Finite Group Databasebeta

← C2×C31×#2449 #21491410

Subgroups — C2×C31×#2449 #21491410

Order 7936.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C4×D4×C31C211yesmaximal, characteristic
4C23×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2449C2116yesmaximal, direct product factor
6C2×C31×#399C211yesmaximal, characteristic, complemented
7C2×C31×#398C211yesmaximal, characteristic, complemented
8C2×C31×#396C211yesmaximal, characteristic, complemented
9C2×C31×#395C211yesmaximal, characteristic, complemented
10C2×C31×#389C211yesmaximal, characteristic, complemented
11C2×C31×#387C211yesmaximal, characteristic, complemented
12C2×C31×#386C211yesmaximal, characteristic
13C2×C31×#386C211yesmaximal, characteristic
14C2×C31×#385C211yesmaximal, characteristic, complemented
15C2×C31×#385C211yesmaximal, characteristic, complemented
16C2×C31×#385C211yesmaximal, characteristic, complemented
17C23×Q8×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C24×C4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C2×C31×C22⋊Q8—28no—
24C2×C31×C22⋊Q8—28no—
25C2×C31×C22⋊Q8C2218yescomplemented
26C2×C31×C22⋊Q8C2218yescomplemented
27C2×C4×D4×C31—28no—
28C2×C4×D4×C31C2218yes—
29C22×C4⋊C4×C31—28no—
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic
37C22×C4⋊C4×C31C2211yescharacteristic
38C22×C4⋊C4×C31C2211yescharacteristic
39C22×C4⋊C4×C31C2211yescharacteristic
40C22×C4⋊C4×C31C2211yescharacteristic
41C22×C4⋊C4×C31C2211yescharacteristic
42C22×C4⋊C4×C31C2218yescomplemented
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×C42×C31C2211yescharacteristic
52C31×#399C2218yescomplemented
53C31×#398C2218yescomplemented
54C31×#396C2218yescomplemented
55C31×#395C2218yescomplemented
56C31×#389C2218yescomplemented
57C31×#387C2218yescomplemented
58C31×#386C2218yes—
59C31×#386C2218yes—
60C31×#385C2218yescomplemented
61C31×#385C2218yescomplemented
62C31×#385C2218yescomplemented
63C2×C31×#95C2211yescharacteristic
64C2×C31×#95C2211yescharacteristic
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2211yescharacteristic
69C2×C31×#95C2211yescharacteristic
70C2×C31×#95C2211yescharacteristic
71C25×C31C2311yescharacteristic
72C25×C31C2311yescharacteristic
73C22×Q8×C31—24no—
74C22×Q8×C31—24no—
75C22×Q8×C31—42no—
76C22×Q8×C31C2314yes—
77C22×D4×C31—24no—
78C22×D4×C31—24no—
79C22×D4×C31Q818yescomplemented
80C22×D4×C31C2314yes—
81C23×C4×C31—24no—
82C23×C4×C31—24no—
83C23×C4×C31—24no—
84C23×C4×C31—24no—
85C23×C4×C31—24no—
86C23×C4×C31—24no—
87C23×C4×C31—24no—
88C23×C4×C31—24no—
89C23×C4×C31—24no—
90C23×C4×C31—42no—
91C23×C4×C31—42no—
92C23×C4×C31—42no—
93C23×C4×C31C2314yes—
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2314yes—
101C23×C4×C31C2314yes—
102C23×C4×C31C2314yes—
103C23×C4×C31C2311yescharacteristic
104C23×C4×C31C2311yescharacteristic
105C23×C4×C31C2311yescharacteristic
106C23×C4×C31C2311yescharacteristic
107C23×C4×C31C2311yescharacteristic
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C31×C22⋊Q8—232no—
111C31×C22⋊Q8—232no—
112C4×D4×C31—232no—
113C2×C4⋊C4×C31—24no—
114C2×C4⋊C4×C31—24no—
115C2×C4⋊C4×C31—24no—
116C2×C4⋊C4×C31—24no—
117C2×C4⋊C4×C31—24no—
118C2×C4⋊C4×C31—24no—
119C2×C4⋊C4×C31—24no—
120C2×C4⋊C4×C31—24no—
121C2×C4⋊C4×C31—24no—
122C2×C4⋊C4×C31—24no—
123C2×C4⋊C4×C31—232no—
124C2×C4⋊C4×C31—42no—
125C2×C4⋊C4×C31D418yescomplemented
126C2×C4⋊C4×C31C2314yes—
127C2×C4⋊C4×C31C2314yes—
128C2×C4⋊C4×C31C2314yes—
129C2×C4⋊C4×C31C2314yes—
130C2×C4⋊C4×C31C2314yes—
131C2×C4⋊C4×C31C2314yes—
132C2×C4⋊C4×C31C2314yes—
133C2×C4⋊C4×C31C2314yes—
134C2×C4⋊C4×C31C2314yes—
135C2×C4⋊C4×C31C2314yes—
136C2×C4⋊C4×C31C2314yes—
137C2×C4⋊C4×C31C2314yes—
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×C31D418yes—
146C2×C22⋊C4×C31C2314yes—
147C2×C22⋊C4×C31C2314yes—
148C2×C22⋊C4×C31C2314yes—
149C2×C22⋊C4×C31C2314yes—
150C2×C22⋊C4×C31C2314yes—
151C2×C22⋊C4×C31C2314yes—
152C2×C22⋊C4×C31C2314yes—
153C2×C22⋊C4×C31C2314yes—
154C2×C42×C31—24no—
155C2×C42×C31C2314yes—
156C31×#95C2314yes—
157C31×#95C2314yes—
158C31×#95C2314yes—
159C31×#95C2314yes—
160C31×#95C2314yes—
161C31×#95C2314yes—
162C31×#95C2314yes—
163C31×#95C2314yes—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31C2×D414yes—
175C24×C31C2×Q814yes—
176C24×C31C2×Q814yes—
177C24×C31#4114yes—
178C24×C31C2412yes—
179C24×C31C2412yes—
180C24×C31C2411yescharacteristic
181C2×Q8×C31—28no—
182C2×Q8×C31—28no—
183C2×Q8×C31—44no—
184C2×Q8×C31—416no—
185C2×D4×C31—232no—
186C2×D4×C31—28no—
187C2×D4×C31—28no—
188C2×D4×C31C2×Q8116yescomplemented
189C22×C4×C31—232no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—28no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—28no—
206C22×C4×C31—28no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—28no—
216C22×C4×C31—28no—
217C22×C4×C31—22no—
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—22no—
226C22×C4×C31—22no—
227C22×C4×C31—28no—
228C22×C4×C31—28no—
229C22×C4×C31—28no—
230C22×C4×C31—28no—
231C22×C4×C31—44no—
232C22×C4×C31—44no—
233C22×C4×C31—44no—
234C22×C4×C31—416no—
235C22×C4×C31—416no—
236C22×C4×C31—416no—
237C22×C4×C31C2×D414yes—
238C22×C4×C31C2×D414yes—
239C22×C4×C31C2×D414yes—
240C22×C4×C31C2×D414yes—
241C22×C4×C31C2×D414yes—
242C22×C4×C31C2×Q814yes—
243C22×C4×C31#4114yes—
244C22×C4×C31C2412yes—
245C22×C4×C31C2412yes—
246C22×C4×C31C2412yes—
247C22×C4×C31C2412yes—
248C22×C4×C31C2412yes—
249C22×C4×C31C2412yes—
250C22×C4×C31C2412yes—
251C22×C4×C31C2412yes—
252C22×C4×C31C2412yes—
253C22×C4×C31C2412yes—
254C22×C4×C31C2412yes—
255C22×C4×C31C2412yes—
256C22×C4×C31C2412yes—
257C4⋊C4×C31—28no—
258C4⋊C4×C31—28no—
259C4⋊C4×C31—28no—
260C4⋊C4×C31—28no—
261C4⋊C4×C31—28no—
262C4⋊C4×C31—28no—
263C4⋊C4×C31—28no—
264C4⋊C4×C31—28no—
265C4⋊C4×C31—28no—
266C4⋊C4×C31—28no—
267C4⋊C4×C31—44no—
268C4⋊C4×C31C2×D4116yescomplemented
269C22⋊C4×C31—28no—
270C22⋊C4×C31—28no—
271C22⋊C4×C31—28no—
272C22⋊C4×C31—28no—
273C22⋊C4×C31—28no—
274C22⋊C4×C31—28no—
275C22⋊C4×C31—44no—
276C22⋊C4×C31C2×D4116yes—
277C42×C31—28no—
278C2×#2449C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—28no—
280C23×C31—28no—
281C23×C31—28no—
282C23×C31—28no—
283C23×C31—28no—
284C23×C31—28no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—28no—
290C23×C31—28no—
291C23×C31—28no—
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—44no—
299C23×C31—44no—
300C23×C31—44no—
301C23×C31—44no—
302C23×C31C22⋊Q8116yescomplemented
303C23×C31C22×D414yes—
304C23×C31C22×D412yes—
305C23×C31C22×D412yes—
306C23×C31C22×Q814yes—
307C23×C31C22×Q814yes—
308C23×C31C22×Q812yes—
309C23×C31C2×#4114yes—
310C23×C31C2×#4112yes—
311C23×C31C2×#4112yes—
312C23×C31H(5,𝔽2)12yes—
313C23×C312−1+412yes—
314C23×C31C2511yescharacteristic
315Q8×C31—416no—
316D4×C31—232no—
317C2×C4×C31—232no—
318C2×C4×C31—28no—
319C2×C4×C31—28no—
320C2×C4×C31—28no—
321C2×C4×C31—28no—
322C2×C4×C31—28no—
323C2×C4×C31—28no—
324C2×C4×C31—28no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
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—416no—
358C2×C4×C31—416no—
359C2×C4×C31—416no—
360C2×C4×C31—44no—
361C2×C4×C31—44no—
362C2×C4×C31—44no—
363C2×C4×C31—44no—
364C2×C4×C31—44no—
365C2×C4×C31—44no—
366C2×C4×C31C22×D414yes—
367C2×C4×C31C22×D414yes—
368C2×C4×C31C22×D414yes—
369C2×C4×C31C22×D414yes—
370C2×C4×C31C22×D414yes—
371C2×C4×C31C22×Q814yes—
372C2×C4×C31C2×#4114yes—
373C22×C22⋊Q8C2×C3111yescharacteristic, complemented
374C22×C22⋊Q8C2×C3111yescharacteristic, complemented
375C22×C4×D4C2×C3111yescharacteristic
376C23×C4⋊C4C2×C3111yescharacteristic, complemented
377#2449C2×C31116yesdirect product factor
378C2×#399C2×C3111yescharacteristic, complemented
379C2×#398C2×C3111yescharacteristic, complemented
380C2×#396C2×C3111yescharacteristic, complemented
381C2×#395C2×C3111yescharacteristic, complemented
382C2×#389C2×C3111yescharacteristic, complemented
383C2×#387C2×C3111yescharacteristic, complemented
384C2×#386C2×C3111yescharacteristic
385C2×#386C2×C3111yescharacteristic
386C2×#385C2×C3111yescharacteristic, complemented
387C2×#385C2×C3111yescharacteristic, complemented
388C2×#385C2×C3111yescharacteristic, complemented
389C22×C31—24no—
390C22×C31—24no—
391C22×C31—24no—
392C22×C31—24no—
393C22×C31—24no—
394C22×C31—24no—
395C22×C31—232no—
396C22×C31—24no—
397C22×C31—24no—
398C22×C31—24no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—416no—
404C22×C31C2×C22⋊Q814yes—
405C22×C31C2×C22⋊Q818yescomplemented
406C22×C31#52514yes—
407C22×C31#53914yes—
408C22×C31D4214yes—
409C22×C31#54714yes—
410C22×C31D4×Q814yes—
411C22×C31#55414yes—
412C22×C31C23×D411yescharacteristic
413C22×C31C23×D411yescharacteristic
414C22×C31C23×Q811yescharacteristic
415C22×C31C22×#4111yescharacteristic
416C22×C31C22×#4111yescharacteristic
417C22×C31C2×H(5,𝔽2)11yescharacteristic
418C22×C31C2×2−1+411yescharacteristic
419C4×C31—24no—
420C4×C31—24no—
421C4×C31—24no—
422C4×C31—24no—
423C4×C31—24no—
424C4×C31—24no—
425C4×C31—24no—
426C4×C31—42no—
427C4×C31—42no—
428C4×C31—42no—
429C4×C31—42no—
430C4×C31—42no—
431C4×C31—42no—
432C23×Q8C22×C3111yescharacteristic
433C23×D4C22×C3111yescharacteristic
434C24×C4C22×C3111yescharacteristic
435C24×C4C22×C3111yescharacteristic
436C24×C4C22×C3111yescharacteristic
437C24×C4C22×C3111yescharacteristic
438C2×C22⋊Q8—28no—
439C2×C22⋊Q8—28no—
440C2×C22⋊Q8C22×C3118yescomplemented
441C2×C22⋊Q8C22×C3118yescomplemented
442C2×C4×D4—28no—
443C2×C4×D4C22×C3118yes—
444C22×C4⋊C4—28no—
445C22×C4⋊C4C22×C3111yescharacteristic
446C22×C4⋊C4C22×C3111yescharacteristic
447C22×C4⋊C4C22×C3111yescharacteristic
448C22×C4⋊C4C22×C3111yescharacteristic
449C22×C4⋊C4C22×C3111yescharacteristic
450C22×C4⋊C4C22×C3111yescharacteristic
451C22×C4⋊C4C22×C3111yescharacteristic
452C22×C4⋊C4C22×C3111yescharacteristic
453C22×C4⋊C4C22×C3111yescharacteristic
454C22×C4⋊C4C22×C3111yescharacteristic
455C22×C4⋊C4C22×C3111yescharacteristic
456C22×C4⋊C4C22×C3111yescharacteristic
457C22×C4⋊C4C22×C3118yescomplemented
458C22×C22⋊C4C22×C3111yescharacteristic
459C22×C22⋊C4C22×C3111yescharacteristic
460C22×C22⋊C4C22×C3111yescharacteristic
461C22×C22⋊C4C22×C3111yescharacteristic
462C22×C22⋊C4C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3111yescharacteristic
464C22×C22⋊C4C22×C3111yescharacteristic
465C22×C22⋊C4C22×C3111yescharacteristic
466C22×C42C22×C3111yescharacteristic
467#399C22×C3118yescomplemented
468#398C22×C3118yescomplemented
469#396C22×C3118yescomplemented
470#395C22×C3118yescomplemented
471#389C22×C3118yescomplemented
472#387C22×C3118yescomplemented
473#386C22×C3118yes—
474#386C22×C3118yes—
475#385C22×C3118yescomplemented
476#385C22×C3118yescomplemented
477#385C22×C3118yescomplemented
478C2×#95C22×C3111yescharacteristic
479C2×#95C22×C3111yescharacteristic
480C2×#95C22×C3111yescharacteristic
481C2×#95C22×C3111yescharacteristic
482C2×#95C22×C3111yescharacteristic
483C2×#95C22×C3111yescharacteristic
484C2×#95C22×C3111yescharacteristic
485C2×#95C22×C3111yescharacteristic
486C2×C31—28no—
487C2×C31—44no—
488C2×C31#244918yesdirect product factor
489C2×C31C22×C22⋊Q811yescharacteristic
490C2×C31C2×#52511yescharacteristic
491C2×C31C2×#53911yescharacteristic
492C2×C31C2×D4211yescharacteristic
493C2×C31C2×#54711yescharacteristic
494C2×C31C2×D4×Q811yescharacteristic
495C2×C31C2×#55411yescharacteristic
496C25C23×C3111yescharacteristic
497C25C23×C3111yescharacteristic
498C22×Q8—24no—
499C22×Q8—24no—
500C22×Q8—42no—
501C22×Q8C23×C3114yes—
502C22×D4—24no—
503C22×D4—24no—
504C22×D4Q8×C3118yescomplemented
505C22×D4C23×C3114yes—
506C23×C4—24no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—24no—
515C23×C4—42no—
516C23×C4—42no—
517C23×C4—42no—
518C23×C4C23×C3111yescharacteristic
519C23×C4C23×C3111yescharacteristic
520C23×C4C23×C3111yescharacteristic
521C23×C4C23×C3111yescharacteristic
522C23×C4C23×C3111yescharacteristic
523C23×C4C23×C3111yescharacteristic
524C23×C4C23×C3114yes—
525C23×C4C23×C3114yes—
526C23×C4C23×C3114yes—
527C23×C4C23×C3114yes—
528C23×C4C23×C3111yescharacteristic
529C23×C4C23×C3111yescharacteristic
530C23×C4C23×C3111yescharacteristic
531C23×C4C23×C3111yescharacteristic
532C23×C4C23×C3111yescharacteristic
533C23×C4C23×C3111yescharacteristic
534C23×C4C23×C3111yescharacteristic
535C22⋊Q8—232no—
536C22⋊Q8—232no—
537C4×D4—232no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—232no—
549C2×C4⋊C4—42no—
550C2×C4⋊C4D4×C3118yescomplemented
551C2×C4⋊C4C23×C3114yes—
552C2×C4⋊C4C23×C3114yes—
553C2×C4⋊C4C23×C3114yes—
554C2×C4⋊C4C23×C3114yes—
555C2×C4⋊C4C23×C3114yes—
556C2×C4⋊C4C23×C3114yes—
557C2×C4⋊C4C23×C3114yes—
558C2×C4⋊C4C23×C3114yes—
559C2×C4⋊C4C23×C3114yes—
560C2×C4⋊C4C23×C3114yes—
561C2×C4⋊C4C23×C3114yes—
562C2×C4⋊C4C23×C3114yes—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4D4×C3118yes—
571C2×C22⋊C4C23×C3114yes—
572C2×C22⋊C4C23×C3114yes—
573C2×C22⋊C4C23×C3114yes—
574C2×C22⋊C4C23×C3114yes—
575C2×C22⋊C4C23×C3114yes—
576C2×C22⋊C4C23×C3114yes—
577C2×C22⋊C4C23×C3114yes—
578C2×C22⋊C4C23×C3114yes—
579C2×C42—24no—
580C2×C42C23×C3114yes—
581#95C23×C3114yes—
582#95C23×C3114yes—
583#95C23×C3114yes—
584#95C23×C3114yes—
585#95C23×C3114yes—
586#95C23×C3114yes—
587#95C23×C3114yes—
588#95C23×C3114yes—
589C31C2×#244911yescharacteristic, direct product factor, Sylow
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24C2×D4×C3114yes—
601C24C2×Q8×C3114yes—
602C24C2×Q8×C3114yes—
603C24#41×C3114yes—
604C24C24×C3112yes—
605C24C24×C3112yes—
606C24C24×C3111yescharacteristic
607C2×Q8—28no—
608C2×Q8—28no—
609C2×Q8—44no—
610C2×Q8—416no—
611C2×D4—232no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4C2×Q8×C31116yescomplemented
615C22×C4—232no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—28no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—28no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—416no—
661C22×C4—416no—
662C22×C4—416no—
663C22×C4C2×D4×C3114yes—
664C22×C4C2×D4×C3114yes—
665C22×C4C2×D4×C3114yes—
666C22×C4C2×D4×C3114yes—
667C22×C4C2×D4×C3114yes—
668C22×C4C2×Q8×C3114yes—
669C22×C4#41×C3114yes—
670C22×C4C24×C3112yes—
671C22×C4C24×C3112yes—
672C22×C4C24×C3112yes—
673C22×C4C24×C3112yes—
674C22×C4C24×C3112yes—
675C22×C4C24×C3112yes—
676C22×C4C24×C3112yes—
677C22×C4C24×C3112yes—
678C22×C4C24×C3112yes—
679C22×C4C24×C3112yes—
680C22×C4C24×C3112yes—
681C22×C4C24×C3112yes—
682C22×C4C24×C3112yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—44no—
694C4⋊C4C2×D4×C31116yescomplemented
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—44no—
702C22⋊C4C2×D4×C31116yes—
703C42—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23C31×C22⋊Q8116yescomplemented
728C23C22×D4×C3114yes—
729C23C22×D4×C3112yes—
730C23C22×D4×C3112yes—
731C23C22×Q8×C3114yes—
732C23C22×Q8×C3114yes—
733C23C22×Q8×C3112yes—
734C23C2×#41×C3114yes—
735C23C2×#41×C3112yes—
736C23C2×#41×C3112yes—
737C23C31×H(5,𝔽2)12yes—
738C23C31×2−1+412yes—
739C23C25×C3111yescharacteristic
740Q8—416no—
741D4—232no—
742C2×C4—232no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4C22×D4×C3114yes—
792C2×C4C22×D4×C3114yes—
793C2×C4C22×D4×C3114yes—
794C2×C4C22×D4×C3114yes—
795C2×C4C22×D4×C3114yes—
796C2×C4C22×Q8×C3114yes—
797C2×C4C2×#41×C3114yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—232no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—416no—
813C22C2×C31×C22⋊Q814yes—
814C22C2×C31×C22⋊Q818yescomplemented
815C22C31×#52514yes—
816C22C31×#53914yes—
817C22D42×C3114yes—
818C22C31×#54714yes—
819C22D4×Q8×C3114yes—
820C22C31×#55414yes—
821C22C23×D4×C3111yescharacteristic
822C22C23×D4×C3111yescharacteristic
823C22C23×Q8×C3111yescharacteristic
824C22C22×#41×C3111yescharacteristic
825C22C22×#41×C3111yescharacteristic
826C22C2×C31×H(5,𝔽2)11yescharacteristic
827C22C2×C31×2−1+411yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—24no—
834C4—24no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C2—28no—
842C2—44no—
843C2C31×#244918yesdirect product factor
844C2C22×C31×C22⋊Q811yescharacteristic
845C2C2×C31×#52511yescharacteristic
846C2C2×C31×#53911yescharacteristic
847C2C2×D42×C3111yescharacteristic
848C2C2×C31×#54711yescharacteristic
849C2C2×D4×Q8×C3111yescharacteristic
850C2C2×C31×#55411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
2. C22×C31×C22⋊Q8C2semidirect
4. C23×C4⋊C4×C31C2semidirect
5. C31×#2449C2direct (N × H)
6. C2×C31×#399C2semidirect
7. C2×C31×#398C2semidirect
8. C2×C31×#396C2semidirect
9. C2×C31×#395C2semidirect
10. C2×C31×#389C2semidirect
11. C2×C31×#387C2semidirect
14. C2×C31×#385C2semidirect
15. C2×C31×#385C2semidirect
16. C2×C31×#385C2semidirect
25. C2×C31×C22⋊Q8C22semidirect
26. C2×C31×C22⋊Q8C22semidirect
42. C22×C4⋊C4×C31C22semidirect
52. C31×#399C22semidirect
53. C31×#398C22semidirect
54. C31×#396C22semidirect
55. C31×#395C22semidirect
56. C31×#389C22semidirect
57. C31×#387C22semidirect
60. C31×#385C22semidirect
61. C31×#385C22semidirect
62. C31×#385C22semidirect
79. C22×D4×C31Q8semidirect
125. C2×C4⋊C4×C31D4semidirect
188. C2×D4×C31C2×Q8semidirect
268. C4⋊C4×C31C2×D4semidirect
278. C2×#2449C31direct (N × H)
302. C23×C31C22⋊Q8semidirect
373. C22×C22⋊Q8C2×C31semidirect
374. C22×C22⋊Q8C2×C31semidirect
376. C23×C4⋊C4C2×C31semidirect
377. #2449C2×C31direct (N × H)
378. C2×#399C2×C31semidirect
379. C2×#398C2×C31semidirect
380. C2×#396C2×C31semidirect
381. C2×#395C2×C31semidirect
382. C2×#389C2×C31semidirect
383. C2×#387C2×C31semidirect
386. C2×#385C2×C31semidirect
387. C2×#385C2×C31semidirect
388. C2×#385C2×C31semidirect
405. C22×C31C2×C22⋊Q8semidirect
440. C2×C22⋊Q8C22×C31semidirect
441. C2×C22⋊Q8C22×C31semidirect
457. C22×C4⋊C4C22×C31semidirect
467. #399C22×C31semidirect
468. #398C22×C31semidirect
469. #396C22×C31semidirect
470. #395C22×C31semidirect
471. #389C22×C31semidirect
472. #387C22×C31semidirect
475. #385C22×C31semidirect
476. #385C22×C31semidirect
477. #385C22×C31semidirect
488. C2×C31#2449direct (N × H)
504. C22×D4Q8×C31semidirect
550. C2×C4⋊C4D4×C31semidirect
589. C31C2×#2449direct (N × H)
614. C2×D4C2×Q8×C31semidirect
694. C4⋊C4C2×D4×C31semidirect
727. C23C31×C22⋊Q8semidirect
814. C22C2×C31×C22⋊Q8semidirect
843. C2C31×#2449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C22×C4×D4×C312
C23×C4⋊C4×C312
C31×#24492
C2×C31×#3992
C2×C31×#3982
C2×C31×#3962
C2×C31×#3952
C2×C31×#3892
C2×C31×#3872
C2×C31×#3862
C2×C31×#3852
C2×#244931