Finite Group Databasebeta

← C31×#25137 #21481896

Subgroups — C31×#25137 #21481896

Order 7936.

1124 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#452C211yesmaximal, characteristic, complemented
3C2×C31×#436C211yesmaximal, characteristic, complemented
4C2×C31×#417C211yesmaximal, characteristic, complemented
5C31×#2417C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2001C211yesmaximal, characteristic, complemented
11C31×#1969C211yesmaximal, characteristic, complemented
12C31×#1934C211yesmaximal, characteristic, complemented
13C31×#1894C211yesmaximal, characteristic, complemented
14C31×#1894C211yesmaximal, characteristic, complemented
15C31×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C31×#468—24no—
28C31×#452—24no—
29C31×#436—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×#107C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C31×#417—24no—
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#398—21no—
46C31×#396—21no—
47C31×#394—21no—
48C31×#392—21no—
49C31×#391C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#386—21no—
54C31×#386—21no—
55C31×#385—21no—
56C31×#380—21no—
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
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×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31D411yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31—41no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C2×M16×C31—22no—
86C2×M16×C31—22no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
89C2×M16×C31—41no—
90C2×M16×C31—41no—
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—41no—
100C31×C22⋊Q8—41no—
101C31×#121—22no—
102C31×#121—41no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—41no—
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#107—41no—
131C31×C4⋊C8—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102D414yescomplemented
140C31×C22⋊C8—22no—
141C31×C22⋊C8D414yescomplemented
142C4×C8×C31—22no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C24×C31C2×D411yescharacteristic
153#41×C31—28no—
154#41×C31—44no—
155#41×C31—44no—
156#41×C31—44no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
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#4112yes—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—41no—
177C2×D4×C31—42no—
178C2×D4×C31—42no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—81no—
183C2×D4×C31C2×D412yes—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
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—21no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31—81no—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D412yes—
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31#4112yes—
213C22×C4×C31C2411yescharacteristic
214Q16×C31—44no—
215SD16×C31—44no—
216M16×C31—44no—
217M16×C31—44no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31C2×D412yes—
228C2×C8×C31C2×D412yes—
229C2×C8×C31C2×D412yes—
230C4⋊C4×C31—22no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—42no—
241C4⋊C4×C31—42no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31—42no—
244C4⋊C4×C31—81no—
245C4⋊C4×C31C2×D412yes—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—81no—
254C22⋊C4×C31—81no—
255C22⋊C4×C31—81no—
256C42×C31—21no—
257C42×C31—21no—
258#25137C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—22no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31#12112yes—
280C23×C31C22×D411yescharacteristic
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—41no—
284Q8×C31—41no—
285Q8×C31—41no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—41no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—44no—
292D4×C31—48no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—84no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—48no—
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—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—84no—
337C2×C4×C31#12112yes—
338C2×C4×C31#13712yes—
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C2×#4111yescharacteristic
342C2×C4×C31C2×#4111yescharacteristic
343C2×C4×C31H(5,𝔽2)11yescharacteristic
344C2×C4×C31H(5,𝔽2)11yescharacteristic
345C8×C31—22no—
346C8×C31—22no—
347C8×C31—22no—
348C8×C31—41no—
349C2×#468C2×C3111yescharacteristic, complemented
350C2×#452C2×C3111yescharacteristic, complemented
351C2×#436C2×C3111yescharacteristic, complemented
352C2×#417C2×C3111yescharacteristic, complemented
353#2417C2×C3111yescharacteristic, complemented
354#2407C2×C3111yescharacteristic
355#2068C2×C3111yescharacteristic, complemented
356#2055C2×C3111yescharacteristic, complemented
357#2033C2×C3111yescharacteristic, complemented
358#2001C2×C3111yescharacteristic, complemented
359#1969C2×C3111yescharacteristic, complemented
360#1934C2×C3111yescharacteristic, complemented
361#1894C2×C3111yescharacteristic, complemented
362#1894C2×C3111yescharacteristic, complemented
363#1852C2×C3111yescharacteristic, complemented
364C22×C31—22no—
365C22×C31—22no—
366C22×C31—22no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—42no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—42no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31C2×#12111yescharacteristic
386C22×C31D4211yescharacteristic
387C22×C31#54611yescharacteristic
388C22×C31C2×#13711yescharacteristic
389C22×C31#57511yescharacteristic
390C22×C31#57611yescharacteristic
391C22×C31#57811yescharacteristic
392C4×C31—22no—
393C4×C31—22no—
394C4×C31—41no—
395C4×C31—42no—
396C4×C31—42no—
397C4×C31—41no—
398C4×C31—81no—
399C4×C31—81no—
400C4×C31—81no—
401C4×C31—81no—
402C4×C31—81no—
403C4×C31#52511yescharacteristic
404C4×C31#53811yescharacteristic
405C4×C31D4211yescharacteristic
406C4×C31#54611yescharacteristic
407C22×#41C22×C3111yescharacteristic
408C22×Q16C22×C3111yescharacteristic
409C22×SD16C22×C3111yescharacteristic
410C22×M16C22×C3111yescharacteristic
411C22×M16C22×C3111yescharacteristic
412C2×C22⋊Q8C22×C3111yescharacteristic
413C2×C22⋊Q8C22×C3111yescharacteristic
414C2×C22⋊Q8C22×C3111yescharacteristic
415C2×#121C22×C3111yescharacteristic
416C2×C4×D4C22×C3111yescharacteristic
417C22×C4⋊C4C22×C3111yescharacteristic
418#468—24no—
419#452—24no—
420#436—24no—
421C2×#107C22×C3111yescharacteristic
422C2×#107C22×C3111yescharacteristic
423C2×C4⋊C8C22×C3111yescharacteristic
424#417—24no—
425C2×#103C22×C3111yescharacteristic
426C2×#103C22×C3111yescharacteristic
427C2×#103C22×C3111yescharacteristic
428C2×#103C22×C3111yescharacteristic
429C2×#103C22×C3111yescharacteristic
430C2×#102C22×C3111yescharacteristic
431C2×#102C22×C3111yescharacteristic
432C2×#102C22×C3111yescharacteristic
433C2×C22⋊C8C22×C3111yescharacteristic
434C2×C22⋊C8C22×C3111yescharacteristic
435C2×C4×C8C22×C3111yescharacteristic
436#398—21no—
437#396—21no—
438#394—21no—
439#392—21no—
440#391C22×C3111yescharacteristic
441#391C22×C3111yescharacteristic
442#390C22×C3111yescharacteristic
443#389C22×C3111yescharacteristic
444#386—21no—
445#386—21no—
446#385—21no—
447#380—21no—
448#380C22×C3111yescharacteristic
449#380C22×C3111yescharacteristic
450#340C22×C3111yescharacteristic
451#340C22×C3111yescharacteristic
452#340C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic
454C2×C31—42no—
455C2×C31—81no—
456C2×C31—82no—
457C2×C31#242411yescharacteristic
458C2×C31#305611yescharacteristic
459C2×C31#306111yescharacteristic
460C2×C31#327311yescharacteristic
461C2×C31#327611yescharacteristic
462C2×C31#332711yescharacteristic
463C2×C31#333311yescharacteristic
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8C23×C3111yescharacteristic
471C22×Q8C23×C3111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4D4×C3111yescharacteristic
475C22×D4C23×C3111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4C23×C3111yescharacteristic
479C23×C4C23×C3111yescharacteristic
480C2×Q16—22no—
481C2×Q16—22no—
482C2×Q16—41no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—41no—
486C2×M16—22no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—41no—
491C2×M16—41no—
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495C22×C8C23×C3111yescharacteristic
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—41no—
501C22⋊Q8—41no—
502#121—22no—
503#121—41no—
504C4×D4—22no—
505C4×D4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C3111yescharacteristic
514C2×C4⋊C4C23×C3111yescharacteristic
515C2×C4⋊C4C23×C3111yescharacteristic
516C2×C4⋊C4C23×C3111yescharacteristic
517C2×C4⋊C4C23×C3111yescharacteristic
518C2×C4⋊C4C23×C3111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4D4×C3111yescharacteristic
528C2×C22⋊C4D4×C3111yescharacteristic
529C2×C42C23×C3111yescharacteristic
530#107—22no—
531#107—41no—
532C4⋊C8—22no—
533#103—22no—
534#103—22no—
535#103—22no—
536#103—22no—
537#103—41no—
538#102—22no—
539#102—22no—
540#102D4×C3114yescomplemented
541C22⋊C8—22no—
542C22⋊C8D4×C3114yescomplemented
543C4×C8—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551C31#2513711yescharacteristic, direct product factor, Sylow
552C24—21no—
553C24C2×D4×C3111yescharacteristic
554C24C2×D4×C3111yescharacteristic
555#41—28no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8#41×C3112yes—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4C2×D4×C3112yes—
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—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3111yescharacteristic
612C22×C4C2×D4×C3112yes—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4#41×C3112yes—
615C22×C4C24×C3111yescharacteristic
616Q16—44no—
617SD16—44no—
618M16—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C2×D4×C3112yes—
630C2×C8C2×D4×C3112yes—
631C2×C8C2×D4×C3112yes—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C3112yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C42—21no—
659C42—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C31×#12112yes—
681C23C22×D4×C3111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—48no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
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×C4C31×#12112yes—
739C2×C4C31×#13712yes—
740C2×C4C22×D4×C3111yescharacteristic
741C2×C4C22×D4×C3111yescharacteristic
742C2×C4C2×#41×C3111yescharacteristic
743C2×C4C2×#41×C3111yescharacteristic
744C2×C4C31×H(5,𝔽2)11yescharacteristic
745C2×C4C31×H(5,𝔽2)11yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C31×#12111yescharacteristic
772C22D42×C3111yescharacteristic
773C22C31×#54611yescharacteristic
774C22C2×C31×#13711yescharacteristic
775C22C31×#57511yescharacteristic
776C22C31×#57611yescharacteristic
777C22C31×#57811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4C31×#52511yescharacteristic
790C4C31×#53811yescharacteristic
791C4D42×C3111yescharacteristic
792C4C31×#54611yescharacteristic
793C2—42no—
794C2—81no—
795C2—82no—
796C2C31×#242411yescharacteristic
797C2C31×#305611yescharacteristic
798C2C31×#306111yescharacteristic
799C2C31×#327311yescharacteristic
800C2C31×#327611yescharacteristic
801C2C31×#332711yescharacteristic
802C2C31×#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×#468C2semidirect
2. C2×C31×#452C2semidirect
3. C2×C31×#436C2semidirect
4. C2×C31×#417C2semidirect
5. C31×#2417C2semidirect
7. C31×#2068C2semidirect
8. C31×#2055C2semidirect
9. C31×#2033C2semidirect
10. C31×#2001C2semidirect
11. C31×#1969C2semidirect
12. C31×#1934C2semidirect
13. C31×#1894C2semidirect
14. C31×#1894C2semidirect
15. C31×#1852C2semidirect
139. C31×#102D4semidirect
141. C31×C22⋊C8D4semidirect
258. #25137C31direct (N × H)
349. C2×#468C2×C31semidirect
350. C2×#452C2×C31semidirect
351. C2×#436C2×C31semidirect
352. C2×#417C2×C31semidirect
353. #2417C2×C31semidirect
355. #2068C2×C31semidirect
356. #2055C2×C31semidirect
357. #2033C2×C31semidirect
358. #2001C2×C31semidirect
359. #1969C2×C31semidirect
360. #1934C2×C31semidirect
361. #1894C2×C31semidirect
362. #1894C2×C31semidirect
363. #1852C2×C31semidirect
540. #102D4×C31semidirect
542. C22⋊C8D4×C31semidirect
551. C31#25137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4522
C2×C31×#4362
C2×C31×#4172
C31×#24172
C31×#24072
C31×#20682
C31×#20552
C31×#20332
C31×#20012
C31×#19692
C31×#19342
C31×#18942
C31×#18522
#2513731