Finite Group Databasebeta

← C31×#25200 #21481959

Subgroups — C31×#25200 #21481959

Order 7936.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C2×C31×#466C211yesmaximal, characteristic
3C31×#2501C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic, complemented
5C31×#2083C211yesmaximal, characteristic, complemented
6C31×#2071C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#1947C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1850C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic, complemented
15C2×C31×#340C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#123—21no—
19C2×C31×#123—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C4×D4×C31—21no—
23C2×C4×D4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C31×#480—24no—
27C31×#466—24no—
28C2×C31×#107C2211yescharacteristic
29C2×C31×#107C2211yescharacteristic
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C31×#399—21no—
41C31×#399—21no—
42C31×#390C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#388—21no—
47C31×#386—21no—
48C31×#385—21no—
49C31×#384C2211yescharacteristic
50C31×#384C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C2×D8×C31—22no—
70C2×D8×C31—22no—
71C2×D8×C31—41no—
72C22×C8×C31—22no—
73C22×C8×C31—22no—
74C22×C8×C31—41no—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×#123—44no—
80C31×#123—44no—
81C31×#121—22no—
82C31×#121—22no—
83C31×#121—22no—
84C31×#121D414yes—
85C4×D4×C31—22no—
86C4×D4×C31—41no—
87C4×D4×C31—44no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C22⋊C4×C31D411yescharacteristic
116C2×C42×C31—21no—
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C31×#107—22no—
120C31×#107—22no—
121C31×#107—22no—
122C31×C4⋊C8—22no—
123C31×C4⋊C8—41no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—41no—
130C31×C22⋊C8—22no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95D411yescharacteristic
134C31×#95D411yescharacteristic
135C24×C31—21no—
136C24×C31—21no—
137C24×C31C2×D411yescharacteristic
138C2×D4×C31—24no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—42no—
151C2×D4×C31—42no—
152C2×D4×C31—42no—
153C2×D4×C31—42no—
154C2×D4×C31—42no—
155C2×D4×C31C2×D412yes—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D412yes—
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31#4112yes—
182C22×C4×C31C2411yescharacteristic
183D8×C31—44no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—44no—
196C2×C8×C31#4112yes—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31C2×D412yes—
215C4⋊C4×C31#4112yes—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—24no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—42no—
221C22⋊C4×C31—42no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—42no—
224C22⋊C4×C31—42no—
225C22⋊C4×C31—81no—
226C22⋊C4×C31D814yescomplemented
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—21no—
230C42×C31—21no—
231C42×C31—42no—
232#25200C3111yesmaximal, characteristic, direct product factor, Sylow
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—22no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31#12112yes—
252C23×C31C2×D812yes—
253C23×C31AGL(1,ℤ/8)12yes—
254C23×C31C22×D411yescharacteristic
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—48no—
258D4×C31—41no—
259D4×C31—41no—
260D4×C31—41no—
261D4×C31—41no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—84no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—21no—
277C2×C4×C31—22no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—84no—
300C2×C4×C31—84no—
301C2×C4×C31—84no—
302C2×C4×C31#12112yes—
303C2×C4×C31C2×D812yes—
304C2×C4×C31C2×D812yes—
305C2×C4×C31C22×D411yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31H(5,𝔽2)11yescharacteristic
310C2×C4×C312−1+411yescharacteristic
311C8×C31—22no—
312C8×C31—41no—
313C8×C31—41no—
314C8×C31—41no—
315C2×#480C2×C3111yescharacteristic, complemented
316C2×#466C2×C3111yescharacteristic
317#2501C2×C3111yescharacteristic, complemented
318#2361C2×C3111yescharacteristic, complemented
319#2083C2×C3111yescharacteristic, complemented
320#2071C2×C3111yescharacteristic, complemented
321#2067C2×C3111yescharacteristic, complemented
322#2054C2×C3111yescharacteristic, complemented
323#1947C2×C3111yescharacteristic, complemented
324#1925C2×C3111yescharacteristic, complemented
325#1879C2×C3111yescharacteristic, complemented
326#1874C2×C3111yescharacteristic, complemented
327#1850C2×C3111yescharacteristic, complemented
328#1802C2×C3111yescharacteristic, complemented
329C2×#340C2×C3111yescharacteristic, complemented
330C22×C31—22no—
331C22×C31—22no—
332C22×C31—22no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—22no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31#45914yes—
351C22×C31C2×#12111yescharacteristic
352C22×C31#54611yescharacteristic
353C22×C31#54711yescharacteristic
354C22×C31C22×D811yescharacteristic
355C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C31#57711yescharacteristic
357C22×C31#57811yescharacteristic
358C4×C31—22no—
359C4×C31—22no—
360C4×C31—22no—
361C4×C31—41no—
362C4×C31—42no—
363C4×C31—42no—
364C4×C31—41no—
365C4×C31—81no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31#52911yescharacteristic
370C4×C31#53911yescharacteristic
371C4×C31#54611yescharacteristic
372C4×C31#54711yescharacteristic
373C22×D8C22×C3111yescharacteristic
374C23×C8C22×C3111yescharacteristic
375C2×#123—21no—
376C2×#123—21no—
377C2×#121C22×C3111yescharacteristic
378C2×#121C22×C3111yescharacteristic
379C2×C4×D4—21no—
380C2×C4×D4C22×C3111yescharacteristic
381C22×C4⋊C4C22×C3111yescharacteristic
382C22×C4⋊C4C22×C3111yescharacteristic
383#480—24no—
384#466—24no—
385C2×#107C22×C3111yescharacteristic
386C2×#107C22×C3111yescharacteristic
387C2×#107C22×C3111yescharacteristic
388C2×C4⋊C8C22×C3111yescharacteristic
389C2×C4⋊C8C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#102C22×C3111yescharacteristic
394C2×#102C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×C22⋊C8C22×C3111yescharacteristic
397#399—21no—
398#399—21no—
399#390C22×C3111yescharacteristic
400#390C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#389C22×C3111yescharacteristic
403#388—21no—
404#386—21no—
405#385—21no—
406#384C22×C3111yescharacteristic
407#384C22×C3111yescharacteristic
408C4×C4⋊C4C22×C3111yescharacteristic
409C4×C22⋊C4C22×C3111yescharacteristic
410#340C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#340C22×C3111yescharacteristic
415#340C22×C3111yescharacteristic
416#336C22×C3111yescharacteristic
417#336C22×C3111yescharacteristic
418C2×C31—24no—
419C2×C31—82no—
420C2×C31—161no—
421C2×C31#242511yescharacteristic
422C2×C31C2×#45911yescharacteristic
423C2×C31#304611yescharacteristic
424C2×C31#329411yescharacteristic
425C2×C31#330811yescharacteristic
426C2×C31#333411yescharacteristic
427C2×C31#334511yescharacteristic
428C22×D4—21no—
429C22×D4—21no—
430C22×D4C23×C3111yescharacteristic
431C22×D4C23×C3111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4C23×C3111yescharacteristic
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—41no—
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8C23×C3111yescharacteristic
443C22×C8C23×C3111yescharacteristic
444C22×C8C23×C3111yescharacteristic
445C22×C8C23×C3111yescharacteristic
446#123—44no—
447#123—44no—
448#121—22no—
449#121—22no—
450#121—22no—
451#121D4×C3114yes—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—44no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4C23×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4D4×C3111yescharacteristic
482C2×C22⋊C4D4×C3111yescharacteristic
483C2×C42—21no—
484C2×C42C23×C3111yescharacteristic
485C2×C42C23×C3111yescharacteristic
486#107—22no—
487#107—22no—
488#107—22no—
489C4⋊C8—22no—
490C4⋊C8—41no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—41no—
497C22⋊C8—22no—
498#95—21no—
499#95—21no—
500#95D4×C3111yescharacteristic
501#95D4×C3111yescharacteristic
502C31#2520011yescharacteristic, direct product factor, Sylow
503C24—21no—
504C24—21no—
505C24C2×D4×C3111yescharacteristic
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×D4×C3112yes—
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—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4C2×D4×C3111yescharacteristic
544C22×C4C2×D4×C3111yescharacteristic
545C22×C4C2×D4×C3111yescharacteristic
546C22×C4C2×D4×C3112yes—
547C22×C4C2×D4×C3111yescharacteristic
548C22×C4C2×D4×C3111yescharacteristic
549C22×C4#41×C3112yes—
550C22×C4C24×C3111yescharacteristic
551D8—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#41×C3112yes—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4C2×D4×C3112yes—
583C4⋊C4#41×C3112yes—
584C22⋊C4—22no—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4D8×C3114yescomplemented
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23C31×#12112yes—
619C23C2×D8×C3112yes—
620C23C31×AGL(1,ℤ/8)12yes—
621C23C22×D4×C3111yescharacteristic
622D4—22no—
623D4—22no—
624D4—48no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—84no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4C31×#12112yes—
670C2×C4C2×D8×C3112yes—
671C2×C4C2×D8×C3112yes—
672C2×C4C22×D4×C3111yescharacteristic
673C2×C4C2×#41×C3111yescharacteristic
674C2×C4C2×#41×C3111yescharacteristic
675C2×C4C2×#41×C3111yescharacteristic
676C2×C4C31×H(5,𝔽2)11yescharacteristic
677C2×C4C31×2−1+411yescharacteristic
678C8—22no—
679C8—41no—
680C8—41no—
681C8—41no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C31×#45914yes—
703C22C2×C31×#12111yescharacteristic
704C22C31×#54611yescharacteristic
705C22C31×#54711yescharacteristic
706C22C22×D8×C3111yescharacteristic
707C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
708C22C31×#57711yescharacteristic
709C22C31×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4C31×#52911yescharacteristic
722C4C31×#53911yescharacteristic
723C4C31×#54611yescharacteristic
724C4C31×#54711yescharacteristic
725C2—24no—
726C2—82no—
727C2—161no—
728C2C31×#242511yescharacteristic
729C2C2×C31×#45911yescharacteristic
730C2C31×#304611yescharacteristic
731C2C31×#329411yescharacteristic
732C2C31×#330811yescharacteristic
733C2C31×#333411yescharacteristic
734C2C31×#334511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#480C2semidirect
3. C31×#2501C2semidirect
4. C31×#2361C2semidirect
5. C31×#2083C2semidirect
6. C31×#2071C2semidirect
7. C31×#2067C2semidirect
8. C31×#2054C2semidirect
9. C31×#1947C2semidirect
10. C31×#1925C2semidirect
11. C31×#1879C2semidirect
12. C31×#1874C2semidirect
13. C31×#1850C2semidirect
14. C31×#1802C2semidirect
15. C2×C31×#340C2semidirect
226. C22⋊C4×C31D8semidirect
232. #25200C31direct (N × H)
315. C2×#480C2×C31semidirect
317. #2501C2×C31semidirect
318. #2361C2×C31semidirect
319. #2083C2×C31semidirect
320. #2071C2×C31semidirect
321. #2067C2×C31semidirect
322. #2054C2×C31semidirect
323. #1947C2×C31semidirect
324. #1925C2×C31semidirect
325. #1879C2×C31semidirect
326. #1874C2×C31semidirect
327. #1850C2×C31semidirect
328. #1802C2×C31semidirect
329. C2×#340C2×C31semidirect
502. C31#25200direct (N × H)
594. C22⋊C4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C2×C31×#4662
C31×#25012
C31×#23612
C31×#20832
C31×#20712
C31×#20672
C31×#20542
C31×#19472
C31×#19252
C31×#18792
C31×#18742
C31×#18502
C31×#18022
C2×C31×#3402
#2520031