Finite Group Databasebeta

← C2×C31×#2055 #21480296

Subgroups — C2×C31×#2055 #21480296

Order 7936.

1702 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C31C211yesmaximal, characteristic
2C22×C31×C4⋊C8C211yesmaximal, characteristic, complemented
3C22×C31×#103C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic
5C2×C31×#391C211yesmaximal, characteristic, complemented
6C2×C31×#390C211yesmaximal, characteristic
7C31×#2055C218yesmaximal, direct product factor
8C2×C31×#340C211yesmaximal, characteristic, complemented
9C23×Q8×C31C2211yescharacteristic
10C23×D4×C31C2211yescharacteristic
11C22×SD16×C31—24no—
12C22×SD16×C31—24no—
13C22×SD16×C31—24no—
14C22×SD16×C31C2214yes—
15C23×C8×C31C2211yescharacteristic
16C23×C8×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31—21no—
20C22×C22⋊C4×C31—21no—
21C22×C42×C31C2211yescharacteristic
22C2×C31×C4⋊C8—24no—
23C2×C31×C4⋊C8C2214yescomplemented
24C2×C31×#103—24no—
25C2×C31×#103C2214yescomplemented
26C2×C31×#102—24no—
27C2×C31×#102C2214yes—
28C31×#391—22no—
29C31×#391C2214yescomplemented
30C31×#390—22no—
31C31×#390C2214yes—
32C2×C31×#95—21no—
33C2×C31×#95—21no—
34C31×#340C2214yescomplemented
35C25×C31—21no—
36C22×Q8×C31—21no—
37C22×Q8×C31—22no—
38C22×Q8×C31—22no—
39C22×Q8×C31—22no—
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31D414yes—
43C22×Q8×C31C2312yes—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31D414yes—
51C22×D4×C31C2312yes—
52C23×C4×C31—21no—
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31D411yescharacteristic
56C23×C4×C31D411yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C2×SD16×C31—232no—
59C2×SD16×C31—28no—
60C2×SD16×C31—28no—
61C2×SD16×C31—28no—
62C22×C8×C31—22no—
63C22×C8×C31—22no—
64C22×C8×C31—22no—
65C22×C8×C31—22no—
66C22×C8×C31—22no—
67C22×C8×C31D414yes—
68C22×C8×C31C2312yes—
69C22×C8×C31C2312yes—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31C2312yes—
77C2×C4⋊C4×C31C2312yes—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—44no—
81C2×C22⋊C4×C31—44no—
82C2×C42×C31—22no—
83C2×C42×C31—22no—
84C2×C42×C31D412yes—
85C2×C42×C31C2312yes—
86C31×C4⋊C8—28no—
87C31×#103—28no—
88C31×#102—28no—
89C31×#95—24no—
90C31×#95—24no—
91C24×C31—24no—
92C24×C31—22no—
93C24×C31—42no—
94C24×C31—42no—
95C24×C31—42no—
96C24×C31—42no—
97C24×C31—42no—
98C24×C31—42no—
99C24×C31C2×D411yescharacteristic
100C2×Q8×C31—24no—
101C2×Q8×C31—22no—
102C2×Q8×C31—28no—
103C2×Q8×C31—28no—
104C2×Q8×C31—22no—
105C2×Q8×C31—22no—
106C2×Q8×C31—22no—
107C2×Q8×C31—22no—
108C2×Q8×C31—42no—
109C2×Q8×C31—42no—
110C2×Q8×C31—44no—
111C2×Q8×C31—44no—
112C2×Q8×C31C2×D414yes—
113C2×D4×C31—28no—
114C2×D4×C31—24no—
115C2×D4×C31—28no—
116C2×D4×C31—22no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31—44no—
124C2×D4×C31—44no—
125C2×D4×C31C2×D414yes—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31SD1614yescomplemented
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31#4112yes—
151C22×C4×C31#4112yes—
152C22×C4×C31#4112yes—
153C22×C4×C31C2411yescharacteristic
154SD16×C31—232no—
155C2×C8×C31—28no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—44no—
162C2×C8×C31C2×D414yes—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—42no—
168C4⋊C4×C31—42no—
169C22⋊C4×C31—48no—
170C22⋊C4×C31—48no—
171C42×C31—24no—
172C42×C31—22no—
173C42×C31—22no—
174C2×#2055C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—24no—
176C23×C31—42no—
177C23×C31—42no—
178C23×C31—42no—
179C23×C31—42no—
180C23×C31—42no—
181C23×C31—42no—
182C23×C31—48no—
183C23×C31—48no—
184C23×C31—48no—
185C23×C31—84no—
186C23×C31—84no—
187C23×C31—84no—
188C23×C31—84no—
189C23×C31#12112yes—
190C23×C31#12112yes—
191C23×C31#12112yes—
192C23×C31C2×SD1612yes—
193C23×C31#13512yes—
194C23×C31AGL(1,ℤ/8)12yes—
195C23×C31#13712yes—
196C23×C31C22×D411yescharacteristic
197Q8×C31—24no—
198Q8×C31—24no—
199Q8×C31—42no—
200Q8×C31—42no—
201Q8×C31—48no—
202D4×C31—24no—
203D4×C31—24no—
204D4×C31—42no—
205D4×C31—42no—
206D4×C31—48no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—28no—
210C2×C4×C31—22no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—48no—
217C2×C4×C31—44no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—84no—
225C2×C4×C31—84no—
226C2×C4×C31#12014yes—
227C2×C4×C31#12112yes—
228C2×C4×C31#12112yes—
229C2×C4×C31#12112yes—
230C2×C4×C31#12314yes—
231C2×C4×C31#12314yes—
232C2×C4×C31#12414yes—
233C2×C4×C31C2×SD1614yescomplemented
234C2×C4×C31C22×D411yescharacteristic
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C22×D411yescharacteristic
237C2×C4×C31C2×#4111yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C31C2×#4111yescharacteristic
240C8×C31—24no—
241C8×C31—42no—
242C23×SD16C2×C3111yescharacteristic
243C22×C4⋊C8C2×C3111yescharacteristic, complemented
244C22×#103C2×C3111yescharacteristic, complemented
245C22×#102C2×C3111yescharacteristic
246C2×#391C2×C3111yescharacteristic, complemented
247C2×#390C2×C3111yescharacteristic
248#2055C2×C3118yesdirect product factor
249C2×#340C2×C3111yescharacteristic, complemented
250C22×C31—44no—
251C22×C31—44no—
252C22×C31—44no—
253C22×C31—816no—
254C22×C31—82no—
255C22×C31—82no—
256C22×C31—82no—
257C22×C31—82no—
258C22×C31#39414yes—
259C22×C31#46014yes—
260C22×C31#46114yes—
261C22×C31#46314yes—
262C22×C31#46414yes—
263C22×C31#46514yes—
264C22×C31#46814yes—
265C22×C31C2×#12111yescharacteristic
266C22×C31C2×#12111yescharacteristic
267C22×C31C2×#12111yescharacteristic
268C22×C31C22×SD1611yescharacteristic
269C22×C31C2×#13511yescharacteristic
270C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C31C2×#13711yescharacteristic
272C4×C31—24no—
273C4×C31—44no—
274C4×C31—42no—
275C4×C31—82no—
276C4×C31—82no—
277C4×C31#39414yes—
278C4×C31C2×#12011yescharacteristic
279C4×C31C2×#12311yescharacteristic
280C4×C31C2×#12311yescharacteristic
281C4×C31C2×#12411yescharacteristic
282C23×Q8C22×C3111yescharacteristic
283C23×D4C22×C3111yescharacteristic
284C22×SD16—24no—
285C22×SD16—24no—
286C22×SD16—24no—
287C22×SD16C22×C3114yes—
288C23×C8C22×C3111yescharacteristic
289C23×C8C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C22⋊C4—21no—
293C22×C22⋊C4—21no—
294C22×C42C22×C3111yescharacteristic
295C2×C4⋊C8—24no—
296C2×C4⋊C8C22×C3114yescomplemented
297C2×#103—24no—
298C2×#103C22×C3114yescomplemented
299C2×#102—24no—
300C2×#102C22×C3114yes—
301#391—22no—
302#391C22×C3114yescomplemented
303#390—22no—
304#390C22×C3114yes—
305C2×#95—21no—
306C2×#95—21no—
307#340C22×C3114yescomplemented
308C2×C31—84no—
309C2×C31#205518yesdirect product factor
310C2×C31C2×#39411yescharacteristic
311C2×C31C2×#46111yescharacteristic
312C2×C31C2×#46311yescharacteristic
313C2×C31C2×#46011yescharacteristic
314C2×C31C2×#46411yescharacteristic
315C2×C31C2×#46511yescharacteristic
316C2×C31C2×#46811yescharacteristic
317C25—21no—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8D4×C3114yes—
325C22×Q8C23×C3112yes—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4D4×C3114yes—
333C22×D4C23×C3112yes—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4D4×C3111yescharacteristic
338C23×C4D4×C3111yescharacteristic
339C23×C4C23×C3111yescharacteristic
340C2×SD16—232no—
341C2×SD16—28no—
342C2×SD16—28no—
343C2×SD16—28no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8D4×C3114yes—
350C22×C8C23×C3112yes—
351C22×C8C23×C3112yes—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C23×C3112yes—
359C2×C4⋊C4C23×C3112yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42D4×C3112yes—
367C2×C42C23×C3112yes—
368C4⋊C8—28no—
369#103—28no—
370#102—28no—
371#95—24no—
372#95—24no—
373C31C2×#205511yescharacteristic, direct product factor, Sylow
374C24—24no—
375C24—22no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24C2×D4×C3111yescharacteristic
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—28no—
386C2×Q8—28no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8C2×D4×C3114yes—
396C2×D4—28no—
397C2×D4—24no—
398C2×D4—28no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4C2×D4×C3114yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4SD16×C3114yescomplemented
427C22×C4C2×D4×C3112yes—
428C22×C4C2×D4×C3112yes—
429C22×C4C2×D4×C3112yes—
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3112yes—
432C22×C4C2×D4×C3111yescharacteristic
433C22×C4#41×C3112yes—
434C22×C4#41×C3112yes—
435C22×C4#41×C3112yes—
436C22×C4C24×C3111yescharacteristic
437SD16—232no—
438C2×C8—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—44no—
445C2×C8C2×D4×C3114yes—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C22⋊C4—48no—
453C22⋊C4—48no—
454C42—24no—
455C42—22no—
456C42—22no—
457C23—24no—
458C23—48no—
459C23—48no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—48no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C31×#12112yes—
472C23C31×#12112yes—
473C23C31×#12112yes—
474C23C2×SD16×C3112yes—
475C23C31×#13512yes—
476C23C31×AGL(1,ℤ/8)12yes—
477C23C31×#13712yes—
478C23C22×D4×C3111yescharacteristic
479Q8—24no—
480Q8—24no—
481Q8—42no—
482Q8—42no—
483Q8—48no—
484D4—24no—
485D4—24no—
486D4—42no—
487D4—42no—
488D4—48no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—48no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—84no—
508C2×C4C31×#12014yes—
509C2×C4C31×#12112yes—
510C2×C4C31×#12112yes—
511C2×C4C31×#12112yes—
512C2×C4C31×#12314yes—
513C2×C4C31×#12314yes—
514C2×C4C31×#12414yes—
515C2×C4C2×SD16×C3114yescomplemented
516C2×C4C22×D4×C3111yescharacteristic
517C2×C4C22×D4×C3111yescharacteristic
518C2×C4C22×D4×C3111yescharacteristic
519C2×C4C2×#41×C3111yescharacteristic
520C2×C4C2×#41×C3111yescharacteristic
521C2×C4C2×#41×C3111yescharacteristic
522C8—24no—
523C8—42no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—816no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22C31×#39414yes—
533C22C31×#46014yes—
534C22C31×#46114yes—
535C22C31×#46314yes—
536C22C31×#46414yes—
537C22C31×#46514yes—
538C22C31×#46814yes—
539C22C2×C31×#12111yescharacteristic
540C22C2×C31×#12111yescharacteristic
541C22C2×C31×#12111yescharacteristic
542C22C22×SD16×C3111yescharacteristic
543C22C2×C31×#13511yescharacteristic
544C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
545C22C2×C31×#13711yescharacteristic
546C4—24no—
547C4—44no—
548C4—42no—
549C4—82no—
550C4—82no—
551C4C31×#39414yes—
552C4C2×C31×#12011yescharacteristic
553C4C2×C31×#12311yescharacteristic
554C4C2×C31×#12311yescharacteristic
555C4C2×C31×#12411yescharacteristic
556C2—84no—
557C2C31×#205518yesdirect product factor
558C2C2×C31×#39411yescharacteristic
559C2C2×C31×#46111yescharacteristic
560C2C2×C31×#46311yescharacteristic
561C2C2×C31×#46011yescharacteristic
562C2C2×C31×#46411yescharacteristic
563C2C2×C31×#46511yescharacteristic
564C2C2×C31×#46811yescharacteristic
subgroupG/H
center, socleC24×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×C4⋊C8C2semidirect
3. C22×C31×#103C2semidirect
5. C2×C31×#391C2semidirect
7. C31×#2055C2direct (N × H)
8. C2×C31×#340C2semidirect
23. C2×C31×C4⋊C8C22semidirect
25. C2×C31×#103C22semidirect
29. C31×#391C22semidirect
34. C31×#340C22semidirect
143. C22×C4×C31SD16semidirect
174. C2×#2055C31direct (N × H)
233. C2×C4×C31C2×SD16semidirect
243. C22×C4⋊C8C2×C31semidirect
244. C22×#103C2×C31semidirect
246. C2×#391C2×C31semidirect
248. #2055C2×C31direct (N × H)
249. C2×#340C2×C31semidirect
296. C2×C4⋊C8C22×C31semidirect
298. C2×#103C22×C31semidirect
302. #391C22×C31semidirect
307. #340C22×C31semidirect
309. C2×C31#2055direct (N × H)
373. C31C2×#2055direct (N × H)
426. C22×C4SD16×C31semidirect
515. C2×C4C2×SD16×C31semidirect
557. C2C31×#2055direct (N × H)

Maximal subgroups

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

subgroupindex
C23×SD16×C312
C22×C31×C4⋊C82
C22×C31×#1032
C22×C31×#1022
C2×C31×#3912
C2×C31×#3902
C31×#20552
C2×C31×#3402
C2×#205531