Finite Group Databasebeta

← C31×#26382 #21483141

Subgroups — C31×#26382 #21483141

Order 7936.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#478C211yesmaximal, characteristic, complemented
2C2×C4×D8×C31C211yesmaximal, characteristic
3C31×#2454C211yesmaximal, characteristic, complemented
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2083C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2059C211yesmaximal, characteristic, complemented
9C31×#1941C211yesmaximal, characteristic, complemented
10C31×#1916C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic
12C31×#1879C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic, complemented
14C31×#1864C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C2×C31×#125C2211yescharacteristic
18C2×C4×D4×C31C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31—21no—
23C31×#478—24no—
24C4×D8×C31—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C31×#399—21no—
39C31×#396—21no—
40C31×#390C2211yescharacteristic
41C31×#390C2211yescharacteristic
42C31×#389C2211yescharacteristic
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#385—21no—
47C31×#385—21no—
48C31×#385—21no—
49C31×#384C2211yescharacteristic
50C31×#380—21no—
51C31×#380—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31C2311yescharacteristic
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C2×D8×C31—22no—
68C2×D8×C31—22no—
69C2×D8×C31Q814yes—
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C31×#125—22no—
75C31×#125—41no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—41no—
82C4×D4×C31—41no—
83C4×D4×C31—41no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—44no—
93C2×C4⋊C4×C31D411yescharacteristic
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C2×C42×C31C2311yescharacteristic
112C31×#107—22no—
113C31×#107—22no—
114C31×#106—22no—
115C31×#106—22no—
116C31×#106—41no—
117C31×C4⋊C8—22no—
118C31×#102—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—41no—
123C31×#102D414yes—
124C4×C8×C31—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95D411yescharacteristic
130C31×#95D411yescharacteristic
131C24×C31—21no—
132C24×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—21no—
137C2×D4×C31—21no—
138C2×D4×C31—21no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31C2×D412yes—
142C2×D4×C31C2×Q812yes—
143C2×D4×C31C2×Q812yes—
144C2×D4×C31#4112yes—
145C22×C4×C31—24no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—42no—
153C22×C4×C31—42no—
154C22×C4×C31—42no—
155C22×C4×C31—42no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—42no—
159C22×C4×C31—42no—
160C22×C4×C31—81no—
161C22×C4×C31—81no—
162C22×C4×C31—81no—
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2411yescharacteristic
170D8×C31—28no—
171C2×C8×C31—21no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31C2×D412yes—
182C2×C8×C31C2×Q812yes—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—42no—
196C4⋊C4×C31—42no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—81no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31—81no—
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31#4112yes—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—42no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—81no—
211C22⋊C4×C31—81no—
212C22⋊C4×C31—81no—
213C42×C31—21no—
214C42×C31—21no—
215C42×C31—21no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219#26382C3111yesmaximal, characteristic, direct product factor, Sylow
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×C31C22×D411yescharacteristic
235D4×C31—22no—
236D4×C31—22no—
237D4×C31—22no—
238D4×C31—22no—
239D4×C31—22no—
240D4×C31—41no—
241D4×C31—41no—
242D4×C31C22⋊Q814yes—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—22no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—48no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—84no—
279C2×C4×C31—84no—
280C2×C4×C31—84no—
281C2×C4×C31#13512yes—
282C2×C4×C31AGL(1,ℤ/8)12yes—
283C2×C4×C31C22×D411yescharacteristic
284C2×C4×C31C22×Q811yescharacteristic
285C2×C4×C31C2×#4111yescharacteristic
286C2×C4×C31C2×#4111yescharacteristic
287C2×C4×C31H(5,𝔽2)11yescharacteristic
288C2×C4×C312−1+411yescharacteristic
289C8×C31—22no—
290C8×C31—22no—
291C8×C31—41no—
292C8×C31—41no—
293C2×#478C2×C3111yescharacteristic, complemented
294C2×C4×D8C2×C3111yescharacteristic
295#2454C2×C3111yescharacteristic, complemented
296D4×C4⋊C4C2×C3111yescharacteristic, complemented
297#2094C2×C3111yescharacteristic, complemented
298#2083C2×C3111yescharacteristic, complemented
299#2065C2×C3111yescharacteristic, complemented
300#2059C2×C3111yescharacteristic, complemented
301#1941C2×C3111yescharacteristic, complemented
302#1916C2×C3111yescharacteristic, complemented
303#1879C2×C3111yescharacteristic
304#1879C2×C3111yescharacteristic
305#1864C2×C3111yescharacteristic, complemented
306#1864C2×C3111yescharacteristic, complemented
307#1862C2×C3111yescharacteristic, complemented
308C22×C31—24no—
309C22×C31—42no—
310C22×C31—42no—
311C22×C31—42no—
312C22×C31—42no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—42no—
316C22×C31—42no—
317C22×C31—42no—
318C22×C31—81no—
319C22×C31—81no—
320C22×C31—81no—
321C22×C31—81no—
322C22×C31#52511yescharacteristic
323C22×C31D4211yescharacteristic
324C22×C31D4×Q811yescharacteristic
325C22×C31C2×#13511yescharacteristic
326C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C31#57611yescharacteristic
328C22×C31#57711yescharacteristic
329C4×C31—22no—
330C4×C31—22no—
331C4×C31—42no—
332C4×C31—41no—
333C4×C31—41no—
334C4×C31—42no—
335C4×C31—41no—
336C4×C31—41no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31—81no—
341C4×C31C2×C22⋊Q811yescharacteristic
342C4×C31#53911yescharacteristic
343C4×C31#54711yescharacteristic
344C4×C31#55411yescharacteristic
345C22×D8C22×C3111yescharacteristic
346C2×#125C22×C3111yescharacteristic
347C2×C4×D4C22×C3111yescharacteristic
348C2×C4×D4C22×C3111yescharacteristic
349C2×C4×D4C22×C3111yescharacteristic
350C2×C4×D4C22×C3111yescharacteristic
351C22×C4⋊C4—21no—
352#478—24no—
353C4×D8—24no—
354C2×#107C22×C3111yescharacteristic
355C2×#107C22×C3111yescharacteristic
356C2×#106C22×C3111yescharacteristic
357C2×#106C22×C3111yescharacteristic
358C2×#106C22×C3111yescharacteristic
359C2×C4⋊C8C22×C3111yescharacteristic
360C2×#102C22×C3111yescharacteristic
361C2×#102C22×C3111yescharacteristic
362C2×#102C22×C3111yescharacteristic
363C2×#102C22×C3111yescharacteristic
364C2×#102C22×C3111yescharacteristic
365C2×#102C22×C3111yescharacteristic
366C2×C4×C8C22×C3111yescharacteristic
367#399—21no—
368#396—21no—
369#390C22×C3111yescharacteristic
370#390C22×C3111yescharacteristic
371#389C22×C3111yescharacteristic
372#389C22×C3111yescharacteristic
373#389C22×C3111yescharacteristic
374#389C22×C3111yescharacteristic
375#385—21no—
376#385—21no—
377#385—21no—
378#384C22×C3111yescharacteristic
379#380—21no—
380#380—21no—
381C4×C4⋊C4C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#336C22×C3111yescharacteristic
387#336C22×C3111yescharacteristic
388#336C22×C3111yescharacteristic
389#336C22×C3111yescharacteristic
390C2×C31—44no—
391C2×C31—82no—
392C2×C31#244911yescharacteristic
393C2×C31#310511yescharacteristic
394C2×C31#311911yescharacteristic
395C2×C31#326411yescharacteristic
396C2×C31#328411yescharacteristic
397C2×C31#338011yescharacteristic
398C2×C31#338411yescharacteristic
399C22×D4C23×C3111yescharacteristic
400C22×D4C23×C3111yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—21no—
405C2×D8—22no—
406C2×D8—22no—
407C2×D8Q8×C3114yes—
408C22×C8C23×C3111yescharacteristic
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C22×C8C23×C3111yescharacteristic
412#125—22no—
413#125—41no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4—41no—
421C4×D4—41no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4D4×C3111yescharacteristic
432C2×C4⋊C4D4×C3111yescharacteristic
433C2×C4⋊C4C23×C3111yescharacteristic
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C4⋊C4C23×C3111yescharacteristic
437C2×C4⋊C4C23×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42C23×C3111yescharacteristic
448C2×C42C23×C3111yescharacteristic
449C2×C42C23×C3111yescharacteristic
450#107—22no—
451#107—22no—
452#106—22no—
453#106—22no—
454#106—41no—
455C4⋊C8—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—41no—
461#102D4×C3114yes—
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C3111yescharacteristic
468#95D4×C3111yescharacteristic
469C31#2638211yescharacteristic, direct product factor, Sylow
470C24—21no—
471C24—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×D4×C3112yes—
481C2×D4C2×Q8×C3112yes—
482C2×D4C2×Q8×C3112yes—
483C2×D4#41×C3112yes—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C24×C3111yescharacteristic
509D8—28no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C3112yes—
521C2×C8C2×Q8×C3112yes—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4C2×D4×C3112yes—
543C4⋊C4#41×C3112yes—
544C22⋊C4—24no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C3111yescharacteristic
573D4—22no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—41no—
579D4—41no—
580D4C31×C22⋊Q814yes—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—48no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4C31×#13512yes—
620C2×C4C31×AGL(1,ℤ/8)12yes—
621C2×C4C22×D4×C3111yescharacteristic
622C2×C4C22×Q8×C3111yescharacteristic
623C2×C4C2×#41×C3111yescharacteristic
624C2×C4C2×#41×C3111yescharacteristic
625C2×C4C31×H(5,𝔽2)11yescharacteristic
626C2×C4C31×2−1+411yescharacteristic
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C31×#52511yescharacteristic
646C22D42×C3111yescharacteristic
647C22D4×Q8×C3111yescharacteristic
648C22C2×C31×#13511yescharacteristic
649C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
650C22C31×#57611yescharacteristic
651C22C31×#57711yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C2×C31×C22⋊Q811yescharacteristic
665C4C31×#53911yescharacteristic
666C4C31×#54711yescharacteristic
667C4C31×#55411yescharacteristic
668C2—44no—
669C2—82no—
670C2C31×#244911yescharacteristic
671C2C31×#310511yescharacteristic
672C2C31×#311911yescharacteristic
673C2C31×#326411yescharacteristic
674C2C31×#328411yescharacteristic
675C2C31×#338011yescharacteristic
676C2C31×#338411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#478C2semidirect
3. C31×#2454C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2083C2semidirect
7. C31×#2065C2semidirect
8. C31×#2059C2semidirect
9. C31×#1941C2semidirect
10. C31×#1916C2semidirect
13. C31×#1864C2semidirect
14. C31×#1864C2semidirect
15. C31×#1862C2semidirect
219. #26382C31direct (N × H)
293. C2×#478C2×C31semidirect
295. #2454C2×C31semidirect
296. D4×C4⋊C4C2×C31semidirect
297. #2094C2×C31semidirect
298. #2083C2×C31semidirect
299. #2065C2×C31semidirect
300. #2059C2×C31semidirect
301. #1941C2×C31semidirect
302. #1916C2×C31semidirect
305. #1864C2×C31semidirect
306. #1864C2×C31semidirect
307. #1862C2×C31semidirect
469. C31#26382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4782
C2×C4×D8×C312
C31×#24542
D4×C4⋊C4×C312
C31×#20942
C31×#20832
C31×#20652
C31×#20592
C31×#19412
C31×#19162
C31×#18792
C31×#18642
C31×#18622
#2638231