Finite Group Databasebeta

← C31×#24861 #21481620

Subgroups — C31×#24861 #21481620

Order 7936.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#480C211yesmaximal, characteristic, complemented
2C22×C31×#102C211yesmaximal, characteristic, complemented
3C31×#2408C211yesmaximal, characteristic
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2093C211yesmaximal, characteristic, complemented
6C31×#2071C211yesmaximal, characteristic, complemented
7C31×#2033C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1925C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1869C211yesmaximal, characteristic, complemented
13C31×#1852C211yesmaximal, characteristic, complemented
14C31×#1808C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#121C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C31×#120—21no—
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic, complemented
25C31×#480—24no—
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#107C2211yescharacteristic, complemented
28C2×C31×#107C2211yescharacteristic, complemented
29C2×C31×#107C2211yescharacteristic, complemented
30C2×C31×#102—24no—
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×C22⋊C8C2211yescharacteristic, complemented
41C2×C31×C22⋊C8C2211yescharacteristic, complemented
42C31×#394—21no—
43C31×#392—21no—
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic
46C31×#389—21no—
47C31×#385—21no—
48C31×#385—21no—
49C31×#384C2211yescharacteristic, complemented
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic, complemented
53C31×#379—21no—
54C4×C4⋊C4×C31C2211yescharacteristic, complemented
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—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31D411yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C22×C8×C31—22no—
79C22×C8×C31—22no—
80C22×C8×C31—41no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#121—22no—
86C31×#121—22no—
87C31×#121—41no—
88C31×#121—41no—
89C31×#120—44no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—44no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31D411yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C22⋊C4×C31D411yescharacteristic
119C2×C42×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×#107—22no—
123C31×#107—41no—
124C31×#107—41no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—41no—
131C31×#102—41no—
132C31×#102D414yescomplemented
133C31×C22⋊C8—22no—
134C31×C22⋊C8—22no—
135C31×C22⋊C8—41no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—42no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31—42no—
146C24×C31—42no—
147C24×C31—81no—
148C24×C31—81no—
149C24×C31C2×D411yescharacteristic
150C24×C31C2×D411yescharacteristic
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—28no—
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—44no—
165C2×D4×C31—44no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—44no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—42no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31D814yes—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
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—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31—81no—
200C22×C4×C31—81no—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31#4112yes—
206C22×C4×C31#4112yes—
207C22×C4×C31C2411yescharacteristic
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×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—44no—
220C2×C8×C31C2×D412yes—
221C4⋊C4×C31—22no—
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—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—42no—
236C4⋊C4×C31—81no—
237C4⋊C4×C31C2×D412yes—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
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—42no—
247C22⋊C4×C31—81no—
248C22⋊C4×C31—81no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—42no—
252#24861C3111yesmaximal, characteristic, direct product factor, Sylow
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—48no—
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—41no—
278C23×C31—84no—
279C23×C31—84no—
280C23×C31—84no—
281C23×C31—84no—
282C23×C31—84no—
283C23×C31—84no—
284C23×C31#12312yes—
285C23×C31C2×D812yes—
286C23×C31C2×D812yes—
287C23×C31#13712yes—
288C23×C31C22×D411yescharacteristic
289D4×C31—28no—
290D4×C31—22no—
291D4×C31—22no—
292D4×C31—22no—
293D4×C31—22no—
294D4×C31—48no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—41no—
299D4×C31—84no—
300D4×C31—84no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
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—41no—
337C2×C4×C31—84no—
338C2×C4×C31—84no—
339C2×C4×C31#12312yes—
340C2×C4×C31C2×D812yes—
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C2×#4111yescharacteristic
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×#480C2×C3111yescharacteristic, complemented
352C22×#102C2×C3111yescharacteristic, complemented
353#2408C2×C3111yescharacteristic
354D4×C4⋊C4C2×C3111yescharacteristic, complemented
355#2093C2×C3111yescharacteristic, complemented
356#2071C2×C3111yescharacteristic, complemented
357#2033C2×C3111yescharacteristic, complemented
358#2033C2×C3111yescharacteristic, complemented
359#1925C2×C3111yescharacteristic, complemented
360#1925C2×C3111yescharacteristic, complemented
361#1874C2×C3111yescharacteristic, complemented
362#1869C2×C3111yescharacteristic, complemented
363#1852C2×C3111yescharacteristic, complemented
364#1808C2×C3111yescharacteristic, complemented
365#1786C2×C3111yescharacteristic, complemented
366C22×C31—22no—
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—22no—
371C22×C31—22no—
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—816no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31#48014yescomplemented
395C22×C31C2×#12311yescharacteristic
396C22×C31D4211yescharacteristic
397C22×C31#54611yescharacteristic
398C22×C31C22×D811yescharacteristic
399C22×C31C2×#13711yescharacteristic
400C22×C31#57611yescharacteristic
401C22×C31#57711yescharacteristic
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—41no—
405C4×C31—41no—
406C4×C31—42no—
407C4×C31—81no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31#52511yescharacteristic
413C4×C31#53811yescharacteristic
414C4×C31#54611yescharacteristic
415C4×C31#55111yescharacteristic
416C23×D4C22×C3111yescharacteristic
417C23×C8C22×C3111yescharacteristic
418C2×#121C22×C3111yescharacteristic
419C2×#121C22×C3111yescharacteristic
420C2×#120—21no—
421C2×C4×D4—21no—
422C2×C4×D4C22×C3111yescharacteristic
423C22×C4⋊C4C22×C3111yescharacteristic
424C22×C4⋊C4C22×C3111yescharacteristic, complemented
425#480—24no—
426C2×#107C22×C3111yescharacteristic, complemented
427C2×#107C22×C3111yescharacteristic, complemented
428C2×#107C22×C3111yescharacteristic, complemented
429C2×#107C22×C3111yescharacteristic, complemented
430C2×#102—24no—
431C2×#102C22×C3111yescharacteristic
432C2×#102C22×C3111yescharacteristic
433C2×#102C22×C3111yescharacteristic
434C2×#102C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×C22⋊C8C22×C3111yescharacteristic
440C2×C22⋊C8C22×C3111yescharacteristic, complemented
441C2×C22⋊C8C22×C3111yescharacteristic, complemented
442#394—21no—
443#392—21no—
444#390C22×C3111yescharacteristic
445#390C22×C3111yescharacteristic
446#389—21no—
447#385—21no—
448#385—21no—
449#384C22×C3111yescharacteristic, complemented
450#380C22×C3111yescharacteristic
451#380C22×C3111yescharacteristic
452#380C22×C3111yescharacteristic, complemented
453#379—21no—
454C4×C4⋊C4C22×C3111yescharacteristic, complemented
455#340C22×C3111yescharacteristic, complemented
456#340C22×C3111yescharacteristic, complemented
457#340C22×C3111yescharacteristic, complemented
458#340C22×C3111yescharacteristic, complemented
459#336C22×C3111yescharacteristic, complemented
460#336C22×C3111yescharacteristic, complemented
461C2×C31—24no—
462C2×C31—42no—
463C2×C31—82no—
464C2×C31—82no—
465C2×C31#241811yescharacteristic
466C2×C31C2×#48011yescharacteristic
467C2×C31#309611yescharacteristic
468C2×C31#326611yescharacteristic
469C2×C31D4×D811yescharacteristic
470C2×C31#329411yescharacteristic
471C2×C31#331411yescharacteristic
472C25—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—41no—
481C22×D4—41no—
482C22×D4D4×C3111yescharacteristic
483C22×D4C23×C3111yescharacteristic
484C22×D4C23×C3111yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4C23×C3111yescharacteristic
488C23×C4C23×C3111yescharacteristic
489C22×C8—22no—
490C22×C8—22no—
491C22×C8—41no—
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494C22×C8C23×C3111yescharacteristic
495C22×C8C23×C3111yescharacteristic
496#121—22no—
497#121—22no—
498#121—41no—
499#121—41no—
500#120—44no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—44no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4D4×C3111yescharacteristic
513C2×C4⋊C4C23×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⋊C4—21no—
528C2×C22⋊C4D4×C3111yescharacteristic
529C2×C22⋊C4D4×C3111yescharacteristic
530C2×C42—21no—
531C2×C42C23×C3111yescharacteristic
532#107—22no—
533#107—22no—
534#107—41no—
535#107—41no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—41no—
542#102—41no—
543#102D4×C3114yescomplemented
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—41no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551C31#2486111yescharacteristic, direct product factor, Sylow
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C3111yescharacteristic
562C24C2×D4×C3111yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4D8×C3114yes—
589C2×D4C2×D4×C3112yes—
590C2×D4#41×C3112yes—
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—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4#41×C3112yes—
618C22×C4#41×C3112yes—
619C22×C4C24×C3111yescharacteristic
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×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C3112yes—
633C4⋊C4—22no—
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—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C3112yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23C31×#12312yes—
696C23C2×D8×C3112yes—
697C23C2×D8×C3112yes—
698C23C31×#13712yes—
699C23C22×D4×C3111yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
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—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4C31×#12312yes—
751C2×C4C2×D8×C3112yes—
752C2×C4C22×D4×C3111yescharacteristic
753C2×C4C2×#41×C3111yescharacteristic
754C2×C4C2×#41×C3111yescharacteristic
755C2×C4C2×#41×C3111yescharacteristic
756C2×C4C31×H(5,𝔽2)11yescharacteristic
757C2×C4C31×H(5,𝔽2)11yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C31×#48014yescomplemented
791C22C2×C31×#12311yescharacteristic
792C22D42×C3111yescharacteristic
793C22C31×#54611yescharacteristic
794C22C22×D8×C3111yescharacteristic
795C22C2×C31×#13711yescharacteristic
796C22C31×#57611yescharacteristic
797C22C31×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4C31×#52511yescharacteristic
809C4C31×#53811yescharacteristic
810C4C31×#54611yescharacteristic
811C4C31×#55111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C31×#241811yescharacteristic
817C2C2×C31×#48011yescharacteristic
818C2C31×#309611yescharacteristic
819C2C31×#326611yescharacteristic
820C2D4×D8×C3111yescharacteristic
821C2C31×#329411yescharacteristic
822C2C31×#331411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2408C2
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×#480C2semidirect
2. C22×C31×#102C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2093C2semidirect
6. C31×#2071C2semidirect
7. C31×#2033C2semidirect
8. C31×#2033C2semidirect
9. C31×#1925C2semidirect
10. C31×#1925C2semidirect
11. C31×#1874C2semidirect
12. C31×#1869C2semidirect
13. C31×#1852C2semidirect
14. C31×#1808C2semidirect
15. C31×#1786C2semidirect
24. C22×C4⋊C4×C31C22semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#107C22semidirect
28. C2×C31×#107C22semidirect
29. C2×C31×#107C22semidirect
40. C2×C31×C22⋊C8C22semidirect
41. C2×C31×C22⋊C8C22semidirect
49. C31×#384C22semidirect
52. C31×#380C22semidirect
54. C4×C4⋊C4×C31C22semidirect
55. C31×#340C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
132. C31×#102D4semidirect
252. #24861C31direct (N × H)
351. C2×#480C2×C31semidirect
352. C22×#102C2×C31semidirect
354. D4×C4⋊C4C2×C31semidirect
355. #2093C2×C31semidirect
356. #2071C2×C31semidirect
357. #2033C2×C31semidirect
358. #2033C2×C31semidirect
359. #1925C2×C31semidirect
360. #1925C2×C31semidirect
361. #1874C2×C31semidirect
362. #1869C2×C31semidirect
363. #1852C2×C31semidirect
364. #1808C2×C31semidirect
365. #1786C2×C31semidirect
394. C22×C31#480semidirect
424. C22×C4⋊C4C22×C31semidirect
426. C2×#107C22×C31semidirect
427. C2×#107C22×C31semidirect
428. C2×#107C22×C31semidirect
429. C2×#107C22×C31semidirect
440. C2×C22⋊C8C22×C31semidirect
441. C2×C22⋊C8C22×C31semidirect
449. #384C22×C31semidirect
452. #380C22×C31semidirect
454. C4×C4⋊C4C22×C31semidirect
455. #340C22×C31semidirect
456. #340C22×C31semidirect
457. #340C22×C31semidirect
458. #340C22×C31semidirect
459. #336C22×C31semidirect
460. #336C22×C31semidirect
543. #102D4×C31semidirect
551. C31#24861direct (N × H)
790. C22C31×#480semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C22×C31×#1022
C31×#24082
D4×C4⋊C4×C312
C31×#20932
C31×#20712
C31×#20332
C31×#19252
C31×#18742
C31×#18692
C31×#18522
C31×#18082
C31×#17862
#2486131