Finite Group Databasebeta

← C31×#23956 #21480715

Subgroups — C31×#23956 #21480715

Order 7936.

1284 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3494C211yesmaximal, characteristic, complemented
2C31×#3005C211yesmaximal, characteristic, complemented
3C31×#2896C211yesmaximal, characteristic, complemented
4C31×#2431C211yesmaximal, characteristic, complemented
5C31×#2028C211yesmaximal, characteristic, complemented
6C31×#2027C211yesmaximal, characteristic, complemented
7C31×#2004C211yesmaximal, characteristic, complemented
8C31×#2002C211yesmaximal, characteristic, complemented
9C31×#1900C211yesmaximal, characteristic, complemented
10C31×#1887C211yesmaximal, characteristic, complemented
11C31×#1885C211yesmaximal, characteristic, complemented
12C31×#1883C211yesmaximal, characteristic, complemented
13C31×#1882C211yesmaximal, characteristic, complemented
14C31×#1871C211yesmaximal, characteristic, complemented
15C31×#1826C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C2×C31×#137C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C31×#555—21no—
21C31×#553—21no—
22C31×#553—21no—
23C31×#551—22no—
24C31×#547—21no—
25C31×#546—22no—
26C31×#544C2211yescharacteristic
27C31×#542—21no—
28C31×#540—21no—
29C31×#535C2211yescharacteristic
30C31×#532—21no—
31C2×C31×#127C2211yescharacteristic
32C31×#529—21no—
33C2×C31×#124C2211yescharacteristic
34C31×#525C2211yescharacteristic
35C2×C31×#121C2211yescharacteristic
36C31×#520C2211yescharacteristic
37C31×#518C2211yescharacteristic
38C2×C31×#117C2211yescharacteristic
39C31×#452—21no—
40C31×#452—21no—
41C31×#449—21no—
42C31×#449—21no—
43C2×C31×#104C2211yescharacteristic
44C2×C31×#104C2211yescharacteristic
45C31×#419C2211yescharacteristic
46C31×#419C2211yescharacteristic
47C31×#419C2211yescharacteristic
48C31×#418C2211yescharacteristic
49C31×#418C2211yescharacteristic
50C31×#418C2211yescharacteristic
51C31×#417—21no—
52C31×#417—21no—
53C31×#416—21no—
54C31×#416—21no—
55C2×C31×#100C2211yescharacteristic
56C2×C31×#100C2211yescharacteristic
57C31×#407C2211yescharacteristic
58C31×#392—22no—
59C31×#391C2211yescharacteristic
60C31×#390C2211yescharacteristic
61C31×#386—22no—
62C4×C22⋊C4×C31C2211yescharacteristic
63C31×#343C2211yescharacteristic
64C31×#343C2211yescharacteristic
65C31×#339C2211yescharacteristic
66C31×#339C2211yescharacteristic
67C31×#339C2211yescharacteristic
68C31×#339C2211yescharacteristic
69C31×#339C2211yescharacteristic
70C31×#339C2211yescharacteristic
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—22no—
74C2×#41×C31—21no—
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C2×#41×C31—21no—
78C2×#41×C31—41no—
79C2×#41×C31—41no—
80C2×#41×C31C2311yescharacteristic
81C22×Q8×C31C2311yescharacteristic
82C22×D4×C31—21no—
83C22×D4×C31—22no—
84C22×D4×C31D412yes—
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C31×#137—22no—
90C31×#137—41no—
91C31×AGL(1,ℤ/8)—22no—
92C31×AGL(1,ℤ/8)—41no—
93C2×Q16×C31—21no—
94C2×SD16×C31—21no—
95C2×SD16×C31—21no—
96C2×D8×C31—21no—
97C2×M16×C31—21no—
98C2×M16×C31—41no—
99C2×M16×C31—41no—
100C2×M16×C31C2311yescharacteristic
101C2×M16×C31C2311yescharacteristic
102C2×M16×C31C2311yescharacteristic
103C2×M16×C31C2311yescharacteristic
104C22×C8×C31—21no—
105C31×C4⋊Q8—21no—
106C31×C4⋊Q8—21no—
107C31×#127—21no—
108C31×#127—22no—
109C31×#127—41no—
110C31×#126—22no—
111C31×#126—22no—
112C31×#125—21no—
113C31×#125—21no—
114C31×#124—22no—
115C31×#124—22no—
116C31×#124—21no—
117C31×#124—22no—
118C31×#124—41no—
119C31×#123—22no—
120C31×#123—22no—
121C31×#123—22no—
122C31×#123—22no—
123C31×#123—21no—
124C31×C22⋊Q8—22no—
125C31×C22⋊Q8—22no—
126C31×C22⋊Q8D411yescharacteristic, complemented
127C31×C22⋊Q8D411yescharacteristic, complemented
128C31×#121—22no—
129C31×#121—22no—
130C31×#121—22no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121D411yescharacteristic, complemented
138C31×#121D411yescharacteristic, complemented
139C31×#120—21no—
140C31×#120—22no—
141C4×Q8×C31—21no—
142C4×D4×C31—22no—
143C4×D4×C31—22no—
144C4×D4×C31—21no—
145C4×D4×C31—22no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C31×#117—22no—
153C31×#117—21no—
154C31×#117—21no—
155C31×#117—21no—
156C31×#117D411yescharacteristic, complemented
157C31×#117D411yescharacteristic, complemented
158C31×#117C2311yescharacteristic
159C31×#117C2311yescharacteristic
160C31×#117C2311yescharacteristic
161C2×C4⋊C4×C31—21no—
162C2×C4⋊C4×C31D411yescharacteristic, complemented
163C2×C4⋊C4×C31D411yescharacteristic, complemented
164C2×C4⋊C4×C31C2311yescharacteristic
165C2×C22⋊C4×C31—21no—
166C2×C22⋊C4×C31—22no—
167C2×C22⋊C4×C31—22no—
168C2×C22⋊C4×C31—21no—
169C2×C22⋊C4×C31—22no—
170C2×C22⋊C4×C31D412yes—
171C2×C42×C31—21no—
172C2×C42×C31C2311yescharacteristic
173C2×C42×C31C2311yescharacteristic
174C31×#104—41no—
175C31×#104—41no—
176C31×#103—21no—
177C31×#103—21no—
178C31×#103—21no—
179C31×#103—21no—
180C31×#103—21no—
181C31×#103—21no—
182C31×#102—21no—
183C31×#102—21no—
184C31×#102—21no—
185C31×#102—21no—
186C31×#102—21no—
187C31×#102—21no—
188C31×#100—41no—
189C31×#100—41no—
190C31×C22⋊C8—21no—
191C31×C22⋊C8—21no—
192C31×#95—21no—
193C31×#95—22no—
194C24×C31—21no—
195C24×C31C2×D412yes—
196C24×C31C2×D411yescharacteristic
197#41×C31—24no—
198#41×C31—24no—
199#41×C31—21no—
200#41×C31—21no—
201#41×C31—21no—
202#41×C31—21no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—42no—
206#41×C31—42no—
207#41×C31—42no—
208#41×C31—42no—
209#41×C31—84no—
210C2×Q8×C31—22no—
211C2×Q8×C31—21no—
212C2×Q8×C31—21no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31—21no—
216C2×Q8×C31C2×D411yescharacteristic
217C2×Q8×C31#4112yescomplemented
218C2×D4×C31—21no—
219C2×D4×C31—22no—
220C2×D4×C31—21no—
221C2×D4×C31—22no—
222C2×D4×C31—22no—
223C2×D4×C31—21no—
224C2×D4×C31—22no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—21no—
236C2×D4×C31—42no—
237C2×D4×C31—44no—
238C2×D4×C31—42no—
239C2×D4×C31—41no—
240C2×D4×C31—41no—
241C2×D4×C31—44no—
242C2×D4×C31—82no—
243C2×D4×C31—82no—
244C2×D4×C31C2×D411yescharacteristic
245C2×D4×C31#4112yescomplemented
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—42no—
260C22×C4×C31—42no—
261C22×C4×C31—41no—
262C22×C4×C31—41no—
263C22×C4×C31C2×D411yescharacteristic
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D412yes—
269C22×C4×C31C2411yescharacteristic
270Q16×C31—42no—
271SD16×C31—42no—
272SD16×C31—42no—
273D8×C31—42no—
274M16×C31—21no—
275M16×C31—21no—
276M16×C31—21no—
277M16×C31—21no—
278M16×C31—21no—
279M16×C31—21no—
280M16×C31—21no—
281M16×C31—21no—
282M16×C31—42no—
283C2×C8×C31—21no—
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31—42no—
288C4⋊C4×C31—22no—
289C4⋊C4×C31—22no—
290C4⋊C4×C31—22no—
291C4⋊C4×C31—22no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31C2×D411yescharacteristic
299C4⋊C4×C31C2×D411yescharacteristic
300C4⋊C4×C31C2×D411yescharacteristic
301C4⋊C4×C31C2×D411yescharacteristic
302C4⋊C4×C31C2×D411yescharacteristic
303C4⋊C4×C31C2×D411yescharacteristic
304C22⋊C4×C31—22no—
305C22⋊C4×C31—22no—
306C22⋊C4×C31—22no—
307C22⋊C4×C31—22no—
308C22⋊C4×C31—22no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—21no—
315C22⋊C4×C31—21no—
316C22⋊C4×C31—22no—
317C22⋊C4×C31—22no—
318C22⋊C4×C31—21no—
319C22⋊C4×C31—21no—
320C22⋊C4×C31—44no—
321C22⋊C4×C31—42no—
322C22⋊C4×C31—82no—
323C42×C31—22no—
324C42×C31—21no—
325C42×C31—21no—
326C42×C31—21no—
327C42×C31—21no—
328C42×C31—21no—
329C42×C31—21no—
330C42×C31—21no—
331C42×C31—21no—
332C42×C31—21no—
333#23956C3111yesmaximal, characteristic, direct product factor, Sylow
334C23×C31—21no—
335C23×C31—21no—
336C23×C31—22no—
337C23×C31—21no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—42no—
346C23×C31—42no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31#12011yescharacteristic
350C23×C31#12011yescharacteristic
351C23×C31C22×D411yescharacteristic
352Q8×C31—22no—
353Q8×C31—21no—
354Q8×C31—22no—
355Q8×C31—21no—
356Q8×C31—41no—
357Q8×C31—41no—
358Q8×C31—82no—
359D4×C31—22no—
360D4×C31—21no—
361D4×C31—22no—
362D4×C31—21no—
363D4×C31—44no—
364D4×C31—42no—
365D4×C31—44no—
366D4×C31—44no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—41no—
374D4×C31—41no—
375D4×C31—81no—
376D4×C31—82no—
377D4×C31—82no—
378D4×C31—82no—
379D4×C31—88no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—21no—
389C2×C4×C31—21no—
390C2×C4×C31—22no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—21no—
397C2×C4×C31—21no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—44no—
401C2×C4×C31—44no—
402C2×C4×C31—41no—
403C2×C4×C31—42no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—42no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—81no—
414C2×C4×C31—82no—
415C2×C4×C31—82no—
416C2×C4×C31—82no—
417C2×C4×C31#12011yescharacteristic
418C2×C4×C31#12011yescharacteristic
419C2×C4×C31C22×D411yescharacteristic
420C2×C4×C31C22×D411yescharacteristic
421C2×C4×C31C2×#4111yescharacteristic
422C2×C4×C31C2×#4111yescharacteristic
423C2×C4×C31H(5,𝔽2)11yescharacteristic
424C2×C4×C31H(5,𝔽2)11yescharacteristic
425C8×C31—41no—
426C8×C31—41no—
427C8×C31—41no—
428C8×C31—41no—
429#3494C2×C3111yescharacteristic, complemented
430#3005C2×C3111yescharacteristic, complemented
431#2896C2×C3111yescharacteristic, complemented
432#2431C2×C3111yescharacteristic, complemented
433#2028C2×C3111yescharacteristic, complemented
434#2027C2×C3111yescharacteristic, complemented
435#2004C2×C3111yescharacteristic, complemented
436#2002C2×C3111yescharacteristic, complemented
437#1900C2×C3111yescharacteristic, complemented
438#1887C2×C3111yescharacteristic, complemented
439#1885C2×C3111yescharacteristic, complemented
440#1883C2×C3111yescharacteristic, complemented
441#1882C2×C3111yescharacteristic, complemented
442#1871C2×C3111yescharacteristic, complemented
443#1826C2×C3111yescharacteristic, complemented
444C22×C31—21no—
445C22×C31—21no—
446C22×C31—21no—
447C22×C31—21no—
448C22×C31—21no—
449C22×C31—21no—
450C22×C31—21no—
451C22×C31—21no—
452C22×C31—44no—
453C22×C31—42no—
454C22×C31—41no—
455C22×C31—42no—
456C22×C31—42no—
457C22×C31—41no—
458C22×C31—41no—
459C22×C31—42no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—82no—
463C22×C31—82no—
464C22×C31—82no—
465C22×C31—81no—
466C22×C31—81no—
467C22×C31C2×#12011yescharacteristic
468C22×C31#54611yescharacteristic
469C22×C31#54611yescharacteristic
470C4×C31—21no—
471C4×C31—21no—
472C4×C31—42no—
473C4×C31—42no—
474C4×C31—41no—
475C4×C31—41no—
476C4×C31—41no—
477C4×C31—41no—
478C4×C31—41no—
479C4×C31—41no—
480C4×C31—42no—
481C4×C31—41no—
482C4×C31—81no—
483C4×C31#52511yescharacteristic
484C4×C31#53511yescharacteristic
485C4×C31#54611yescharacteristic
486C4×C31#54611yescharacteristic
487C22×#41C22×C3111yescharacteristic
488C2×#137C22×C3111yescharacteristic
489C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
490C22×M16C22×C3111yescharacteristic
491#555—21no—
492#553—21no—
493#553—21no—
494#551—22no—
495#547—21no—
496#546—22no—
497#544C22×C3111yescharacteristic
498#542—21no—
499#540—21no—
500#535C22×C3111yescharacteristic
501#532—21no—
502C2×#127C22×C3111yescharacteristic
503#529—21no—
504C2×#124C22×C3111yescharacteristic
505#525C22×C3111yescharacteristic
506C2×#121C22×C3111yescharacteristic
507#520C22×C3111yescharacteristic
508#518C22×C3111yescharacteristic
509C2×#117C22×C3111yescharacteristic
510#452—21no—
511#452—21no—
512#449—21no—
513#449—21no—
514C2×#104C22×C3111yescharacteristic
515C2×#104C22×C3111yescharacteristic
516#419C22×C3111yescharacteristic
517#419C22×C3111yescharacteristic
518#419C22×C3111yescharacteristic
519#418C22×C3111yescharacteristic
520#418C22×C3111yescharacteristic
521#418C22×C3111yescharacteristic
522#417—21no—
523#417—21no—
524#416—21no—
525#416—21no—
526C2×#100C22×C3111yescharacteristic
527C2×#100C22×C3111yescharacteristic
528#407C22×C3111yescharacteristic
529#392—22no—
530#391C22×C3111yescharacteristic
531#390C22×C3111yescharacteristic
532#386—22no—
533C4×C22⋊C4C22×C3111yescharacteristic
534#343C22×C3111yescharacteristic
535#343C22×C3111yescharacteristic
536#339C22×C3111yescharacteristic
537#339C22×C3111yescharacteristic
538#339C22×C3111yescharacteristic
539#339C22×C3111yescharacteristic
540#339C22×C3111yescharacteristic
541#339C22×C3111yescharacteristic
542C2×C31—21no—
543C2×C31—21no—
544C2×C31—41no—
545C2×C31—41no—
546C2×C31—81no—
547C2×C31—82no—
548C2×C31—82no—
549C2×C31#240411yescharacteristic
550C2×C31#301811yescharacteristic
551C2×C31#301911yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—41no—
560C2×#41—41no—
561C2×#41C23×C3111yescharacteristic
562C22×Q8C23×C3111yescharacteristic
563C22×D4—21no—
564C22×D4—22no—
565C22×D4D4×C3112yes—
566C22×D4C23×C3111yescharacteristic
567C22×D4C23×C3111yescharacteristic
568C23×C4—21no—
569C23×C4C23×C3111yescharacteristic
570#137—22no—
571#137—41no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—41no—
574C2×Q16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×D8—21no—
578C2×M16—21no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16C23×C3111yescharacteristic
582C2×M16C23×C3111yescharacteristic
583C2×M16C23×C3111yescharacteristic
584C2×M16C23×C3111yescharacteristic
585C22×C8—21no—
586C4⋊Q8—21no—
587C4⋊Q8—21no—
588#127—21no—
589#127—22no—
590#127—41no—
591#126—22no—
592#126—22no—
593#125—21no—
594#125—21no—
595#124—22no—
596#124—22no—
597#124—21no—
598#124—22no—
599#124—41no—
600#123—22no—
601#123—22no—
602#123—22no—
603#123—22no—
604#123—21no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8D4×C3111yescharacteristic, complemented
608C22⋊Q8D4×C3111yescharacteristic, complemented
609#121—22no—
610#121—22no—
611#121—22no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121D4×C3111yescharacteristic, complemented
619#121D4×C3111yescharacteristic, complemented
620#120—21no—
621#120—22no—
622C4×Q8—21no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—21no—
626C4×D4—22no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633#117—22no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C3111yescharacteristic, complemented
638#117D4×C3111yescharacteristic, complemented
639#117C23×C3111yescharacteristic
640#117C23×C3111yescharacteristic
641#117C23×C3111yescharacteristic
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C3111yescharacteristic, complemented
644C2×C4⋊C4D4×C3111yescharacteristic, complemented
645C2×C4⋊C4C23×C3111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4D4×C3112yes—
652C2×C42—21no—
653C2×C42C23×C3111yescharacteristic
654C2×C42C23×C3111yescharacteristic
655#104—41no—
656#104—41no—
657#103—21no—
658#103—21no—
659#103—21no—
660#103—21no—
661#103—21no—
662#103—21no—
663#102—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#100—41no—
670#100—41no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673#95—21no—
674#95—22no—
675C31#2395611yescharacteristic, direct product factor, Sylow
676C24—21no—
677C24C2×D4×C3112yes—
678C24C2×D4×C3111yescharacteristic
679#41—24no—
680#41—24no—
681#41—21no—
682#41—21no—
683#41—21no—
684#41—21no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41—42no—
690#41—42no—
691#41—84no—
692C2×Q8—22no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8C2×D4×C3111yescharacteristic
699C2×Q8#41×C3112yescomplemented
700C2×D4—21no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—22no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—42no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—44no—
724C2×D4—82no—
725C2×D4—82no—
726C2×D4C2×D4×C3111yescharacteristic
727C2×D4#41×C3112yescomplemented
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4C2×D4×C3111yescharacteristic
746C22×C4C2×D4×C3111yescharacteristic
747C22×C4C2×D4×C3111yescharacteristic
748C22×C4C2×D4×C3111yescharacteristic
749C22×C4C2×D4×C3111yescharacteristic
750C22×C4C2×D4×C3112yes—
751C22×C4C24×C3111yescharacteristic
752Q16—42no—
753SD16—42no—
754SD16—42no—
755D8—42no—
756M16—21no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—42no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—42no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4C2×D4×C3111yescharacteristic
781C4⋊C4C2×D4×C3111yescharacteristic
782C4⋊C4C2×D4×C3111yescharacteristic
783C4⋊C4C2×D4×C3111yescharacteristic
784C4⋊C4C2×D4×C3111yescharacteristic
785C4⋊C4C2×D4×C3111yescharacteristic
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—44no—
803C22⋊C4—42no—
804C22⋊C4—82no—
805C42—22no—
806C42—21no—
807C42—21no—
808C42—21no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C23—21no—
816C23—21no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—41no—
829C23—41no—
830C23C31×#12011yescharacteristic
831C23C31×#12011yescharacteristic
832C23C22×D4×C3111yescharacteristic
833Q8—22no—
834Q8—21no—
835Q8—22no—
836Q8—21no—
837Q8—41no—
838Q8—41no—
839Q8—82no—
840D4—22no—
841D4—21no—
842D4—22no—
843D4—21no—
844D4—44no—
845D4—42no—
846D4—44no—
847D4—44no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—82no—
858D4—82no—
859D4—82no—
860D4—88no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—81no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4C31×#12011yescharacteristic
899C2×C4C31×#12011yescharacteristic
900C2×C4C22×D4×C3111yescharacteristic
901C2×C4C22×D4×C3111yescharacteristic
902C2×C4C2×#41×C3111yescharacteristic
903C2×C4C2×#41×C3111yescharacteristic
904C2×C4C31×H(5,𝔽2)11yescharacteristic
905C2×C4C31×H(5,𝔽2)11yescharacteristic
906C8—41no—
907C8—41no—
908C8—41no—
909C8—41no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—44no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—81no—
932C22—81no—
933C22C2×C31×#12011yescharacteristic
934C22C31×#54611yescharacteristic
935C22C31×#54611yescharacteristic
936C4—21no—
937C4—21no—
938C4—42no—
939C4—42no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—81no—
949C4C31×#52511yescharacteristic
950C4C31×#53511yescharacteristic
951C4C31×#54611yescharacteristic
952C4C31×#54611yescharacteristic
953C2—21no—
954C2—21no—
955C2—41no—
956C2—41no—
957C2—82no—
958C2—82no—
959C2—81no—
960C2C31×#240411yescharacteristic
961C2C31×#301811yescharacteristic
962C2C31×#301911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3494C2semidirect
2. C31×#3005C2semidirect
3. C31×#2896C2semidirect
4. C31×#2431C2semidirect
5. C31×#2028C2semidirect
6. C31×#2027C2semidirect
7. C31×#2004C2semidirect
8. C31×#2002C2semidirect
9. C31×#1900C2semidirect
10. C31×#1887C2semidirect
11. C31×#1885C2semidirect
12. C31×#1883C2semidirect
13. C31×#1882C2semidirect
14. C31×#1871C2semidirect
15. C31×#1826C2semidirect
126. C31×C22⋊Q8D4semidirect
127. C31×C22⋊Q8D4semidirect
137. C31×#121D4semidirect
138. C31×#121D4semidirect
156. C31×#117D4semidirect
157. C31×#117D4semidirect
162. C2×C4⋊C4×C31D4semidirect
163. C2×C4⋊C4×C31D4semidirect
217. C2×Q8×C31#41semidirect
245. C2×D4×C31#41semidirect
333. #23956C31direct (N × H)
429. #3494C2×C31semidirect
430. #3005C2×C31semidirect
431. #2896C2×C31semidirect
432. #2431C2×C31semidirect
433. #2028C2×C31semidirect
434. #2027C2×C31semidirect
435. #2004C2×C31semidirect
436. #2002C2×C31semidirect
437. #1900C2×C31semidirect
438. #1887C2×C31semidirect
439. #1885C2×C31semidirect
440. #1883C2×C31semidirect
441. #1882C2×C31semidirect
442. #1871C2×C31semidirect
443. #1826C2×C31semidirect
607. C22⋊Q8D4×C31semidirect
608. C22⋊Q8D4×C31semidirect
618. #121D4×C31semidirect
619. #121D4×C31semidirect
637. #117D4×C31semidirect
638. #117D4×C31semidirect
643. C2×C4⋊C4D4×C31semidirect
644. C2×C4⋊C4D4×C31semidirect
675. C31#23956direct (N × H)
699. C2×Q8#41×C31semidirect
727. C2×D4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34942
C31×#30052
C31×#28962
C31×#24312
C31×#20282
C31×#20272
C31×#20042
C31×#20022
C31×#19002
C31×#18872
C31×#18852
C31×#18832
C31×#18822
C31×#18712
C31×#18262
#2395631