Finite Group Databasebeta

← C2×C31×#2480 #21491419

Subgroups — C2×C31×#2480 #21491419

Order 7936.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#126C211yesmaximal, characteristic, complemented
2C23×C22⋊C4×C31C211yesmaximal, characteristic
3C31×#2480C2116yesmaximal, direct product factor
4C2×C31×#397C211yesmaximal, characteristic, complemented
5C2×C31×#397C211yesmaximal, characteristic, complemented
6C2×C31×#397C211yesmaximal, characteristic, complemented
7C2×C31×#396C211yesmaximal, characteristic, complemented
8C2×C31×#388C211yesmaximal, characteristic, complemented
9C2×C31×#388C211yesmaximal, characteristic, complemented
10C2×C31×#388C211yesmaximal, characteristic, complemented
11C2×C31×#385C211yesmaximal, characteristic, complemented
12C2×C31×#385C211yesmaximal, characteristic, complemented
13C2×C31×#380C211yesmaximal, characteristic, complemented
14C2×C31×#379C211yesmaximal, characteristic
15C2×C31×#379C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
17C26×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C2×C31×#126—28no—
21C2×C31×#126C2218yescomplemented
22C22×C4⋊C4×C31C2211yescharacteristic, complemented
23C22×C4⋊C4×C31C2211yescharacteristic, complemented
24C22×C4⋊C4×C31C2211yescharacteristic, complemented
25C22×C4⋊C4×C31C2211yescharacteristic, complemented
26C22×C4⋊C4×C31C2211yescharacteristic, complemented
27C22×C4⋊C4×C31C2211yescharacteristic, complemented
28C22×C22⋊C4×C31—28no—
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2218yes—
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊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×C42×C31C2211yescharacteristic, complemented
47C22×C42×C31C2211yescharacteristic, complemented
48C31×#397C2218yescomplemented
49C31×#397C2218yescomplemented
50C31×#397C2218yescomplemented
51C31×#396C2218yescomplemented
52C31×#388C2218yescomplemented
53C31×#388C2218yescomplemented
54C31×#388C2218yescomplemented
55C31×#385C2218yescomplemented
56C31×#385C2218yescomplemented
57C31×#380C2218yescomplemented
58C31×#379C2218yes—
59C31×#379C2218yes—
60C4×C22⋊C4×C31C2218yescomplemented
61C2×C31×#95C2211yescharacteristic, complemented
62C2×C31×#95C2211yescharacteristic, complemented
63C2×C31×#95C2211yescharacteristic, complemented
64C2×C31×#95C2211yescharacteristic, complemented
65C2×C31×#95C2211yescharacteristic, complemented
66C2×C31×#95C2211yescharacteristic, complemented
67C2×C31×#95C2211yescharacteristic, complemented
68C2×C31×#95C2211yescharacteristic, complemented
69C25×C31—24no—
70C25×C31—24no—
71C25×C31—24no—
72C25×C31—24no—
73C25×C31—24no—
74C25×C31—42no—
75C25×C31—42no—
76C25×C31C2311yescharacteristic
77C25×C31C2311yescharacteristic
78C25×C31C2314yes—
79C25×C31C2311yescharacteristic
80C23×C4×C31—24no—
81C23×C4×C31—24no—
82C23×C4×C31—24no—
83C23×C4×C31—24no—
84C23×C4×C31—42no—
85C23×C4×C31—42no—
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2314yes—
97C23×C4×C31C2314yes—
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C31×#126—232no—
101C2×C4⋊C4×C31—24no—
102C2×C4⋊C4×C31—24no—
103C2×C4⋊C4×C31—24no—
104C2×C4⋊C4×C31—42no—
105C2×C4⋊C4×C31—42no—
106C2×C4⋊C4×C31—42no—
107C2×C4⋊C4×C31C2314yescomplemented
108C2×C4⋊C4×C31C2314yescomplemented
109C2×C4⋊C4×C31C2314yescomplemented
110C2×C4⋊C4×C31C2314yescomplemented
111C2×C4⋊C4×C31C2314yescomplemented
112C2×C4⋊C4×C31C2314yescomplemented
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—24no—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—24no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—232no—
125C2×C22⋊C4×C31—42no—
126C2×C22⋊C4×C31—42no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31D418yes—
130C2×C22⋊C4×C31C2314yes—
131C2×C22⋊C4×C31C2314yes—
132C2×C22⋊C4×C31C2314yes—
133C2×C22⋊C4×C31C2314yes—
134C2×C22⋊C4×C31C2314yes—
135C2×C22⋊C4×C31C2314yes—
136C2×C22⋊C4×C31C2314yes—
137C2×C22⋊C4×C31C2314yes—
138C2×C22⋊C4×C31C2314yes—
139C2×C22⋊C4×C31C2314yes—
140C2×C22⋊C4×C31C2314yes—
141C2×C22⋊C4×C31C2314yes—
142C2×C22⋊C4×C31C2314yes—
143C2×C22⋊C4×C31C2314yes—
144C2×C22⋊C4×C31C2314yes—
145C2×C22⋊C4×C31C2314yes—
146C2×C42×C31—24no—
147C2×C42×C31—42no—
148C2×C42×C31C2314yescomplemented
149C2×C42×C31C2314yescomplemented
150C31×#95C2314yescomplemented
151C31×#95C2314yescomplemented
152C31×#95C2314yescomplemented
153C31×#95C2314yescomplemented
154C31×#95C2314yescomplemented
155C31×#95C2314yescomplemented
156C31×#95C2314yescomplemented
157C31×#95C2314yescomplemented
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—232no—
163C24×C31—28no—
164C24×C31—22no—
165C24×C31—28no—
166C24×C31—28no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—22no—
177C24×C31—22no—
178C24×C31—28no—
179C24×C31—28no—
180C24×C31—44no—
181C24×C31—44no—
182C24×C31—416no—
183C24×C31—416no—
184C24×C31—416no—
185C24×C31—416no—
186C24×C31—416no—
187C24×C31—416no—
188C24×C31C2×D414yes—
189C24×C31#4114yes—
190C24×C31#4114yes—
191C24×C31#4114yes—
192C24×C31#4114yes—
193C24×C31C2412yes—
194C24×C31C2412yes—
195C24×C31C2412yes—
196C24×C31C2411yescharacteristic
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—22no—
206C22×C4×C31—22no—
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—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—28no—
220C22×C4×C31—28no—
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—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—28no—
234C22×C4×C31—28no—
235C22×C4×C31—44no—
236C22×C4×C31—44no—
237C22×C4×C31—416no—
238C22×C4×C31—416no—
239C22×C4×C31C2×D414yes—
240C22×C4×C31C2×D414yes—
241C22×C4×C31C2412yes—
242C22×C4×C31C2412yes—
243C22×C4×C31C2412yes—
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—
253C4⋊C4×C31—28no—
254C4⋊C4×C31—28no—
255C4⋊C4×C31—28no—
256C4⋊C4×C31—44no—
257C4⋊C4×C31—44no—
258C4⋊C4×C31—44no—
259C22⋊C4×C31—28no—
260C22⋊C4×C31—28no—
261C22⋊C4×C31—28no—
262C22⋊C4×C31—28no—
263C22⋊C4×C31—28no—
264C22⋊C4×C31—28no—
265C22⋊C4×C31—28no—
266C22⋊C4×C31—28no—
267C22⋊C4×C31—28no—
268C22⋊C4×C31—28no—
269C22⋊C4×C31—28no—
270C22⋊C4×C31—44no—
271C22⋊C4×C31—44no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—44no—
274C22⋊C4×C31C2×D4116yes—
275C42×C31—28no—
276C42×C31—44no—
277C2×#2480C3111yesmaximal, characteristic, direct product factor, Sylow
278C23×C31—28no—
279C23×C31—28no—
280C23×C31—28no—
281C23×C31—28no—
282C23×C31—28no—
283C23×C31—28no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—232no—
289C23×C31—28no—
290C23×C31—28no—
291C23×C31—28no—
292C23×C31—28no—
293C23×C31—28no—
294C23×C31—28no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—416no—
308C23×C31—416no—
309C23×C31—416no—
310C23×C31—416no—
311C23×C31—416no—
312C23×C31—4128no—
313C23×C31—44no—
314C23×C31—44no—
315C23×C31—416no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—44no—
320C23×C31—44no—
321C23×C31—44no—
322C23×C31#126116yescomplemented
323C23×C31C22×D414yes—
324C23×C31C22×D412yes—
325C23×C31C2×#4114yes—
326C23×C31C2×#4114yes—
327C23×C31C2×#4114yes—
328C23×C31C2×#4114yes—
329C23×C31C2×#4112yes—
330C23×C31C2×#4112yes—
331C23×C31C2×#4112yes—
332C23×C31C2×#4112yes—
333C23×C31H(5,𝔽2)12yes—
334C23×C31H(5,𝔽2)12yes—
335C23×C31C2511yescharacteristic
336C2×C4×C31—28no—
337C2×C4×C31—28no—
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—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—416no—
373C2×C4×C31—416no—
374C2×C4×C31—44no—
375C2×C4×C31—44no—
376C2×C4×C31—44no—
377C2×C4×C31—44no—
378C2×C4×C31—44no—
379C2×C4×C31—44no—
380C2×C4×C31—44no—
381C2×C4×C31—44no—
382C2×C4×C31—44no—
383C2×C4×C31—44no—
384C2×C4×C31C22×D414yes—
385C2×C4×C31C22×D414yes—
386C22×#126C2×C3111yescharacteristic, complemented
387C23×C22⋊C4C2×C3111yescharacteristic
388#2480C2×C31116yesdirect product factor
389C2×#397C2×C3111yescharacteristic, complemented
390C2×#397C2×C3111yescharacteristic, complemented
391C2×#397C2×C3111yescharacteristic, complemented
392C2×#396C2×C3111yescharacteristic, complemented
393C2×#388C2×C3111yescharacteristic, complemented
394C2×#388C2×C3111yescharacteristic, complemented
395C2×#388C2×C3111yescharacteristic, complemented
396C2×#385C2×C3111yescharacteristic, complemented
397C2×#385C2×C3111yescharacteristic, complemented
398C2×#380C2×C3111yescharacteristic, complemented
399C2×#379C2×C3111yescharacteristic
400C2×#379C2×C3111yescharacteristic
401C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
402C22×C31—24no—
403C22×C31—24no—
404C22×C31—24no—
405C22×C31—24no—
406C22×C31—24no—
407C22×C31—24no—
408C22×C31—232no—
409C22×C31—24no—
410C22×C31—24no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—24no—
414C22×C31—24no—
415C22×C31—464no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—416no—
425C22×C31—416no—
426C22×C31#52514yes—
427C22×C31C2×#12614yes—
428C22×C31C2×#12618yescomplemented
429C22×C31#53814yes—
430C22×C31#54614yes—
431C22×C31#54614yes—
432C22×C31#55114yes—
433C22×C31#55114yes—
434C22×C31C23×D411yescharacteristic
435C22×C31C22×#4111yescharacteristic
436C22×C31C22×#4111yescharacteristic
437C22×C31C22×#4111yescharacteristic
438C22×C31C22×#4111yescharacteristic
439C22×C31C2×H(5,𝔽2)11yescharacteristic
440C22×C31C2×H(5,𝔽2)11yescharacteristic
441C4×C31—24no—
442C4×C31—24no—
443C4×C31—42no—
444C4×C31—42no—
445C4×C31—42no—
446C4×C31—42no—
447C4×C31—42no—
448C4×C31—42no—
449C4×C31—42no—
450C4×C31—42no—
451C4×C31—42no—
452C4×C31—42no—
453C26C22×C3111yescharacteristic
454C24×C4C22×C3111yescharacteristic
455C24×C4C22×C3111yescharacteristic
456C2×#126—28no—
457C2×#126C22×C3118yescomplemented
458C22×C4⋊C4C22×C3111yescharacteristic, complemented
459C22×C4⋊C4C22×C3111yescharacteristic, complemented
460C22×C4⋊C4C22×C3111yescharacteristic, complemented
461C22×C4⋊C4C22×C3111yescharacteristic, complemented
462C22×C4⋊C4C22×C3111yescharacteristic, complemented
463C22×C4⋊C4C22×C3111yescharacteristic, complemented
464C22×C22⋊C4—28no—
465C22×C22⋊C4C22×C3111yescharacteristic
466C22×C22⋊C4C22×C3111yescharacteristic
467C22×C22⋊C4C22×C3111yescharacteristic
468C22×C22⋊C4C22×C3111yescharacteristic
469C22×C22⋊C4C22×C3111yescharacteristic
470C22×C22⋊C4C22×C3111yescharacteristic
471C22×C22⋊C4C22×C3118yes—
472C22×C22⋊C4C22×C3111yescharacteristic
473C22×C22⋊C4C22×C3111yescharacteristic
474C22×C22⋊C4C22×C3111yescharacteristic
475C22×C22⋊C4C22×C3111yescharacteristic
476C22×C22⋊C4C22×C3111yescharacteristic
477C22×C22⋊C4C22×C3111yescharacteristic
478C22×C22⋊C4C22×C3111yescharacteristic
479C22×C22⋊C4C22×C3111yescharacteristic
480C22×C22⋊C4C22×C3111yescharacteristic
481C22×C22⋊C4C22×C3111yescharacteristic
482C22×C42C22×C3111yescharacteristic, complemented
483C22×C42C22×C3111yescharacteristic, complemented
484#397C22×C3118yescomplemented
485#397C22×C3118yescomplemented
486#397C22×C3118yescomplemented
487#396C22×C3118yescomplemented
488#388C22×C3118yescomplemented
489#388C22×C3118yescomplemented
490#388C22×C3118yescomplemented
491#385C22×C3118yescomplemented
492#385C22×C3118yescomplemented
493#380C22×C3118yescomplemented
494#379C22×C3118yes—
495#379C22×C3118yes—
496C4×C22⋊C4C22×C3118yescomplemented
497C2×#95C22×C3111yescharacteristic, complemented
498C2×#95C22×C3111yescharacteristic, complemented
499C2×#95C22×C3111yescharacteristic, complemented
500C2×#95C22×C3111yescharacteristic, complemented
501C2×#95C22×C3111yescharacteristic, complemented
502C2×#95C22×C3111yescharacteristic, complemented
503C2×#95C22×C3111yescharacteristic, complemented
504C2×#95C22×C3111yescharacteristic, complemented
505C2×C31—28no—
506C2×C31—44no—
507C2×C31—44no—
508C2×C31#248018yesdirect product factor
509C2×C31C2×#52511yescharacteristic
510C2×C31C22×#12611yescharacteristic
511C2×C31C2×#53811yescharacteristic
512C2×C31C2×#54611yescharacteristic
513C2×C31C2×#54611yescharacteristic
514C2×C31C2×#55111yescharacteristic
515C2×C31C2×#55111yescharacteristic
516C25—24no—
517C25—24no—
518C25—24no—
519C25—24no—
520C25—24no—
521C25—42no—
522C25—42no—
523C25C23×C3111yescharacteristic
524C25C23×C3111yescharacteristic
525C25C23×C3114yes—
526C25C23×C3111yescharacteristic
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C23×C3111yescharacteristic
534C23×C4C23×C3111yescharacteristic
535C23×C4C23×C3111yescharacteristic
536C23×C4C23×C3111yescharacteristic
537C23×C4C23×C3111yescharacteristic
538C23×C4C23×C3111yescharacteristic
539C23×C4C23×C3111yescharacteristic
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C23×C4C23×C3111yescharacteristic
543C23×C4C23×C3114yes—
544C23×C4C23×C3114yes—
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3111yescharacteristic
547#126—232no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—42no—
552C2×C4⋊C4—42no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4C23×C3114yescomplemented
555C2×C4⋊C4C23×C3114yescomplemented
556C2×C4⋊C4C23×C3114yescomplemented
557C2×C4⋊C4C23×C3114yescomplemented
558C2×C4⋊C4C23×C3114yescomplemented
559C2×C4⋊C4C23×C3114yescomplemented
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
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—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—232no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4D4×C3118yes—
577C2×C22⋊C4C23×C3114yes—
578C2×C22⋊C4C23×C3114yes—
579C2×C22⋊C4C23×C3114yes—
580C2×C22⋊C4C23×C3114yes—
581C2×C22⋊C4C23×C3114yes—
582C2×C22⋊C4C23×C3114yes—
583C2×C22⋊C4C23×C3114yes—
584C2×C22⋊C4C23×C3114yes—
585C2×C22⋊C4C23×C3114yes—
586C2×C22⋊C4C23×C3114yes—
587C2×C22⋊C4C23×C3114yes—
588C2×C22⋊C4C23×C3114yes—
589C2×C22⋊C4C23×C3114yes—
590C2×C22⋊C4C23×C3114yes—
591C2×C22⋊C4C23×C3114yes—
592C2×C22⋊C4C23×C3114yes—
593C2×C42—24no—
594C2×C42—42no—
595C2×C42C23×C3114yescomplemented
596C2×C42C23×C3114yescomplemented
597#95C23×C3114yescomplemented
598#95C23×C3114yescomplemented
599#95C23×C3114yescomplemented
600#95C23×C3114yescomplemented
601#95C23×C3114yescomplemented
602#95C23×C3114yescomplemented
603#95C23×C3114yescomplemented
604#95C23×C3114yescomplemented
605C31C2×#248011yescharacteristic, direct product factor, Sylow
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—232no—
611C24—28no—
612C24—22no—
613C24—28no—
614C24—28no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—28no—
627C24—28no—
628C24—44no—
629C24—44no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24—416no—
636C24C2×D4×C3114yes—
637C24#41×C3114yes—
638C24#41×C3114yes—
639C24#41×C3114yes—
640C24#41×C3114yes—
641C24C24×C3112yes—
642C24C24×C3112yes—
643C24C24×C3112yes—
644C24C24×C3111yescharacteristic
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—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—416no—
686C22×C4—416no—
687C22×C4C2×D4×C3114yes—
688C22×C4C2×D4×C3114yes—
689C22×C4C24×C3112yes—
690C22×C4C24×C3112yes—
691C22×C4C24×C3112yes—
692C22×C4C24×C3112yes—
693C22×C4C24×C3112yes—
694C22×C4C24×C3112yes—
695C22×C4C24×C3112yes—
696C22×C4C24×C3112yes—
697C22×C4C24×C3112yes—
698C22×C4C24×C3112yes—
699C22×C4C24×C3112yes—
700C22×C4C24×C3112yes—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4C2×D4×C31116yes—
723C42—28no—
724C42—44no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—232no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—4128no—
760C23—44no—
761C23—44no—
762C23—416no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23C31×#126116yescomplemented
770C23C22×D4×C3114yes—
771C23C22×D4×C3112yes—
772C23C2×#41×C3114yes—
773C23C2×#41×C3114yes—
774C23C2×#41×C3114yes—
775C23C2×#41×C3114yes—
776C23C2×#41×C3112yes—
777C23C2×#41×C3112yes—
778C23C2×#41×C3112yes—
779C23C2×#41×C3112yes—
780C23C31×H(5,𝔽2)12yes—
781C23C31×H(5,𝔽2)12yes—
782C23C25×C3111yescharacteristic
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4C22×D4×C3114yes—
832C2×C4C22×D4×C3114yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—232no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—416no—
856C22—416no—
857C22C31×#52514yes—
858C22C2×C31×#12614yes—
859C22C2×C31×#12618yescomplemented
860C22C31×#53814yes—
861C22C31×#54614yes—
862C22C31×#54614yes—
863C22C31×#55114yes—
864C22C31×#55114yes—
865C22C23×D4×C3111yescharacteristic
866C22C22×#41×C3111yescharacteristic
867C22C22×#41×C3111yescharacteristic
868C22C22×#41×C3111yescharacteristic
869C22C22×#41×C3111yescharacteristic
870C22C2×C31×H(5,𝔽2)11yescharacteristic
871C22C2×C31×H(5,𝔽2)11yescharacteristic
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2C31×#248018yesdirect product factor
888C2C2×C31×#52511yescharacteristic
889C2C22×C31×#12611yescharacteristic
890C2C2×C31×#53811yescharacteristic
891C2C2×C31×#54611yescharacteristic
892C2C2×C31×#54611yescharacteristic
893C2C2×C31×#55111yescharacteristic
894C2C2×C31×#55111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC26×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×#126C2semidirect
3. C31×#2480C2direct (N × H)
4. C2×C31×#397C2semidirect
5. C2×C31×#397C2semidirect
6. C2×C31×#397C2semidirect
7. C2×C31×#396C2semidirect
8. C2×C31×#388C2semidirect
9. C2×C31×#388C2semidirect
10. C2×C31×#388C2semidirect
11. C2×C31×#385C2semidirect
12. C2×C31×#385C2semidirect
13. C2×C31×#380C2semidirect
16. C2×C4×C22⋊C4×C31C2semidirect
21. C2×C31×#126C22semidirect
22. C22×C4⋊C4×C31C22semidirect
23. C22×C4⋊C4×C31C22semidirect
24. C22×C4⋊C4×C31C22semidirect
25. C22×C4⋊C4×C31C22semidirect
26. C22×C4⋊C4×C31C22semidirect
27. C22×C4⋊C4×C31C22semidirect
46. C22×C42×C31C22semidirect
47. C22×C42×C31C22semidirect
48. C31×#397C22semidirect
49. C31×#397C22semidirect
50. C31×#397C22semidirect
51. C31×#396C22semidirect
52. C31×#388C22semidirect
53. C31×#388C22semidirect
54. C31×#388C22semidirect
55. C31×#385C22semidirect
56. C31×#385C22semidirect
57. C31×#380C22semidirect
60. C4×C22⋊C4×C31C22semidirect
61. C2×C31×#95C22semidirect
62. C2×C31×#95C22semidirect
63. C2×C31×#95C22semidirect
64. C2×C31×#95C22semidirect
65. C2×C31×#95C22semidirect
66. C2×C31×#95C22semidirect
67. C2×C31×#95C22semidirect
68. C2×C31×#95C22semidirect
107. C2×C4⋊C4×C31C23semidirect
108. C2×C4⋊C4×C31C23semidirect
109. C2×C4⋊C4×C31C23semidirect
110. C2×C4⋊C4×C31C23semidirect
111. C2×C4⋊C4×C31C23semidirect
112. C2×C4⋊C4×C31C23semidirect
148. C2×C42×C31C23semidirect
149. C2×C42×C31C23semidirect
150. C31×#95C23semidirect
151. C31×#95C23semidirect
152. C31×#95C23semidirect
153. C31×#95C23semidirect
154. C31×#95C23semidirect
155. C31×#95C23semidirect
156. C31×#95C23semidirect
157. C31×#95C23semidirect
277. C2×#2480C31direct (N × H)
322. C23×C31#126semidirect
386. C22×#126C2×C31semidirect
388. #2480C2×C31direct (N × H)
389. C2×#397C2×C31semidirect
390. C2×#397C2×C31semidirect
391. C2×#397C2×C31semidirect
392. C2×#396C2×C31semidirect
393. C2×#388C2×C31semidirect
394. C2×#388C2×C31semidirect
395. C2×#388C2×C31semidirect
396. C2×#385C2×C31semidirect
397. C2×#385C2×C31semidirect
398. C2×#380C2×C31semidirect
401. C2×C4×C22⋊C4C2×C31semidirect
428. C22×C31C2×#126semidirect
457. C2×#126C22×C31semidirect
458. C22×C4⋊C4C22×C31semidirect
459. C22×C4⋊C4C22×C31semidirect
460. C22×C4⋊C4C22×C31semidirect
461. C22×C4⋊C4C22×C31semidirect
462. C22×C4⋊C4C22×C31semidirect
463. C22×C4⋊C4C22×C31semidirect
482. C22×C42C22×C31semidirect
483. C22×C42C22×C31semidirect
484. #397C22×C31semidirect
485. #397C22×C31semidirect
486. #397C22×C31semidirect
487. #396C22×C31semidirect
488. #388C22×C31semidirect
489. #388C22×C31semidirect
490. #388C22×C31semidirect
491. #385C22×C31semidirect
492. #385C22×C31semidirect
493. #380C22×C31semidirect
496. C4×C22⋊C4C22×C31semidirect
497. C2×#95C22×C31semidirect
498. C2×#95C22×C31semidirect
499. C2×#95C22×C31semidirect
500. C2×#95C22×C31semidirect
501. C2×#95C22×C31semidirect
502. C2×#95C22×C31semidirect
503. C2×#95C22×C31semidirect
504. C2×#95C22×C31semidirect
508. C2×C31#2480direct (N × H)
554. C2×C4⋊C4C23×C31semidirect
555. C2×C4⋊C4C23×C31semidirect
556. C2×C4⋊C4C23×C31semidirect
557. C2×C4⋊C4C23×C31semidirect
558. C2×C4⋊C4C23×C31semidirect
559. C2×C4⋊C4C23×C31semidirect
595. C2×C42C23×C31semidirect
596. C2×C42C23×C31semidirect
597. #95C23×C31semidirect
598. #95C23×C31semidirect
599. #95C23×C31semidirect
600. #95C23×C31semidirect
601. #95C23×C31semidirect
602. #95C23×C31semidirect
603. #95C23×C31semidirect
604. #95C23×C31semidirect
605. C31C2×#2480direct (N × H)
769. C23C31×#126semidirect
859. C22C2×C31×#126semidirect
887. C2C31×#2480direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1262
C23×C22⋊C4×C312
C31×#24802
C2×C31×#3972
C2×C31×#3962
C2×C31×#3882
C2×C31×#3852
C2×C31×#3802
C2×C31×#3792
C2×C4×C22⋊C4×C312
C2×#248031