Finite Group Databasebeta

← C31×#23580 #21480339

Subgroups — C31×#23580 #21480339

Order 7936.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#540C211yesmaximal, characteristic, complemented
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic, complemented
4C31×#2324C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2025C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1999C211yesmaximal, characteristic, complemented
12C31×#1999C211yesmaximal, characteristic, complemented
13C31×#1762C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C31×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C31×#540—24no—
19C31×#540—24no—
20C2×C31×#127C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C31×#123—21no—
24C2×C31×#121—21no—
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C31×#442—24no—
34C4×D8×C31—24no—
35C2×C31×#107C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×#97C2211yescharacteristic
48C2×C4×C8×C31C2211yescharacteristic
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#386—21no—
54C31×#385—21no—
55C31×#380C2211yescharacteristic
56C4×C4⋊C4×C31C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31C2311yescharacteristic
69C22×D4×C31C2311yescharacteristic
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C22×C8×C31C2311yescharacteristic
84C22×C8×C31C2311yescharacteristic
85C31×#127—22no—
86C31×#127—22no—
87C31×#125—22no—
88C31×#125—22no—
89C31×#123—28no—
90C31×#123—28no—
91C31×#121—28no—
92C31×#121—28no—
93C31×#121—22no—
94C31×#121—22no—
95C31×#121—22no—
96C31×#121—22no—
97C31×#121—22no—
98C31×#121—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31D414yescomplemented
104C4×D4×C31D414yescomplemented
105C31×#117—22no—
106C31×#117—22no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31D411yescharacteristic
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#107—22no—
132C31×#106—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×#102—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×C22⋊C8—22no—
143C31×#97—22no—
144C4×C8×C31—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C2×D4×C31—24no—
153C2×D4×C31—24no—
154C2×D4×C31—24no—
155C2×D4×C31—24no—
156C2×D4×C31—24no—
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—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31—81no—
178C2×D4×C31—81no—
179C2×D4×C31—81no—
180C2×D4×C31—81no—
181C2×D4×C31—81no—
182C2×D4×C31C2×D412yes—
183C2×D4×C31C2×D412yes—
184C2×D4×C31#4112yes—
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—24no—
195C22×C4×C31—24no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—42no—
199C22×C4×C31—81no—
200C22×C4×C31—81no—
201C22×C4×C31—81no—
202C22×C4×C31—81no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2411yescharacteristic
211D8×C31—28no—
212D8×C31—28no—
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#4112yes—
224C2×C8×C31#4112yes—
225C4⋊C4×C31—24no—
226C4⋊C4×C31—24no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—22no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—81no—
237C4⋊C4×C31C2×D412yes—
238C4⋊C4×C31C2×D412yes—
239C4⋊C4×C31#4112yes—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—81no—
249C22⋊C4×C31—81no—
250C22⋊C4×C31—81no—
251C42×C31—21no—
252C42×C31—21no—
253C42×C31—81no—
254C42×C31C2×D412yes—
255C42×C31C2×D412yes—
256#23580C3111yesmaximal, characteristic, direct product factor, Sylow
257C23×C31—21no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
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—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31C22×D411yescharacteristic
286D4×C31—22no—
287D4×C31—22no—
288D4×C31—22no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—22no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—41no—
298D4×C31—84no—
299D4×C31—84no—
300D4×C31—84no—
301D4×C31—84no—
302D4×C31—84no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
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—84no—
336C2×C4×C31—84no—
337C2×C4×C31—84no—
338C2×C4×C31#12012yes—
339C2×C4×C31#12012yes—
340C2×C4×C31C22×D411yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C2×#4111yescharacteristic
343C2×C4×C31C2×#4111yescharacteristic
344C2×C4×C31C2×#4111yescharacteristic
345C2×C4×C31C2×#4111yescharacteristic
346C8×C31—22no—
347C8×C31—22no—
348C8×C31—41no—
349C8×C31—41no—
350C2×#540C2×C3111yescharacteristic, complemented
351C2×#442C2×C3111yescharacteristic, complemented
352C2×C4×D8C2×C3111yescharacteristic, complemented
353#2324C2×C3111yescharacteristic, complemented
354#2059C2×C3111yescharacteristic, complemented
355#2041C2×C3111yescharacteristic, complemented
356#2034C2×C3111yescharacteristic, complemented
357#2033C2×C3111yescharacteristic, complemented
358#2025C2×C3111yescharacteristic, complemented
359#2011C2×C3111yescharacteristic, complemented
360#1999C2×C3111yescharacteristic, complemented
361#1999C2×C3111yescharacteristic, complemented
362#1762C2×C3111yescharacteristic, complemented
363C4×#102C2×C3111yescharacteristic, complemented
364#1750C2×C3111yescharacteristic, complemented
365C22×C31—41no—
366C22×C31—42no—
367C22×C31—41no—
368C22×C31—42no—
369C22×C31—41no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31—42no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—42no—
376C22×C31—41no—
377C22×C31—42no—
378C22×C31—42no—
379C22×C31—41no—
380C22×C31—42no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31—81no—
384C22×C31—81no—
385C22×C31—81no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31C2×#12011yescharacteristic
394C22×C31#52511yescharacteristic
395C22×C31#53211yescharacteristic
396C22×C31#57611yescharacteristic
397C22×C31#57611yescharacteristic
398C22×C31#57611yescharacteristic
399C22×C31#57711yescharacteristic
400C4×C31—22no—
401C4×C31—22no—
402C4×C31—42no—
403C4×C31—41no—
404C4×C31—41no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—42no—
408C4×C31—81no—
409C4×C31—81no—
410C4×C31#52511yescharacteristic
411C4×C31#52511yescharacteristic
412C4×C31#53211yescharacteristic
413C4×C31#53211yescharacteristic
414C22×D8C22×C3111yescharacteristic
415C22×D8C22×C3111yescharacteristic
416#540—24no—
417#540—24no—
418C2×#127C22×C3111yescharacteristic
419C2×#125C22×C3111yescharacteristic
420C2×#123—21no—
421C2×#123—21no—
422C2×#121—21no—
423C2×#121—21no—
424C2×#121C22×C3111yescharacteristic
425C2×#121C22×C3111yescharacteristic
426C2×#121C22×C3111yescharacteristic
427C2×C4×D4C22×C3111yescharacteristic
428C2×C4×D4C22×C3111yescharacteristic
429C2×C4×D4C22×C3111yescharacteristic
430C2×#117C22×C3111yescharacteristic
431#442—24no—
432C4×D8—24no—
433C2×#107C22×C3111yescharacteristic
434C2×#106C22×C3111yescharacteristic
435C2×#102C22×C3111yescharacteristic
436C2×#102C22×C3111yescharacteristic
437C2×#102C22×C3111yescharacteristic
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445C2×#97C22×C3111yescharacteristic
446C2×C4×C8C22×C3111yescharacteristic
447#390—21no—
448#390C22×C3111yescharacteristic
449#389C22×C3111yescharacteristic
450#388—21no—
451#386—21no—
452#385—21no—
453#380C22×C3111yescharacteristic
454C4×C4⋊C4C22×C3111yescharacteristic
455#340C22×C3111yescharacteristic
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459#336C22×C3111yescharacteristic
460#336C22×C3111yescharacteristic
461C2×C31—81no—
462C2×C31—82no—
463C2×C31—82no—
464C2×C31—82no—
465C2×C31#238811yescharacteristic
466C2×C31#300811yescharacteristic
467C2×C31#301211yescharacteristic
468C2×C31#311911yescharacteristic
469C2×C31#312211yescharacteristic
470C2×C31#317611yescharacteristic
471C2×C31#317911yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C3111yescharacteristic
478C22×D4C23×C3111yescharacteristic
479C22×D4C23×C3111yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4C23×C3111yescharacteristic
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C22×C8C23×C3111yescharacteristic
491C22×C8C23×C3111yescharacteristic
492C22×C8C23×C3111yescharacteristic
493C22×C8C23×C3111yescharacteristic
494#127—22no—
495#127—22no—
496#125—22no—
497#125—22no—
498#123—28no—
499#123—28no—
500#121—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4D4×C3114yescomplemented
513C4×D4D4×C3114yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C3111yescharacteristic
520C2×C4⋊C4D4×C3111yescharacteristic
521C2×C4⋊C4C23×C3111yescharacteristic
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4D4×C3111yescharacteristic
536C2×C22⋊C4D4×C3111yescharacteristic
537C2×C42—21no—
538C2×C42C23×C3111yescharacteristic
539C2×C42C23×C3111yescharacteristic
540#107—22no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552#97—22no—
553C4×C8—22no—
554#95—21no—
555#95—21no—
556#95—21no—
557C31#2358011yescharacteristic, direct product factor, Sylow
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C3111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
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—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C3112yes—
593C2×D4C2×D4×C3112yes—
594C2×D4#41×C3112yes—
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—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3111yescharacteristic
619C22×C4C2×D4×C3111yescharacteristic
620C22×C4C24×C3111yescharacteristic
621D8—28no—
622D8—28no—
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—21no—
632C2×C8—21no—
633C2×C8#41×C3112yes—
634C2×C8#41×C3112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C3112yes—
648C4⋊C4C2×D4×C3112yes—
649C4⋊C4#41×C3112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C3112yes—
665C42C2×D4×C3112yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
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—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C3111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
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—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4C31×#12012yes—
748C2×C4C31×#12012yes—
749C2×C4C22×D4×C3111yescharacteristic
750C2×C4C22×D4×C3111yescharacteristic
751C2×C4C2×#41×C3111yescharacteristic
752C2×C4C2×#41×C3111yescharacteristic
753C2×C4C2×#41×C3111yescharacteristic
754C2×C4C2×#41×C3111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×C31×#12011yescharacteristic
788C22C31×#52511yescharacteristic
789C22C31×#53211yescharacteristic
790C22C31×#57611yescharacteristic
791C22C31×#57611yescharacteristic
792C22C31×#57611yescharacteristic
793C22C31×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C31×#52511yescharacteristic
805C4C31×#52511yescharacteristic
806C4C31×#53211yescharacteristic
807C4C31×#53211yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C31×#238811yescharacteristic
813C2C31×#300811yescharacteristic
814C2C31×#301211yescharacteristic
815C2C31×#311911yescharacteristic
816C2C31×#312211yescharacteristic
817C2C31×#317611yescharacteristic
818C2C31×#317911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#540C2semidirect
2. C2×C31×#442C2semidirect
3. C2×C4×D8×C31C2semidirect
4. C31×#2324C2semidirect
5. C31×#2059C2semidirect
6. C31×#2041C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#2025C2semidirect
10. C31×#2011C2semidirect
11. C31×#1999C2semidirect
12. C31×#1999C2semidirect
13. C31×#1762C2semidirect
14. C4×C31×#102C2semidirect
15. C31×#1750C2semidirect
103. C4×D4×C31D4semidirect
104. C4×D4×C31D4semidirect
256. #23580C31direct (N × H)
350. C2×#540C2×C31semidirect
351. C2×#442C2×C31semidirect
352. C2×C4×D8C2×C31semidirect
353. #2324C2×C31semidirect
354. #2059C2×C31semidirect
355. #2041C2×C31semidirect
356. #2034C2×C31semidirect
357. #2033C2×C31semidirect
358. #2025C2×C31semidirect
359. #2011C2×C31semidirect
360. #1999C2×C31semidirect
361. #1999C2×C31semidirect
362. #1762C2×C31semidirect
363. C4×#102C2×C31semidirect
364. #1750C2×C31semidirect
512. C4×D4D4×C31semidirect
513. C4×D4D4×C31semidirect
557. C31#23580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5402
C2×C31×#4422
C2×C4×D8×C312
C31×#23242
C31×#20592
C31×#20412
C31×#20342
C31×#20332
C31×#20252
C31×#20112
C31×#19992
C31×#17622
C4×C31×#1022
C31×#17502
#2358031