Finite Group Databasebeta

← C31×#24909 #21481668

Subgroups — C31×#24909 #21481668

Order 7936.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#447C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C31×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2092C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2054C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1936C211yesmaximal, characteristic, complemented
10C31×#1924C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1862C211yesmaximal, characteristic, complemented
14C31×#1804C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic, complemented
23C22×C22⋊C4×C31—21no—
24C31×#447—24no—
25C31×#442—24no—
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×C4⋊C8C2211yescharacteristic, complemented
29C2×C31×#102C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic, complemented
36C2×C31×#102C2211yescharacteristic, complemented
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic, complemented
40C31×#397—21no—
41C31×#394—21no—
42C31×#390C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic, complemented
45C31×#389C2211yescharacteristic, complemented
46C31×#386—21no—
47C31×#386—21no—
48C31×#386—21no—
49C31×#382C2211yescharacteristic, complemented
50C31×#381—21no—
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic, complemented
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31—21no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2311yescharacteristic
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31—41no—
82C2×D8×C31D414yes—
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C31×#121—22no—
88C31×#121—41no—
89C4×D4×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—41no—
93C4×D4×C31—41no—
94C4×D4×C31—41no—
95C2×C4⋊C4×C31—21no—
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×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—44no—
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C22⋊C4×C31D411yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C31×#107—41no—
119C31×#106—22no—
120C31×C4⋊C8—41no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—41no—
128C31×#102—41no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—41no—
131C31×#97—22no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95D411yescharacteristic
138C31×#95D411yescharacteristic
139C24×C31—21no—
140C24×C31—24no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—42no—
147C24×C31—81no—
148C24×C31—81no—
149C24×C31C2×D411yescharacteristic
150C2×D4×C31—24no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—44no—
167C2×D4×C31—44no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—81no—
173C2×D4×C31C2×D412yes—
174C2×D4×C31C2×D412yes—
175C2×D4×C31#4112yes—
176C2×D4×C31#4112yes—
177C2×D4×C31#4112yes—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—81no—
196C22×C4×C31—81no—
197C22×C4×C31—81no—
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2411yescharacteristic
204D8×C31—28no—
205D8×C31—44no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31C2×D412yes—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—81no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—41no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—81no—
239C22⋊C4×C31—81no—
240C22⋊C4×C31—81no—
241C22⋊C4×C31—81no—
242C22⋊C4×C31—81no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31—21no—
246C42×C31—21no—
247#24909C3111yesmaximal, characteristic, direct product factor, Sylow
248C23×C31—21no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—48no—
260C23×C31—48no—
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—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—84no—
278C23×C31—84no—
279C23×C31—84no—
280C23×C31—84no—
281C23×C31—84no—
282C23×C31AGL(1,ℤ/8)12yes—
283C23×C31C22×D411yescharacteristic
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—48no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—84no—
297D4×C31#12314yes—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
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—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—84no—
333C2×C4×C31—84no—
334C2×C4×C31—84no—
335C2×C4×C31C22×D411yescharacteristic
336C2×C4×C31C2×#4111yescharacteristic
337C2×C4×C31C2×#4111yescharacteristic
338C2×C4×C31C2×#4111yescharacteristic
339C2×C4×C31H(5,𝔽2)11yescharacteristic
340C2×C4×C31H(5,𝔽2)11yescharacteristic
341C8×C31—22no—
342C8×C31—41no—
343C8×C31—41no—
344C8×C31—41no—
345C2×#447C2×C3111yescharacteristic
346C2×#442C2×C3111yescharacteristic, complemented
347#2420C2×C3111yescharacteristic, complemented
348D4×C22⋊C4C2×C3111yescharacteristic, complemented
349#2092C2×C3111yescharacteristic, complemented
350#2077C2×C3111yescharacteristic, complemented
351#2054C2×C3111yescharacteristic, complemented
352#2033C2×C3111yescharacteristic, complemented
353#1936C2×C3111yescharacteristic, complemented
354#1924C2×C3111yescharacteristic, complemented
355#1879C2×C3111yescharacteristic, complemented
356#1879C2×C3111yescharacteristic, complemented
357#1862C2×C3111yescharacteristic, complemented
358#1804C2×C3111yescharacteristic, complemented
359#1786C2×C3111yescharacteristic, complemented
360C22×C31—22no—
361C22×C31—24no—
362C22×C31—22no—
363C22×C31—22no—
364C22×C31—42no—
365C22×C31—41no—
366C22×C31—42no—
367C22×C31—41no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—816no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31#52511yescharacteristic
390C22×C31D4211yescharacteristic
391C22×C31#54611yescharacteristic
392C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C31#57511yescharacteristic
394C22×C31#57611yescharacteristic
395C22×C31#57611yescharacteristic
396C4×C31—41no—
397C4×C31—41no—
398C4×C31—41no—
399C4×C31—41no—
400C4×C31—41no—
401C4×C31—81no—
402C4×C31—81no—
403C4×C31—81no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31C2×#12311yescharacteristic
407C4×C31#53811yescharacteristic
408C4×C31#54611yescharacteristic
409C4×C31#55111yescharacteristic
410C23×D4C22×C3111yescharacteristic
411C22×D8C22×C3111yescharacteristic
412C22×D8C22×C3111yescharacteristic
413C2×#121C22×C3111yescharacteristic
414C2×C4×D4C22×C3111yescharacteristic
415C2×C4×D4C22×C3111yescharacteristic
416C2×C4×D4C22×C3111yescharacteristic, complemented
417C22×C22⋊C4—21no—
418#447—24no—
419#442—24no—
420C2×#107C22×C3111yescharacteristic, complemented
421C2×#106C22×C3111yescharacteristic, complemented
422C2×C4⋊C8C22×C3111yescharacteristic, complemented
423C2×#102C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×#102C22×C3111yescharacteristic
427C2×#102C22×C3111yescharacteristic
428C2×#102C22×C3111yescharacteristic
429C2×#102C22×C3111yescharacteristic, complemented
430C2×#102C22×C3111yescharacteristic, complemented
431C2×C22⋊C8C22×C3111yescharacteristic
432C2×C22⋊C8C22×C3111yescharacteristic
433C2×#97C22×C3111yescharacteristic, complemented
434#397—21no—
435#394—21no—
436#390C22×C3111yescharacteristic
437#390C22×C3111yescharacteristic
438#390C22×C3111yescharacteristic, complemented
439#389C22×C3111yescharacteristic, complemented
440#386—21no—
441#386—21no—
442#386—21no—
443#382C22×C3111yescharacteristic, complemented
444#381—21no—
445#380C22×C3111yescharacteristic
446#380C22×C3111yescharacteristic
447#379—21no—
448C4×C22⋊C4C22×C3111yescharacteristic
449#340C22×C3111yescharacteristic, complemented
450#340C22×C3111yescharacteristic, complemented
451#340C22×C3111yescharacteristic, complemented
452#340C22×C3111yescharacteristic, complemented
453#336C22×C3111yescharacteristic, complemented
454#336C22×C3111yescharacteristic, complemented
455C2×C31—42no—
456C2×C31—44no—
457C2×C31—82no—
458C2×C31—82no—
459C2×C31#241811yescharacteristic
460C2×C31#311411yescharacteristic
461C2×C31#312211yescharacteristic
462C2×C31#326411yescharacteristic
463C2×C31#327311yescharacteristic
464C2×C31#331811yescharacteristic
465C2×C31#331911yescharacteristic
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4C23×C3111yescharacteristic
476C22×D4C23×C3111yescharacteristic
477C22×D4C23×C3111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C3111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—41no—
487C2×D8D4×C3114yes—
488C22×C8C23×C3111yescharacteristic
489C22×C8C23×C3111yescharacteristic
490C22×C8C23×C3111yescharacteristic
491C22×C8C23×C3111yescharacteristic
492#121—22no—
493#121—41no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—41no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—44no—
519C2×C22⋊C4D4×C3111yescharacteristic
520C2×C22⋊C4D4×C3111yescharacteristic
521C2×C42C23×C3111yescharacteristic
522C2×C42C23×C3111yescharacteristic
523#107—41no—
524#106—22no—
525C4⋊C8—41no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—41no—
533#102—41no—
534C22⋊C8—22no—
535C22⋊C8—41no—
536#97—22no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95D4×C3111yescharacteristic
543#95D4×C3111yescharacteristic
544C31#2490911yescharacteristic, direct product factor, Sylow
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C3111yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C3112yes—
580C2×D4C2×D4×C3112yes—
581C2×D4#41×C3112yes—
582C2×D4#41×C3112yes—
583C2×D4#41×C3112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C24×C3111yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C3112yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23C31×AGL(1,ℤ/8)12yes—
688C23C22×D4×C3111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4C31×#12314yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
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—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C22×D4×C3111yescharacteristic
741C2×C4C2×#41×C3111yescharacteristic
742C2×C4C2×#41×C3111yescharacteristic
743C2×C4C2×#41×C3111yescharacteristic
744C2×C4C31×H(5,𝔽2)11yescharacteristic
745C2×C4C31×H(5,𝔽2)11yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C31×#52511yescharacteristic
780C22D42×C3111yescharacteristic
781C22C31×#54611yescharacteristic
782C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
783C22C31×#57511yescharacteristic
784C22C31×#57611yescharacteristic
785C22C31×#57611yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×C31×#12311yescharacteristic
797C4C31×#53811yescharacteristic
798C4C31×#54611yescharacteristic
799C4C31×#55111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C31×#241811yescharacteristic
805C2C31×#311411yescharacteristic
806C2C31×#312211yescharacteristic
807C2C31×#326411yescharacteristic
808C2C31×#327311yescharacteristic
809C2C31×#331811yescharacteristic
810C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
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
2. C2×C31×#442C2semidirect
3. C31×#2420C2semidirect
4. D4×C22⋊C4×C31C2semidirect
5. C31×#2092C2semidirect
6. C31×#2077C2semidirect
7. C31×#2054C2semidirect
8. C31×#2033C2semidirect
9. C31×#1936C2semidirect
10. C31×#1924C2semidirect
11. C31×#1879C2semidirect
12. C31×#1879C2semidirect
13. C31×#1862C2semidirect
14. C31×#1804C2semidirect
15. C31×#1786C2semidirect
22. C2×C4×D4×C31C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#106C22semidirect
28. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#102C22semidirect
36. C2×C31×#102C22semidirect
39. C2×C31×#97C22semidirect
44. C31×#390C22semidirect
45. C31×#389C22semidirect
49. C31×#382C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
247. #24909C31direct (N × H)
346. C2×#442C2×C31semidirect
347. #2420C2×C31semidirect
348. D4×C22⋊C4C2×C31semidirect
349. #2092C2×C31semidirect
350. #2077C2×C31semidirect
351. #2054C2×C31semidirect
352. #2033C2×C31semidirect
353. #1936C2×C31semidirect
354. #1924C2×C31semidirect
355. #1879C2×C31semidirect
356. #1879C2×C31semidirect
357. #1862C2×C31semidirect
358. #1804C2×C31semidirect
359. #1786C2×C31semidirect
416. C2×C4×D4C22×C31semidirect
420. C2×#107C22×C31semidirect
421. C2×#106C22×C31semidirect
422. C2×C4⋊C8C22×C31semidirect
429. C2×#102C22×C31semidirect
430. C2×#102C22×C31semidirect
433. C2×#97C22×C31semidirect
438. #390C22×C31semidirect
439. #389C22×C31semidirect
443. #382C22×C31semidirect
449. #340C22×C31semidirect
450. #340C22×C31semidirect
451. #340C22×C31semidirect
452. #340C22×C31semidirect
453. #336C22×C31semidirect
454. #336C22×C31semidirect
544. C31#24909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C2×C31×#4422
C31×#24202
D4×C22⋊C4×C312
C31×#20922
C31×#20772
C31×#20542
C31×#20332
C31×#19362
C31×#19242
C31×#18792
C31×#18622
C31×#18042
C31×#17862
#2490931