Finite Group Databasebeta

← C2×C31×#2461 #21491435

Subgroups — C2×C31×#2461 #21491435

Order 7936.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic, complemented
2C22×C31×#123C211yesmaximal, characteristic, complemented
3C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
4C22×C4×D4×C31C211yesmaximal, characteristic, complemented
5C31×#2461C2116yesmaximal, direct product factor
6C2×C31×#396C211yesmaximal, characteristic, complemented
7C2×C31×#395C211yesmaximal, characteristic, complemented
8C2×C31×#394C211yesmaximal, characteristic, complemented
9C2×C31×#392C211yesmaximal, characteristic
10C2×C31×#390C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic, complemented
12C2×C31×#388C211yesmaximal, characteristic, complemented
13C2×C31×#388C211yesmaximal, characteristic, complemented
14C2×C31×#386C211yesmaximal, characteristic, complemented
15C2×C31×#385C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
17C23×Q8×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C23×D4×C31C2211yescharacteristic
21C24×C4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C2×C31×#124—28no—
24C2×C31×#124C2218yescomplemented
25C2×C31×#123—28no—
26C2×C31×#123C2218yescomplemented
27C2×C31×C22⋊Q8—28no—
28C2×C31×C22⋊Q8C2218yescomplemented
29C2×C4×D4×C31—28no—
30C2×C4×D4×C31C2218yescomplemented
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×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×C22⋊C4×C31C2211yescharacteristic
47C22×C22⋊C4×C31C2211yescharacteristic
48C22×C22⋊C4×C31C2211yescharacteristic
49C22×C22⋊C4×C31C2211yescharacteristic
50C22×C22⋊C4×C31C2211yescharacteristic
51C22×C42×C31C2211yescharacteristic
52C22×C42×C31C2211yescharacteristic
53C22×C42×C31C2211yescharacteristic
54C31×#396C2218yescomplemented
55C31×#395C2218yescomplemented
56C31×#394C2218yescomplemented
57C31×#392C2218yes—
58C31×#390C2218yescomplemented
59C31×#388C2218yescomplemented
60C31×#388C2218yescomplemented
61C31×#388C2218yescomplemented
62C31×#386C2218yescomplemented
63C31×#385C2218yescomplemented
64C4×C4⋊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
74C22×Q8×C31—24no—
75C22×Q8×C31—24no—
76C22×Q8×C31—42no—
77C22×Q8×C31C2314yes—
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—42no—
86C22×D4×C31—42no—
87C22×D4×C31C2314yes—
88C22×D4×C31C2314yes—
89C22×D4×C31C2314yes—
90C23×C4×C31—24no—
91C23×C4×C31—24no—
92C23×C4×C31—24no—
93C23×C4×C31—24no—
94C23×C4×C31—42no—
95C23×C4×C31—42no—
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
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×#124—232no—
111C31×#123—232no—
112C31×C22⋊Q8—232no—
113C4×D4×C31—232no—
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—42no—
120C2×C4⋊C4×C31D418yescomplemented
121C2×C4⋊C4×C31C2314yes—
122C2×C4⋊C4×C31C2314yes—
123C2×C4⋊C4×C31C2314yes—
124C2×C4⋊C4×C31C2314yes—
125C2×C4⋊C4×C31C2314yes—
126C2×C4⋊C4×C31C2314yes—
127C2×C4⋊C4×C31C2314yes—
128C2×C22⋊C4×C31—24no—
129C2×C22⋊C4×C31—24no—
130C2×C22⋊C4×C31—24no—
131C2×C22⋊C4×C31—24no—
132C2×C22⋊C4×C31—24no—
133C2×C22⋊C4×C31—24no—
134C2×C22⋊C4×C31—24no—
135C2×C22⋊C4×C31—24no—
136C2×C22⋊C4×C31—24no—
137C2×C22⋊C4×C31—24no—
138C2×C22⋊C4×C31—24no—
139C2×C22⋊C4×C31—24no—
140C2×C22⋊C4×C31D418yescomplemented
141C2×C22⋊C4×C31C2314yes—
142C2×C22⋊C4×C31C2314yes—
143C2×C22⋊C4×C31C2314yes—
144C2×C22⋊C4×C31C2314yes—
145C2×C22⋊C4×C31C2314yes—
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×C31—24no—
156C2×C42×C31—24no—
157C2×C42×C31C2314yes—
158C2×C42×C31C2314yes—
159C2×C42×C31C2314yes—
160C31×#95C2314yes—
161C31×#95C2314yes—
162C31×#95C2314yes—
163C31×#95C2314yes—
164C31×#95C2314yes—
165C31×#95C2314yes—
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×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×C31C2×D414yes—
186C24×C31#4114yes—
187C24×C31C2412yes—
188C24×C31C2412yes—
189C24×C31C2412yes—
190C24×C31C2411yescharacteristic
191C2×Q8×C31—28no—
192C2×Q8×C31—28no—
193C2×Q8×C31—44no—
194C2×Q8×C31—416no—
195C2×D4×C31—232no—
196C2×D4×C31—28no—
197C2×D4×C31—28no—
198C2×D4×C31—28no—
199C2×D4×C31—28no—
200C2×D4×C31—28no—
201C2×D4×C31—28no—
202C2×D4×C31—28no—
203C2×D4×C31—44no—
204C2×D4×C31—44no—
205C2×D4×C31—416no—
206C2×D4×C31—416no—
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—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—22no—
228C22×C4×C31—28no—
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—28no—
238C22×C4×C31—28no—
239C22×C4×C31—28no—
240C22×C4×C31—44no—
241C22×C4×C31—44no—
242C22×C4×C31—416no—
243C22×C4×C31—416no—
244C22×C4×C31C2×D414yes—
245C22×C4×C31C2×D414yes—
246C22×C4×C31C2×D414yes—
247C22×C4×C31C2×D414yes—
248C22×C4×C31C2×D414yes—
249C22×C4×C31#4114yes—
250C22×C4×C31#4114yes—
251C22×C4×C31C2412yes—
252C22×C4×C31C2412yes—
253C22×C4×C31C2412yes—
254C22×C4×C31C2412yes—
255C22×C4×C31C2412yes—
256C22×C4×C31C2412yes—
257C22×C4×C31C2412yes—
258C22×C4×C31C2412yes—
259C22×C4×C31C2412yes—
260C22×C4×C31C2412yes—
261C22×C4×C31C2412yes—
262C22×C4×C31C2412yes—
263C4⋊C4×C31—28no—
264C4⋊C4×C31—28no—
265C4⋊C4×C31—28no—
266C4⋊C4×C31—28no—
267C4⋊C4×C31—28no—
268C4⋊C4×C31—44no—
269C4⋊C4×C31C2×D4116yescomplemented
270C22⋊C4×C31—28no—
271C22⋊C4×C31—28no—
272C22⋊C4×C31—28no—
273C22⋊C4×C31—28no—
274C22⋊C4×C31—28no—
275C22⋊C4×C31—28no—
276C22⋊C4×C31—28no—
277C22⋊C4×C31—28no—
278C22⋊C4×C31—28no—
279C22⋊C4×C31—28no—
280C22⋊C4×C31—28no—
281C22⋊C4×C31—28no—
282C22⋊C4×C31C2×D4116yescomplemented
283C42×C31—28no—
284C42×C31—28no—
285C42×C31—28no—
286C2×#2461C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—28no—
288C23×C31—28no—
289C23×C31—28no—
290C23×C31—28no—
291C23×C31—28no—
292C23×C31—28no—
293C23×C31—22no—
294C23×C31—22no—
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—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—44no—
313C23×C31—44no—
314C23×C31—44no—
315C23×C31—44no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—44no—
320C23×C31—44no—
321C23×C31—44no—
322C23×C31—44no—
323C23×C31—44no—
324C23×C31—44no—
325C23×C31—44no—
326C23×C31—44no—
327C23×C31C22×D414yes—
328C23×C31C22×D412yes—
329C23×C31C22×D412yes—
330C23×C31C2×#4114yes—
331C23×C31C2×#4112yes—
332C23×C31C2×#4112yes—
333C23×C31C2×#4112yes—
334C23×C31H(5,𝔽2)12yes—
335C23×C312−1+412yes—
336C23×C31C2511yescharacteristic
337Q8×C31—416no—
338D4×C31—232no—
339D4×C31—416no—
340D4×C31—416no—
341C2×C4×C31—28no—
342C2×C4×C31—28no—
343C2×C4×C31—28no—
344C2×C4×C31—28no—
345C2×C4×C31—28no—
346C2×C4×C31—28no—
347C2×C4×C31—28no—
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—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—416no—
378C2×C4×C31—416no—
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—
386C2×C4×C31C22×D414yes—
387C2×C4×C31C22×D414yes—
388C2×C4×C31C22×D414yes—
389C2×C4×C31C2×#4114yes—
390C2×C4×C31C2×#4114yes—
391C22×#124C2×C3111yescharacteristic, complemented
392C22×#123C2×C3111yescharacteristic, complemented
393C22×C22⋊Q8C2×C3111yescharacteristic, complemented
394C22×C4×D4C2×C3111yescharacteristic, complemented
395#2461C2×C31116yesdirect product factor
396C2×#396C2×C3111yescharacteristic, complemented
397C2×#395C2×C3111yescharacteristic, complemented
398C2×#394C2×C3111yescharacteristic, complemented
399C2×#392C2×C3111yescharacteristic
400C2×#390C2×C3111yescharacteristic, complemented
401C2×#388C2×C3111yescharacteristic, complemented
402C2×#388C2×C3111yescharacteristic, complemented
403C2×#388C2×C3111yescharacteristic, complemented
404C2×#386C2×C3111yescharacteristic, complemented
405C2×#385C2×C3111yescharacteristic, complemented
406C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
407C22×C31—24no—
408C22×C31—24no—
409C22×C31—24no—
410C22×C31—24no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—416no—
422C22×C31—416no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—88no—
431C22×C31#52514yes—
432C22×C31#53214yes—
433C22×C31#54214yes—
434C22×C31D4214yes—
435C22×C31#54714yes—
436C22×C31#54814yes—
437C22×C31#55114yes—
438C22×C31C23×D411yescharacteristic
439C22×C31C23×D411yescharacteristic
440C22×C31C22×#4111yescharacteristic
441C22×C31C22×#4111yescharacteristic
442C22×C31C22×#4111yescharacteristic
443C22×C31C2×H(5,𝔽2)11yescharacteristic
444C22×C31C2×2−1+411yescharacteristic
445C4×C31—24no—
446C4×C31—24no—
447C4×C31—24no—
448C4×C31—24no—
449C4×C31—24no—
450C4×C31—24no—
451C4×C31—24no—
452C4×C31—42no—
453C4×C31—42no—
454C4×C31—42no—
455C4×C31—42no—
456C4×C31—42no—
457C23×Q8C22×C3111yescharacteristic
458C23×D4C22×C3111yescharacteristic
459C23×D4C22×C3111yescharacteristic
460C23×D4C22×C3111yescharacteristic
461C24×C4C22×C3111yescharacteristic
462C24×C4C22×C3111yescharacteristic
463C2×#124—28no—
464C2×#124C22×C3118yescomplemented
465C2×#123—28no—
466C2×#123C22×C3118yescomplemented
467C2×C22⋊Q8—28no—
468C2×C22⋊Q8C22×C3118yescomplemented
469C2×C4×D4—28no—
470C2×C4×D4C22×C3118yescomplemented
471C22×C4⋊C4C22×C3111yescharacteristic
472C22×C4⋊C4C22×C3111yescharacteristic
473C22×C4⋊C4C22×C3111yescharacteristic
474C22×C4⋊C4C22×C3111yescharacteristic
475C22×C4⋊C4C22×C3111yescharacteristic
476C22×C4⋊C4C22×C3111yescharacteristic
477C22×C4⋊C4C22×C3111yescharacteristic
478C22×C22⋊C4C22×C3111yescharacteristic
479C22×C22⋊C4C22×C3111yescharacteristic
480C22×C22⋊C4C22×C3111yescharacteristic
481C22×C22⋊C4C22×C3111yescharacteristic
482C22×C22⋊C4C22×C3111yescharacteristic
483C22×C22⋊C4C22×C3111yescharacteristic
484C22×C22⋊C4C22×C3111yescharacteristic
485C22×C22⋊C4C22×C3111yescharacteristic
486C22×C22⋊C4C22×C3111yescharacteristic
487C22×C22⋊C4C22×C3111yescharacteristic
488C22×C22⋊C4C22×C3111yescharacteristic
489C22×C22⋊C4C22×C3111yescharacteristic
490C22×C22⋊C4C22×C3111yescharacteristic
491C22×C42C22×C3111yescharacteristic
492C22×C42C22×C3111yescharacteristic
493C22×C42C22×C3111yescharacteristic
494#396C22×C3118yescomplemented
495#395C22×C3118yescomplemented
496#394C22×C3118yescomplemented
497#392C22×C3118yes—
498#390C22×C3118yescomplemented
499#388C22×C3118yescomplemented
500#388C22×C3118yescomplemented
501#388C22×C3118yescomplemented
502#386C22×C3118yescomplemented
503#385C22×C3118yescomplemented
504C4×C4⋊C4C22×C3118yescomplemented
505C2×#95C22×C3111yescharacteristic
506C2×#95C22×C3111yescharacteristic
507C2×#95C22×C3111yescharacteristic
508C2×#95C22×C3111yescharacteristic
509C2×#95C22×C3111yescharacteristic
510C2×#95C22×C3111yescharacteristic
511C2×C31—44no—
512C2×C31—44no—
513C2×C31—82no—
514C2×C31#246118yesdirect product factor
515C2×C31C2×#52511yescharacteristic
516C2×C31C2×#53211yescharacteristic
517C2×C31C2×#54211yescharacteristic
518C2×C31C2×D4211yescharacteristic
519C2×C31C2×#54711yescharacteristic
520C2×C31C2×#54811yescharacteristic
521C2×C31C2×#55111yescharacteristic
522C25C23×C3111yescharacteristic
523C25C23×C3111yescharacteristic
524C25C23×C3111yescharacteristic
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—42no—
528C22×Q8C23×C3114yes—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4C23×C3114yes—
539C22×D4C23×C3114yes—
540C22×D4C23×C3114yes—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—42no—
547C23×C4C23×C3111yescharacteristic
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C23×C4C23×C3111yescharacteristic
551C23×C4C23×C3111yescharacteristic
552C23×C4C23×C3114yes—
553C23×C4C23×C3114yes—
554C23×C4C23×C3111yescharacteristic
555C23×C4C23×C3111yescharacteristic
556C23×C4C23×C3111yescharacteristic
557C23×C4C23×C3111yescharacteristic
558C23×C4C23×C3111yescharacteristic
559C23×C4C23×C3111yescharacteristic
560C23×C4C23×C3111yescharacteristic
561#124—232no—
562#123—232no—
563C22⋊Q8—232no—
564C4×D4—232no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—42no—
571C2×C4⋊C4D4×C3118yescomplemented
572C2×C4⋊C4C23×C3114yes—
573C2×C4⋊C4C23×C3114yes—
574C2×C4⋊C4C23×C3114yes—
575C2×C4⋊C4C23×C3114yes—
576C2×C4⋊C4C23×C3114yes—
577C2×C4⋊C4C23×C3114yes—
578C2×C4⋊C4C23×C3114yes—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4D4×C3118yescomplemented
592C2×C22⋊C4C23×C3114yes—
593C2×C22⋊C4C23×C3114yes—
594C2×C22⋊C4C23×C3114yes—
595C2×C22⋊C4C23×C3114yes—
596C2×C22⋊C4C23×C3114yes—
597C2×C22⋊C4C23×C3114yes—
598C2×C22⋊C4C23×C3114yes—
599C2×C22⋊C4C23×C3114yes—
600C2×C22⋊C4C23×C3114yes—
601C2×C22⋊C4C23×C3114yes—
602C2×C22⋊C4C23×C3114yes—
603C2×C22⋊C4C23×C3114yes—
604C2×C22⋊C4C23×C3114yes—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42C23×C3114yes—
609C2×C42C23×C3114yes—
610C2×C42C23×C3114yes—
611#95C23×C3114yes—
612#95C23×C3114yes—
613#95C23×C3114yes—
614#95C23×C3114yes—
615#95C23×C3114yes—
616#95C23×C3114yes—
617C31C2×#246111yescharacteristic, direct product factor, Sylow
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24C2×D4×C3114yes—
638C24#41×C3114yes—
639C24C24×C3112yes—
640C24C24×C3112yes—
641C24C24×C3112yes—
642C24C24×C3111yescharacteristic
643C2×Q8—28no—
644C2×Q8—28no—
645C2×Q8—44no—
646C2×Q8—416no—
647C2×D4—232no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—416no—
658C2×D4—416no—
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—22no—
668C22×C4—22no—
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—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—416no—
695C22×C4—416no—
696C22×C4C2×D4×C3114yes—
697C22×C4C2×D4×C3114yes—
698C22×C4C2×D4×C3114yes—
699C22×C4C2×D4×C3114yes—
700C22×C4C2×D4×C3114yes—
701C22×C4#41×C3114yes—
702C22×C4#41×C3114yes—
703C22×C4C24×C3112yes—
704C22×C4C24×C3112yes—
705C22×C4C24×C3112yes—
706C22×C4C24×C3112yes—
707C22×C4C24×C3112yes—
708C22×C4C24×C3112yes—
709C22×C4C24×C3112yes—
710C22×C4C24×C3112yes—
711C22×C4C24×C3112yes—
712C22×C4C24×C3112yes—
713C22×C4C24×C3112yes—
714C22×C4C24×C3112yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4C2×D4×C31116yescomplemented
722C22⋊C4—28no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4C2×D4×C31116yescomplemented
735C42—28no—
736C42—28no—
737C42—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23C22×D4×C3114yes—
779C23C22×D4×C3112yes—
780C23C22×D4×C3112yes—
781C23C2×#41×C3114yes—
782C23C2×#41×C3112yes—
783C23C2×#41×C3112yes—
784C23C2×#41×C3112yes—
785C23C31×H(5,𝔽2)12yes—
786C23C31×2−1+412yes—
787C23C25×C3111yescharacteristic
788Q8—416no—
789D4—232no—
790D4—416no—
791D4—416no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
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—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4C22×D4×C3114yes—
836C2×C4C22×D4×C3114yes—
837C2×C4C22×D4×C3114yes—
838C2×C4C22×D4×C3114yes—
839C2×C4C22×D4×C3114yes—
840C2×C4C2×#41×C3114yes—
841C2×C4C2×#41×C3114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—88no—
866C22C31×#52514yes—
867C22C31×#53214yes—
868C22C31×#54214yes—
869C22D42×C3114yes—
870C22C31×#54714yes—
871C22C31×#54814yes—
872C22C31×#55114yes—
873C22C23×D4×C3111yescharacteristic
874C22C23×D4×C3111yescharacteristic
875C22C22×#41×C3111yescharacteristic
876C22C22×#41×C3111yescharacteristic
877C22C22×#41×C3111yescharacteristic
878C22C2×C31×H(5,𝔽2)11yescharacteristic
879C22C2×C31×2−1+411yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—42no—
892C2—44no—
893C2—44no—
894C2—82no—
895C2C31×#246118yesdirect product factor
896C2C2×C31×#52511yescharacteristic
897C2C2×C31×#53211yescharacteristic
898C2C2×C31×#54211yescharacteristic
899C2C2×D42×C3111yescharacteristic
900C2C2×C31×#54711yescharacteristic
901C2C2×C31×#54811yescharacteristic
902C2C2×C31×#55111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#124C2semidirect
2. C22×C31×#123C2semidirect
3. C22×C31×C22⋊Q8C2semidirect
4. C22×C4×D4×C31C2semidirect
5. C31×#2461C2direct (N × H)
6. C2×C31×#396C2semidirect
7. C2×C31×#395C2semidirect
8. C2×C31×#394C2semidirect
10. C2×C31×#390C2semidirect
11. C2×C31×#388C2semidirect
12. C2×C31×#388C2semidirect
13. C2×C31×#388C2semidirect
14. C2×C31×#386C2semidirect
15. C2×C31×#385C2semidirect
16. C2×C4×C4⋊C4×C31C2semidirect
24. C2×C31×#124C22semidirect
26. C2×C31×#123C22semidirect
28. C2×C31×C22⋊Q8C22semidirect
30. C2×C4×D4×C31C22semidirect
54. C31×#396C22semidirect
55. C31×#395C22semidirect
56. C31×#394C22semidirect
58. C31×#390C22semidirect
59. C31×#388C22semidirect
60. C31×#388C22semidirect
61. C31×#388C22semidirect
62. C31×#386C22semidirect
63. C31×#385C22semidirect
64. C4×C4⋊C4×C31C22semidirect
120. C2×C4⋊C4×C31D4semidirect
140. C2×C22⋊C4×C31D4semidirect
269. C4⋊C4×C31C2×D4semidirect
282. C22⋊C4×C31C2×D4semidirect
286. C2×#2461C31direct (N × H)
391. C22×#124C2×C31semidirect
392. C22×#123C2×C31semidirect
393. C22×C22⋊Q8C2×C31semidirect
394. C22×C4×D4C2×C31semidirect
395. #2461C2×C31direct (N × H)
396. C2×#396C2×C31semidirect
397. C2×#395C2×C31semidirect
398. C2×#394C2×C31semidirect
400. C2×#390C2×C31semidirect
401. C2×#388C2×C31semidirect
402. C2×#388C2×C31semidirect
403. C2×#388C2×C31semidirect
404. C2×#386C2×C31semidirect
405. C2×#385C2×C31semidirect
406. C2×C4×C4⋊C4C2×C31semidirect
464. C2×#124C22×C31semidirect
466. C2×#123C22×C31semidirect
468. C2×C22⋊Q8C22×C31semidirect
470. C2×C4×D4C22×C31semidirect
494. #396C22×C31semidirect
495. #395C22×C31semidirect
496. #394C22×C31semidirect
498. #390C22×C31semidirect
499. #388C22×C31semidirect
500. #388C22×C31semidirect
501. #388C22×C31semidirect
502. #386C22×C31semidirect
503. #385C22×C31semidirect
504. C4×C4⋊C4C22×C31semidirect
514. C2×C31#2461direct (N × H)
571. C2×C4⋊C4D4×C31semidirect
591. C2×C22⋊C4D4×C31semidirect
617. C31C2×#2461direct (N × H)
721. C4⋊C4C2×D4×C31semidirect
734. C22⋊C4C2×D4×C31semidirect
895. C2C31×#2461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C31×#1232
C22×C31×C22⋊Q82
C22×C4×D4×C312
C31×#24612
C2×C31×#3962
C2×C31×#3952
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C4×C4⋊C4×C312
C2×#246131