Finite Group Databasebeta

← C31×#17592 #21474351

Subgroups — C31×#17592 #21474351

Order 7936.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C2×C31×#380C211yesmaximal, characteristic, complemented
4C31×#1520C212yesmaximal, complemented
5C31×#1519C212yesmaximal, complemented
6C31×#1513C214yesmaximal, complemented
7C31×#1504C214yesmaximal, complemented
8C22×#41×C31C411yescharacteristic, complemented
9C24×C4×C31C2211yescharacteristic
10C22×M16×C31—21no—
11C31×#525—21no—
12C31×#525—21no—
13C31×#525—21no—
14C31×#525—21no—
15C31×#525C412yescomplemented
16C31×#525C412yescomplemented
17C31×#525C2212yes—
18C31×#525C2212yes—
19C2×C31×#123—21no—
20C2×C31×C22⋊Q8C411yescharacteristic, complemented
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#121C411yescharacteristic, complemented
23C2×C31×#121C2211yescharacteristic
24C2×C31×#120—21no—
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31—21no—
27C2×C31×#117C411yescharacteristic, complemented
28C22×C4⋊C4×C31—21no—
29C22×C22⋊C4×C31—21no—
30C31×#407—21no—
31C31×#407—21no—
32C31×#407C2212yescomplemented
33C31×#407C2212yescomplemented
34C2×C31×C22⋊C8—21no—
35C2×C31×C22⋊C8C2212yes—
36C31×#380—21no—
37C31×#380—21no—
38C31×#380C2212yes—
39C31×#380C2212yescomplemented
40C2×C31×#95C2212yescomplemented
41C31×#328C2218yescomplemented
42C31×#327C2218yescomplemented
43C25×C31D411yescharacteristic
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—44no—
47C2×#41×C31C2×C412yes—
48C2×#41×C31C2×C412yescomplemented
49C22×Q8×C31C2×C411yescharacteristic, complemented
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31C2×C411yescharacteristic, complemented
54C23×C4×C31—21no—
55C23×C4×C31—22no—
56C23×C4×C31—44no—
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31C2×C411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31D411yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—44no—
74C22×C8×C31—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—22no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8C2×C412yes—
84C31×C22⋊Q8C2×C412yescomplemented
85C31×C22⋊Q8C2×C412yescomplemented
86C31×C22⋊Q8C2312yes—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121C2×C412yes—
92C31×#121C2×C412yescomplemented
93C31×#121C2×C412yescomplemented
94C31×#121C2312yes—
95C31×#120—22no—
96C31×#120—22no—
97C31×#120—22no—
98C31×#120—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117C2×C412yes—
110C31×#117C2×C412yescomplemented
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—44no—
116C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
117C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—44no—
126C2×C42×C31—21no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8C2314yes—
131C31×#95—22no—
132C31×#95C2314yes—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—21no—
136C24×C31—42no—
137C24×C31—42no—
138C24×C31C22⋊C411yescharacteristic
139C24×C31C22⋊C411yescharacteristic
140C24×C31C22⋊C411yescharacteristic
141C24×C31C22⋊C411yescharacteristic
142C24×C31C2×D411yescharacteristic
143C24×C31C2×D411yescharacteristic
144C24×C31C2×D411yescharacteristic
145#41×C31—44no—
146#41×C31—44no—
147#41×C31—44no—
148#41×C31—44no—
149C2×Q8×C31—21no—
150C2×Q8×C31—42no—
151C2×Q8×C31C22×C412yes—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—21no—
159C2×D4×C31—42no—
160C2×D4×C31—44no—
161C2×D4×C31—44no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31C22×C412yes—
165C22×C4×C31—24no—
166C22×C4×C31—24no—
167C22×C4×C31—24no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—24no—
174C22×C4×C31—42no—
175C22×C4×C31—42no—
176C22×C4×C31—42no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—42no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—42no—
183C22×C4×C31—42no—
184C22×C4×C31—42no—
185C22×C4×C31—44no—
186C22×C4×C31—44no—
187C22×C4×C31—44no—
188C22×C4×C31—44no—
189C22×C4×C31C22⋊C411yescharacteristic
190C22×C4×C31C22⋊C411yescharacteristic
191C22×C4×C31C22⋊C411yescharacteristic
192C22×C4×C31C22⋊C411yescharacteristic
193C22×C4×C31C22⋊C411yescharacteristic
194C22×C4×C31C22⋊C411yescharacteristic
195C22×C4×C31C22⋊C411yescharacteristic
196C22×C4×C31C22⋊C411yescharacteristic
197C22×C4×C31C22⋊C411yescharacteristic
198C22×C4×C31C22⋊C411yescharacteristic
199C22×C4×C31C22⋊C411yescharacteristic
200C22×C4×C31C22⋊C411yescharacteristic
201C22×C4×C31C22×C411yescharacteristic
202C22×C4×C31C22×C411yescharacteristic
203C22×C4×C31C22×C411yescharacteristic
204C22×C4×C31C22×C411yescharacteristic
205C22×C4×C31C22×C411yescharacteristic
206C22×C4×C31C22×C411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2411yescharacteristic
217M16×C31—44no—
218M16×C31—44no—
219C2×C8×C31—24no—
220C2×C8×C31—44no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—44no—
228C4⋊C4×C31—44no—
229C4⋊C4×C31C22×C412yes—
230C4⋊C4×C31C22×C412yes—
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—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—44no—
242C22⋊C4×C31—44no—
243C42×C31—22no—
244C42×C31—22no—
245#17592C3111yesmaximal, characteristic, direct product factor, Sylow
246C23×C31—21no—
247C23×C31—21no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—48no—
270C23×C31—48no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31C2×C22⋊C411yescharacteristic
275C23×C31C2×C22⋊C411yescharacteristic
276C23×C31C2×C22⋊C411yescharacteristic
277C23×C31C2×C22⋊C411yescharacteristic
278C23×C31C2×C22⋊C411yescharacteristic
279C23×C31C2×C22⋊C411yescharacteristic
280C23×C31AGL(1,ℤ/8)12yes—
281C23×C31#13712yes—
282C23×C31C22×D411yescharacteristic
283Q8×C31—42no—
284Q8×C31—42no—
285D4×C31—42no—
286D4×C31—44no—
287D4×C31—44no—
288D4×C31—42no—
289D4×C31—42no—
290D4×C31—44no—
291D4×C31—44no—
292D4×C31—44no—
293D4×C31—42no—
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—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—44no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—44no—
329C2×C4×C31—44no—
330C2×C4×C31—44no—
331C2×C4×C31—44no—
332C2×C4×C31—88no—
333C2×C4×C31#9914yes—
334C2×C4×C31C2×C22⋊C411yescharacteristic
335C2×C4×C31C2×C22⋊C411yescharacteristic
336C2×C4×C31C2×C22⋊C411yescharacteristic
337C2×C4×C31C2×C22⋊C411yescharacteristic
338C2×C4×C31C2×C22⋊C411yescharacteristic
339C2×C4×C31C2×C22⋊C411yescharacteristic
340C2×C4×C31C23×C411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C8×C31—44no—
343C2×#525C2×C3111yescharacteristic
344C2×#407C2×C3111yescharacteristic, complemented
345C2×#380C2×C3111yescharacteristic, complemented
346#1520C2×C3112yescomplemented
347#1519C2×C3112yescomplemented
348#1513C2×C3114yescomplemented
349#1504C2×C3114yescomplemented
350C22×C31—24no—
351C22×C31—24no—
352C22×C31—21no—
353C22×C31—21no—
354C22×C31—21no—
355C22×C31—21no—
356C22×C31—21no—
357C22×C31—21no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—21no—
365C22×C31—21no—
366C22×C31—21no—
367C22×C31—21no—
368C22×C31—42no—
369C22×C31—42no—
370C22×C31—44no—
371C22×C31—44no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—84no—
380C22×C31C2×#9912yes—
381C22×C31#41712yes—
382C22×C31#41712yes—
383C22×C31#42112yes—
384C22×C31C22×C22⋊C411yescharacteristic
385C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C31C2×#13711yescharacteristic
387C4×C31—21no—
388C4×C31—21no—
389C4×C31—21no—
390C4×C31—21no—
391C4×C31—21no—
392C4×C31—21no—
393C4×C31—42no—
394C4×C31—42no—
395C4×C31—42no—
396C4×C31—84no—
397C4×C31C2×#9912yes—
398C4×C31C2×#9912yes—
399C22×#41C4×C3111yescharacteristic, complemented
400C24×C4C22×C3111yescharacteristic
401C22×M16—21no—
402#525—21no—
403#525—21no—
404#525—21no—
405#525—21no—
406#525C4×C3112yescomplemented
407#525C4×C3112yescomplemented
408#525C22×C3112yes—
409#525C22×C3112yes—
410C2×#123—21no—
411C2×C22⋊Q8C4×C3111yescharacteristic, complemented
412C2×C22⋊Q8C22×C3111yescharacteristic
413C2×#121C4×C3111yescharacteristic, complemented
414C2×#121C22×C3111yescharacteristic
415C2×#120—21no—
416C2×C4×D4—21no—
417C2×C4×D4—21no—
418C2×#117C4×C3111yescharacteristic, complemented
419C22×C4⋊C4—21no—
420C22×C22⋊C4—21no—
421#407—21no—
422#407—21no—
423#407C22×C3112yescomplemented
424#407C22×C3112yescomplemented
425C2×C22⋊C8—21no—
426C2×C22⋊C8C22×C3112yes—
427#380—21no—
428#380—21no—
429#380C22×C3112yes—
430#380C22×C3112yescomplemented
431C2×#95C22×C3112yescomplemented
432#328C22×C3118yescomplemented
433#327C22×C3118yescomplemented
434C2×C31—21no—
435C2×C31—21no—
436C2×C31—22no—
437C2×C31—22no—
438C2×C31—22no—
439C2×C31—22no—
440C2×C31—41no—
441C2×C31—41no—
442C2×C31—82no—
443C2×C31C22×#9911yescharacteristic
444C2×C31C2×#41711yescharacteristic
445C2×C31C2×#42111yescharacteristic
446C25D4×C3111yescharacteristic
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—44no—
450C2×#41C2×C4×C3112yes—
451C2×#41C2×C4×C3112yescomplemented
452C22×Q8C2×C4×C3111yescharacteristic, complemented
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4C2×C4×C3111yescharacteristic, complemented
457C23×C4—21no—
458C23×C4—22no—
459C23×C4—44no—
460C23×C4C2×C4×C3111yescharacteristic
461C23×C4C2×C4×C3111yescharacteristic
462C23×C4C2×C4×C3111yescharacteristic
463C23×C4C2×C4×C3111yescharacteristic
464C23×C4D4×C3111yescharacteristic
465C23×C4D4×C3111yescharacteristic
466C23×C4D4×C3111yescharacteristic
467C23×C4D4×C3111yescharacteristic
468C23×C4D4×C3111yescharacteristic
469C23×C4D4×C3111yescharacteristic
470C23×C4D4×C3111yescharacteristic
471C23×C4C23×C3111yescharacteristic
472C23×C4C23×C3111yescharacteristic
473C23×C4C23×C3111yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—44no—
477C22×C8—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8C2×C4×C3112yes—
487C22⋊Q8C2×C4×C3112yescomplemented
488C22⋊Q8C2×C4×C3112yescomplemented
489C22⋊Q8C23×C3112yes—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121C2×C4×C3112yes—
495#121C2×C4×C3112yescomplemented
496#121C2×C4×C3112yescomplemented
497#121C23×C3112yes—
498#120—22no—
499#120—22no—
500#120—22no—
501#120—22no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—21no—
511#117—21no—
512#117C2×C4×C3112yes—
513#117C2×C4×C3112yescomplemented
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—44no—
519C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
520C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—44no—
529C2×C42—21no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8C23×C3114yes—
534#95—22no—
535#95C23×C3114yes—
536C31#1759211yescharacteristic, direct product factor, Sylow
537C24—22no—
538C24—22no—
539C24—21no—
540C24—42no—
541C24—42no—
542C24C22⋊C4×C3111yescharacteristic
543C24C22⋊C4×C3111yescharacteristic
544C24C22⋊C4×C3111yescharacteristic
545C24C22⋊C4×C3111yescharacteristic
546C24C2×D4×C3111yescharacteristic
547C24C2×D4×C3111yescharacteristic
548C24C2×D4×C3111yescharacteristic
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—42no—
555C2×Q8C22×C4×C3112yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C22×C4×C3112yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4C22⋊C4×C3111yescharacteristic
594C22×C4C22⋊C4×C3111yescharacteristic
595C22×C4C22⋊C4×C3111yescharacteristic
596C22×C4C22⋊C4×C3111yescharacteristic
597C22×C4C22⋊C4×C3111yescharacteristic
598C22×C4C22⋊C4×C3111yescharacteristic
599C22×C4C22⋊C4×C3111yescharacteristic
600C22×C4C22⋊C4×C3111yescharacteristic
601C22×C4C22⋊C4×C3111yescharacteristic
602C22×C4C22⋊C4×C3111yescharacteristic
603C22×C4C22⋊C4×C3111yescharacteristic
604C22×C4C22⋊C4×C3111yescharacteristic
605C22×C4C22×C4×C3111yescharacteristic
606C22×C4C22×C4×C3111yescharacteristic
607C22×C4C22×C4×C3111yescharacteristic
608C22×C4C22×C4×C3111yescharacteristic
609C22×C4C22×C4×C3111yescharacteristic
610C22×C4C22×C4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3111yescharacteristic
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C24×C3111yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—24no—
624C2×C8—44no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4C22×C4×C3112yes—
634C4⋊C4C22×C4×C3112yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C42—22no—
648C42—22no—
649C23—22no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—48no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C2×C22⋊C4×C3111yescharacteristic
678C23C2×C22⋊C4×C3111yescharacteristic
679C23C2×C22⋊C4×C3111yescharacteristic
680C23C2×C22⋊C4×C3111yescharacteristic
681C23C2×C22⋊C4×C3111yescharacteristic
682C23C2×C22⋊C4×C3111yescharacteristic
683C23C31×AGL(1,ℤ/8)12yes—
684C23C31×#13712yes—
685C23C22×D4×C3111yescharacteristic
686Q8—42no—
687Q8—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—88no—
736C2×C4C31×#9914yes—
737C2×C4C2×C22⋊C4×C3111yescharacteristic
738C2×C4C2×C22⋊C4×C3111yescharacteristic
739C2×C4C2×C22⋊C4×C3111yescharacteristic
740C2×C4C2×C22⋊C4×C3111yescharacteristic
741C2×C4C2×C22⋊C4×C3111yescharacteristic
742C2×C4C2×C22⋊C4×C3111yescharacteristic
743C2×C4C23×C4×C3111yescharacteristic
744C2×C4C22×D4×C3111yescharacteristic
745C8—44no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22C2×C31×#9912yes—
777C22C31×#41712yes—
778C22C31×#41712yes—
779C22C31×#42112yes—
780C22C22×C22⋊C4×C3111yescharacteristic
781C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
782C22C2×C31×#13711yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—84no—
793C4C2×C31×#9912yes—
794C4C2×C31×#9912yes—
795C2—21no—
796C2—22no—
797C2—22no—
798C2—21no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—82no—
804C2C22×C31×#9911yescharacteristic
805C2C2×C31×#41711yescharacteristic
806C2C2×C31×#42111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#525C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#407C2semidirect
3. C2×C31×#380C2semidirect
4. C31×#1520C2semidirect
5. C31×#1519C2semidirect
6. C31×#1513C2semidirect
7. C31×#1504C2semidirect
8. C22×#41×C31C4semidirect
15. C31×#525C4semidirect
16. C31×#525C4semidirect
20. C2×C31×C22⋊Q8C4semidirect
22. C2×C31×#121C4semidirect
27. C2×C31×#117C4semidirect
32. C31×#407C22semidirect
33. C31×#407C22semidirect
39. C31×#380C22semidirect
40. C2×C31×#95C22semidirect
41. C31×#328C22semidirect
42. C31×#327C22semidirect
48. C2×#41×C31C2×C4semidirect
49. C22×Q8×C31C2×C4semidirect
53. C22×D4×C31C2×C4semidirect
84. C31×C22⋊Q8C2×C4semidirect
85. C31×C22⋊Q8C2×C4semidirect
92. C31×#121C2×C4semidirect
93. C31×#121C2×C4semidirect
110. C31×#117C2×C4semidirect
116. C2×C4⋊C4×C31C2×C4semidirect
117. C2×C4⋊C4×C31C2×C4semidirect
245. #17592C31direct (N × H)
344. C2×#407C2×C31semidirect
345. C2×#380C2×C31semidirect
346. #1520C2×C31semidirect
347. #1519C2×C31semidirect
348. #1513C2×C31semidirect
349. #1504C2×C31semidirect
399. C22×#41C4×C31semidirect
406. #525C4×C31semidirect
407. #525C4×C31semidirect
411. C2×C22⋊Q8C4×C31semidirect
413. C2×#121C4×C31semidirect
418. C2×#117C4×C31semidirect
423. #407C22×C31semidirect
424. #407C22×C31semidirect
430. #380C22×C31semidirect
431. C2×#95C22×C31semidirect
432. #328C22×C31semidirect
433. #327C22×C31semidirect
451. C2×#41C2×C4×C31semidirect
452. C22×Q8C2×C4×C31semidirect
456. C22×D4C2×C4×C31semidirect
487. C22⋊Q8C2×C4×C31semidirect
488. C22⋊Q8C2×C4×C31semidirect
495. #121C2×C4×C31semidirect
496. #121C2×C4×C31semidirect
513. #117C2×C4×C31semidirect
519. C2×C4⋊C4C2×C4×C31semidirect
520. C2×C4⋊C4C2×C4×C31semidirect
536. C31#17592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4072
C2×C31×#3802
C31×#15202
C31×#15192
C31×#15132
C31×#15042
#1759231