Finite Group Databasebeta

← C31×#15183 #21471942

Subgroups — C31×#15183 #21471942

Order 7936.

1586 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic, complemented
2C2×C31×#380C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
5C31×#1445C212yesmaximal, complemented
6C31×#1443C212yesmaximal, complemented
7C31×#1440C212yesmaximal
8C31×#1439C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C31×C4⋊#95C211yesmaximal, characteristic, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#389—24no—
25C31×#380—24no—
26C31×#380—24no—
27C4×C22⋊C4×C31—24no—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C25×C31C2311yescharacteristic
40C23×C4×C31—22no—
41C23×C4×C31—22no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31—22no—
46C23×C4×C31D414yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—42no—
71C2×C4⋊C4×C31D414yes—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31Q814yes—
84C2×C42×C31—22no—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31—22no—
89C2×C42×C31—22no—
90C31×#95—22no—
91C31×#95—22no—
92C31×#95—24no—
93C31×#95—24no—
94C31×#95—24no—
95C31×#95—24no—
96C31×#95—42no—
97C31×#95—42no—
98C31×#95—42no—
99C31×#95—42no—
100C31×#95—42no—
101C24×C31—21no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—21no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31C2×D412yes—
114C24×C31C2×Q812yes—
115C24×C31#4112yes—
116C24×C31C2411yescharacteristic
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—28no—
154C22×C4×C31—28no—
155C22×C4×C31—28no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
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—44no—
178C22×C4×C31—44no—
179C22×C4×C31—44no—
180C22×C4×C31—44no—
181C22×C4×C31C2×D412yes—
182C22×C4×C31C2×D414yes—
183C22×C4×C31C2×D412yes—
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×Q812yes—
186C22×C4×C31C2×Q812yes—
187C22×C4×C31#4112yes—
188C22×C4×C31#4112yes—
189C22×C4×C31#4112yes—
190C22×C4×C31#4112yes—
191C22×C4×C31#4112yes—
192C22×C4×C31#4112yes—
193C22×C4×C31#4112yes—
194C4⋊C4×C31—28no—
195C4⋊C4×C31—48no—
196C4⋊C4×C31—44no—
197C4⋊C4×C31—44no—
198C4⋊C4×C31—44no—
199C22⋊C4×C31—28no—
200C22⋊C4×C31—28no—
201C22⋊C4×C31—48no—
202C22⋊C4×C31—48no—
203C42×C31—44no—
204C42×C31—44no—
205#15183C3111yesmaximal, characteristic, direct product factor, Sylow
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—22no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—22no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31C22⋊Q814yes—
241C23×C31C22×D411yescharacteristic
242C23×C31C22×D411yescharacteristic
243C23×C31C22×Q811yescharacteristic
244C23×C31C2×#4111yescharacteristic
245C23×C31C2×#4111yescharacteristic
246C23×C31C2×#4111yescharacteristic
247C23×C31C2×#4111yescharacteristic
248C23×C31C2×#4111yescharacteristic
249C23×C31C2×#4111yescharacteristic
250C23×C31C2×#4111yescharacteristic
251C23×C31C2×#4111yescharacteristic
252C23×C31H(5,𝔽2)11yescharacteristic
253C23×C31H(5,𝔽2)11yescharacteristic
254C23×C31H(5,𝔽2)11yescharacteristic
255C23×C312−1+411yescharacteristic
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—24no—
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—24no—
265C2×C4×C31—22no—
266C2×C4×C31—24no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—42no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—42no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—42no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—42no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—416no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31#12114yes—
321C2×C4×C31#12314yes—
322C2×C4×C31#12314yes—
323C2×C4×C31#12314yes—
324C2×C4×C31#12414yes—
325C2×C4×C31#12614yes—
326C2×C4×C31#12614yes—
327C2×#389C2×C3111yescharacteristic, complemented
328C2×#380C2×C3111yescharacteristic
329C2×#380C2×C3111yescharacteristic
330C2×C4×C22⋊C4C2×C3111yescharacteristic
331#1445C2×C3112yescomplemented
332#1443C2×C3112yescomplemented
333#1440C2×C3112yes—
334#1439C2×C3112yes—
335C4⋊#95C2×C3111yescharacteristic, complemented
336C4⋊#95C2×C3111yescharacteristic, complemented
337C4⋊#95C2×C3111yescharacteristic, complemented
338C22×C31—24no—
339C22×C31—24no—
340C22×C31—24no—
341C22×C31—42no—
342C22×C31—42no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—42no—
346C22×C31—42no—
347C22×C31—42no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—42no—
351C22×C31—42no—
352C22×C31—42no—
353C22×C31C2×#12111yescharacteristic
354C22×C31C2×C22⋊Q811yescharacteristic
355C22×C31C2×#12311yescharacteristic
356C22×C31C2×#12311yescharacteristic
357C22×C31C2×#12311yescharacteristic
358C22×C31#52511yescharacteristic
359C22×C31C2×#12411yescharacteristic
360C22×C31C2×#12611yescharacteristic
361C22×C31C2×#12611yescharacteristic
362C22×C31#52911yescharacteristic
363C22×C31#52911yescharacteristic
364C22×C31#53311yescharacteristic
365C22×C31#53311yescharacteristic
366C22×C31#53511yescharacteristic
367C22×C31#53711yescharacteristic
368C22×C31#54011yescharacteristic
369C22×C31#54011yescharacteristic
370C22×C31#54211yescharacteristic
371C22×C31#54211yescharacteristic
372C22×C31#54611yescharacteristic
373C22×C31#54611yescharacteristic
374C22×C31D4×Q811yescharacteristic
375C22×C31#55011yescharacteristic
376C22×C31#55211yescharacteristic
377C22×C31#55211yescharacteristic
378C22×C31#55311yescharacteristic
379C22×C31#55311yescharacteristic
380C22×C31#55311yescharacteristic
381C22×C31#55311yescharacteristic
382C22×C31#55411yescharacteristic
383C22×C31#55411yescharacteristic
384C22×C31#55411yescharacteristic
385C22×C31#55511yescharacteristic
386C22×C31#55511yescharacteristic
387C22×C31#55611yescharacteristic
388C4×C31—42no—
389C4×C31—42no—
390C4×C31—42no—
391C4×C31—44no—
392C4×C31—42no—
393C4×C31—42no—
394C4×C31—82no—
395C4×C31—82no—
396C4×C31—82no—
397C4×C31#39718yes—
398C24×C4C22×C3111yescharacteristic
399C22×C4⋊C4C22×C3111yescharacteristic
400C22×C4⋊C4C22×C3111yescharacteristic
401C22×C4⋊C4C22×C3111yescharacteristic
402C22×C4⋊C4C22×C3112yes—
403C22×C4⋊C4C22×C3111yescharacteristic
404C22×C22⋊C4C22×C3111yescharacteristic
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3111yescharacteristic
407C22×C22⋊C4C22×C3112yes—
408C22×C42C22×C3111yescharacteristic
409C22×C42C22×C3111yescharacteristic
410#389—24no—
411#380—24no—
412#380—24no—
413C4×C22⋊C4—24no—
414C2×#95C22×C3112yes—
415C2×#95C22×C3112yes—
416C2×#95C22×C3111yescharacteristic
417C2×#95C22×C3112yes—
418C2×#95C22×C3112yes—
419C2×#95C22×C3111yescharacteristic
420C2×#95C22×C3112yes—
421C2×#95C22×C3112yes—
422C2×#95C22×C3112yes—
423C2×#95C22×C3112yes—
424C2×#95C22×C3112yes—
425C2×C31—44no—
426C2×C31C2×#39711yescharacteristic
427C2×C31#241411yescharacteristic
428C2×C31#241711yescharacteristic
429C2×C31#242011yescharacteristic
430C2×C31#242311yescharacteristic
431C2×C31#248511yescharacteristic
432C2×C31#248711yescharacteristic
433C2×C31#249011yescharacteristic
434C2×C31#249211yescharacteristic
435C2×C31#249411yescharacteristic
436C2×C31#249511yescharacteristic
437C2×C31#249711yescharacteristic
438C2×C31#249711yescharacteristic
439C2×C31#262411yescharacteristic
440C2×C31#285511yescharacteristic
441C25C23×C3111yescharacteristic
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4D4×C3114yes—
449C23×C4C23×C3112yes—
450C23×C4C23×C3112yes—
451C23×C4C23×C3112yes—
452C23×C4C23×C3112yes—
453C23×C4C23×C3111yescharacteristic
454C23×C4C23×C3111yescharacteristic
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C23×C4C23×C3111yescharacteristic
458C23×C4C23×C3111yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4D4×C3114yes—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4Q8×C3114yes—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492#95—22no—
493#95—22no—
494#95—24no—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—42no—
499#95—42no—
500#95—42no—
501#95—42no—
502#95—42no—
503C31#1518311yescharacteristic, direct product factor, Sylow
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24C2×D4×C3112yes—
517C24C2×Q8×C3112yes—
518C24#41×C3112yes—
519C24C24×C3111yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
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—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4C2×D4×C3112yes—
585C22×C4C2×D4×C3114yes—
586C22×C4C2×D4×C3112yes—
587C22×C4C2×D4×C3112yes—
588C22×C4C2×Q8×C3112yes—
589C22×C4C2×Q8×C3112yes—
590C22×C4#41×C3112yes—
591C22×C4#41×C3112yes—
592C22×C4#41×C3112yes—
593C22×C4#41×C3112yes—
594C22×C4#41×C3112yes—
595C22×C4#41×C3112yes—
596C22×C4#41×C3112yes—
597C4⋊C4—28no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C42—44no—
607C42—44no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C31×C22⋊Q814yes—
643C23C22×D4×C3111yescharacteristic
644C23C22×D4×C3111yescharacteristic
645C23C22×Q8×C3111yescharacteristic
646C23C2×#41×C3111yescharacteristic
647C23C2×#41×C3111yescharacteristic
648C23C2×#41×C3111yescharacteristic
649C23C2×#41×C3111yescharacteristic
650C23C2×#41×C3111yescharacteristic
651C23C2×#41×C3111yescharacteristic
652C23C2×#41×C3111yescharacteristic
653C23C2×#41×C3111yescharacteristic
654C23C31×H(5,𝔽2)11yescharacteristic
655C23C31×H(5,𝔽2)11yescharacteristic
656C23C31×H(5,𝔽2)11yescharacteristic
657C23C31×2−1+411yescharacteristic
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—416no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C31×#12114yes—
723C2×C4C31×#12314yes—
724C2×C4C31×#12314yes—
725C2×C4C31×#12314yes—
726C2×C4C31×#12414yes—
727C2×C4C31×#12614yes—
728C2×C4C31×#12614yes—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22C2×C31×#12111yescharacteristic
745C22C2×C31×C22⋊Q811yescharacteristic
746C22C2×C31×#12311yescharacteristic
747C22C2×C31×#12311yescharacteristic
748C22C2×C31×#12311yescharacteristic
749C22C31×#52511yescharacteristic
750C22C2×C31×#12411yescharacteristic
751C22C2×C31×#12611yescharacteristic
752C22C2×C31×#12611yescharacteristic
753C22C31×#52911yescharacteristic
754C22C31×#52911yescharacteristic
755C22C31×#53311yescharacteristic
756C22C31×#53311yescharacteristic
757C22C31×#53511yescharacteristic
758C22C31×#53711yescharacteristic
759C22C31×#54011yescharacteristic
760C22C31×#54011yescharacteristic
761C22C31×#54211yescharacteristic
762C22C31×#54211yescharacteristic
763C22C31×#54611yescharacteristic
764C22C31×#54611yescharacteristic
765C22D4×Q8×C3111yescharacteristic
766C22C31×#55011yescharacteristic
767C22C31×#55211yescharacteristic
768C22C31×#55211yescharacteristic
769C22C31×#55311yescharacteristic
770C22C31×#55311yescharacteristic
771C22C31×#55311yescharacteristic
772C22C31×#55311yescharacteristic
773C22C31×#55411yescharacteristic
774C22C31×#55411yescharacteristic
775C22C31×#55411yescharacteristic
776C22C31×#55511yescharacteristic
777C22C31×#55511yescharacteristic
778C22C31×#55611yescharacteristic
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—42no—
784C4—42no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4C31×#39718yes—
789C2—44no—
790C2C2×C31×#39711yescharacteristic
791C2C31×#241411yescharacteristic
792C2C31×#241711yescharacteristic
793C2C31×#242011yescharacteristic
794C2C31×#242311yescharacteristic
795C2C31×#248511yescharacteristic
796C2C31×#248711yescharacteristic
797C2C31×#249011yescharacteristic
798C2C31×#249211yescharacteristic
799C2C31×#249411yescharacteristic
800C2C31×#249511yescharacteristic
801C2C31×#249711yescharacteristic
802C2C31×#249711yescharacteristic
803C2C31×#262411yescharacteristic
804C2C31×#285511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#389C2semidirect
5. C31×#1445C2semidirect
6. C31×#1443C2semidirect
9. C31×C4⋊#95C2semidirect
10. C31×C4⋊#95C2semidirect
11. C31×C4⋊#95C2semidirect
205. #15183C31direct (N × H)
327. C2×#389C2×C31semidirect
331. #1445C2×C31semidirect
332. #1443C2×C31semidirect
335. C4⋊#95C2×C31semidirect
336. C4⋊#95C2×C31semidirect
337. C4⋊#95C2×C31semidirect
503. C31#15183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14452
C31×#14432
C31×#14402
C31×#14392
C31×C4⋊#952
#1518331