Finite Group Databasebeta

← C31×#22554 #21479313

Subgroups — C31×#22554 #21479313

Order 7936.

1224 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×#432C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊C8C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1924C212yesmaximal, complemented
5C31×#1924C212yesmaximal, complemented
6C31×#1850C212yesmaximal, complemented
7C31×#1817C211yesmaximal, characteristic, complemented
8C31×#1797C211yesmaximal, characteristic, complemented
9C31×#1779C211yesmaximal, characteristic
10C31×#1752C212yesmaximal, complemented
11C31×#1749C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C23×C8×C31C2212yes—
14C22×C22⋊C4×C31C411yescharacteristic
15C22×C22⋊C4×C31C411yescharacteristic
16C22×C42×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C31×#432—24no—
19C2×C31×C4⋊C8C2212yescomplemented
20C2×C31×C4⋊C8C2212yescomplemented
21C2×C31×C22⋊C8—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×C31×#97C2212yescomplemented
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
60C22×C8×C31—24no—
61C22×C8×C31—24no—
62C22×C8×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—24no—
98C31×#97—42no—
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—41no—
112C24×C31—41no—
113C24×C31M1614yes—
114C24×C31C22×C411yescharacteristic
115C24×C31C22×C411yescharacteristic
116C24×C31C22×C411yescharacteristic
117C22×C4×C31—21no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
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—22no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
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—41no—
147C22×C4×C31—48no—
148C22×C4×C31—48no—
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
164C2×C8×C31—22no—
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—48no—
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×C31M1614yes—
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#22554C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—21no—
197C23×C31—21no—
198C23×C31—21no—
199C23×C31—21no—
200C23×C31—21no—
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—28no—
211C23×C31—28no—
212C23×C31—44no—
213C23×C31—44no—
214C23×C31—44no—
215C23×C31—44no—
216C23×C31—44no—
217C23×C31#11712yes—
218C23×C31C4×D412yes—
219C23×C31C2×M1612yes—
220C23×C31C2×M1612yes—
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—24no—
234C2×C4×C31—24no—
235C2×C4×C31—24no—
236C2×C4×C31—24no—
237C2×C4×C31—21no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
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—21no—
258C2×C4×C31—44no—
259C2×C4×C31—44no—
260C2×C4×C31—44no—
261C2×C4×C31—44no—
262C2×C4×C31—44no—
263C2×C4×C31—44no—
264C2×C4×C31—44no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31#11712yes—
268C2×C4×C31C4×D412yes—
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×#432C2×C3111yescharacteristic, complemented
280C22×C22⋊C8C2×C3111yescharacteristic
281C2×C4×C22⋊C4C2×C3111yescharacteristic
282#1924C2×C3112yescomplemented
283#1924C2×C3112yescomplemented
284#1850C2×C3112yescomplemented
285#1817C2×C3111yescharacteristic, complemented
286#1797C2×C3111yescharacteristic, complemented
287#1779C2×C3111yescharacteristic
288#1752C2×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—22no—
303C22×C31—22no—
304C22×C31—22no—
305C22×C31—416no—
306C22×C31—41no—
307C22×C31—41no—
308C22×C31—41no—
309C22×C31—41no—
310C22×C31#43214yescomplemented
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—41no—
324C4×C31—41no—
325C4×C31—41no—
326C4×C31—41no—
327C4×C31—41no—
328C4×C31—41no—
329C4×C31—41no—
330C4×C31#54612yes—
331C4×C31#55112yes—
332C24×C4C22×C3111yescharacteristic
333C23×C8C22×C3112yes—
334C22×C22⋊C4C4×C3111yescharacteristic
335C22×C22⋊C4C4×C3111yescharacteristic
336C22×C42C22×C3111yescharacteristic
337C22×C42C22×C3111yescharacteristic
338#432—24no—
339C2×C4⋊C8C22×C3112yescomplemented
340C2×C4⋊C8C22×C3112yescomplemented
341C2×C22⋊C8—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×#97C22×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—24no—
367C2×C31—42no—
368C2×C31#234211yescharacteristic
369C2×C31C2×#43211yescharacteristic
370C2×C31#292411yescharacteristic
371C2×C31C2×#43511yescharacteristic
372C2×C31D4×M1611yescharacteristic
373C2×C31#297311yescharacteristic
374C2×C31#297411yescharacteristic
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
390C22×C8—24no—
391C22×C8—24no—
392C22×C8—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—24no—
428#97—42no—
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#2255411yescharacteristic, direct product factor, Sylow
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—41no—
443C24—41no—
444C24M16×C3114yes—
445C24C22×C4×C3111yescharacteristic
446C24C22×C4×C3111yescharacteristic
447C24C22×C4×C3111yescharacteristic
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
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—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—48no—
479C22×C4—48no—
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
495C2×C8—22no—
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—48no—
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×C3114yes—
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—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—28no—
535C23—28no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23C31×#11712yes—
548C23C4×D4×C3112yes—
549C23C2×M16×C3112yes—
550C23C2×M16×C3112yes—
551C23C2×M16×C3112yes—
552C23C2×M16×C3112yes—
553C23C31×#13112yes—
554C23C23×C4×C3111yescharacteristic
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
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—21no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C31×#11712yes—
598C2×C4C4×D4×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—22no—
622C22—22no—
623C22—22no—
624C22—416no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22C31×#43214yescomplemented
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—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4C31×#54612yes—
650C4C31×#55112yes—
651C2—24no—
652C2—24no—
653C2—42no—
654C2C31×#234211yescharacteristic
655C2C2×C31×#43211yescharacteristic
656C2C31×#292411yescharacteristic
657C2C2×C31×#43511yescharacteristic
658C2D4×M16×C3111yescharacteristic
659C2C31×#297311yescharacteristic
660C2C31×#297411yescharacteristic
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×#432C2semidirect
4. C31×#1924C2semidirect
5. C31×#1924C2semidirect
6. C31×#1850C2semidirect
7. C31×#1817C2semidirect
8. C31×#1797C2semidirect
10. C31×#1752C2semidirect
11. C31×#1749C2semidirect
19. C2×C31×C4⋊C8C22semidirect
20. C2×C31×C4⋊C8C22semidirect
29. C2×C31×#97C22semidirect
30. C2×C31×#97C22semidirect
41. C31×#336C22semidirect
42. C31×#336C22semidirect
43. C31×#336C22semidirect
44. C31×#336C22semidirect
195. #22554C31direct (N × H)
279. C2×#432C2×C31semidirect
282. #1924C2×C31semidirect
283. #1924C2×C31semidirect
284. #1850C2×C31semidirect
285. #1817C2×C31semidirect
286. #1797C2×C31semidirect
288. #1752C2×C31semidirect
289. #1749C2×C31semidirect
310. C22×C31#432semidirect
339. C2×C4⋊C8C22×C31semidirect
340. C2×C4⋊C8C22×C31semidirect
349. C2×#97C22×C31semidirect
350. C2×#97C22×C31semidirect
361. #336C22×C31semidirect
362. #336C22×C31semidirect
363. #336C22×C31semidirect
364. #336C22×C31semidirect
437. C31#22554direct (N × H)
629. C22C31×#432semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4322
C22×C31×C22⋊C82
C2×C4×C22⋊C4×C312
C31×#19242
C31×#18502
C31×#18172
C31×#17972
C31×#17792
C31×#17522
C31×#17492
#2255431