Finite Group Databasebeta

← C2×C31×#2837 #21493417

Subgroups — C2×C31×#2837 #21493417

Order 7936.

2110 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2837C2116yesmaximal, direct product factor
2C2×C31×#400C211yesmaximal, characteristic, complemented
3C2×C31×#399C211yesmaximal, characteristic, complemented
4C2×C31×#399C211yesmaximal, characteristic, complemented
5C2×C31×#398C211yesmaximal, characteristic, complemented
6C2×C31×#398C211yesmaximal, characteristic, complemented
7C2×C31×#397C211yesmaximal, characteristic, complemented
8C2×C31×#397C211yesmaximal, characteristic, complemented
9C2×C31×#396C211yesmaximal, characteristic, complemented
10C2×C31×#396C211yesmaximal, characteristic, complemented
11C2×C31×#394C211yesmaximal, characteristic
12C2×C31×#394C211yesmaximal, characteristic
13C2×C31×#394C211yesmaximal, characteristic
14C2×C31×#389C211yesmaximal, characteristic, complemented
15C2×C31×#388C211yesmaximal, characteristic, complemented
16C2×C31×#388C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
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×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×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C42×C31C2211yescharacteristic
42C31×#400C2218yescomplemented
43C31×#399C2218yescomplemented
44C31×#399C2218yescomplemented
45C31×#398C2218yescomplemented
46C31×#398C2218yescomplemented
47C31×#397C2218yescomplemented
48C31×#397C2218yescomplemented
49C31×#396C2218yescomplemented
50C31×#396C2218yescomplemented
51C31×#394C2218yes—
52C31×#394C2218yes—
53C31×#394C2218yes—
54C31×#389C2218yescomplemented
55C31×#388C2218yescomplemented
56C31×#388C2218yescomplemented
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
67C25×C31C2311yescharacteristic
68C25×C31C2311yescharacteristic
69C22×D4×C31—42no—
70C22×D4×C31—42no—
71C22×D4×C31—42no—
72C22×D4×C31C2314yes—
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—42no—
88C2×C4⋊C4×C31—42no—
89C2×C4⋊C4×C31—42no—
90C2×C4⋊C4×C31—42no—
91C2×C4⋊C4×C31—42no—
92C2×C4⋊C4×C31—42no—
93C2×C4⋊C4×C31—42no—
94C2×C4⋊C4×C31—42no—
95C2×C4⋊C4×C31—42no—
96C2×C4⋊C4×C31—42no—
97C2×C4⋊C4×C31C2314yes—
98C2×C4⋊C4×C31C2314yes—
99C2×C4⋊C4×C31C2314yes—
100C2×C4⋊C4×C31C2314yes—
101C2×C4⋊C4×C31C2314yes—
102C2×C4⋊C4×C31C2314yes—
103C2×C4⋊C4×C31C2314yes—
104C2×C4⋊C4×C31C2314yes—
105C2×C4⋊C4×C31C2314yes—
106C2×C4⋊C4×C31C2314yes—
107C2×C4⋊C4×C31C2314yes—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31—42no—
112C2×C22⋊C4×C31—42no—
113C2×C22⋊C4×C31—42no—
114C2×C22⋊C4×C31—42no—
115C2×C22⋊C4×C31—42no—
116C2×C22⋊C4×C31—42no—
117C2×C22⋊C4×C31—42no—
118C2×C22⋊C4×C31—42no—
119C2×C22⋊C4×C31—42no—
120C2×C22⋊C4×C31C2314yes—
121C2×C22⋊C4×C31C2314yes—
122C2×C22⋊C4×C31C2314yes—
123C2×C22⋊C4×C31C2314yes—
124C2×C22⋊C4×C31C2314yes—
125C2×C22⋊C4×C31C2314yes—
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—42no—
133C2×C42×C31C2314yes—
134C31×#95C2314yes—
135C31×#95C2314yes—
136C31×#95C2314yes—
137C31×#95C2314yes—
138C31×#95C2314yes—
139C31×#95C2314yes—
140C31×#95C2314yes—
141C31×#95C2314yes—
142C31×#95C2314yes—
143C31×#95C2314yes—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—22no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31C2412yes—
159C24×C31C2412yes—
160C24×C31C2411yescharacteristic
161C2×D4×C31—44no—
162C2×D4×C31—44no—
163C2×D4×C31—44no—
164C2×D4×C31—416no—
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—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31#4114yes—
204C22×C4×C31C2412yes—
205C22×C4×C31C2412yes—
206C22×C4×C31C2412yes—
207C22×C4×C31C2412yes—
208C22×C4×C31C2412yes—
209C22×C4×C31C2412yes—
210C22×C4×C31C2412yes—
211C22×C4×C31C2412yes—
212C22×C4×C31C2412yes—
213C22×C4×C31C2412yes—
214C22×C4×C31C2412yes—
215C22×C4×C31C2412yes—
216C22×C4×C31C2412yes—
217C4⋊C4×C31—28no—
218C4⋊C4×C31—44no—
219C4⋊C4×C31—44no—
220C4⋊C4×C31—44no—
221C4⋊C4×C31—44no—
222C4⋊C4×C31—44no—
223C4⋊C4×C31—44no—
224C4⋊C4×C31—44no—
225C4⋊C4×C31—44no—
226C4⋊C4×C31—44no—
227C4⋊C4×C31—44no—
228C22⋊C4×C31—28no—
229C22⋊C4×C31—28no—
230C22⋊C4×C31—44no—
231C22⋊C4×C31—44no—
232C22⋊C4×C31—44no—
233C22⋊C4×C31—44no—
234C22⋊C4×C31—44no—
235C22⋊C4×C31—44no—
236C22⋊C4×C31—44no—
237C22⋊C4×C31—44no—
238C22⋊C4×C31—44no—
239C22⋊C4×C31—44no—
240C42×C31—44no—
241C2×#2837C3111yesmaximal, characteristic, direct product factor, Sylow
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—22no—
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×C31—44no—
261C23×C31—44no—
262C23×C31—44no—
263C23×C31—44no—
264C23×C31—44no—
265C23×C31—44no—
266C23×C31—44no—
267C23×C31—44no—
268C23×C31—44no—
269C23×C31—44no—
270C23×C31C2×#4112yes—
271C23×C31H(5,𝔽2)12yes—
272C23×C31H(5,𝔽2)12yes—
273C23×C31H(5,𝔽2)12yes—
274C23×C31H(5,𝔽2)12yes—
275C23×C312−1+412yes—
276C23×C312−1+412yes—
277C23×C31C2511yescharacteristic
278D4×C31—416no—
279C2×C4×C31—28no—
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—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—44no—
319C2×C4×C31—44no—
320C2×C4×C31—44no—
321C2×C4×C31—44no—
322C2×C4×C31—44no—
323C2×C4×C31—44no—
324C2×C4×C31—44no—
325C2×C4×C31—44no—
326C2×C4×C31—44no—
327C2×C4×C31—44no—
328C2×C4×C31—44no—
329C2×C4×C31—44no—
330C2×C4×C31C2×#4114yes—
331#2837C2×C31116yesdirect product factor
332C2×#400C2×C3111yescharacteristic, complemented
333C2×#399C2×C3111yescharacteristic, complemented
334C2×#399C2×C3111yescharacteristic, complemented
335C2×#398C2×C3111yescharacteristic, complemented
336C2×#398C2×C3111yescharacteristic, complemented
337C2×#397C2×C3111yescharacteristic, complemented
338C2×#397C2×C3111yescharacteristic, complemented
339C2×#396C2×C3111yescharacteristic, complemented
340C2×#396C2×C3111yescharacteristic, complemented
341C2×#394C2×C3111yescharacteristic
342C2×#394C2×C3111yescharacteristic
343C2×#394C2×C3111yescharacteristic
344C2×#389C2×C3111yescharacteristic, complemented
345C2×#388C2×C3111yescharacteristic, complemented
346C2×#388C2×C3111yescharacteristic, complemented
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31—42no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—88no—
362C22×C31—88no—
363C22×C31#53914yes—
364C22×C31#54014yes—
365C22×C31#54214yes—
366C22×C31#56014yes—
367C22×C31#56214yes—
368C22×C31#56214yes—
369C22×C31#56314yes—
370C22×C31C22×#4111yescharacteristic
371C22×C31C2×H(5,𝔽2)11yescharacteristic
372C22×C31C2×H(5,𝔽2)11yescharacteristic
373C22×C31C2×H(5,𝔽2)11yescharacteristic
374C22×C31C2×H(5,𝔽2)11yescharacteristic
375C22×C31C2×2−1+411yescharacteristic
376C22×C31C2×2−1+411yescharacteristic
377C4×C31—24no—
378C4×C31—42no—
379C4×C31—42no—
380C4×C31—42no—
381C4×C31—42no—
382C4×C31—42no—
383C4×C31—42no—
384C4×C31—42no—
385C4×C31—42no—
386C4×C31—42no—
387C4×C31—42no—
388C4×C31—42no—
389C4×C31—42no—
390C23×D4C22×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×C4⋊C4C22×C3111yescharacteristic
399C22×C4⋊C4C22×C3111yescharacteristic
400C22×C4⋊C4C22×C3111yescharacteristic
401C22×C4⋊C4C22×C3111yescharacteristic
402C22×C22⋊C4C22×C3111yescharacteristic
403C22×C22⋊C4C22×C3111yescharacteristic
404C22×C22⋊C4C22×C3111yescharacteristic
405C22×C22⋊C4C22×C3111yescharacteristic
406C22×C22⋊C4C22×C3111yescharacteristic
407C22×C22⋊C4C22×C3111yescharacteristic
408C22×C22⋊C4C22×C3111yescharacteristic
409C22×C22⋊C4C22×C3111yescharacteristic
410C22×C22⋊C4C22×C3111yescharacteristic
411C22×C22⋊C4C22×C3111yescharacteristic
412C22×C22⋊C4C22×C3111yescharacteristic
413C22×C22⋊C4C22×C3111yescharacteristic
414C22×C42C22×C3111yescharacteristic
415#400C22×C3118yescomplemented
416#399C22×C3118yescomplemented
417#399C22×C3118yescomplemented
418#398C22×C3118yescomplemented
419#398C22×C3118yescomplemented
420#397C22×C3118yescomplemented
421#397C22×C3118yescomplemented
422#396C22×C3118yescomplemented
423#396C22×C3118yescomplemented
424#394C22×C3118yes—
425#394C22×C3118yes—
426#394C22×C3118yes—
427#389C22×C3118yescomplemented
428#388C22×C3118yescomplemented
429#388C22×C3118yescomplemented
430C2×#95C22×C3111yescharacteristic
431C2×#95C22×C3111yescharacteristic
432C2×#95C22×C3111yescharacteristic
433C2×#95C22×C3111yescharacteristic
434C2×#95C22×C3111yescharacteristic
435C2×#95C22×C3111yescharacteristic
436C2×#95C22×C3111yescharacteristic
437C2×#95C22×C3111yescharacteristic
438C2×#95C22×C3111yescharacteristic
439C2×#95C22×C3111yescharacteristic
440C2×C31—82no—
441C2×C31—82no—
442C2×C31#283718yesdirect product factor
443C2×C31C2×#53911yescharacteristic
444C2×C31C2×#54011yescharacteristic
445C2×C31C2×#54211yescharacteristic
446C2×C31C2×#56011yescharacteristic
447C2×C31C2×#56211yescharacteristic
448C2×C31C2×#56211yescharacteristic
449C2×C31C2×#56311yescharacteristic
450C25C23×C3111yescharacteristic
451C25C23×C3111yescharacteristic
452C22×D4—42no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4C23×C3114yes—
456C23×C4C23×C3111yescharacteristic
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C23×C4C23×C3111yescharacteristic
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3111yescharacteristic
465C23×C4C23×C3111yescharacteristic
466C23×C4C23×C3111yescharacteristic
467C23×C4C23×C3111yescharacteristic
468C23×C4C23×C3111yescharacteristic
469C2×C4⋊C4—24no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
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—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4C23×C3114yes—
504C2×C22⋊C4C23×C3114yes—
505C2×C22⋊C4C23×C3114yes—
506C2×C22⋊C4C23×C3114yes—
507C2×C22⋊C4C23×C3114yes—
508C2×C22⋊C4C23×C3114yes—
509C2×C22⋊C4C23×C3114yes—
510C2×C22⋊C4C23×C3114yes—
511C2×C22⋊C4C23×C3114yes—
512C2×C22⋊C4C23×C3114yes—
513C2×C22⋊C4C23×C3114yes—
514C2×C22⋊C4C23×C3114yes—
515C2×C42—42no—
516C2×C42C23×C3114yes—
517#95C23×C3114yes—
518#95C23×C3114yes—
519#95C23×C3114yes—
520#95C23×C3114yes—
521#95C23×C3114yes—
522#95C23×C3114yes—
523#95C23×C3114yes—
524#95C23×C3114yes—
525#95C23×C3114yes—
526#95C23×C3114yes—
527C31C2×#283711yescharacteristic, direct product factor, Sylow
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C24×C3112yes—
543C24C24×C3112yes—
544C24C24×C3111yescharacteristic
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—416no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4#41×C3114yes—
588C22×C4C24×C3112yes—
589C22×C4C24×C3112yes—
590C22×C4C24×C3112yes—
591C22×C4C24×C3112yes—
592C22×C4C24×C3112yes—
593C22×C4C24×C3112yes—
594C22×C4C24×C3112yes—
595C22×C4C24×C3112yes—
596C22×C4C24×C3112yes—
597C22×C4C24×C3112yes—
598C22×C4C24×C3112yes—
599C22×C4C24×C3112yes—
600C22×C4C24×C3112yes—
601C4⋊C4—28no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C42—44no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23C2×#41×C3112yes—
654C23C31×H(5,𝔽2)12yes—
655C23C31×H(5,𝔽2)12yes—
656C23C31×H(5,𝔽2)12yes—
657C23C31×H(5,𝔽2)12yes—
658C23C31×2−1+412yes—
659C23C31×2−1+412yes—
660C23C25×C3111yescharacteristic
661D4—416no—
662C2×C4—28no—
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4C2×#41×C3114yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22C31×#53914yes—
731C22C31×#54014yes—
732C22C31×#54214yes—
733C22C31×#56014yes—
734C22C31×#56214yes—
735C22C31×#56214yes—
736C22C31×#56314yes—
737C22C22×#41×C3111yescharacteristic
738C22C2×C31×H(5,𝔽2)11yescharacteristic
739C22C2×C31×H(5,𝔽2)11yescharacteristic
740C22C2×C31×H(5,𝔽2)11yescharacteristic
741C22C2×C31×H(5,𝔽2)11yescharacteristic
742C22C2×C31×2−1+411yescharacteristic
743C22C2×C31×2−1+411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C2—82no—
758C2—82no—
759C2C31×#283718yesdirect product factor
760C2C2×C31×#53911yescharacteristic
761C2C2×C31×#54011yescharacteristic
762C2C2×C31×#54211yescharacteristic
763C2C2×C31×#56011yescharacteristic
764C2C2×C31×#56211yescharacteristic
765C2C2×C31×#56211yescharacteristic
766C2C2×C31×#56311yescharacteristic
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. C31×#2837C2direct (N × H)
2. C2×C31×#400C2semidirect
3. C2×C31×#399C2semidirect
4. C2×C31×#399C2semidirect
5. C2×C31×#398C2semidirect
6. C2×C31×#398C2semidirect
7. C2×C31×#397C2semidirect
8. C2×C31×#397C2semidirect
9. C2×C31×#396C2semidirect
10. C2×C31×#396C2semidirect
14. C2×C31×#389C2semidirect
15. C2×C31×#388C2semidirect
16. C2×C31×#388C2semidirect
42. C31×#400C22semidirect
43. C31×#399C22semidirect
44. C31×#399C22semidirect
45. C31×#398C22semidirect
46. C31×#398C22semidirect
47. C31×#397C22semidirect
48. C31×#397C22semidirect
49. C31×#396C22semidirect
50. C31×#396C22semidirect
54. C31×#389C22semidirect
55. C31×#388C22semidirect
56. C31×#388C22semidirect
241. C2×#2837C31direct (N × H)
331. #2837C2×C31direct (N × H)
332. C2×#400C2×C31semidirect
333. C2×#399C2×C31semidirect
334. C2×#399C2×C31semidirect
335. C2×#398C2×C31semidirect
336. C2×#398C2×C31semidirect
337. C2×#397C2×C31semidirect
338. C2×#397C2×C31semidirect
339. C2×#396C2×C31semidirect
340. C2×#396C2×C31semidirect
344. C2×#389C2×C31semidirect
345. C2×#388C2×C31semidirect
346. C2×#388C2×C31semidirect
415. #400C22×C31semidirect
416. #399C22×C31semidirect
417. #399C22×C31semidirect
418. #398C22×C31semidirect
419. #398C22×C31semidirect
420. #397C22×C31semidirect
421. #397C22×C31semidirect
422. #396C22×C31semidirect
423. #396C22×C31semidirect
427. #389C22×C31semidirect
428. #388C22×C31semidirect
429. #388C22×C31semidirect
442. C2×C31#2837direct (N × H)
527. C31C2×#2837direct (N × H)
759. C2C31×#2837direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28372
C2×C31×#4002
C2×C31×#3992
C2×C31×#3982
C2×C31×#3972
C2×C31×#3962
C2×C31×#3942
C2×C31×#3892
C2×C31×#3882
C2×#283731