C2×#41×C3114yes—
913C2×C4C2×#41×C3114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—416no—
936C22—416no—
937C22—416no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—88no—
946C22C31×#52514yes—
947C22C31×#53214yes—
948C22C31×#54014yes—
949C22D42×C3114yes—
950C22C31×#54614yes—
951C22C31×#54614yes—
952C22C31×#55314yes—
953C22C23×D4×C3111yescharacteristic
954C22C23×D4×C3111yescharacteristic
955C22C22×#41×C3111yescharacteristic
956C22C22×#41×C3111yescharacteristic
957C22C22×#41×C3111yescharacteristic
958C22C2×C31×H(5,𝔽2)11yescharacteristic
959C22C2×C31×H(5,𝔽2)11yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C2—44no—
972C2—44no—
973C2—44no—
974C2—82no—
975C2C31×#246418yesdirect product factor
976C2C2×C31×#52511yescharacteristic
977C2C2×C31×#53211yescharacteristic
978C2C2×C31×#54011yescharacteristic
979C2C2×D42×C3111yescharacteristic
980C2C2×C31×#54611yescharacteristic
981C2C2×C31×#54611yescharacteristic
982C2C2×C31×#55311yescharacteristic
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×#123C2semidirect
2. C22×C31×#121C2semidirect
3. C22×C31×#121C2semidirect
4. C22×C4×D4×C31C2semidirect
5. C31×#2464C2direct (N × H)
6. C2×C31×#398C2semidirect
7. C2×C31×#394C2semidirect
8. C2×C31×#392C2semidirect
9. C2×C31×#392C2semidirect
10. C2×C31×#390C2semidirect
11. C2×C31×#388C2semidirect
12. C2×C31×#388C2semidirect
13. C2×C31×#386C2semidirect
14. C2×C31×#386C2semidirect
15. C2×C31×#385C2semidirect
16. C2×C4×C22⋊C4×C31C2semidirect
27. C2×C31×#123C22semidirect
30. C2×C31×#121C22semidirect
31. C2×C31×#121C22semidirect
33. C2×C4×D4×C31C22semidirect
54. C31×#398C22semidirect
55. C31×#394C22semidirect
56. C31×#392C22semidirect
57. C31×#392C22semidirect
58. C31×#390C22semidirect
59. C31×#388C22semidirect
60. C31×#388C22semidirect
61. C31×#386C22semidirect
62. C31×#386C22semidirect
63. C31×#385C22semidirect
64. C4×C22⋊C4×C31C22semidirect
147. C2×C22⋊C4×C31D4semidirect
148. C2×C22⋊C4×C31D4semidirect
301. C22⋊C4×C31C2×D4semidirect
302. C22⋊C4×C31C2×D4semidirect
305. C2×#2464C31direct (N × H)
423. C22×#123C2×C31semidirect
424. C22×#121C2×C31semidirect
425. C22×#121C2×C31semidirect
426. C22×C4×D4C2×C31semidirect
427. #2464C2×C31direct (N × H)
428. C2×#398C2×C31semidirect
429. C2×#394C2×C31semidirect
430. C2×#392C2×C31semidirect
431. C2×#392C2×C31semidirect
432. C2×#390C2×C31semidirect
433. C2×#388C2×C31semidirect
434. C2×#388C2×C31semidirect
435. C2×#386C2×C31semidirect
436. C2×#386C2×C31semidirect
437. C2×#385C2×C31semidirect
438. C2×C4×C22⋊C4C2×C31semidirect
506. C2×#123C22×C31semidirect
509. C2×#121C22×C31semidirect
510. C2×#121C22×C31semidirect
512. C2×C4×D4C22×C31semidirect
533. #398C22×C31semidirect
534. #394C22×C31semidirect
535. #392C22×C31semidirect
536. #392C22×C31semidirect
537. #390C22×C31semidirect
538. #388C22×C31semidirect
539. #388C22×C31semidirect
540. #386C22×C31semidirect
541. #386C22×C31semidirect
542. #385C22×C31semidirect
543. C4×C22⋊C4C22×C31semidirect
554. C2×C31#2464direct (N × H)
638. C2×C22⋊C4D4×C31semidirect
639. C2×C22⋊C4D4×C31semidirect
663. C31C2×#2464direct (N × H)
793. C22⋊C4C2×D4×C31semidirect
794. C22⋊C4C2×D4×C31semidirect
975. C2C31×#2464direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#1212
C22×C4×D4×C312
C31×#24642
C2×C31×#3982
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C4×C22⋊C4×C312
C2×#246431