Finite Group Databasebeta

← C31×#25151 #21481910

Subgroups — C31×#25151 #21481910

Order 7936.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#462C211yesmaximal, characteristic, complemented
2C2×C31×#452C211yesmaximal, characteristic
3C2×C31×#452C211yesmaximal, characteristic
4C2×C4×Q16×C31C211yesmaximal, characteristic, complemented
5C31×#2429C211yesmaximal, characteristic, complemented
6C31×#2341C211yesmaximal, characteristic
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#2035C211yesmaximal, characteristic, complemented
10C31×#2013C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1878C211yesmaximal, characteristic, complemented
15C31×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C31×#462—24no—
28C31×#452—24no—
29C31×#452—24no—
30C4×Q16×C31—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×#106C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
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×#391C2211yescharacteristic
48C31×#390—21no—
49C31×#390—21no—
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#389—21no—
53C31×#389C2211yescharacteristic
54C31×#388—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
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×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C2×Q16×C31—22no—
77C2×Q16×C31—22no—
78C2×Q16×C31—22no—
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31D414yes—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—41no—
87C2×SD16×C31—41no—
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×C4⋊Q8—22no—
93C31×C4⋊Q8—41no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—41no—
97C31×C22⋊Q8—41no—
98C4×Q8×C31—22no—
99C4×Q8×C31—22no—
100C4×Q8×C31—22no—
101C4×Q8×C31—41no—
102C4×Q8×C31—41no—
103C4×Q8×C31—41no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
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×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×#107—22no—
131C31×#106—41no—
132C31×C4⋊C8—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—41no—
138C31×#103D414yes—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×C22⋊C8—22no—
143C4×C8×C31—22no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152#41×C31—44no—
153#41×C31—44no—
154#41×C31—44no—
155#41×C31—44no—
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—21no—
170C2×Q8×C31C2×D412yes—
171C2×Q8×C31C2×D412yes—
172C2×Q8×C31C2×D412yes—
173C2×Q8×C31#4112yes—
174C2×D4×C31—24no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31#4112yes—
183C22×C4×C31—21no—
184C22×C4×C31—24no—
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—42no—
198C22×C4×C31—42no—
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2411yescharacteristic
205Q16×C31—28no—
206Q16×C31—44no—
207SD16×C31—44no—
208SD16×C31—44no—
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×C31C2×D412yes—
220C2×C8×C31C2×D412yes—
221C4⋊C4×C31—21no—
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—42no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—42no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—42no—
236C4⋊C4×C31C2×D412yes—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—81no—
244C22⋊C4×C31—81no—
245C22⋊C4×C31—81no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—42no—
251C42×C31—42no—
252C42×C31—42no—
253#25151C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—22no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31C22×D411yescharacteristic
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—22no—
272Q8×C31—22no—
273Q8×C31—22no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31#12114yes—
281D4×C31—22no—
282D4×C31—22no—
283D4×C31—48no—
284D4×C31—41no—
285D4×C31—41no—
286C2×C4×C31—22no—
287C2×C4×C31—21no—
288C2×C4×C31—21no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—21no—
292C2×C4×C31—21no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—48no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
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#13512yes—
326C2×C4×C31#13712yes—
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C22×D411yescharacteristic
329C2×C4×C31C2×#4111yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31H(5,𝔽2)11yescharacteristic
332C2×C4×C31H(5,𝔽2)11yescharacteristic
333C8×C31—22no—
334C8×C31—22no—
335C8×C31—41no—
336C8×C31—41no—
337C2×#462C2×C3111yescharacteristic, complemented
338C2×#452C2×C3111yescharacteristic
339C2×#452C2×C3111yescharacteristic
340C2×C4×Q16C2×C3111yescharacteristic, complemented
341#2429C2×C3111yescharacteristic, complemented
342#2341C2×C3111yescharacteristic
343#2067C2×C3111yescharacteristic, complemented
344#2036C2×C3111yescharacteristic, complemented
345#2035C2×C3111yescharacteristic, complemented
346#2013C2×C3111yescharacteristic, complemented
347#1968C2×C3111yescharacteristic, complemented
348#1923C2×C3111yescharacteristic, complemented
349#1880C2×C3111yescharacteristic, complemented
350#1878C2×C3111yescharacteristic, complemented
351#1865C2×C3111yescharacteristic, complemented
352C22×C31—41no—
353C22×C31—42no—
354C22×C31—41no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31#52511yescharacteristic
367C22×C31D4211yescharacteristic
368C22×C31D4211yescharacteristic
369C22×C31C2×#13511yescharacteristic
370C22×C31C2×#13711yescharacteristic
371C22×C31#57711yescharacteristic
372C22×C31#57811yescharacteristic
373C4×C31—24no—
374C4×C31—22no—
375C4×C31—22no—
376C4×C31—41no—
377C4×C31—42no—
378C4×C31—41no—
379C4×C31—41no—
380C4×C31—42no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31C2×#12111yescharacteristic
386C4×C31#53811yescharacteristic
387C4×C31#54611yescharacteristic
388C4×C31#54611yescharacteristic
389C22×#41C22×C3111yescharacteristic
390C22×Q16C22×C3111yescharacteristic
391C22×Q16C22×C3111yescharacteristic
392C22×SD16C22×C3111yescharacteristic
393C22×SD16C22×C3111yescharacteristic
394C2×C4⋊Q8C22×C3111yescharacteristic
395C2×C22⋊Q8C22×C3111yescharacteristic
396C2×C22⋊Q8C22×C3111yescharacteristic
397C2×C4×Q8C22×C3111yescharacteristic
398C2×C4×Q8C22×C3111yescharacteristic
399C2×C4×Q8C22×C3111yescharacteristic
400#462—24no—
401#452—24no—
402#452—24no—
403C4×Q16—24no—
404C2×#107C22×C3111yescharacteristic
405C2×#106C22×C3111yescharacteristic
406C2×C4⋊C8C22×C3111yescharacteristic
407C2×#103C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417C2×C4×C8C22×C3111yescharacteristic
418#398—21no—
419#396—21no—
420#391C22×C3111yescharacteristic
421#390—21no—
422#390—21no—
423#390C22×C3111yescharacteristic
424#390C22×C3111yescharacteristic
425#389—21no—
426#389C22×C3111yescharacteristic
427#388—21no—
428#380—21no—
429#380C22×C3111yescharacteristic
430C4×C22⋊C4—21no—
431C4×C22⋊C4C22×C3111yescharacteristic
432#340C22×C3111yescharacteristic
433#340C22×C3111yescharacteristic
434#336C22×C3111yescharacteristic
435#336C22×C3111yescharacteristic
436C2×C31—81no—
437C2×C31—82no—
438C2×C31#242411yescharacteristic
439C2×C31#310711yescharacteristic
440C2×C31#312011yescharacteristic
441C2×C31#327011yescharacteristic
442C2×C31#327811yescharacteristic
443C2×C31#328411yescharacteristic
444C2×C31#328511yescharacteristic
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—41no—
450C2×#41—41no—
451C22×Q8C23×C3111yescharacteristic
452C22×Q8C23×C3111yescharacteristic
453C22×Q8C23×C3111yescharacteristic
454C22×D4—21no—
455C22×D4C23×C3111yescharacteristic
456C23×C4—21no—
457C23×C4C23×C3111yescharacteristic
458C2×Q16—22no—
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×Q16D4×C3114yes—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16—41no—
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C22×C8C23×C3111yescharacteristic
473C22×C8C23×C3111yescharacteristic
474C4⋊Q8—22no—
475C4⋊Q8—41no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—41no—
479C22⋊Q8—41no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—41no—
484C4×Q8—41no—
485C4×Q8—41no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C4⋊C4C23×C3111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C3111yescharacteristic
506C2×C22⋊C4D4×C3111yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C3111yescharacteristic
511C2×C42C23×C3111yescharacteristic
512#107—22no—
513#106—41no—
514C4⋊C8—22no—
515#103—22no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—41no—
520#103D4×C3114yes—
521#102—22no—
522#102—22no—
523C22⋊C8—22no—
524C22⋊C8—22no—
525C4×C8—22no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95D4×C3111yescharacteristic
531#95D4×C3111yescharacteristic
532C31#2515111yescharacteristic, direct product factor, Sylow
533C24—21no—
534C24C2×D4×C3111yescharacteristic
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
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×Q8C2×D4×C3112yes—
554C2×Q8C2×D4×C3112yes—
555C2×Q8C2×D4×C3112yes—
556C2×Q8#41×C3112yes—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4#41×C3112yes—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C24×C3111yescharacteristic
588Q16—28no—
589Q16—44no—
590SD16—44no—
591SD16—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C3112yes—
603C2×C8C2×D4×C3112yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4C2×D4×C3112yes—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—42no—
634C42—42no—
635C42—42no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×D4×C3111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8C31×#12114yes—
663D4—22no—
664D4—22no—
665D4—48no—
666D4—41no—
667D4—41no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—48no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
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×C4C31×#13512yes—
708C2×C4C31×#13712yes—
709C2×C4C22×D4×C3111yescharacteristic
710C2×C4C22×D4×C3111yescharacteristic
711C2×C4C2×#41×C3111yescharacteristic
712C2×C4C2×#41×C3111yescharacteristic
713C2×C4C31×H(5,𝔽2)11yescharacteristic
714C2×C4C31×H(5,𝔽2)11yescharacteristic
715C8—22no—
716C8—22no—
717C8—41no—
718C8—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C31×#52511yescharacteristic
734C22D42×C3111yescharacteristic
735C22D42×C3111yescharacteristic
736C22C2×C31×#13511yescharacteristic
737C22C2×C31×#13711yescharacteristic
738C22C31×#57711yescharacteristic
739C22C31×#57811yescharacteristic
740C4—24no—
741C4—22no—
742C4—22no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4C2×C31×#12111yescharacteristic
753C4C31×#53811yescharacteristic
754C4C31×#54611yescharacteristic
755C4C31×#54611yescharacteristic
756C2—81no—
757C2—82no—
758C2C31×#242411yescharacteristic
759C2C31×#310711yescharacteristic
760C2C31×#312011yescharacteristic
761C2C31×#327011yescharacteristic
762C2C31×#327811yescharacteristic
763C2C31×#328411yescharacteristic
764C2C31×#328511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×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×#462C2semidirect
4. C2×C4×Q16×C31C2semidirect
5. C31×#2429C2semidirect
7. C31×#2067C2semidirect
8. C31×#2036C2semidirect
9. C31×#2035C2semidirect
10. C31×#2013C2semidirect
11. C31×#1968C2semidirect
12. C31×#1923C2semidirect
13. C31×#1880C2semidirect
14. C31×#1878C2semidirect
15. C31×#1865C2semidirect
253. #25151C31direct (N × H)
337. C2×#462C2×C31semidirect
340. C2×C4×Q16C2×C31semidirect
341. #2429C2×C31semidirect
343. #2067C2×C31semidirect
344. #2036C2×C31semidirect
345. #2035C2×C31semidirect
346. #2013C2×C31semidirect
347. #1968C2×C31semidirect
348. #1923C2×C31semidirect
349. #1880C2×C31semidirect
350. #1878C2×C31semidirect
351. #1865C2×C31semidirect
532. C31#25151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4622
C2×C31×#4522
C2×C4×Q16×C312
C31×#24292
C31×#23412
C31×#20672
C31×#20362
C31×#20352
C31×#20132
C31×#19682
C31×#19232
C31×#18802
C31×#18782
C31×#18652
#2515131