Finite Group Databasebeta

← C31×#22553 #21479312

Subgroups — C31×#22553 #21479312

Order 7936.

1212 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#431C211yesmaximal, characteristic, complemented
2C2×C31×#407C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1924C212yesmaximal, complemented
5C31×#1923C212yesmaximal, complemented
6C31×#1851C212yesmaximal, complemented
7C31×#1817C211yesmaximal, characteristic, complemented
8C31×#1797C211yesmaximal, characteristic, complemented
9C31×#1779C211yesmaximal, characteristic
10C31×#1753C212yesmaximal, complemented
11C31×#1749C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×M16×C31C2212yes—
14C22×C22⋊C4×C31C411yescharacteristic
15C22×C22⋊C4×C31C411yescharacteristic
16C22×C42×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C31×#431—24no—
19C2×C31×C4⋊C8C2212yescomplemented
20C2×C31×C4⋊C8C2212yescomplemented
21C31×#407—24no—
22C2×C31×C22⋊C8C2211yescharacteristic
23C2×C31×C22⋊C8C2211yescharacteristic
24C2×C31×C22⋊C8C2211yescharacteristic
25C2×C31×C22⋊C8C2212yes—
26C2×C31×C22⋊C8C2212yes—
27C2×C31×C22⋊C8C2212yes—
28C2×C31×C22⋊C8C2211yescharacteristic
29C2×C31×#97C2212yescomplemented
30C2×C4×C8×C31C2212yescomplemented
31C4×C22⋊C4×C31C411yescharacteristic
32C4×C22⋊C4×C31C411yescharacteristic
33C4×C22⋊C4×C31C411yescharacteristic
34C4×C22⋊C4×C31C411yescharacteristic
35C4×C22⋊C4×C31C2211yescharacteristic
36C4×C22⋊C4×C31C2211yescharacteristic
37C4×C22⋊C4×C31C2211yescharacteristic
38C4×C22⋊C4×C31C2211yescharacteristic
39C2×C31×#95C411yescharacteristic
40C2×C31×#95C411yescharacteristic
41C31×#336C2212yescomplemented
42C31×#336C2212yescomplemented
43C31×#336C2212yescomplemented
44C31×#336C2212yescomplemented
45C25×C31C2×C411yescharacteristic
46C23×C4×C31—22no—
47C23×C4×C31—24no—
48C23×C4×C31—22no—
49C23×C4×C31—42no—
50C23×C4×C31C2×C411yescharacteristic
51C23×C4×C31C2×C411yescharacteristic
52C23×C4×C31C2×C411yescharacteristic
53C23×C4×C31C2×C411yescharacteristic
54C23×C4×C31C2×C411yescharacteristic
55C23×C4×C31C2×C411yescharacteristic
56C23×C4×C31C2×C411yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C2×M16×C31—24no—
61C2×M16×C31—24no—
62C2×M16×C31—42no—
63C22×C8×C31C2312yes—
64C22×C8×C31C2312yes—
65C22×C8×C31C2312yes—
66C22×C8×C31C2312yes—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31C2×C411yescharacteristic
70C2×C22⋊C4×C31C2×C411yescharacteristic
71C2×C22⋊C4×C31C2×C411yescharacteristic
72C2×C22⋊C4×C31C2×C411yescharacteristic
73C2×C22⋊C4×C31C2×C411yescharacteristic
74C2×C22⋊C4×C31C2×C411yescharacteristic
75C2×C22⋊C4×C31C2×C411yescharacteristic
76C2×C22⋊C4×C31C2×C411yescharacteristic
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31—42no—
80C2×C42×C31C2×C411yescharacteristic
81C2×C42×C31C2×C411yescharacteristic
82C2×C42×C31C2×C411yescharacteristic
83C2×C42×C31C2×C411yescharacteristic
84C2×C42×C31C2311yescharacteristic
85C2×C42×C31C2311yescharacteristic
86C2×C42×C31C2311yescharacteristic
87C2×C42×C31C2311yescharacteristic
88C31×C4⋊C8—24no—
89C31×C4⋊C8—42no—
90C31×C22⋊C8—22no—
91C31×C22⋊C8—22no—
92C31×C22⋊C8—24no—
93C31×C22⋊C8—22no—
94C31×C22⋊C8—24no—
95C31×C22⋊C8—42no—
96C31×C22⋊C8D414yes—
97C31×#97—42no—
98C4×C8×C31—24no—
99C31×#95C2×C411yescharacteristic
100C31×#95C2×C411yescharacteristic
101C31×#95C2×C411yescharacteristic
102C31×#95C2×C411yescharacteristic
103C31×#95C2×C411yescharacteristic
104C31×#95C2×C411yescharacteristic
105C31×#95C2×C411yescharacteristic
106C31×#95C2×C411yescharacteristic
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—41no—
113C24×C31—41no—
114C24×C31C22×C411yescharacteristic
115C24×C31C22×C411yescharacteristic
116C24×C31C22×C411yescharacteristic
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—41no—
140C22×C4×C31—41no—
141C22×C4×C31—41no—
142C22×C4×C31—41no—
143C22×C4×C31—41no—
144C22×C4×C31—41no—
145C22×C4×C31—41no—
146C22×C4×C31—48no—
147C22×C4×C31—48no—
148C22×C4×C31M1614yescomplemented
149C22×C4×C31C22×C411yescharacteristic
150C22×C4×C31C22×C411yescharacteristic
151C22×C4×C31C22×C411yescharacteristic
152C22×C4×C31C22×C411yescharacteristic
153C22×C4×C31C22×C411yescharacteristic
154C22×C4×C31C22×C411yescharacteristic
155C22×C4×C31C22×C411yescharacteristic
156C22×C4×C31C22×C411yescharacteristic
157C22×C4×C31C22×C411yescharacteristic
158C22×C4×C31C22×C411yescharacteristic
159C22×C4×C31C22×C411yescharacteristic
160C22×C4×C31C2×D412yes—
161C22×C4×C31#4114yes—
162C22×C4×C31#4112yes—
163C22×C4×C31C2411yescharacteristic
164M16×C31—48no—
165C2×C8×C31—22no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31C2×D414yes—
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×C31M1614yescomplemented
185C42×C31—22no—
186C42×C31—22no—
187C42×C31—21no—
188C42×C31—21no—
189C42×C31—21no—
190C42×C31—21no—
191C42×C31—22no—
192C42×C31—22no—
193C42×C31—41no—
194C42×C31—41no—
195#22553C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—21no—
197C23×C31—21no—
198C23×C31—21no—
199C23×C31—21no—
200C23×C31—28no—
201C23×C31—21no—
202C23×C31—21no—
203C23×C31—21no—
204C23×C31—21no—
205C23×C31—21no—
206C23×C31—21no—
207C23×C31—21no—
208C23×C31—21no—
209C23×C31—21no—
210C23×C31—21no—
211C23×C31—21no—
212C23×C31—21no—
213C23×C31—44no—
214C23×C31—44no—
215C23×C31—44no—
216C23×C31—44no—
217C23×C31—44no—
218C23×C31—44no—
219C23×C31#11712yes—
220C23×C31C4×D412yes—
221C23×C31C2×M1612yes—
222C23×C31C2×M1612yes—
223C23×C31#13112yes—
224C23×C31C23×C411yescharacteristic
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—21no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
237C2×C4×C31—28no—
238C2×C4×C31—24no—
239C2×C4×C31—24no—
240C2×C4×C31—24no—
241C2×C4×C31—24no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—44no—
258C2×C4×C31—44no—
259C2×C4×C31—44no—
260C2×C4×C31—44no—
261C2×C4×C31—44no—
262C2×C4×C31—44no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31#11712yes—
266C2×C4×C31C4×D412yes—
267C2×C4×C31C2×M1612yes—
268C2×C4×C31C2×M1612yes—
269C2×C4×C31C2×M1612yes—
270C2×C4×C31C2×M1612yes—
271C2×C4×C31C22×D411yescharacteristic
272C2×C4×C31C2×#4112yes—
273C2×C4×C31C2×#4111yescharacteristic
274C2×C4×C31H(5,𝔽2)12yes—
275C8×C31—24no—
276C8×C31—42no—
277C8×C31—42no—
278C8×C31—42no—
279C2×#431C2×C3111yescharacteristic, complemented
280C2×#407C2×C3111yescharacteristic
281C2×C4×C22⋊C4C2×C3111yescharacteristic
282#1924C2×C3112yescomplemented
283#1923C2×C3112yescomplemented
284#1851C2×C3112yescomplemented
285#1817C2×C3111yescharacteristic, complemented
286#1797C2×C3111yescharacteristic, complemented
287#1779C2×C3111yescharacteristic
288#1753C2×C3112yescomplemented
289#1749C2×C3111yescharacteristic, complemented
290C22×C31—22no—
291C22×C31—22no—
292C22×C31—22no—
293C22×C31—22no—
294C22×C31—22no—
295C22×C31—22no—
296C22×C31—22no—
297C22×C31—22no—
298C22×C31—22no—
299C22×C31—22no—
300C22×C31—22no—
301C22×C31—22no—
302C22×C31—416no—
303C22×C31—41no—
304C22×C31—41no—
305C22×C31—41no—
306C22×C31—41no—
307C22×C31—41no—
308C22×C31—41no—
309C22×C31—41no—
310C22×C31—41no—
311C22×C31#43514yes—
312C22×C31C2×#11711yescharacteristic
313C22×C31C2×C4×D411yescharacteristic
314C22×C31#51811yescharacteristic
315C22×C31C22×M1611yescharacteristic
316C22×C31C22×M1611yescharacteristic
317C22×C31C2×#13111yescharacteristic
318C22×C31#56811yescharacteristic
319C4×C31—22no—
320C4×C31—22no—
321C4×C31—22no—
322C4×C31—22no—
323C4×C31—22no—
324C4×C31—22no—
325C4×C31—41no—
326C4×C31—41no—
327C4×C31—41no—
328C4×C31—41no—
329C4×C31—41no—
330C4×C31#54612yes—
331C4×C31#55112yes—
332C24×C4C22×C3111yescharacteristic
333C22×M16C22×C3112yes—
334C22×C22⋊C4C4×C3111yescharacteristic
335C22×C22⋊C4C4×C3111yescharacteristic
336C22×C42C22×C3111yescharacteristic
337C22×C42C22×C3111yescharacteristic
338#431—24no—
339C2×C4⋊C8C22×C3112yescomplemented
340C2×C4⋊C8C22×C3112yescomplemented
341#407—24no—
342C2×C22⋊C8C22×C3111yescharacteristic
343C2×C22⋊C8C22×C3111yescharacteristic
344C2×C22⋊C8C22×C3111yescharacteristic
345C2×C22⋊C8C22×C3112yes—
346C2×C22⋊C8C22×C3112yes—
347C2×C22⋊C8C22×C3112yes—
348C2×C22⋊C8C22×C3111yescharacteristic
349C2×#97C22×C3112yescomplemented
350C2×C4×C8C22×C3112yescomplemented
351C4×C22⋊C4C4×C3111yescharacteristic
352C4×C22⋊C4C4×C3111yescharacteristic
353C4×C22⋊C4C4×C3111yescharacteristic
354C4×C22⋊C4C4×C3111yescharacteristic
355C4×C22⋊C4C22×C3111yescharacteristic
356C4×C22⋊C4C22×C3111yescharacteristic
357C4×C22⋊C4C22×C3111yescharacteristic
358C4×C22⋊C4C22×C3111yescharacteristic
359C2×#95C4×C3111yescharacteristic
360C2×#95C4×C3111yescharacteristic
361#336C22×C3112yescomplemented
362#336C22×C3112yescomplemented
363#336C22×C3112yescomplemented
364#336C22×C3112yescomplemented
365C2×C31—24no—
366C2×C31—42no—
367C2×C31—42no—
368C2×C31#234211yescharacteristic
369C2×C31#292011yescharacteristic
370C2×C31#292411yescharacteristic
371C2×C31C2×#43511yescharacteristic
372C2×C31D4×M1611yescharacteristic
373C2×C31#297411yescharacteristic
374C2×C31#297511yescharacteristic
375C25C2×C4×C3111yescharacteristic
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—42no—
380C23×C4C2×C4×C3111yescharacteristic
381C23×C4C2×C4×C3111yescharacteristic
382C23×C4C2×C4×C3111yescharacteristic
383C23×C4C2×C4×C3111yescharacteristic
384C23×C4C2×C4×C3111yescharacteristic
385C23×C4C2×C4×C3111yescharacteristic
386C23×C4C2×C4×C3111yescharacteristic
387C23×C4C23×C3111yescharacteristic
388C23×C4C23×C3111yescharacteristic
389C23×C4C23×C3111yescharacteristic
390C2×M16—24no—
391C2×M16—24no—
392C2×M16—42no—
393C22×C8C23×C3112yes—
394C22×C8C23×C3112yes—
395C22×C8C23×C3112yes—
396C22×C8C23×C3112yes—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4C2×C4×C3111yescharacteristic
400C2×C22⋊C4C2×C4×C3111yescharacteristic
401C2×C22⋊C4C2×C4×C3111yescharacteristic
402C2×C22⋊C4C2×C4×C3111yescharacteristic
403C2×C22⋊C4C2×C4×C3111yescharacteristic
404C2×C22⋊C4C2×C4×C3111yescharacteristic
405C2×C22⋊C4C2×C4×C3111yescharacteristic
406C2×C22⋊C4C2×C4×C3111yescharacteristic
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—42no—
410C2×C42C2×C4×C3111yescharacteristic
411C2×C42C2×C4×C3111yescharacteristic
412C2×C42C2×C4×C3111yescharacteristic
413C2×C42C2×C4×C3111yescharacteristic
414C2×C42C23×C3111yescharacteristic
415C2×C42C23×C3111yescharacteristic
416C2×C42C23×C3111yescharacteristic
417C2×C42C23×C3111yescharacteristic
418C4⋊C8—24no—
419C4⋊C8—42no—
420C22⋊C8—22no—
421C22⋊C8—22no—
422C22⋊C8—24no—
423C22⋊C8—22no—
424C22⋊C8—24no—
425C22⋊C8—42no—
426C22⋊C8D4×C3114yes—
427#97—42no—
428C4×C8—24no—
429#95C2×C4×C3111yescharacteristic
430#95C2×C4×C3111yescharacteristic
431#95C2×C4×C3111yescharacteristic
432#95C2×C4×C3111yescharacteristic
433#95C2×C4×C3111yescharacteristic
434#95C2×C4×C3111yescharacteristic
435#95C2×C4×C3111yescharacteristic
436#95C2×C4×C3111yescharacteristic
437C31#2255311yescharacteristic, direct product factor, Sylow
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—41no—
444C24—41no—
445C24C22×C4×C3111yescharacteristic
446C24C22×C4×C3111yescharacteristic
447C24C22×C4×C3111yescharacteristic
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4M16×C3114yescomplemented
480C22×C4C22×C4×C3111yescharacteristic
481C22×C4C22×C4×C3111yescharacteristic
482C22×C4C22×C4×C3111yescharacteristic
483C22×C4C22×C4×C3111yescharacteristic
484C22×C4C22×C4×C3111yescharacteristic
485C22×C4C22×C4×C3111yescharacteristic
486C22×C4C22×C4×C3111yescharacteristic
487C22×C4C22×C4×C3111yescharacteristic
488C22×C4C22×C4×C3111yescharacteristic
489C22×C4C22×C4×C3111yescharacteristic
490C22×C4C22×C4×C3111yescharacteristic
491C22×C4C2×D4×C3112yes—
492C22×C4#41×C3114yes—
493C22×C4#41×C3112yes—
494C22×C4C24×C3111yescharacteristic
495M16—48no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8C2×D4×C3114yes—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4M16×C3114yescomplemented
516C42—22no—
517C42—22no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—28no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—44no—
548C23—44no—
549C23C31×#11712yes—
550C23C4×D4×C3112yes—
551C23C2×M16×C3112yes—
552C23C2×M16×C3112yes—
553C23C31×#13112yes—
554C23C23×C4×C3111yescharacteristic
555C2×C4—28no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4C31×#11712yes—
596C2×C4C4×D4×C3112yes—
597C2×C4C2×M16×C3112yes—
598C2×C4C2×M16×C3112yes—
599C2×C4C2×M16×C3112yes—
600C2×C4C2×M16×C3112yes—
601C2×C4C22×D4×C3111yescharacteristic
602C2×C4C2×#41×C3112yes—
603C2×C4C2×#41×C3111yescharacteristic
604C2×C4C31×H(5,𝔽2)12yes—
605C8—24no—
606C8—42no—
607C8—42no—
608C8—42no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—416no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22C31×#43514yes—
631C22C2×C31×#11711yescharacteristic
632C22C2×C4×D4×C3111yescharacteristic
633C22C31×#51811yescharacteristic
634C22C22×M16×C3111yescharacteristic
635C22C22×M16×C3111yescharacteristic
636C22C2×C31×#13111yescharacteristic
637C22C31×#56811yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4C31×#54612yes—
650C4C31×#55112yes—
651C2—24no—
652C2—42no—
653C2—42no—
654C2C31×#234211yescharacteristic
655C2C31×#292011yescharacteristic
656C2C31×#292411yescharacteristic
657C2C2×C31×#43511yescharacteristic
658C2D4×M16×C3111yescharacteristic
659C2C31×#297411yescharacteristic
660C2C31×#297511yescharacteristic
subgroupG/H
centerC22×C4×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C23×C4
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#431C2semidirect
4. C31×#1924C2semidirect
5. C31×#1923C2semidirect
6. C31×#1851C2semidirect
7. C31×#1817C2semidirect
8. C31×#1797C2semidirect
10. C31×#1753C2semidirect
11. C31×#1749C2semidirect
19. C2×C31×C4⋊C8C22semidirect
20. C2×C31×C4⋊C8C22semidirect
29. C2×C31×#97C22semidirect
30. C2×C4×C8×C31C22semidirect
41. C31×#336C22semidirect
42. C31×#336C22semidirect
43. C31×#336C22semidirect
44. C31×#336C22semidirect
148. C22×C4×C31M16semidirect
184. C22⋊C4×C31M16semidirect
195. #22553C31direct (N × H)
279. C2×#431C2×C31semidirect
282. #1924C2×C31semidirect
283. #1923C2×C31semidirect
284. #1851C2×C31semidirect
285. #1817C2×C31semidirect
286. #1797C2×C31semidirect
288. #1753C2×C31semidirect
289. #1749C2×C31semidirect
339. C2×C4⋊C8C22×C31semidirect
340. C2×C4⋊C8C22×C31semidirect
349. C2×#97C22×C31semidirect
350. C2×C4×C8C22×C31semidirect
361. #336C22×C31semidirect
362. #336C22×C31semidirect
363. #336C22×C31semidirect
364. #336C22×C31semidirect
437. C31#22553direct (N × H)
479. C22×C4M16×C31semidirect
515. C22⋊C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4312
C2×C31×#4072
C2×C4×C22⋊C4×C312
C31×#19242
C31×#19232
C31×#18512
C31×#18172
C31×#17972
C31×#17792
C31×#17532
C31×#17492
#2255331