Finite Group Databasebeta

← C31×#23981 #21480740

Subgroups — C31×#23981 #21480740

Order 7936.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic, complemented
2C2×C31×#452C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C31×#2407C211yesmaximal, characteristic
5C31×#2024C211yesmaximal, characteristic, complemented
6C31×#2023C211yesmaximal, characteristic, complemented
7C31×#2001C211yesmaximal, characteristic, complemented
8C31×#2000C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1880C211yesmaximal, characteristic, complemented
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1872C211yesmaximal, characteristic, complemented
14C31×#1870C211yesmaximal, characteristic, complemented
15C31×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C31×#554—24no—
21C31×#554—24no—
22C2×C31×C4⋊Q8C2211yescharacteristic
23C2×C31×#125—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×C22⋊Q8C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C4×Q8×C31C2211yescharacteristic
31C2×C4×D4×C31—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C31×#452—24no—
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#386—21no—
53C31×#385—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31—21no—
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C2×Q16×C31—22no—
82C2×Q16×C31—22no—
83C2×Q16×C31—41no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—41no—
87C2×M16×C31—22no—
88C2×M16×C31—41no—
89C2×M16×C31—41no—
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×C4⋊Q8—22no—
95C31×C4⋊Q8—22no—
96C31×#125—28no—
97C31×C22⋊Q8—28no—
98C31×C22⋊Q8—28no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8—22no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8—41no—
104C31×C22⋊Q8D414yescomplemented
105C31×#121—22no—
106C31×#121—41no—
107C4×Q8×C31—22no—
108C4×Q8×C31—22no—
109C4×D4×C31—28no—
110C4×D4×C31—22no—
111C4×D4×C31—22no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—22no—
120C2×C4⋊C4×C31—22no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31D411yescharacteristic
123C2×C4⋊C4×C31D414yescomplemented
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C4⋊C4×C31C2311yescharacteristic
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C4⋊C4×C31C2311yescharacteristic
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
137C2×C22⋊C4×C31D411yescharacteristic
138C2×C42×C31—21no—
139C2×C42×C31C2311yescharacteristic
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#103—41no—
144C31×#103—41no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×C22⋊C8—22no—
149C31×C22⋊C8—41no—
150C31×C22⋊C8—41no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D411yescharacteristic
157#41×C31—28no—
158#41×C31—44no—
159#41×C31—44no—
160#41×C31—44no—
161C2×Q8×C31—24no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—81no—
173C2×Q8×C31—81no—
174C2×Q8×C31C2×D412yes—
175C2×Q8×C31#4112yes—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—81no—
190C2×D4×C31#4112yes—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—24no—
201C22×C4×C31—24no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31—81no—
214C22×C4×C31—81no—
215C22×C4×C31—81no—
216C22×C4×C31—81no—
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2×D412yes—
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2411yescharacteristic
224Q16×C31—44no—
225SD16×C31—44no—
226M16×C31—44no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C4⋊C4×C31—24no—
240C4⋊C4×C31—24no—
241C4⋊C4×C31—24no—
242C4⋊C4×C31—24no—
243C4⋊C4×C31—24no—
244C4⋊C4×C31—24no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—42no—
254C4⋊C4×C31C2×D412yes—
255C4⋊C4×C31C2×D412yes—
256C4⋊C4×C31C2×D412yes—
257C22⋊C4×C31—24no—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—81no—
265C22⋊C4×C31—81no—
266C42×C31—24no—
267C42×C31—21no—
268C42×C31—21no—
269#23981C3111yesmaximal, characteristic, direct product factor, Sylow
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—22no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31#12012yes—
290C23×C31#13712yes—
291C23×C31C22×D411yescharacteristic
292Q8×C31—22no—
293Q8×C31—22no—
294Q8×C31—22no—
295Q8×C31—22no—
296Q8×C31—41no—
297Q8×C31—41no—
298Q8×C31—41no—
299Q8×C31—41no—
300Q8×C31—84no—
301D4×C31—28no—
302D4×C31—22no—
303D4×C31—22no—
304D4×C31—48no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—84no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—21no—
323C2×C4×C31—22no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—48no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
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—84no—
349C2×C4×C31—84no—
350C2×C4×C31#12012yes—
351C2×C4×C31#13712yes—
352C2×C4×C31C22×D411yescharacteristic
353C2×C4×C31C22×D411yescharacteristic
354C2×C4×C31C2×#4111yescharacteristic
355C2×C4×C31C2×#4111yescharacteristic
356C2×C4×C31H(5,𝔽2)11yescharacteristic
357C2×C4×C31H(5,𝔽2)11yescharacteristic
358C8×C31—41no—
359C8×C31—41no—
360C8×C31—41no—
361C8×C31—41no—
362C2×#554C2×C3111yescharacteristic, complemented
363C2×#452C2×C3111yescharacteristic, complemented
364C2×#417C2×C3111yescharacteristic, complemented
365#2407C2×C3111yescharacteristic
366#2024C2×C3111yescharacteristic, complemented
367#2023C2×C3111yescharacteristic, complemented
368#2001C2×C3111yescharacteristic, complemented
369#2000C2×C3111yescharacteristic, complemented
370#1894C2×C3111yescharacteristic, complemented
371#1880C2×C3111yescharacteristic, complemented
372#1878C2×C3111yescharacteristic, complemented
373#1874C2×C3111yescharacteristic, complemented
374#1872C2×C3111yescharacteristic, complemented
375#1870C2×C3111yescharacteristic, complemented
376#1823C2×C3111yescharacteristic, complemented
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—22no—
381C22×C31—22no—
382C22×C31—22no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—42no—
392C22×C31—42no—
393C22×C31—42no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31C2×#12011yescharacteristic
399C22×C31#54611yescharacteristic
400C22×C31#54611yescharacteristic
401C22×C31C2×#13711yescharacteristic
402C22×C31C2×#13711yescharacteristic
403C22×C31#57611yescharacteristic
404C22×C31#57711yescharacteristic
405C4×C31—22no—
406C4×C31—22no—
407C4×C31—41no—
408C4×C31—42no—
409C4×C31—42no—
410C4×C31—41no—
411C4×C31—42no—
412C4×C31—42no—
413C4×C31—42no—
414C4×C31—81no—
415C4×C31—81no—
416C4×C31#52511yescharacteristic
417C4×C31#53511yescharacteristic
418C4×C31#54611yescharacteristic
419C4×C31#54611yescharacteristic
420C22×#41C22×C3111yescharacteristic
421C22×Q16C22×C3111yescharacteristic
422C22×SD16C22×C3111yescharacteristic
423C22×M16C22×C3111yescharacteristic
424#554—24no—
425#554—24no—
426C2×C4⋊Q8C22×C3111yescharacteristic
427C2×#125—21no—
428C2×C22⋊Q8—21no—
429C2×C22⋊Q8—21no—
430C2×C22⋊Q8C22×C3111yescharacteristic
431C2×C22⋊Q8C22×C3111yescharacteristic
432C2×C22⋊Q8C22×C3111yescharacteristic
433C2×#121C22×C3111yescharacteristic
434C2×C4×Q8C22×C3111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C3111yescharacteristic
437C22×C4⋊C4C22×C3111yescharacteristic
438C22×C4⋊C4C22×C3111yescharacteristic
439#452—24no—
440#417—24no—
441C2×#103C22×C3111yescharacteristic
442C2×#103C22×C3111yescharacteristic
443C2×#103C22×C3111yescharacteristic
444C2×#103C22×C3111yescharacteristic
445C2×#103C22×C3111yescharacteristic
446C2×#102C22×C3111yescharacteristic
447C2×#102C22×C3111yescharacteristic
448C2×#102C22×C3111yescharacteristic
449C2×C22⋊C8C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451C2×C22⋊C8C22×C3111yescharacteristic
452#394—21no—
453#392—21no—
454#391C22×C3111yescharacteristic
455#390C22×C3111yescharacteristic
456#386—21no—
457#385—21no—
458#380C22×C3111yescharacteristic
459#340C22×C3111yescharacteristic
460#340C22×C3111yescharacteristic
461#340C22×C3111yescharacteristic
462#340C22×C3111yescharacteristic
463#340C22×C3111yescharacteristic
464#340C22×C3111yescharacteristic
465#336C22×C3111yescharacteristic
466#336C22×C3111yescharacteristic
467C2×C31—42no—
468C2×C31—42no—
469C2×C31—82no—
470C2×C31#240411yescharacteristic
471C2×C31#300411yescharacteristic
472C2×C31#301211yescharacteristic
473C2×C31#331411yescharacteristic
474C2×C31#331611yescharacteristic
475C2×C31#333111yescharacteristic
476C2×C31#333311yescharacteristic
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—41no—
482C2×#41—41no—
483C22×Q8—21no—
484C22×Q8C23×C3111yescharacteristic
485C22×Q8C23×C3111yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C3111yescharacteristic
489C22×D4C23×C3111yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C23×C3111yescharacteristic
494C23×C4C23×C3111yescharacteristic
495C2×Q16—22no—
496C2×Q16—22no—
497C2×Q16—41no—
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×M16—22no—
502C2×M16—41no—
503C2×M16—41no—
504C22×C8C23×C3111yescharacteristic
505C22×C8C23×C3111yescharacteristic
506C22×C8C23×C3111yescharacteristic
507C22×C8C23×C3111yescharacteristic
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510#125—28no—
511C22⋊Q8—28no—
512C22⋊Q8—28no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518C22⋊Q8D4×C3114yescomplemented
519#121—22no—
520#121—41no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×D4—28no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4D4×C3111yescharacteristic
537C2×C4⋊C4D4×C3114yescomplemented
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C22⋊C4—21no—
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×C42C23×C3111yescharacteristic
554#103—22no—
555#103—22no—
556#103—22no—
557#103—41no—
558#103—41no—
559#102—22no—
560#102—22no—
561#102—22no—
562C22⋊C8—22no—
563C22⋊C8—41no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567#95—21no—
568C31#2398111yescharacteristic, direct product factor, Sylow
569C24—21no—
570C24C2×D4×C3111yescharacteristic
571C24C2×D4×C3111yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—24no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—81no—
588C2×Q8—81no—
589C2×Q8C2×D4×C3112yes—
590C2×Q8#41×C3112yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4#41×C3112yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C2×D4×C3111yescharacteristic
634C22×C4C2×D4×C3111yescharacteristic
635C22×C4C2×D4×C3112yes—
636C22×C4C2×D4×C3112yes—
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C24×C3111yescharacteristic
639Q16—44no—
640SD16—44no—
641M16—44no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4C2×D4×C3112yes—
670C4⋊C4C2×D4×C3112yes—
671C4⋊C4C2×D4×C3112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—24no—
682C42—21no—
683C42—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23C31×#12012yes—
704C23C31×#13712yes—
705C23C22×D4×C3111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—84no—
715D4—28no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—41no—
720D4—41no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—48no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
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—84no—
763C2×C4—84no—
764C2×C4C31×#12012yes—
765C2×C4C31×#13712yes—
766C2×C4C22×D4×C3111yescharacteristic
767C2×C4C22×D4×C3111yescharacteristic
768C2×C4C2×#41×C3111yescharacteristic
769C2×C4C2×#41×C3111yescharacteristic
770C2×C4C31×H(5,𝔽2)11yescharacteristic
771C2×C4C31×H(5,𝔽2)11yescharacteristic
772C8—41no—
773C8—41no—
774C8—41no—
775C8—41no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22C2×C31×#12011yescharacteristic
798C22C31×#54611yescharacteristic
799C22C31×#54611yescharacteristic
800C22C2×C31×#13711yescharacteristic
801C22C2×C31×#13711yescharacteristic
802C22C31×#57611yescharacteristic
803C22C31×#57711yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4C31×#52511yescharacteristic
816C4C31×#53511yescharacteristic
817C4C31×#54611yescharacteristic
818C4C31×#54611yescharacteristic
819C2—42no—
820C2—42no—
821C2—82no—
822C2C31×#240411yescharacteristic
823C2C31×#300411yescharacteristic
824C2C31×#301211yescharacteristic
825C2C31×#331411yescharacteristic
826C2C31×#331611yescharacteristic
827C2C31×#333111yescharacteristic
828C2C31×#333311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2407C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#554C2semidirect
2. C2×C31×#452C2semidirect
3. C2×C31×#417C2semidirect
5. C31×#2024C2semidirect
6. C31×#2023C2semidirect
7. C31×#2001C2semidirect
8. C31×#2000C2semidirect
9. C31×#1894C2semidirect
10. C31×#1880C2semidirect
11. C31×#1878C2semidirect
12. C31×#1874C2semidirect
13. C31×#1872C2semidirect
14. C31×#1870C2semidirect
15. C31×#1823C2semidirect
104. C31×C22⋊Q8D4semidirect
123. C2×C4⋊C4×C31D4semidirect
269. #23981C31direct (N × H)
362. C2×#554C2×C31semidirect
363. C2×#452C2×C31semidirect
364. C2×#417C2×C31semidirect
366. #2024C2×C31semidirect
367. #2023C2×C31semidirect
368. #2001C2×C31semidirect
369. #2000C2×C31semidirect
370. #1894C2×C31semidirect
371. #1880C2×C31semidirect
372. #1878C2×C31semidirect
373. #1874C2×C31semidirect
374. #1872C2×C31semidirect
375. #1870C2×C31semidirect
376. #1823C2×C31semidirect
518. C22⋊Q8D4×C31semidirect
537. C2×C4⋊C4D4×C31semidirect
568. C31#23981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4522
C2×C31×#4172
C31×#24072
C31×#20242
C31×#20232
C31×#20012
C31×#20002
C31×#18942
C31×#18802
C31×#18782
C31×#18742
C31×#18722
C31×#18702
C31×#18232
#2398131