Finite Group Databasebeta

← C2×C31×#2556 #21491583

Subgroups — C2×C31×#2556 #21491583

Order 7936.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#125C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic
3C31×#2556C2116yesmaximal, direct product factor
4C2×C31×#399C211yesmaximal, characteristic
5C2×C31×#398C211yesmaximal, characteristic, complemented
6C2×C31×#396C211yesmaximal, characteristic
7C2×C31×#395C211yesmaximal, characteristic, complemented
8C2×C31×#391C211yesmaximal, characteristic, complemented
9C2×C31×#389C211yesmaximal, characteristic, complemented
10C2×C31×#389C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic
12C2×C31×#388C211yesmaximal, characteristic
13C2×C31×#387C211yesmaximal, characteristic, complemented
14C2×C31×#385C211yesmaximal, characteristic
15C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
17C23×Q8×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C2×C31×#125—28no—
20C2×C31×#125C2218yescomplemented
21C2×C31×C22⋊Q8—28no—
22C2×C31×C22⋊Q8C2218yes—
23C22×C4⋊C4×C31C2211yescharacteristic
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×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C22×C4⋊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
44C22×C42×C31C2211yescharacteristic
45C22×C42×C31C2211yescharacteristic
46C31×#399C2218yes—
47C31×#398C2218yescomplemented
48C31×#396C2218yes—
49C31×#395C2218yescomplemented
50C31×#391C2218yescomplemented
51C31×#389C2218yescomplemented
52C31×#389C2218yescomplemented
53C31×#388C2218yes—
54C31×#388C2218yes—
55C31×#387C2218yescomplemented
56C31×#385C2218yes—
57C4×C4⋊C4×C31C2218yescomplemented
58C4×C22⋊C4×C31C2218yes—
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
70C22×Q8×C31—24no—
71C22×Q8×C31—24no—
72C22×Q8×C31—42no—
73C22×Q8×C31C2314yes—
74C23×C4×C31—24no—
75C23×C4×C31—24no—
76C23×C4×C31—42no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2314yes—
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C31×#125—232no—
93C31×C22⋊Q8—232no—
94C2×C4⋊C4×C31—24no—
95C2×C4⋊C4×C31—24no—
96C2×C4⋊C4×C31—24no—
97C2×C4⋊C4×C31—24no—
98C2×C4⋊C4×C31—24no—
99C2×C4⋊C4×C31—24no—
100C2×C4⋊C4×C31—24no—
101C2×C4⋊C4×C31—24no—
102C2×C4⋊C4×C31—24no—
103C2×C4⋊C4×C31—24no—
104C2×C4⋊C4×C31—24no—
105C2×C4⋊C4×C31—42no—
106C2×C4⋊C4×C31D418yes—
107C2×C4⋊C4×C31C2314yes—
108C2×C4⋊C4×C31C2314yes—
109C2×C4⋊C4×C31C2314yes—
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×C4⋊C4×C31C2314yes—
119C2×C4⋊C4×C31C2314yes—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—42no—
125C2×C22⋊C4×C31Q818yescomplemented
126C2×C22⋊C4×C31C2314yes—
127C2×C22⋊C4×C31C2314yes—
128C2×C22⋊C4×C31C2314yes—
129C2×C22⋊C4×C31C2314yes—
130C2×C22⋊C4×C31C2314yes—
131C2×C22⋊C4×C31C2314yes—
132C2×C42×C31—24no—
133C2×C42×C31—24no—
134C2×C42×C31—42no—
135C2×C42×C31—42no—
136C2×C42×C31C2314yes—
137C2×C42×C31C2314yes—
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—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31C2×Q814yes—
157C24×C31C2412yes—
158C24×C31C2411yescharacteristic
159C2×Q8×C31—28no—
160C2×Q8×C31—28no—
161C2×Q8×C31—44no—
162C2×Q8×C31—416no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
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—22no—
184C22×C4×C31—22no—
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—28no—
198C22×C4×C31—28no—
199C22×C4×C31—44no—
200C22×C4×C31—416no—
201C22×C4×C31C2×D414yes—
202C22×C4×C31C2×D414yes—
203C22×C4×C31C2×D414yes—
204C22×C4×C31C2×Q814yes—
205C22×C4×C31C2×Q814yes—
206C22×C4×C31#4114yes—
207C22×C4×C31#4114yes—
208C22×C4×C31#4114yes—
209C22×C4×C31C2412yes—
210C22×C4×C31C2412yes—
211C22×C4×C31C2412yes—
212C22×C4×C31C2412yes—
213C22×C4×C31C2412yes—
214C22×C4×C31C2412yes—
215C22×C4×C31C2412yes—
216C22×C4×C31C2412yes—
217C22×C4×C31C2412yes—
218C22×C4×C31C2412yes—
219C22×C4×C31C2412yes—
220C22×C4×C31C2412yes—
221C22×C4×C31C2412yes—
222C22×C4×C31C2412yes—
223C4⋊C4×C31—28no—
224C4⋊C4×C31—28no—
225C4⋊C4×C31—28no—
226C4⋊C4×C31—28no—
227C4⋊C4×C31—28no—
228C4⋊C4×C31—28no—
229C4⋊C4×C31—28no—
230C4⋊C4×C31—28no—
231C4⋊C4×C31—28no—
232C4⋊C4×C31—28no—
233C4⋊C4×C31—28no—
234C4⋊C4×C31—44no—
235C4⋊C4×C31C2×D4116yes—
236C22⋊C4×C31—28no—
237C22⋊C4×C31—28no—
238C22⋊C4×C31—28no—
239C22⋊C4×C31—28no—
240C22⋊C4×C31—44no—
241C22⋊C4×C31C2×Q8116yescomplemented
242C42×C31—28no—
243C42×C31—28no—
244C42×C31—44no—
245C42×C31—44no—
246C2×#2556C3111yesmaximal, characteristic, direct product factor, Sylow
247C23×C31—28no—
248C23×C31—28no—
249C23×C31—28no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—44no—
257C23×C31—44no—
258C23×C31—44no—
259C23×C31—44no—
260C23×C31C22×D412yes—
261C23×C31C22×Q814yes—
262C23×C31C22×Q812yes—
263C23×C31C2×#4112yes—
264C23×C31C2×#4112yes—
265C23×C31C2×#4112yes—
266C23×C31H(5,𝔽2)12yes—
267C23×C312−1+412yes—
268C23×C31C2511yescharacteristic
269Q8×C31—416no—
270C2×C4×C31—28no—
271C2×C4×C31—28no—
272C2×C4×C31—28no—
273C2×C4×C31—28no—
274C2×C4×C31—28no—
275C2×C4×C31—28no—
276C2×C4×C31—28no—
277C2×C4×C31—28no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
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—416no—
313C2×C4×C31—44no—
314C2×C4×C31—44no—
315C2×C4×C31—44no—
316C2×C4×C31—44no—
317C2×C4×C31—44no—
318C2×C4×C31—44no—
319C2×C4×C31C22×D414yes—
320C2×C4×C31C22×D414yes—
321C2×C4×C31C22×D414yes—
322C2×C4×C31C22×Q814yes—
323C2×C4×C31C22×Q814yes—
324C2×C4×C31C2×#4114yes—
325C2×C4×C31C2×#4114yes—
326C2×C4×C31C2×#4114yes—
327C22×#125C2×C3111yescharacteristic, complemented
328C22×C22⋊Q8C2×C3111yescharacteristic
329#2556C2×C31116yesdirect product factor
330C2×#399C2×C3111yescharacteristic
331C2×#398C2×C3111yescharacteristic, complemented
332C2×#396C2×C3111yescharacteristic
333C2×#395C2×C3111yescharacteristic, complemented
334C2×#391C2×C3111yescharacteristic, complemented
335C2×#389C2×C3111yescharacteristic, complemented
336C2×#389C2×C3111yescharacteristic, complemented
337C2×#388C2×C3111yescharacteristic
338C2×#388C2×C3111yescharacteristic
339C2×#387C2×C3111yescharacteristic, complemented
340C2×#385C2×C3111yescharacteristic
341C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
342C2×C4×C22⋊C4C2×C3111yescharacteristic
343C22×C31—24no—
344C22×C31—24no—
345C22×C31—24no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—416no—
351C22×C31#53214yes—
352C22×C31#53314yes—
353C22×C31#53914yes—
354C22×C31#54614yes—
355C22×C31D4×Q814yes—
356C22×C31#55214yes—
357C22×C31#55414yes—
358C22×C31C23×D411yescharacteristic
359C22×C31C23×Q811yescharacteristic
360C22×C31C22×#4111yescharacteristic
361C22×C31C22×#4111yescharacteristic
362C22×C31C22×#4111yescharacteristic
363C22×C31C2×H(5,𝔽2)11yescharacteristic
364C22×C31C2×2−1+411yescharacteristic
365C4×C31—24no—
366C4×C31—24no—
367C4×C31—24no—
368C4×C31—24no—
369C4×C31—24no—
370C4×C31—24no—
371C4×C31—24no—
372C4×C31—24no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—42no—
378C4×C31—42no—
379C23×Q8C22×C3111yescharacteristic
380C24×C4C22×C3111yescharacteristic
381C2×#125—28no—
382C2×#125C22×C3118yescomplemented
383C2×C22⋊Q8—28no—
384C2×C22⋊Q8C22×C3118yes—
385C22×C4⋊C4C22×C3111yescharacteristic
386C22×C4⋊C4C22×C3111yescharacteristic
387C22×C4⋊C4C22×C3111yescharacteristic
388C22×C4⋊C4C22×C3111yescharacteristic
389C22×C4⋊C4C22×C3111yescharacteristic
390C22×C4⋊C4C22×C3111yescharacteristic
391C22×C4⋊C4C22×C3111yescharacteristic
392C22×C4⋊C4C22×C3111yescharacteristic
393C22×C4⋊C4C22×C3111yescharacteristic
394C22×C4⋊C4C22×C3111yescharacteristic
395C22×C4⋊C4C22×C3111yescharacteristic
396C22×C4⋊C4C22×C3111yescharacteristic
397C22×C4⋊C4C22×C3111yescharacteristic
398C22×C22⋊C4C22×C3111yescharacteristic
399C22×C22⋊C4C22×C3111yescharacteristic
400C22×C22⋊C4C22×C3111yescharacteristic
401C22×C22⋊C4C22×C3111yescharacteristic
402C22×C22⋊C4C22×C3111yescharacteristic
403C22×C22⋊C4C22×C3111yescharacteristic
404C22×C42C22×C3111yescharacteristic
405C22×C42C22×C3111yescharacteristic
406C22×C42C22×C3111yescharacteristic
407C22×C42C22×C3111yescharacteristic
408#399C22×C3118yes—
409#398C22×C3118yescomplemented
410#396C22×C3118yes—
411#395C22×C3118yescomplemented
412#391C22×C3118yescomplemented
413#389C22×C3118yescomplemented
414#389C22×C3118yescomplemented
415#388C22×C3118yes—
416#388C22×C3118yes—
417#387C22×C3118yescomplemented
418#385C22×C3118yes—
419C4×C4⋊C4C22×C3118yescomplemented
420C4×C22⋊C4C22×C3118yes—
421C2×#95C22×C3111yescharacteristic
422C2×#95C22×C3111yescharacteristic
423C2×#95C22×C3111yescharacteristic
424C2×#95C22×C3111yescharacteristic
425C2×#95C22×C3111yescharacteristic
426C2×#95C22×C3111yescharacteristic
427C2×#95C22×C3111yescharacteristic
428C2×#95C22×C3111yescharacteristic
429C2×#95C22×C3111yescharacteristic
430C2×#95C22×C3111yescharacteristic
431C2×C31—44no—
432C2×C31#255618yesdirect product factor
433C2×C31C2×#53211yescharacteristic
434C2×C31C2×#53311yescharacteristic
435C2×C31C2×#53911yescharacteristic
436C2×C31C2×#54611yescharacteristic
437C2×C31C2×D4×Q811yescharacteristic
438C2×C31C2×#55211yescharacteristic
439C2×C31C2×#55411yescharacteristic
440C25C23×C3111yescharacteristic
441C22×Q8—24no—
442C22×Q8—24no—
443C22×Q8—42no—
444C22×Q8C23×C3114yes—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—42no—
448C23×C4C23×C3111yescharacteristic
449C23×C4C23×C3111yescharacteristic
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3111yescharacteristic
452C23×C4C23×C3111yescharacteristic
453C23×C4C23×C3111yescharacteristic
454C23×C4C23×C3114yes—
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C23×C4C23×C3111yescharacteristic
463#125—232no—
464C22⋊Q8—232no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4D4×C3118yes—
478C2×C4⋊C4C23×C3114yes—
479C2×C4⋊C4C23×C3114yes—
480C2×C4⋊C4C23×C3114yes—
481C2×C4⋊C4C23×C3114yes—
482C2×C4⋊C4C23×C3114yes—
483C2×C4⋊C4C23×C3114yes—
484C2×C4⋊C4C23×C3114yes—
485C2×C4⋊C4C23×C3114yes—
486C2×C4⋊C4C23×C3114yes—
487C2×C4⋊C4C23×C3114yes—
488C2×C4⋊C4C23×C3114yes—
489C2×C4⋊C4C23×C3114yes—
490C2×C4⋊C4C23×C3114yes—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4Q8×C3118yescomplemented
497C2×C22⋊C4C23×C3114yes—
498C2×C22⋊C4C23×C3114yes—
499C2×C22⋊C4C23×C3114yes—
500C2×C22⋊C4C23×C3114yes—
501C2×C22⋊C4C23×C3114yes—
502C2×C22⋊C4C23×C3114yes—
503C2×C42—24no—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42—42no—
507C2×C42C23×C3114yes—
508C2×C42C23×C3114yes—
509C2×C42C23×C3114yes—
510C2×C42C23×C3114yes—
511#95C23×C3114yes—
512#95C23×C3114yes—
513#95C23×C3114yes—
514#95C23×C3114yes—
515#95C23×C3114yes—
516#95C23×C3114yes—
517#95C23×C3114yes—
518#95C23×C3114yes—
519#95C23×C3114yes—
520#95C23×C3114yes—
521C31C2×#255611yescharacteristic, direct product factor, Sylow
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24C2×Q8×C3114yes—
529C24C24×C3112yes—
530C24C24×C3111yescharacteristic
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—44no—
534C2×Q8—416no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—44no—
572C22×C4—416no—
573C22×C4C2×D4×C3114yes—
574C22×C4C2×D4×C3114yes—
575C22×C4C2×D4×C3114yes—
576C22×C4C2×Q8×C3114yes—
577C22×C4C2×Q8×C3114yes—
578C22×C4#41×C3114yes—
579C22×C4#41×C3114yes—
580C22×C4#41×C3114yes—
581C22×C4C24×C3112yes—
582C22×C4C24×C3112yes—
583C22×C4C24×C3112yes—
584C22×C4C24×C3112yes—
585C22×C4C24×C3112yes—
586C22×C4C24×C3112yes—
587C22×C4C24×C3112yes—
588C22×C4C24×C3112yes—
589C22×C4C24×C3112yes—
590C22×C4C24×C3112yes—
591C22×C4C24×C3112yes—
592C22×C4C24×C3112yes—
593C22×C4C24×C3112yes—
594C22×C4C24×C3112yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—44no—
607C4⋊C4C2×D4×C31116yes—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—44no—
613C22⋊C4C2×Q8×C31116yescomplemented
614C42—28no—
615C42—28no—
616C42—44no—
617C42—44no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C22×D4×C3112yes—
632C23C22×Q8×C3114yes—
633C23C22×Q8×C3112yes—
634C23C2×#41×C3112yes—
635C23C2×#41×C3112yes—
636C23C2×#41×C3112yes—
637C23C31×H(5,𝔽2)12yes—
638C23C31×2−1+412yes—
639C23C25×C3111yescharacteristic
640Q8—416no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4C22×D4×C3114yes—
691C2×C4C22×D4×C3114yes—
692C2×C4C22×D4×C3114yes—
693C2×C4C22×Q8×C3114yes—
694C2×C4C22×Q8×C3114yes—
695C2×C4C2×#41×C3114yes—
696C2×C4C2×#41×C3114yes—
697C2×C4C2×#41×C3114yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—416no—
706C22C31×#53214yes—
707C22C31×#53314yes—
708C22C31×#53914yes—
709C22C31×#54614yes—
710C22D4×Q8×C3114yes—
711C22C31×#55214yes—
712C22C31×#55414yes—
713C22C23×D4×C3111yescharacteristic
714C22C23×Q8×C3111yescharacteristic
715C22C22×#41×C3111yescharacteristic
716C22C22×#41×C3111yescharacteristic
717C22C22×#41×C3111yescharacteristic
718C22C2×C31×H(5,𝔽2)11yescharacteristic
719C22C2×C31×2−1+411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C2—44no—
735C2C31×#255618yesdirect product factor
736C2C2×C31×#53211yescharacteristic
737C2C2×C31×#53311yescharacteristic
738C2C2×C31×#53911yescharacteristic
739C2C2×C31×#54611yescharacteristic
740C2C2×D4×Q8×C3111yescharacteristic
741C2C2×C31×#55211yescharacteristic
742C2C2×C31×#55411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#125C2semidirect
3. C31×#2556C2direct (N × H)
5. C2×C31×#398C2semidirect
7. C2×C31×#395C2semidirect
8. C2×C31×#391C2semidirect
9. C2×C31×#389C2semidirect
10. C2×C31×#389C2semidirect
13. C2×C31×#387C2semidirect
15. C2×C4×C4⋊C4×C31C2semidirect
20. C2×C31×#125C22semidirect
47. C31×#398C22semidirect
49. C31×#395C22semidirect
50. C31×#391C22semidirect
51. C31×#389C22semidirect
52. C31×#389C22semidirect
55. C31×#387C22semidirect
57. C4×C4⋊C4×C31C22semidirect
125. C2×C22⋊C4×C31Q8semidirect
241. C22⋊C4×C31C2×Q8semidirect
246. C2×#2556C31direct (N × H)
327. C22×#125C2×C31semidirect
329. #2556C2×C31direct (N × H)
331. C2×#398C2×C31semidirect
333. C2×#395C2×C31semidirect
334. C2×#391C2×C31semidirect
335. C2×#389C2×C31semidirect
336. C2×#389C2×C31semidirect
339. C2×#387C2×C31semidirect
341. C2×C4×C4⋊C4C2×C31semidirect
382. C2×#125C22×C31semidirect
409. #398C22×C31semidirect
411. #395C22×C31semidirect
412. #391C22×C31semidirect
413. #389C22×C31semidirect
414. #389C22×C31semidirect
417. #387C22×C31semidirect
419. C4×C4⋊C4C22×C31semidirect
432. C2×C31#2556direct (N × H)
496. C2×C22⋊C4Q8×C31semidirect
521. C31C2×#2556direct (N × H)
613. C22⋊C4C2×Q8×C31semidirect
735. C2C31×#2556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1252
C22×C31×C22⋊Q82
C31×#25562
C2×C31×#3992
C2×C31×#3982
C2×C31×#3962
C2×C31×#3952
C2×C31×#3912
C2×C31×#3892
C2×C31×#3882
C2×C31×#3872
C2×C31×#3852
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C2×#255631