Finite Group Databasebeta

← C31×#25105 #21481864

Subgroups — C31×#25105 #21481864

Order 7936.

1192 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#470C211yesmaximal, characteristic, complemented
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic
4C2×C31×#418C211yesmaximal, characteristic
5C31×#2435C211yesmaximal, characteristic
6C31×#2362C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2042C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1926C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1873C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic, complemented
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic, complemented
26C2×C31×#117C2211yescharacteristic
27C31×#470—24no—
28C31×#464—24no—
29C31×#450—24no—
30C2×C31×#106C2211yescharacteristic, complemented
31C2×C31×C4⋊C8C2211yescharacteristic, complemented
32C2×C31×C4⋊C8C2211yescharacteristic, complemented
33C31×#418—24no—
34C2×C31×#103C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#391C2211yescharacteristic, complemented
48C31×#390C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389C2211yescharacteristic, complemented
51C31×#388—21no—
52C31×#388—21no—
53C31×#387—21no—
54C31×#379—21no—
55C31×#379—21no—
56C4×C4⋊C4×C31—21no—
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—22no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C2×Q16×C31—22no—
77C2×Q16×C31—22no—
78C2×Q16×C31—41no—
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—41no—
84C2×SD16×C31—41no—
85C2×M16×C31—22no—
86C2×M16×C31—22no—
87C2×M16×C31—41no—
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×#124—22no—
93C31×#124—22no—
94C31×#124—41no—
95C31×#124—41no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8D414yes—
100C4×Q8×C31—22no—
101C4×Q8×C31—41no—
102C31×#117—22no—
103C31×#117—41no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
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×C31D411yescharacteristic
124C2×C22⋊C4×C31D411yescharacteristic
125C2×C42×C31—21no—
126C2×C42×C31—21no—
127C2×C42×C31—21no—
128C2×C42×C31C2311yescharacteristic
129C2×C42×C31C2311yescharacteristic
130C31×#106—22no—
131C31×C4⋊C8—22no—
132C31×C4⋊C8—41no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102D414yes—
143C31×C22⋊C8—22no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—42no—
153C24×C31—42no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—81no—
158C24×C31—81no—
159C24×C31C2×D411yescharacteristic
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—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31C2×D412yes—
172C2×D4×C31—28no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—44no—
184C2×D4×C31—44no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
189C2×D4×C31C2×D412yes—
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—21no—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D412yes—
207C22×C4×C31#4112yes—
208C22×C4×C31C2411yescharacteristic
209Q16×C31—44no—
210SD16×C31—44no—
211SD16×C31—44no—
212M16×C31—44no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
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×C31C2×D412yes—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31C2×D412yes—
236C4⋊C4×C31C2×D412yes—
237C22⋊C4×C31—24no—
238C22⋊C4×C31—41no—
239C22⋊C4×C31—41no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—81no—
247C22⋊C4×C31—81no—
248C22⋊C4×C31—81no—
249C22⋊C4×C31—81no—
250C42×C31—21no—
251C42×C31—21no—
252C42×C31—21no—
253C42×C31—21no—
254C42×C31—42no—
255C42×C31—42no—
256C42×C31—42no—
257#25105C3111yesmaximal, characteristic, direct product factor, Sylow
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—48no—
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—41no—
278C23×C31—41no—
279C23×C31—84no—
280C23×C31—84no—
281C23×C31—84no—
282C23×C31—84no—
283C23×C31—84no—
284C23×C31—84no—
285C23×C31#12112yes—
286C23×C31C22×D411yescharacteristic
287Q8×C31—22no—
288Q8×C31—22no—
289Q8×C31—41no—
290Q8×C31—41no—
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—41no—
294Q8×C31—41no—
295D4×C31—22no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—22no—
299D4×C31—48no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
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—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31#12112yes—
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C2×#4111yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C2×C4×C31H(5,𝔽2)11yescharacteristic
346C2×C4×C31H(5,𝔽2)11yescharacteristic
347C8×C31—22no—
348C8×C31—41no—
349C8×C31—41no—
350C8×C31—41no—
351C2×#470C2×C3111yescharacteristic, complemented
352C2×#464C2×C3111yescharacteristic, complemented
353C2×#450C2×C3111yescharacteristic
354C2×#418C2×C3111yescharacteristic
355#2435C2×C3111yescharacteristic
356#2362C2×C3111yescharacteristic, complemented
357#2065C2×C3111yescharacteristic, complemented
358#2055C2×C3111yescharacteristic, complemented
359#2042C2×C3111yescharacteristic, complemented
360#2015C2×C3111yescharacteristic, complemented
361#1983C2×C3111yescharacteristic, complemented
362#1926C2×C3111yescharacteristic, complemented
363#1880C2×C3111yescharacteristic, complemented
364#1873C2×C3111yescharacteristic, complemented
365#1851C2×C3111yescharacteristic, complemented
366C22×C31—22no—
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—816no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31C2×#12111yescharacteristic
389C22×C31D4211yescharacteristic
390C22×C31#54611yescharacteristic
391C22×C31#57511yescharacteristic
392C22×C31#57511yescharacteristic
393C22×C31#57711yescharacteristic
394C22×C31#57711yescharacteristic
395C4×C31—22no—
396C4×C31—42no—
397C4×C31—41no—
398C4×C31—42no—
399C4×C31—41no—
400C4×C31—42no—
401C4×C31—41no—
402C4×C31—41no—
403C4×C31—81no—
404C4×C31—81no—
405C4×C31—81no—
406C4×C31#52511yescharacteristic
407C4×C31#53811yescharacteristic
408C4×C31D4211yescharacteristic
409C4×C31#54611yescharacteristic
410C23×D4C22×C3111yescharacteristic
411C22×Q16C22×C3111yescharacteristic, complemented
412C22×SD16C22×C3111yescharacteristic
413C22×SD16C22×C3111yescharacteristic
414C22×M16C22×C3111yescharacteristic
415C2×#124C22×C3111yescharacteristic
416C2×#124C22×C3111yescharacteristic
417C2×C22⋊Q8C22×C3111yescharacteristic
418C2×C22⋊Q8C22×C3111yescharacteristic
419C2×C4×Q8C22×C3111yescharacteristic, complemented
420C2×#117C22×C3111yescharacteristic
421#470—24no—
422#464—24no—
423#450—24no—
424C2×#106C22×C3111yescharacteristic, complemented
425C2×C4⋊C8C22×C3111yescharacteristic, complemented
426C2×C4⋊C8C22×C3111yescharacteristic, complemented
427#418—24no—
428C2×#103C22×C3111yescharacteristic, complemented
429C2×#103C22×C3111yescharacteristic, complemented
430C2×#103C22×C3111yescharacteristic, complemented
431C2×#103C22×C3111yescharacteristic, complemented
432C2×#102C22×C3111yescharacteristic
433C2×#102C22×C3111yescharacteristic
434C2×#102C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×C22⋊C8C22×C3111yescharacteristic
439#394—21no—
440#394—21no—
441#391C22×C3111yescharacteristic, complemented
442#390C22×C3111yescharacteristic
443#390C22×C3111yescharacteristic
444#389C22×C3111yescharacteristic, complemented
445#388—21no—
446#388—21no—
447#387—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C22×C3111yescharacteristic, complemented
452C4×C22⋊C4C22×C3111yescharacteristic
453#340C22×C3111yescharacteristic, complemented
454#340C22×C3111yescharacteristic, complemented
455#336C22×C3111yescharacteristic, complemented
456#336C22×C3111yescharacteristic, complemented
457C2×C31—42no—
458C2×C31—82no—
459C2×C31—82no—
460C2×C31#242411yescharacteristic
461C2×C31#304011yescharacteristic
462C2×C31#304311yescharacteristic
463C2×C31#326711yescharacteristic
464C2×C31#327511yescharacteristic
465C2×C31#331111yescharacteristic
466C2×C31#332311yescharacteristic
467C25—21no—
468C22×Q8C23×C3111yescharacteristic
469C22×Q8C23×C3111yescharacteristic
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4C23×C3111yescharacteristic
478C22×D4C23×C3111yescharacteristic
479C23×C4C23×C3111yescharacteristic
480C2×Q16—22no—
481C2×Q16—22no—
482C2×Q16—41no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495C22×C8C23×C3111yescharacteristic
496#124—22no—
497#124—22no—
498#124—41no—
499#124—41no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8D4×C3114yes—
504C4×Q8—22no—
505C4×Q8—41no—
506#117—22no—
507#117—41no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4C23×C3111yescharacteristic
513C2×C4⋊C4C23×C3111yescharacteristic
514C2×C4⋊C4C23×C3111yescharacteristic
515C2×C4⋊C4C23×C3111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
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×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42C23×C3111yescharacteristic
533C2×C42C23×C3111yescharacteristic
534#106—22no—
535C4⋊C8—22no—
536C4⋊C8—41no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—41no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102D4×C3114yes—
547C22⋊C8—22no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95D4×C3111yescharacteristic
553#95D4×C3111yescharacteristic
554C31#2510511yescharacteristic, direct product factor, Sylow
555C24—21no—
556C24—21no—
557C24—42no—
558C24—42no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—81no—
563C24—81no—
564C24C2×D4×C3111yescharacteristic
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8C2×D4×C3112yes—
577C2×D4—28no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4C2×D4×C3112yes—
595C2×D4#41×C3112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C2×D4×C3111yescharacteristic
609C22×C4C2×D4×C3111yescharacteristic
610C22×C4C2×D4×C3111yescharacteristic
611C22×C4C2×D4×C3112yes—
612C22×C4#41×C3112yes—
613C22×C4C24×C3111yescharacteristic
614Q16—44no—
615SD16—44no—
616SD16—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
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—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C3112yes—
641C4⋊C4C2×D4×C3112yes—
642C22⋊C4—24no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—42no—
660C42—42no—
661C42—42no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23C31×#12112yes—
690C23C22×D4×C3111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
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—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4C31×#12112yes—
745C2×C4C22×D4×C3111yescharacteristic
746C2×C4C22×D4×C3111yescharacteristic
747C2×C4C2×#41×C3111yescharacteristic
748C2×C4C2×#41×C3111yescharacteristic
749C2×C4C31×H(5,𝔽2)11yescharacteristic
750C2×C4C31×H(5,𝔽2)11yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×C31×#12111yescharacteristic
778C22D42×C3111yescharacteristic
779C22C31×#54611yescharacteristic
780C22C31×#57511yescharacteristic
781C22C31×#57511yescharacteristic
782C22C31×#57711yescharacteristic
783C22C31×#57711yescharacteristic
784C4—22no—
785C4—42no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—41no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4C31×#52511yescharacteristic
796C4C31×#53811yescharacteristic
797C4D42×C3111yescharacteristic
798C4C31×#54611yescharacteristic
799C2—42no—
800C2—82no—
801C2—82no—
802C2C31×#242411yescharacteristic
803C2C31×#304011yescharacteristic
804C2C31×#304311yescharacteristic
805C2C31×#326711yescharacteristic
806C2C31×#327511yescharacteristic
807C2C31×#331111yescharacteristic
808C2C31×#332311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×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
1. C2×C31×#470C2semidirect
2. C2×C31×#464C2semidirect
6. C31×#2362C2semidirect
7. C31×#2065C2semidirect
8. C31×#2055C2semidirect
9. C31×#2042C2semidirect
10. C31×#2015C2semidirect
11. C31×#1983C2semidirect
12. C31×#1926C2semidirect
13. C31×#1880C2semidirect
14. C31×#1873C2semidirect
15. C31×#1851C2semidirect
17. C22×Q16×C31C22semidirect
25. C2×C4×Q8×C31C22semidirect
30. C2×C31×#106C22semidirect
31. C2×C31×C4⋊C8C22semidirect
32. C2×C31×C4⋊C8C22semidirect
34. C2×C31×#103C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
37. C2×C31×#103C22semidirect
47. C31×#391C22semidirect
50. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
257. #25105C31direct (N × H)
351. C2×#470C2×C31semidirect
352. C2×#464C2×C31semidirect
356. #2362C2×C31semidirect
357. #2065C2×C31semidirect
358. #2055C2×C31semidirect
359. #2042C2×C31semidirect
360. #2015C2×C31semidirect
361. #1983C2×C31semidirect
362. #1926C2×C31semidirect
363. #1880C2×C31semidirect
364. #1873C2×C31semidirect
365. #1851C2×C31semidirect
411. C22×Q16C22×C31semidirect
419. C2×C4×Q8C22×C31semidirect
424. C2×#106C22×C31semidirect
425. C2×C4⋊C8C22×C31semidirect
426. C2×C4⋊C8C22×C31semidirect
428. C2×#103C22×C31semidirect
429. C2×#103C22×C31semidirect
430. C2×#103C22×C31semidirect
431. C2×#103C22×C31semidirect
441. #391C22×C31semidirect
444. #389C22×C31semidirect
451. C4×C4⋊C4C22×C31semidirect
453. #340C22×C31semidirect
454. #340C22×C31semidirect
455. #336C22×C31semidirect
456. #336C22×C31semidirect
554. C31#25105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4702
C2×C31×#4642
C2×C31×#4502
C2×C31×#4182
C31×#24352
C31×#23622
C31×#20652
C31×#20552
C31×#20422
C31×#20152
C31×#19832
C31×#19262
C31×#18802
C31×#18732
C31×#18512
#2510531