Finite Group Databasebeta

← C31×#25099 #21481858

Subgroups — C31×#25099 #21481858

Order 7936.

1104 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic
2C2×C31×#461C211yesmaximal, characteristic, complemented
3C2×C31×#448C211yesmaximal, characteristic
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C31×#2434C211yesmaximal, characteristic, complemented
6C31×#2363C211yesmaximal, characteristic
7C31×#2068C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2013C211yesmaximal, characteristic, complemented
11C31×#1981C211yesmaximal, characteristic, complemented
12C31×#1928C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1873C211yesmaximal, characteristic, complemented
15C31×#1851C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×C4⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C31×#117C2211yescharacteristic
27C31×#468—24no—
28C31×#461—24no—
29C31×#448—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C31×#419—24no—
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#395—21no—
46C31×#395—21no—
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#388—21no—
53C31×#386—21no—
54C31×#385—21no—
55C31×#385—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—22no—
67C22×Q8×C31—22no—
68C22×Q8×C31—41no—
69C22×Q8×C31—41no—
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
85C2×SD16×C31—41no—
86C2×SD16×C31—41no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
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×C4⋊Q8—41no—
97C31×C4⋊Q8—41no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×#121—22no—
101C31×#121D414yes—
102C4×D4×C31—22no—
103C4×D4×C31—41no—
104C31×#117—22no—
105C31×#117—41no—
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—21no—
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
123C2×C22⋊C4×C31D411yescharacteristic
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31C2311yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×C4⋊C8—22no—
130C31×C4⋊C8—41no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—41no—
139C31×#103D414yescomplemented
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—28no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
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—21no—
169C2×Q8×C31—42no—
170C2×Q8×C31—42no—
171C2×Q8×C31—44no—
172C2×Q8×C31—44no—
173C2×Q8×C31—44no—
174C2×Q8×C31—42no—
175C2×Q8×C31C2×D412yes—
176C2×Q8×C31#4112yes—
177C2×D4×C31—24no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—81no—
184C2×D4×C31—81no—
185C2×D4×C31C2×D412yes—
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—42no—
198C22×C4×C31—42no—
199C22×C4×C31—42no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31—81no—
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D412yes—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31#4112yes—
210C22×C4×C31C2411yescharacteristic
211SD16×C31—44no—
212SD16×C31—44no—
213SD16×C31—44no—
214M16×C31—44no—
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×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31C2×D412yes—
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—42no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31—81no—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D412yes—
241C22⋊C4×C31—24no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—81no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—21no—
252C42×C31—21no—
253C42×C31—42no—
254C42×C31—81no—
255#25099C3111yesmaximal, characteristic, direct product factor, Sylow
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—22no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31#12112yes—
270C23×C31C22×D411yescharacteristic
271Q8×C31—22no—
272Q8×C31—22no—
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—48no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31—41no—
281Q8×C31—41no—
282Q8×C31—41no—
283Q8×C31—41no—
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—84no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—21no—
304C2×C4×C31—22no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—48no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
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—84no—
328C2×C4×C31#12112yes—
329C2×C4×C31#13712yes—
330C2×C4×C31#13712yes—
331C2×C4×C31C22×D411yescharacteristic
332C2×C4×C31C22×D411yescharacteristic
333C2×C4×C31C2×#4111yescharacteristic
334C2×C4×C31C2×#4111yescharacteristic
335C2×C4×C31H(5,𝔽2)11yescharacteristic
336C2×C4×C31H(5,𝔽2)11yescharacteristic
337C8×C31—22no—
338C8×C31—41no—
339C8×C31—41no—
340C8×C31—41no—
341C2×#468C2×C3111yescharacteristic
342C2×#461C2×C3111yescharacteristic, complemented
343C2×#448C2×C3111yescharacteristic
344C2×#419C2×C3111yescharacteristic, complemented
345#2434C2×C3111yescharacteristic, complemented
346#2363C2×C3111yescharacteristic
347#2068C2×C3111yescharacteristic, complemented
348#2055C2×C3111yescharacteristic, complemented
349#2043C2×C3111yescharacteristic, complemented
350#2013C2×C3111yescharacteristic, complemented
351#1981C2×C3111yescharacteristic, complemented
352#1928C2×C3111yescharacteristic, complemented
353#1877C2×C3111yescharacteristic, complemented
354#1873C2×C3111yescharacteristic, complemented
355#1851C2×C3111yescharacteristic, complemented
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—22no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31C2×#12111yescharacteristic
371C22×C31D4211yescharacteristic
372C22×C31#54611yescharacteristic
373C22×C31C2×#13711yescharacteristic
374C22×C31C2×#13711yescharacteristic
375C22×C31#57711yescharacteristic
376C22×C31#57711yescharacteristic
377C4×C31—22no—
378C4×C31—22no—
379C4×C31—22no—
380C4×C31—41no—
381C4×C31—42no—
382C4×C31—42no—
383C4×C31—42no—
384C4×C31—41no—
385C4×C31—42no—
386C4×C31—81no—
387C4×C31—81no—
388C4×C31—81no—
389C4×C31#52511yescharacteristic
390C4×C31#53811yescharacteristic
391C4×C31D4211yescharacteristic
392C4×C31#54611yescharacteristic
393C23×Q8C22×C3111yescharacteristic
394C22×SD16C22×C3111yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396C22×SD16C22×C3111yescharacteristic
397C22×M16C22×C3111yescharacteristic
398C2×C4⋊Q8C22×C3111yescharacteristic
399C2×C4⋊Q8C22×C3111yescharacteristic
400C2×C22⋊Q8C22×C3111yescharacteristic
401C2×#121C22×C3111yescharacteristic
402C2×C4×D4C22×C3111yescharacteristic
403C2×#117C22×C3111yescharacteristic
404#468—24no—
405#461—24no—
406#448—24no—
407C2×#107C22×C3111yescharacteristic
408C2×C4⋊C8C22×C3111yescharacteristic
409C2×C4⋊C8C22×C3111yescharacteristic
410#419—24no—
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#103C22×C3111yescharacteristic
415C2×#103C22×C3111yescharacteristic
416C2×#103C22×C3111yescharacteristic
417C2×#103C22×C3111yescharacteristic
418C2×#103C22×C3111yescharacteristic
419C2×#103C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×C22⋊C8C22×C3111yescharacteristic
422#395—21no—
423#395—21no—
424#391C22×C3111yescharacteristic
425#391C22×C3111yescharacteristic
426#390—21no—
427#390C22×C3111yescharacteristic
428#389C22×C3111yescharacteristic
429#388—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433C4×C4⋊C4C22×C3111yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4C22×C3111yescharacteristic
436#340C22×C3111yescharacteristic
437#340C22×C3111yescharacteristic
438#336C22×C3111yescharacteristic
439#336C22×C3111yescharacteristic
440C2×C31—42no—
441C2×C31—82no—
442C2×C31#242411yescharacteristic
443C2×C31#303911yescharacteristic
444C2×C31#304211yescharacteristic
445C2×C31#326611yescharacteristic
446C2×C31#327811yescharacteristic
447C2×C31#332011yescharacteristic
448C2×C31#332911yescharacteristic
449C22×Q8—21no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—41no—
455C22×Q8—41no—
456C22×Q8C23×C3111yescharacteristic
457C22×Q8C23×C3111yescharacteristic
458C22×Q8C23×C3111yescharacteristic
459C22×D4—21no—
460C22×D4C23×C3111yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C3111yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—41no—
471C2×SD16—41no—
472C2×SD16—41no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—41no—
476C22×C8C23×C3111yescharacteristic
477C22×C8C23×C3111yescharacteristic
478C22×C8C23×C3111yescharacteristic
479C22×C8C23×C3111yescharacteristic
480C4⋊Q8—22no—
481C4⋊Q8—22no—
482C4⋊Q8—41no—
483C4⋊Q8—41no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486#121—22no—
487#121D4×C3114yes—
488C4×D4—22no—
489C4×D4—41no—
490#117—22no—
491#117—41no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4C23×C3111yescharacteristic
499C2×C4⋊C4C23×C3111yescharacteristic
500C2×C4⋊C4C23×C3111yescharacteristic
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4D4×C3111yescharacteristic
509C2×C22⋊C4D4×C3111yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C23×C3111yescharacteristic
513C2×C42C23×C3111yescharacteristic
514#107—22no—
515C4⋊C8—22no—
516C4⋊C8—41no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103—22no—
521#103—22no—
522#103—22no—
523#103—22no—
524#103—41no—
525#103D4×C3114yescomplemented
526#102—22no—
527C22⋊C8—22no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95D4×C3111yescharacteristic
535#95D4×C3111yescharacteristic
536C31#2509911yescharacteristic, direct product factor, Sylow
537C24—21no—
538C24C2×D4×C3111yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—28no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—42no—
562C2×Q8C2×D4×C3112yes—
563C2×Q8#41×C3112yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4C2×D4×C3112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—81no—
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3112yes—
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4#41×C3112yes—
597C22×C4C24×C3111yescharacteristic
598SD16—44no—
599SD16—44no—
600SD16—44no—
601M16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8C2×D4×C3112yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C3112yes—
627C4⋊C4C2×D4×C3112yes—
628C22⋊C4—24no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—42no—
641C42—81no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C31×#12112yes—
656C23C22×D4×C3111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—48no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—48no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—84no—
714C2×C4C31×#12112yes—
715C2×C4C31×#13712yes—
716C2×C4C31×#13712yes—
717C2×C4C22×D4×C3111yescharacteristic
718C2×C4C22×D4×C3111yescharacteristic
719C2×C4C2×#41×C3111yescharacteristic
720C2×C4C2×#41×C3111yescharacteristic
721C2×C4C31×H(5,𝔽2)11yescharacteristic
722C2×C4C31×H(5,𝔽2)11yescharacteristic
723C8—22no—
724C8—41no—
725C8—41no—
726C8—41no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22C2×C31×#12111yescharacteristic
742C22D42×C3111yescharacteristic
743C22C31×#54611yescharacteristic
744C22C2×C31×#13711yescharacteristic
745C22C2×C31×#13711yescharacteristic
746C22C31×#57711yescharacteristic
747C22C31×#57711yescharacteristic
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4C31×#52511yescharacteristic
761C4C31×#53811yescharacteristic
762C4D42×C3111yescharacteristic
763C4C31×#54611yescharacteristic
764C2—42no—
765C2—82no—
766C2C31×#242411yescharacteristic
767C2C31×#303911yescharacteristic
768C2C31×#304211yescharacteristic
769C2C31×#326611yescharacteristic
770C2C31×#327811yescharacteristic
771C2C31×#332011yescharacteristic
772C2C31×#332911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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
2. C2×C31×#461C2semidirect
4. C2×C31×#419C2semidirect
5. C31×#2434C2semidirect
7. C31×#2068C2semidirect
8. C31×#2055C2semidirect
9. C31×#2043C2semidirect
10. C31×#2013C2semidirect
11. C31×#1981C2semidirect
12. C31×#1928C2semidirect
13. C31×#1877C2semidirect
14. C31×#1873C2semidirect
15. C31×#1851C2semidirect
139. C31×#103D4semidirect
255. #25099C31direct (N × H)
342. C2×#461C2×C31semidirect
344. C2×#419C2×C31semidirect
345. #2434C2×C31semidirect
347. #2068C2×C31semidirect
348. #2055C2×C31semidirect
349. #2043C2×C31semidirect
350. #2013C2×C31semidirect
351. #1981C2×C31semidirect
352. #1928C2×C31semidirect
353. #1877C2×C31semidirect
354. #1873C2×C31semidirect
355. #1851C2×C31semidirect
525. #103D4×C31semidirect
536. C31#25099direct (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×#4612
C2×C31×#4482
C2×C31×#4192
C31×#24342
C31×#23632
C31×#20682
C31×#20552
C31×#20432
C31×#20132
C31×#19812
C31×#19282
C31×#18772
C31×#18732
C31×#18512
#2509931