Finite Group Databasebeta

← C2×C31×#1899 #21477741

Subgroups — C2×C31×#1899 #21477741

Order 7936.

2066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C22×C31×#117C211yesmaximal, characteristic, complemented
3C22×C31×#99C212yesmaximal
4C2×C31×#381C211yesmaximal, characteristic, complemented
5C31×#1899C218yesmaximal, direct product factor
6C2×C31×#342C212yesmaximal, complemented
7C23×D4×C31C2211yescharacteristic
8C24×C4×C31C2211yescharacteristic
9C2×C31×#123—21no—
10C2×C31×#123—21no—
11C2×C31×#123—22no—
12C2×C31×#123—22no—
13C2×C31×#123—22no—
14C2×C31×#123C414yescomplemented
15C2×C31×#123C2214yes—
16C2×C31×#117—22no—
17C2×C31×#117—28no—
18C2×C31×#117C2214yescomplemented
19C22×C4⋊C4×C31—21no—
20C22×C4⋊C4×C31C412yescomplemented
21C22×C22⋊C4×C31C412yescomplemented
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C42×C31—21no—
26C2×C31×#99—28no—
27C2×C31×#99C2218yes—
28C31×#381—22no—
29C31×#381C2214yescomplemented
30C2×C31×#95—22no—
31C31×#342C2218yescomplemented
32C25×C31C2×C411yescharacteristic
33C25×C31C2311yescharacteristic
34C22×D4×C31—24no—
35C22×D4×C31—21no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—24no—
40C22×D4×C31C2×C412yes—
41C22×D4×C31C2312yes—
42C23×C4×C31—24no—
43C23×C4×C31—24no—
44C23×C4×C31—22no—
45C23×C4×C31—22no—
46C23×C4×C31C2×C411yescharacteristic
47C23×C4×C31C2×C412yes—
48C23×C4×C31C2×C412yes—
49C23×C4×C31C2×C412yes—
50C23×C4×C31D411yescharacteristic
51C23×C4×C31D411yescharacteristic
52C23×C4×C31D412yes—
53C23×C4×C31D412yes—
54C23×C4×C31D412yes—
55C23×C4×C31C2312yes—
56C31×#123—24no—
57C31×#123—24no—
58C31×#123—28no—
59C31×#123—28no—
60C31×#123—24no—
61C31×#123—24no—
62C31×#117—216no—
63C31×#117—216no—
64C2×C4⋊C4×C31—28no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31C2×C418yescomplemented
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—21no—
73C2×C22⋊C4×C31—21no—
74C2×C22⋊C4×C31—21no—
75C2×C22⋊C4×C31—21no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31C2×C412yes—
83C2×C22⋊C4×C31C2×C418yescomplemented
84C2×C22⋊C4×C31D418yes—
85C2×C22⋊C4×C31C2314yes—
86C2×C22⋊C4×C31C2312yes—
87C2×C22⋊C4×C31C2314yes—
88C2×C42×C31—28no—
89C2×C42×C31—24no—
90C31×#99—216no—
91C31×#95—28no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—24no—
95C24×C31—44no—
96C24×C31—44no—
97C24×C31C22×C411yescharacteristic
98C24×C31C22×C412yes—
99C24×C31C22×C411yescharacteristic
100C24×C31C2×D411yescharacteristic
101C24×C31C2×D411yescharacteristic
102C24×C31C2×D411yescharacteristic
103C24×C31C2×D411yescharacteristic
104C24×C31C2×D414yes—
105C24×C31#4114yes—
106C24×C31C2411yescharacteristic
107C2×D4×C31—22no—
108C2×D4×C31—22no—
109C2×D4×C31—28no—
110C2×D4×C31—24no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—24no—
114C2×D4×C31—42no—
115C2×D4×C31—42no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C2×D4×C31—42no—
119C2×D4×C31—42no—
120C22×C4×C31—28no—
121C22×C4×C31—28no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—24no—
125C22×C4×C31—28no—
126C22×C4×C31—28no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—24no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—24no—
137C22×C4×C31—28no—
138C22×C4×C31—24no—
139C22×C4×C31—24no—
140C22×C4×C31—48no—
141C22×C4×C31—44no—
142C22×C4×C31—48no—
143C22×C4×C31—44no—
144C22×C4×C31C22⋊C414yes—
145C22×C4×C31C22⋊C412yes—
146C22×C4×C31C22⋊C412yes—
147C22×C4×C31C22⋊C414yes—
148C22×C4×C31C22⋊C412yes—
149C22×C4×C31C22⋊C412yes—
150C22×C4×C31C22×C412yes—
151C22×C4×C31C22×C414yes—
152C22×C4×C31C22×C414yes—
153C22×C4×C31C2×D414yes—
154C22×C4×C31C2×D412yes—
155C22×C4×C31C2×D412yes—
156C4⋊C4×C31—216no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—28no—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—28no—
162C22⋊C4×C31—24no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—28no—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—44no—
170C22⋊C4×C31C2×D418yes—
171C42×C31—216no—
172C2×#1899C3111yesmaximal, characteristic, direct product factor, Sylow
173C23×C31—24no—
174C23×C31—24no—
175C23×C31—24no—
176C23×C31—22no—
177C23×C31—24no—
178C23×C31—42no—
179C23×C31—42no—
180C23×C31—42no—
181C23×C31—48no—
182C23×C31—48no—
183C23×C31—42no—
184C23×C31—44no—
185C23×C31—44no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—44no—
189C23×C31—88no—
190C23×C31C2×C22⋊C411yescharacteristic
191C23×C31C2×C22⋊C411yescharacteristic
192C23×C31C2×C22⋊C411yescharacteristic
193C23×C31C2×C22⋊C411yescharacteristic
194C23×C31C4×D414yes—
195C23×C31C4×D414yes—
196C23×C31#12012yes—
197C23×C31#12012yes—
198C23×C31#12114yes—
199C23×C31#12114yes—
200C23×C31#12312yes—
201C23×C31#12312yes—
202C23×C31C23×C411yescharacteristic
203C23×C31C22×D411yescharacteristic
204C23×C31C22×D411yescharacteristic
205C23×C31C22×D412yes—
206C23×C31C2×#4112yes—
207D4×C31—42no—
208D4×C31—44no—
209D4×C31—42no—
210D4×C31—44no—
211D4×C31—44no—
212C2×C4×C31—28no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—28no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—28no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—28no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—22no—
226C2×C4×C31—24no—
227C2×C4×C31—28no—
228C2×C4×C31—48no—
229C2×C4×C31—416no—
230C2×C4×C31—44no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—44no—
234C2×C4×C31—44no—
235C2×C4×C31—48no—
236C2×C4×C31—44no—
237C2×C4×C31—88no—
238C2×C4×C31C2×C22⋊C414yes—
239C2×C4×C31C2×C22⋊C414yes—
240C22×#123C2×C3111yescharacteristic
241C22×#117C2×C3111yescharacteristic, complemented
242C22×#99C2×C3112yes—
243C2×#381C2×C3111yescharacteristic, complemented
244#1899C2×C3118yesdirect product factor
245C2×#342C2×C3112yescomplemented
246C22×C31—22no—
247C22×C31—22no—
248C22×C31—22no—
249C22×C31—22no—
250C22×C31—22no—
251C22×C31—22no—
252C22×C31—24no—
253C22×C31—28no—
254C22×C31—28no—
255C22×C31—24no—
256C22×C31—44no—
257C22×C31—42no—
258C22×C31—44no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—44no—
263C22×C31—42no—
264C22×C31—84no—
265C22×C31—84no—
266C22×C31—84no—
267C22×C31#38612yes—
268C22×C31#38612yes—
269C22×C31#38612yes—
270C22×C31#38612yes—
271C22×C31#41014yes—
272C22×C31C22×C22⋊C411yescharacteristic
273C22×C31C2×C4×D412yes—
274C22×C31C2×#12011yescharacteristic
275C22×C31C2×#12112yes—
276C22×C31C2×#12311yescharacteristic
277C4×C31—24no—
278C4×C31—24no—
279C4×C31—48no—
280C4×C31—44no—
281C4×C31—42no—
282C4×C31—84no—
283C23×D4C22×C3111yescharacteristic
284C24×C4C22×C3111yescharacteristic
285C2×#123—21no—
286C2×#123—22no—
287C2×#123—22no—
288C2×#123—22no—
289C2×#123—21no—
290C2×#123C4×C3114yescomplemented
291C2×#123C22×C3114yes—
292C2×#117—22no—
293C2×#117—28no—
294C2×#117C22×C3114yescomplemented
295C22×C4⋊C4—21no—
296C22×C4⋊C4C4×C3112yescomplemented
297C22×C22⋊C4C4×C3112yescomplemented
298C22×C22⋊C4C22×C3112yes—
299C22×C22⋊C4C22×C3111yescharacteristic
300C22×C22⋊C4C22×C3112yes—
301C22×C42—21no—
302C2×#99—28no—
303C2×#99C22×C3118yes—
304#381—22no—
305#381C22×C3114yescomplemented
306C2×#95—22no—
307#342C22×C3118yescomplemented
308C2×C31—21no—
309C2×C31—22no—
310C2×C31—22no—
311C2×C31—22no—
312C2×C31—21no—
313C2×C31—22no—
314C2×C31—22no—
315C2×C31—82no—
316C2×C31#189914yesdirect product factor
317C2×C31C2×#38611yescharacteristic
318C2×C31C2×#41012yes—
319C25C2×C4×C3111yescharacteristic
320C25C23×C3111yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4C2×C4×C3112yes—
328C22×D4C23×C3112yes—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4C2×C4×C3111yescharacteristic
334C23×C4C2×C4×C3112yes—
335C23×C4C2×C4×C3112yes—
336C23×C4C2×C4×C3112yes—
337C23×C4D4×C3111yescharacteristic
338C23×C4D4×C3112yes—
339C23×C4D4×C3112yes—
340C23×C4D4×C3112yes—
341C23×C4D4×C3111yescharacteristic
342C23×C4C23×C3112yes—
343#123—24no—
344#123—28no—
345#123—24no—
346#123—28no—
347#123—24no—
348#123—24no—
349#117—216no—
350#117—216no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4C2×C4×C3118yescomplemented
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4C2×C4×C3112yes—
370C2×C22⋊C4C2×C4×C3118yescomplemented
371C2×C22⋊C4D4×C3118yes—
372C2×C22⋊C4C23×C3114yes—
373C2×C22⋊C4C23×C3112yes—
374C2×C22⋊C4C23×C3114yes—
375C2×C42—28no—
376C2×C42—24no—
377#99—216no—
378#95—28no—
379C31C2×#189911yescharacteristic, direct product factor, Sylow
380C24—21no—
381C24—21no—
382C24—24no—
383C24—44no—
384C24—44no—
385C24C22×C4×C3111yescharacteristic
386C24C22×C4×C3112yes—
387C24C22×C4×C3111yescharacteristic
388C24C2×D4×C3111yescharacteristic
389C24C2×D4×C3111yescharacteristic
390C24C2×D4×C3111yescharacteristic
391C24C2×D4×C3111yescharacteristic
392C24C2×D4×C3114yes—
393C24#41×C3114yes—
394C24C24×C3111yescharacteristic
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—28no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—42no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—28no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—48no—
429C22×C4—44no—
430C22×C4—48no—
431C22×C4—44no—
432C22×C4C22⋊C4×C3114yes—
433C22×C4C22⋊C4×C3112yes—
434C22×C4C22⋊C4×C3112yes—
435C22×C4C22⋊C4×C3112yes—
436C22×C4C22⋊C4×C3114yes—
437C22×C4C22⋊C4×C3112yes—
438C22×C4C22×C4×C3112yes—
439C22×C4C22×C4×C3114yes—
440C22×C4C22×C4×C3114yes—
441C22×C4C2×D4×C3114yes—
442C22×C4C2×D4×C3112yes—
443C22×C4C2×D4×C3112yes—
444C4⋊C4—216no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—28no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4C2×D4×C3118yes—
459C42—216no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—48no—
469C23—48no—
470C23—42no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—42no—
475C23—42no—
476C23—88no—
477C23C2×C22⋊C4×C3111yescharacteristic
478C23C2×C22⋊C4×C3111yescharacteristic
479C23C2×C22⋊C4×C3111yescharacteristic
480C23C2×C22⋊C4×C3111yescharacteristic
481C23C4×D4×C3114yes—
482C23C4×D4×C3114yes—
483C23C31×#12012yes—
484C23C31×#12012yes—
485C23C31×#12114yes—
486C23C31×#12114yes—
487C23C31×#12312yes—
488C23C31×#12312yes—
489C23C23×C4×C3111yescharacteristic
490C23C22×D4×C3111yescharacteristic
491C23C22×D4×C3111yescharacteristic
492C23C22×D4×C3112yes—
493C23C2×#41×C3112yes—
494D4—42no—
495D4—44no—
496D4—42no—
497D4—44no—
498D4—44no—
499C2×C4—28no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—28no—
515C2×C4—48no—
516C2×C4—416no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—44no—
524C2×C4—88no—
525C2×C4C2×C22⋊C4×C3114yes—
526C2×C4C2×C22⋊C4×C3114yes—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—24no—
534C22—28no—
535C22—28no—
536C22—24no—
537C22—44no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22—42no—
545C22—84no—
546C22—84no—
547C22—84no—
548C22C31×#38612yes—
549C22C31×#38612yes—
550C22C31×#38612yes—
551C22C31×#38612yes—
552C22C31×#41014yes—
553C22C22×C22⋊C4×C3111yescharacteristic
554C22C2×C4×D4×C3112yes—
555C22C2×C31×#12011yescharacteristic
556C22C2×C31×#12112yes—
557C22C2×C31×#12311yescharacteristic
558C4—24no—
559C4—24no—
560C4—48no—
561C4—44no—
562C4—42no—
563C4—84no—
564C2—21no—
565C2—22no—
566C2—22no—
567C2—22no—
568C2—21no—
569C2—22no—
570C2—22no—
571C2—82no—
572C2C31×#189914yesdirect product factor
573C2C2×C31×#38611yescharacteristic
574C2C2×C31×#41012yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#117C2semidirect
4. C2×C31×#381C2semidirect
5. C31×#1899C2direct (N × H)
6. C2×C31×#342C2semidirect
14. C2×C31×#123C4semidirect
18. C2×C31×#117C22semidirect
20. C22×C4⋊C4×C31C4semidirect
21. C22×C22⋊C4×C31C4semidirect
29. C31×#381C22semidirect
31. C31×#342C22semidirect
69. C2×C4⋊C4×C31C2×C4semidirect
83. C2×C22⋊C4×C31C2×C4semidirect
172. C2×#1899C31direct (N × H)
241. C22×#117C2×C31semidirect
243. C2×#381C2×C31semidirect
244. #1899C2×C31direct (N × H)
245. C2×#342C2×C31semidirect
290. C2×#123C4×C31semidirect
294. C2×#117C22×C31semidirect
296. C22×C4⋊C4C4×C31semidirect
297. C22×C22⋊C4C4×C31semidirect
305. #381C22×C31semidirect
307. #342C22×C31semidirect
316. C2×C31#1899direct (N × H)
356. C2×C4⋊C4C2×C4×C31semidirect
370. C2×C22⋊C4C2×C4×C31semidirect
379. C31C2×#1899direct (N × H)
572. C2C31×#1899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#1172
C22×C31×#992
C2×C31×#3812
C31×#18992
C2×C31×#3422
C2×#189931