Finite Group Databasebeta

← C31×#24369 #21481128

Subgroups — C31×#24369 #21481128

Order 7936.

1388 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C2×C31×#451C211yesmaximal, characteristic, complemented
5C31×#2432C211yesmaximal, characteristic
6Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2056C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2016C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1851C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C2×C31×#137—24no—
19C2×C31×#137—24no—
20C2×C31×#137—24no—
21C22×Q16×C31C2211yescharacteristic
22C22×Q16×C31C2211yescharacteristic
23C22×Q16×C31C2211yescharacteristic
24C22×Q16×C31C2211yescharacteristic
25C22×SD16×C31C2211yescharacteristic
26C22×SD16×C31C2211yescharacteristic
27C22×M16×C31C2211yescharacteristic
28C2×C31×C4⋊Q8C2211yescharacteristic
29C2×C31×#124C2211yescharacteristic
30C2×C31×C22⋊Q8C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C31×#464—24no—
34C31×#462—24no—
35C31×#451—24no—
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#394—21no—
48C31×#394—21no—
49C31×#391—21no—
50C31×#391—21no—
51C31×#391C2211yescharacteristic
52C31×#391C2211yescharacteristic
53C31×#391C2211yescharacteristic
54C31×#390C2211yescharacteristic
55C31×#385—21no—
56C31×#385—21no—
57C31×#380—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—41no—
70C2×#41×C31—41no—
71C22×Q8×C31—21no—
72C22×Q8×C31—22no—
73C22×Q8×C31—22no—
74C22×Q8×C31—22no—
75C22×Q8×C31—41no—
76C22×Q8×C31—41no—
77C22×Q8×C31D414yes—
78C22×Q8×C31C2311yescharacteristic
79C22×Q8×C31C2311yescharacteristic
80C22×Q8×C31C2311yescharacteristic
81C22×Q8×C31C2311yescharacteristic
82C22×D4×C31—21no—
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31C2311yescharacteristic
87C31×#137—232no—
88C2×Q16×C31—22no—
89C2×Q16×C31—22no—
90C2×Q16×C31—22no—
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31—22no—
94C2×Q16×C31—22no—
95C2×Q16×C31—22no—
96C2×Q16×C31—22no—
97C2×Q16×C31—41no—
98C2×Q16×C31—41no—
99C2×Q16×C31D414yes—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—22no—
103C2×SD16×C31—22no—
104C2×SD16×C31—22no—
105C2×SD16×C31D414yes—
106C2×M16×C31—22no—
107C2×M16×C31—22no—
108C2×M16×C31—22no—
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C31×C4⋊Q8—22no—
114C31×C4⋊Q8—41no—
115C31×#124—22no—
116C31×#124—41no—
117C31×C22⋊Q8—22no—
118C31×C22⋊Q8—22no—
119C4×Q8×C31—22no—
120C4×Q8×C31—22no—
121C4×Q8×C31—41no—
122C4×Q8×C31—41no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31D411yescharacteristic
138C2×C22⋊C4×C31D411yescharacteristic
139C2×C42×C31—21no—
140C2×C42×C31—21no—
141C2×C42×C31C2311yescharacteristic
142C2×C42×C31C2311yescharacteristic
143C31×C4⋊C8—22no—
144C31×C4⋊C8—22no—
145C31×#103—22no—
146C31×#103—22no—
147C31×#103—22no—
148C31×#103—22no—
149C31×#103—22no—
150C31×#103—41no—
151C31×#102—22no—
152C31×#102—41no—
153C31×C22⋊C8—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95D411yescharacteristic
162C31×#95D411yescharacteristic
163C24×C31—21no—
164C24×C31C2×D411yescharacteristic
165#41×C31—28no—
166#41×C31—44no—
167#41×C31—44no—
168#41×C31—44no—
169C2×Q8×C31—24no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31—21no—
175C2×Q8×C31—28no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—42no—
191C2×Q8×C31—42no—
192C2×Q8×C31—44no—
193C2×Q8×C31—44no—
194C2×Q8×C31—44no—
195C2×Q8×C31C2×D412yes—
196C2×Q8×C31C2×D412yes—
197C2×Q8×C31C2×D412yes—
198C2×Q8×C31C2×D412yes—
199C2×Q8×C31C2×D412yes—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31C2×D412yes—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—24no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31#4112yes—
233C22×C4×C31C2411yescharacteristic
234Q16×C31—28no—
235Q16×C31—28no—
236Q16×C31—44no—
237Q16×C31—44no—
238SD16×C31—28no—
239SD16×C31—28no—
240M16×C31—28no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31C2×D412yes—
252C2×C8×C31C2×D412yes—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—42no—
260C4⋊C4×C31—42no—
261C4⋊C4×C31—42no—
262C4⋊C4×C31—42no—
263C4⋊C4×C31—42no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—41no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C42×C31—21no—
273C42×C31—21no—
274C42×C31—21no—
275C42×C31—21no—
276C42×C31—42no—
277C42×C31—42no—
278#24369C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—22no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31#12112yes—
293C23×C31C22×D411yescharacteristic
294Q8×C31—22no—
295Q8×C31—22no—
296Q8×C31—22no—
297Q8×C31—22no—
298Q8×C31—22no—
299Q8×C31—22no—
300Q8×C31—22no—
301Q8×C31—48no—
302Q8×C31—41no—
303Q8×C31—41no—
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31—41no—
307Q8×C31—41no—
308Q8×C31—41no—
309Q8×C31—41no—
310Q8×C31#12014yes—
311D4×C31—22no—
312D4×C31—22no—
313D4×C31—48no—
314D4×C31—41no—
315D4×C31—41no—
316C2×C4×C31—22no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—22no—
332C2×C4×C31—21no—
333C2×C4×C31—21no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—48no—
339C2×C4×C31—48no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31#12112yes—
357C2×C4×C31#13712yescomplemented
358C2×C4×C31C22×D411yescharacteristic
359C2×C4×C31C22×D411yescharacteristic
360C2×C4×C31C22×D411yescharacteristic
361C2×C4×C31C2×#4111yescharacteristic
362C2×C4×C31H(5,𝔽2)11yescharacteristic
363C2×C4×C31H(5,𝔽2)11yescharacteristic
364C8×C31—22no—
365C8×C31—22no—
366C8×C31—41no—
367C8×C31—41no—
368C22×#137C2×C3111yescharacteristic
369C2×#464C2×C3111yescharacteristic, complemented
370C2×#462C2×C3111yescharacteristic, complemented
371C2×#451C2×C3111yescharacteristic, complemented
372#2432C2×C3111yescharacteristic
373Q8×C22⋊C4C2×C3111yescharacteristic, complemented
374#2056C2×C3111yescharacteristic, complemented
375#2055C2×C3111yescharacteristic, complemented
376#2016C2×C3111yescharacteristic, complemented
377#2015C2×C3111yescharacteristic, complemented
378#1894C2×C3111yescharacteristic, complemented
379#1880C2×C3111yescharacteristic, complemented
380#1878C2×C3111yescharacteristic, complemented
381#1851C2×C3111yescharacteristic, complemented
382#1788C2×C3111yescharacteristic
383C22×C31—22no—
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31C2×#12111yescharacteristic
398C22×C31D4211yescharacteristic
399C22×C31D4211yescharacteristic
400C22×C31C2×#13711yescharacteristic
401C22×C31#57511yescharacteristic
402C22×C31#57811yescharacteristic
403C22×C31#57811yescharacteristic
404C4×C31—22no—
405C4×C31—24no—
406C4×C31—22no—
407C4×C31—42no—
408C4×C31—42no—
409C4×C31—41no—
410C4×C31—41no—
411C4×C31—41no—
412C4×C31—81no—
413C4×C31—81no—
414C4×C31—81no—
415C4×C31—81no—
416C4×C31C2×#12011yescharacteristic
417C4×C31#53411yescharacteristic
418C4×C31#54611yescharacteristic
419C4×C31#54611yescharacteristic
420C22×#41C22×C3111yescharacteristic
421C23×Q8C22×C3111yescharacteristic
422C2×#137—24no—
423C2×#137—24no—
424C2×#137—24no—
425C22×Q16C22×C3111yescharacteristic
426C22×Q16C22×C3111yescharacteristic
427C22×Q16C22×C3111yescharacteristic
428C22×Q16C22×C3111yescharacteristic
429C22×SD16C22×C3111yescharacteristic
430C22×SD16C22×C3111yescharacteristic
431C22×M16C22×C3111yescharacteristic
432C2×C4⋊Q8C22×C3111yescharacteristic
433C2×#124C22×C3111yescharacteristic
434C2×C22⋊Q8C22×C3111yescharacteristic
435C2×C4×Q8C22×C3111yescharacteristic
436C2×C4×Q8C22×C3111yescharacteristic
437#464—24no—
438#462—24no—
439#451—24no—
440C2×C4⋊C8C22×C3111yescharacteristic
441C2×C4⋊C8C22×C3111yescharacteristic
442C2×#103C22×C3111yescharacteristic
443C2×#103C22×C3111yescharacteristic
444C2×#103C22×C3111yescharacteristic
445C2×#103C22×C3111yescharacteristic
446C2×#103C22×C3111yescharacteristic
447C2×#103C22×C3111yescharacteristic
448C2×#102C22×C3111yescharacteristic
449C2×#102C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451#394—21no—
452#394—21no—
453#391—21no—
454#391—21no—
455#391C22×C3111yescharacteristic
456#391C22×C3111yescharacteristic
457#391C22×C3111yescharacteristic
458#390C22×C3111yescharacteristic
459#385—21no—
460#385—21no—
461#380—21no—
462#380C22×C3111yescharacteristic
463C4×C22⋊C4—21no—
464C4×C22⋊C4C22×C3111yescharacteristic
465#340C22×C3111yescharacteristic
466#340C22×C3111yescharacteristic
467#336C22×C3111yescharacteristic
468#336C22×C3111yescharacteristic
469C2×C31—42no—
470C2×C31—82no—
471C2×C31#241011yescharacteristic
472C2×C31#303711yescharacteristic
473C2×C31#304411yescharacteristic
474C2×C31#326911yescharacteristic
475C2×C31#327011yescharacteristic
476C2×C31#327611yescharacteristic
477C2×C31#327711yescharacteristic
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—21no—
485C22×Q8—22no—
486C22×Q8—22no—
487C22×Q8—22no—
488C22×Q8—41no—
489C22×Q8—41no—
490C22×Q8D4×C3114yes—
491C22×Q8C23×C3111yescharacteristic
492C22×Q8C23×C3111yescharacteristic
493C22×Q8C23×C3111yescharacteristic
494C22×Q8C23×C3111yescharacteristic
495C22×D4—21no—
496C22×D4C23×C3111yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C3111yescharacteristic
500#137—232no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×Q16—22no—
504C2×Q16—22no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16D4×C3114yes—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16D4×C3114yes—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—22no—
522C22×C8C23×C3111yescharacteristic
523C22×C8C23×C3111yescharacteristic
524C22×C8C23×C3111yescharacteristic
525C22×C8C23×C3111yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528#124—22no—
529#124—41no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—41no—
535C4×Q8—41no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C3111yescharacteristic
551C2×C22⋊C4D4×C3111yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C3111yescharacteristic
555C2×C42C23×C3111yescharacteristic
556C4⋊C8—22no—
557C4⋊C8—22no—
558#103—22no—
559#103—22no—
560#103—22no—
561#103—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—41no—
566C22⋊C8—22no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C3111yescharacteristic
575#95D4×C3111yescharacteristic
576C31#2436911yescharacteristic, direct product factor, Sylow
577C24—21no—
578C24C2×D4×C3111yescharacteristic
579#41—28no—
580#41—44no—
581#41—44no—
582#41—44no—
583C2×Q8—24no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—28no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8C2×D4×C3112yes—
610C2×Q8C2×D4×C3112yes—
611C2×Q8C2×D4×C3112yes—
612C2×Q8C2×D4×C3112yes—
613C2×Q8C2×D4×C3112yes—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4C2×D4×C3112yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4C2×D4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3112yes—
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4#41×C3112yes—
647C22×C4C24×C3111yescharacteristic
648Q16—28no—
649Q16—28no—
650Q16—44no—
651Q16—44no—
652SD16—28no—
653SD16—28no—
654M16—28no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C3112yes—
666C2×C8C2×D4×C3112yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C22⋊C4—22no—
679C22⋊C4—41no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—42no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23C31×#12112yes—
706C23C22×D4×C3111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—22no—
714Q8—48no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8C31×#12014yes—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4C31×#12112yes—
770C2×C4C31×#13712yescomplemented
771C2×C4C22×D4×C3111yescharacteristic
772C2×C4C22×D4×C3111yescharacteristic
773C2×C4C22×D4×C3111yescharacteristic
774C2×C4C2×#41×C3111yescharacteristic
775C2×C4C31×H(5,𝔽2)11yescharacteristic
776C2×C4C31×H(5,𝔽2)11yescharacteristic
777C8—22no—
778C8—22no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C31×#12111yescharacteristic
796C22D42×C3111yescharacteristic
797C22D42×C3111yescharacteristic
798C22C2×C31×#13711yescharacteristic
799C22C31×#57511yescharacteristic
800C22C31×#57811yescharacteristic
801C22C31×#57811yescharacteristic
802C4—22no—
803C4—24no—
804C4—22no—
805C4—42no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4C2×C31×#12011yescharacteristic
815C4C31×#53411yescharacteristic
816C4C31×#54611yescharacteristic
817C4C31×#54611yescharacteristic
818C2—42no—
819C2—82no—
820C2C31×#241011yescharacteristic
821C2C31×#303711yescharacteristic
822C2C31×#304411yescharacteristic
823C2C31×#326911yescharacteristic
824C2C31×#327011yescharacteristic
825C2C31×#327611yescharacteristic
826C2C31×#327711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
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×#464C2semidirect
3. C2×C31×#462C2semidirect
4. C2×C31×#451C2semidirect
6. Q8×C22⋊C4×C31C2semidirect
7. C31×#2056C2semidirect
8. C31×#2055C2semidirect
9. C31×#2016C2semidirect
10. C31×#2015C2semidirect
11. C31×#1894C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1851C2semidirect
278. #24369C31direct (N × H)
357. C2×C4×C31#137semidirect
369. C2×#464C2×C31semidirect
370. C2×#462C2×C31semidirect
371. C2×#451C2×C31semidirect
373. Q8×C22⋊C4C2×C31semidirect
374. #2056C2×C31semidirect
375. #2055C2×C31semidirect
376. #2016C2×C31semidirect
377. #2015C2×C31semidirect
378. #1894C2×C31semidirect
379. #1880C2×C31semidirect
380. #1878C2×C31semidirect
381. #1851C2×C31semidirect
576. C31#24369direct (N × H)
770. C2×C4C31×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×C31×#4642
C2×C31×#4622
C2×C31×#4512
C31×#24322
Q8×C22⋊C4×C312
C31×#20562
C31×#20552
C31×#20162
C31×#20152
C31×#18942
C31×#18802
C31×#18782
C31×#18512
C31×#17882
#2436931