Finite Group Databasebeta

← C2×C31×#2481 #21491420

Subgroups — C2×C31×#2481 #21491420

Order 7936.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#126C211yesmaximal, characteristic, complemented
2C23×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C31×#2481C2116yesmaximal, direct product factor
4C2×C31×#400C211yesmaximal, characteristic, complemented
5C2×C31×#400C211yesmaximal, characteristic, complemented
6C2×C31×#397C211yesmaximal, characteristic, complemented
7C2×C31×#396C211yesmaximal, characteristic, complemented
8C2×C31×#388C211yesmaximal, characteristic, complemented
9C2×C31×#387C211yesmaximal, characteristic, complemented
10C2×C31×#387C211yesmaximal, characteristic, complemented
11C2×C31×#386C211yesmaximal, characteristic
12C2×C31×#386C211yesmaximal, characteristic
13C2×C31×#386C211yesmaximal, characteristic
14C2×C31×#385C211yesmaximal, characteristic, complemented
15C2×C31×#380C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C2×C31×#126—28no—
22C2×C31×#126C2218yescomplemented
23C22×C4⋊C4×C31—28no—
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C4⋊C4×C31C2218yescomplemented
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
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×C42×C31C2211yescharacteristic
43C22×C42×C31C2211yescharacteristic
44C31×#400C2218yescomplemented
45C31×#400C2218yescomplemented
46C31×#397C2218yescomplemented
47C31×#396C2218yescomplemented
48C31×#388C2218yescomplemented
49C31×#387C2218yescomplemented
50C31×#387C2218yescomplemented
51C31×#386C2218yes—
52C31×#386C2218yes—
53C31×#386C2218yes—
54C31×#385C2218yescomplemented
55C31×#380C2218yescomplemented
56C4×C22⋊C4×C31C2218yescomplemented
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C2×C31×#95C2211yescharacteristic
62C2×C31×#95C2211yescharacteristic
63C2×C31×#95C2211yescharacteristic
64C2×C31×#95C2211yescharacteristic
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2211yescharacteristic
69C25×C31C2311yescharacteristic
70C25×C31C2311yescharacteristic
71C22×D4×C31—24no—
72C22×D4×C31—24no—
73C22×D4×C31—24no—
74C22×D4×C31C2314yes—
75C23×C4×C31—24no—
76C23×C4×C31—24no—
77C23×C4×C31—24no—
78C23×C4×C31—24no—
79C23×C4×C31—24no—
80C23×C4×C31—24no—
81C23×C4×C31—24no—
82C23×C4×C31—42no—
83C23×C4×C31—42no—
84C23×C4×C31C2314yes—
85C23×C4×C31C2311yescharacteristic
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×C31C2314yes—
95C23×C4×C31C2314yes—
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
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—24no—
105C2×C4⋊C4×C31—24no—
106C2×C4⋊C4×C31—24no—
107C2×C4⋊C4×C31—232no—
108C2×C4⋊C4×C31—42no—
109C2×C4⋊C4×C31D418yescomplemented
110C2×C4⋊C4×C31C2314yes—
111C2×C4⋊C4×C31C2314yes—
112C2×C4⋊C4×C31C2314yes—
113C2×C4⋊C4×C31C2314yes—
114C2×C4⋊C4×C31C2314yes—
115C2×C4⋊C4×C31C2314yes—
116C2×C4⋊C4×C31C2314yes—
117C2×C4⋊C4×C31C2314yes—
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—24no—
125C2×C22⋊C4×C31—42no—
126C2×C22⋊C4×C31—42no—
127C2×C22⋊C4×C31C2314yes—
128C2×C22⋊C4×C31C2314yes—
129C2×C22⋊C4×C31C2314yes—
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×C42×C31—24no—
137C2×C42×C31—42no—
138C2×C42×C31C2314yes—
139C2×C42×C31C2314yes—
140C31×#95C2314yes—
141C31×#95C2314yes—
142C31×#95C2314yes—
143C31×#95C2314yes—
144C31×#95C2314yes—
145C31×#95C2314yes—
146C31×#95C2314yes—
147C31×#95C2314yes—
148C31×#95C2314yes—
149C31×#95C2314yes—
150C31×#95C2314yes—
151C31×#95C2314yes—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31#4114yes—
164C24×C31#4114yes—
165C24×C31#4114yes—
166C24×C31C2412yes—
167C24×C31C2412yes—
168C24×C31C2411yescharacteristic
169C2×D4×C31—28no—
170C2×D4×C31—28no—
171C2×D4×C31—28no—
172C2×D4×C31—416no—
173C22×C4×C31—232no—
174C22×C4×C31—22no—
175C22×C4×C31—28no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—28no—
184C22×C4×C31—28no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
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—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—28no—
200C22×C4×C31—28no—
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—28no—
215C22×C4×C31—28no—
216C22×C4×C31—44no—
217C22×C4×C31—44no—
218C22×C4×C31—416no—
219C22×C4×C31—416no—
220C22×C4×C31C2×D414yes—
221C22×C4×C31C2×D414yes—
222C22×C4×C31C2×D414yes—
223C22×C4×C31#4114yes—
224C22×C4×C31C2412yes—
225C22×C4×C31C2412yes—
226C22×C4×C31C2412yes—
227C22×C4×C31C2412yes—
228C22×C4×C31C2412yes—
229C22×C4×C31C2412yes—
230C22×C4×C31C2412yes—
231C22×C4×C31C2412yes—
232C22×C4×C31C2412yes—
233C22×C4×C31C2412yes—
234C22×C4×C31C2412yes—
235C22×C4×C31C2412yes—
236C22×C4×C31C2412yes—
237C4⋊C4×C31—28no—
238C4⋊C4×C31—28no—
239C4⋊C4×C31—28no—
240C4⋊C4×C31—28no—
241C4⋊C4×C31—28no—
242C4⋊C4×C31—28no—
243C4⋊C4×C31—44no—
244C4⋊C4×C31C2×D4116yescomplemented
245C22⋊C4×C31—28no—
246C22⋊C4×C31—28no—
247C22⋊C4×C31—28no—
248C22⋊C4×C31—28no—
249C22⋊C4×C31—28no—
250C22⋊C4×C31—28no—
251C22⋊C4×C31—28no—
252C22⋊C4×C31—44no—
253C22⋊C4×C31—44no—
254C42×C31—28no—
255C42×C31—44no—
256C2×#2481C3111yesmaximal, characteristic, direct product factor, Sylow
257C23×C31—28no—
258C23×C31—28no—
259C23×C31—28no—
260C23×C31—28no—
261C23×C31—28no—
262C23×C31—28no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—44no—
275C23×C31—44no—
276C23×C31—44no—
277C23×C31—44no—
278C23×C31—44no—
279C23×C31—44no—
280C23×C31—44no—
281C23×C31#126116yescomplemented
282C23×C31C22×D412yes—
283C23×C31C2×#4114yes—
284C23×C31C2×#4114yes—
285C23×C31C2×#4114yes—
286C23×C31C2×#4112yes—
287C23×C31C2×#4112yes—
288C23×C31C2×#4112yes—
289C23×C31C2×#4112yes—
290C23×C31H(5,𝔽2)12yes—
291C23×C312−1+412yes—
292C23×C31C2511yescharacteristic
293D4×C31—416no—
294C2×C4×C31—232no—
295C2×C4×C31—28no—
296C2×C4×C31—28no—
297C2×C4×C31—28no—
298C2×C4×C31—28no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
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—416no—
335C2×C4×C31—416no—
336C2×C4×C31—44no—
337C2×C4×C31—44no—
338C2×C4×C31—44no—
339C2×C4×C31—44no—
340C2×C4×C31—44no—
341C2×C4×C31—44no—
342C2×C4×C31—44no—
343C2×C4×C31—44no—
344C2×C4×C31—44no—
345C2×C4×C31C22×D414yes—
346C2×C4×C31C22×D414yes—
347C2×C4×C31C22×D414yes—
348C2×C4×C31C2×#4114yes—
349C22×#126C2×C3111yescharacteristic, complemented
350C23×C4⋊C4C2×C3111yescharacteristic, complemented
351#2481C2×C31116yesdirect product factor
352C2×#400C2×C3111yescharacteristic, complemented
353C2×#400C2×C3111yescharacteristic, complemented
354C2×#397C2×C3111yescharacteristic, complemented
355C2×#396C2×C3111yescharacteristic, complemented
356C2×#388C2×C3111yescharacteristic, complemented
357C2×#387C2×C3111yescharacteristic, complemented
358C2×#387C2×C3111yescharacteristic, complemented
359C2×#386C2×C3111yescharacteristic
360C2×#386C2×C3111yescharacteristic
361C2×#386C2×C3111yescharacteristic
362C2×#385C2×C3111yescharacteristic, complemented
363C2×#380C2×C3111yescharacteristic, complemented
364C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
365C22×C31—24no—
366C22×C31—24no—
367C22×C31—24no—
368C22×C31—24no—
369C22×C31—24no—
370C22×C31—24no—
371C22×C31—232no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—88no—
380C22×C31#52514yes—
381C22×C31C2×#12614yes—
382C22×C31C2×#12618yescomplemented
383C22×C31#53914yes—
384C22×C31#54614yes—
385C22×C31#54814yes—
386C22×C31#55214yes—
387C22×C31#55314yes—
388C22×C31C23×D411yescharacteristic
389C22×C31C22×#4111yescharacteristic
390C22×C31C22×#4111yescharacteristic
391C22×C31C22×#4111yescharacteristic
392C22×C31C22×#4111yescharacteristic
393C22×C31C2×H(5,𝔽2)11yescharacteristic
394C22×C31C2×2−1+411yescharacteristic
395C4×C31—24no—
396C4×C31—24no—
397C4×C31—24no—
398C4×C31—24no—
399C4×C31—42no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—42no—
403C4×C31—42no—
404C4×C31—42no—
405C4×C31—42no—
406C4×C31—42no—
407C4×C31—42no—
408C23×D4C22×C3111yescharacteristic
409C24×C4C22×C3111yescharacteristic
410C24×C4C22×C3111yescharacteristic
411C24×C4C22×C3111yescharacteristic
412C2×#126—28no—
413C2×#126C22×C3118yescomplemented
414C22×C4⋊C4—28no—
415C22×C4⋊C4C22×C3111yescharacteristic
416C22×C4⋊C4C22×C3111yescharacteristic
417C22×C4⋊C4C22×C3111yescharacteristic
418C22×C4⋊C4C22×C3111yescharacteristic
419C22×C4⋊C4C22×C3111yescharacteristic
420C22×C4⋊C4C22×C3111yescharacteristic
421C22×C4⋊C4C22×C3111yescharacteristic
422C22×C4⋊C4C22×C3111yescharacteristic
423C22×C4⋊C4C22×C3118yescomplemented
424C22×C22⋊C4C22×C3111yescharacteristic
425C22×C22⋊C4C22×C3111yescharacteristic
426C22×C22⋊C4C22×C3111yescharacteristic
427C22×C22⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3111yescharacteristic
429C22×C22⋊C4C22×C3111yescharacteristic
430C22×C22⋊C4C22×C3111yescharacteristic
431C22×C22⋊C4C22×C3111yescharacteristic
432C22×C22⋊C4C22×C3111yescharacteristic
433C22×C42C22×C3111yescharacteristic
434C22×C42C22×C3111yescharacteristic
435#400C22×C3118yescomplemented
436#400C22×C3118yescomplemented
437#397C22×C3118yescomplemented
438#396C22×C3118yescomplemented
439#388C22×C3118yescomplemented
440#387C22×C3118yescomplemented
441#387C22×C3118yescomplemented
442#386C22×C3118yes—
443#386C22×C3118yes—
444#386C22×C3118yes—
445#385C22×C3118yescomplemented
446#380C22×C3118yescomplemented
447C4×C22⋊C4C22×C3118yescomplemented
448C2×#95C22×C3111yescharacteristic
449C2×#95C22×C3111yescharacteristic
450C2×#95C22×C3111yescharacteristic
451C2×#95C22×C3111yescharacteristic
452C2×#95C22×C3111yescharacteristic
453C2×#95C22×C3111yescharacteristic
454C2×#95C22×C3111yescharacteristic
455C2×#95C22×C3111yescharacteristic
456C2×#95C22×C3111yescharacteristic
457C2×#95C22×C3111yescharacteristic
458C2×#95C22×C3111yescharacteristic
459C2×#95C22×C3111yescharacteristic
460C2×C31—28no—
461C2×C31—82no—
462C2×C31#248118yesdirect product factor
463C2×C31C2×#52511yescharacteristic
464C2×C31C22×#12611yescharacteristic
465C2×C31C2×#53911yescharacteristic
466C2×C31C2×#54611yescharacteristic
467C2×C31C2×#54811yescharacteristic
468C2×C31C2×#55211yescharacteristic
469C2×C31C2×#55311yescharacteristic
470C25C23×C3111yescharacteristic
471C25C23×C3111yescharacteristic
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4C23×C3114yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—42no—
484C23×C4—42no—
485C23×C4C23×C3111yescharacteristic
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3111yescharacteristic
488C23×C4C23×C3111yescharacteristic
489C23×C4C23×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491C23×C4C23×C3111yescharacteristic
492C23×C4C23×C3111yescharacteristic
493C23×C4C23×C3114yes—
494C23×C4C23×C3111yescharacteristic
495C23×C4C23×C3114yes—
496C23×C4C23×C3114yes—
497C23×C4C23×C3111yescharacteristic
498C23×C4C23×C3111yescharacteristic
499C23×C4C23×C3111yescharacteristic
500C23×C4C23×C3111yescharacteristic
501#126—232no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—232no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4D4×C3118yescomplemented
511C2×C4⋊C4C23×C3114yes—
512C2×C4⋊C4C23×C3114yes—
513C2×C4⋊C4C23×C3114yes—
514C2×C4⋊C4C23×C3114yes—
515C2×C4⋊C4C23×C3114yes—
516C2×C4⋊C4C23×C3114yes—
517C2×C4⋊C4C23×C3114yes—
518C2×C4⋊C4C23×C3114yes—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4C23×C3114yes—
529C2×C22⋊C4C23×C3114yes—
530C2×C22⋊C4C23×C3114yes—
531C2×C22⋊C4C23×C3114yes—
532C2×C22⋊C4C23×C3114yes—
533C2×C22⋊C4C23×C3114yes—
534C2×C22⋊C4C23×C3114yes—
535C2×C22⋊C4C23×C3114yes—
536C2×C22⋊C4C23×C3114yes—
537C2×C42—24no—
538C2×C42—42no—
539C2×C42C23×C3114yes—
540C2×C42C23×C3114yes—
541#95C23×C3114yes—
542#95C23×C3114yes—
543#95C23×C3114yes—
544#95C23×C3114yes—
545#95C23×C3114yes—
546#95C23×C3114yes—
547#95C23×C3114yes—
548#95C23×C3114yes—
549#95C23×C3114yes—
550#95C23×C3114yes—
551#95C23×C3114yes—
552#95C23×C3114yes—
553C31C2×#248111yescharacteristic, direct product factor, Sylow
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24#41×C3114yes—
566C24#41×C3114yes—
567C24#41×C3114yes—
568C24C24×C3112yes—
569C24C24×C3112yes—
570C24C24×C3111yescharacteristic
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—416no—
575C22×C4—232no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—416no—
621C22×C4—416no—
622C22×C4C2×D4×C3114yes—
623C22×C4C2×D4×C3114yes—
624C22×C4C2×D4×C3114yes—
625C22×C4#41×C3114yes—
626C22×C4C24×C3112yes—
627C22×C4C24×C3112yes—
628C22×C4C24×C3112yes—
629C22×C4C24×C3112yes—
630C22×C4C24×C3112yes—
631C22×C4C24×C3112yes—
632C22×C4C24×C3112yes—
633C22×C4C24×C3112yes—
634C22×C4C24×C3112yes—
635C22×C4C24×C3112yes—
636C22×C4C24×C3112yes—
637C22×C4C24×C3112yes—
638C22×C4C24×C3112yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—44no—
646C4⋊C4C2×D4×C31116yescomplemented
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C42—28no—
657C42—44no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23C31×#126116yescomplemented
683C23C22×D4×C3112yes—
684C23C2×#41×C3114yes—
685C23C2×#41×C3114yes—
686C23C2×#41×C3114yes—
687C23C2×#41×C3112yes—
688C23C2×#41×C3112yes—
689C23C2×#41×C3112yes—
690C23C2×#41×C3112yes—
691C23C31×H(5,𝔽2)12yes—
692C23C31×2−1+412yes—
693C23C25×C3111yescharacteristic
694D4—416no—
695C2×C4—232no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—416no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4C22×D4×C3114yes—
747C2×C4C22×D4×C3114yes—
748C2×C4C22×D4×C3114yes—
749C2×C4C2×#41×C3114yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—232no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—88no—
765C22C31×#52514yes—
766C22C2×C31×#12614yes—
767C22C2×C31×#12618yescomplemented
768C22C31×#53914yes—
769C22C31×#54614yes—
770C22C31×#54814yes—
771C22C31×#55214yes—
772C22C31×#55314yes—
773C22C23×D4×C3111yescharacteristic
774C22C22×#41×C3111yescharacteristic
775C22C22×#41×C3111yescharacteristic
776C22C22×#41×C3111yescharacteristic
777C22C22×#41×C3111yescharacteristic
778C22C2×C31×H(5,𝔽2)11yescharacteristic
779C22C2×C31×2−1+411yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C2—28no—
794C2—82no—
795C2C31×#248118yesdirect product factor
796C2C2×C31×#52511yescharacteristic
797C2C22×C31×#12611yescharacteristic
798C2C2×C31×#53911yescharacteristic
799C2C2×C31×#54611yescharacteristic
800C2C2×C31×#54811yescharacteristic
801C2C2×C31×#55211yescharacteristic
802C2C2×C31×#55311yescharacteristic
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×#126C2semidirect
2. C23×C4⋊C4×C31C2semidirect
3. C31×#2481C2direct (N × H)
4. C2×C31×#400C2semidirect
5. C2×C31×#400C2semidirect
6. C2×C31×#397C2semidirect
7. C2×C31×#396C2semidirect
8. C2×C31×#388C2semidirect
9. C2×C31×#387C2semidirect
10. C2×C31×#387C2semidirect
14. C2×C31×#385C2semidirect
15. C2×C31×#380C2semidirect
16. C2×C4×C22⋊C4×C31C2semidirect
22. C2×C31×#126C22semidirect
32. C22×C4⋊C4×C31C22semidirect
44. C31×#400C22semidirect
45. C31×#400C22semidirect
46. C31×#397C22semidirect
47. C31×#396C22semidirect
48. C31×#388C22semidirect
49. C31×#387C22semidirect
50. C31×#387C22semidirect
54. C31×#385C22semidirect
55. C31×#380C22semidirect
56. C4×C22⋊C4×C31C22semidirect
109. C2×C4⋊C4×C31D4semidirect
244. C4⋊C4×C31C2×D4semidirect
256. C2×#2481C31direct (N × H)
281. C23×C31#126semidirect
349. C22×#126C2×C31semidirect
350. C23×C4⋊C4C2×C31semidirect
351. #2481C2×C31direct (N × H)
352. C2×#400C2×C31semidirect
353. C2×#400C2×C31semidirect
354. C2×#397C2×C31semidirect
355. C2×#396C2×C31semidirect
356. C2×#388C2×C31semidirect
357. C2×#387C2×C31semidirect
358. C2×#387C2×C31semidirect
362. C2×#385C2×C31semidirect
363. C2×#380C2×C31semidirect
364. C2×C4×C22⋊C4C2×C31semidirect
382. C22×C31C2×#126semidirect
413. C2×#126C22×C31semidirect
423. C22×C4⋊C4C22×C31semidirect
435. #400C22×C31semidirect
436. #400C22×C31semidirect
437. #397C22×C31semidirect
438. #396C22×C31semidirect
439. #388C22×C31semidirect
440. #387C22×C31semidirect
441. #387C22×C31semidirect
445. #385C22×C31semidirect
446. #380C22×C31semidirect
447. C4×C22⋊C4C22×C31semidirect
462. C2×C31#2481direct (N × H)
510. C2×C4⋊C4D4×C31semidirect
553. C31C2×#2481direct (N × H)
646. C4⋊C4C2×D4×C31semidirect
682. C23C31×#126semidirect
767. C22C2×C31×#126semidirect
795. C2C31×#2481direct (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×C4⋊C4×C312
C31×#24812
C2×C31×#4002
C2×C31×#3972
C2×C31×#3962
C2×C31×#3882
C2×C31×#3872
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C2×C4×C22⋊C4×C312
C2×#248131