Finite Group Databasebeta

← C2×#23763820 #34289929

Subgroups — C2×#23763820 #34289929

Order 20224.

2094 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
1C23×C8×D79C211yesmaximal, characteristic
2C22×#14579137C211yesmaximal, characteristic
3C22×#14579085C211yesmaximal, characteristic, complemented
4C2×#19098420C211yesmaximal, characteristic
5#23763820C218yesmaximal, direct product factor
6C2×#19098326C211yesmaximal, characteristic, complemented
7C2×#19098325C211yesmaximal, characteristic, complemented
8C22×#103×C79C211yesmaximal, characteristic, complemented
9C23×C4×D79C2211yescharacteristic
10C23×C79⋊C8C2211yescharacteristic
11C22×C8×D79—24no—
12C22×C8×D79—24no—
13C22×C8×D79—24no—
14C22×C8×D79C2214yes—
15C2×#14579137—24no—
16C2×#14579137—22no—
17C2×#14579137C418yescomplemented
18C2×#14579137C2214yes—
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4—21no—
22C22×(C2×D79)⋊C4—21no—
23C22×(C2×D79)⋊C4—21no—
24C2×#14579085—24no—
25C2×#14579085C2214yescomplemented
26#19098420—22no—
27#19098420C2214yes—
28C2×C79⋊#95—21no—
29#19098326C2214yescomplemented
30#19098325C2214yescomplemented
31C23×Q8×C79C2211yescharacteristic
32C23×C8×C79C2211yescharacteristic
33C22×C4⋊C4×C79C2211yescharacteristic
34C2×#103×C79—24no—
35C2×#103×C79C2214yescomplemented
36C24×D79D411yescharacteristic
37C23×Dic79—21no—
38C23×Dic79—21no—
39C23×Dic79D411yescharacteristic
40C22×C4×D79—22no—
41C22×C4×D79—22no—
42C22×C4×D79—22no—
43C22×C4×D79—22no—
44C22×C4×D79C2×C414yes—
45C22×C4×D79D412yes—
46C22×C4×D79D414yes—
47C22×C4×D79C2312yes—
48C22×C79⋊C8—22no—
49C22×C79⋊C8—22no—
50C22×C79⋊C8D414yes—
51C22×C79⋊C8C2312yes—
52C2×C8×D79—232no—
53C2×C8×D79—28no—
54C2×C8×D79—28no—
55C2×C8×D79—28no—
56#14579137—216no—
57#14579137—28no—
58#14579137C2×C4116yescomplemented
59C2×C4⋊Dic79—21no—
60C2×C4⋊Dic79—22no—
61C2×C4⋊Dic79—22no—
62C2×C4⋊Dic79—22no—
63C2×C4⋊Dic79—21no—
64C2×C4⋊Dic79C2×C414yes—
65C2×C4⋊Dic79C2312yes—
66C2×C4⋊Dic79C2312yes—
67C2×Dic79⋊C4—28no—
68C2×Dic79⋊C4—24no—
69C2×(C2×D79)⋊C4—28no—
70C2×(C2×D79)⋊C4—24no—
71C2×(C2×D79)⋊C4—24no—
72C2×(C2×D79)⋊C4—44no—
73#14579085—28no—
74C79⋊#95—24no—
75C22×Q8×C79—22no—
76C22×Q8×C79—21no—
77C22×Q8×C79—22no—
78C22×Q8×C79—22no—
79C22×Q8×C79—22no—
80C22×Q8×C79—22no—
81C22×Q8×C79C2×C414yes—
82C22×Q8×C79C2312yes—
83C23×C4×C79—21no—
84C23×C4×C79—21no—
85C23×C4×C79C2311yescharacteristic
86C22×C8×C79—22no—
87C22×C8×C79—22no—
88C22×C8×C79D414yes—
89C22×C8×C79C2312yes—
90C2×C4⋊C4×C79—22no—
91C2×C4⋊C4×C79—22no—
92C2×C4⋊C4×C79—21no—
93C2×C4⋊C4×C79C2312yes—
94#103×C79—28no—
95C23×D79—22no—
96C23×D79—22no—
97C23×D79—22no—
98C23×D79—22no—
99C23×D79C22⋊C414yes—
100C23×D79SD1614yes—
101C23×D79Q1614yes—
102C23×D79C2×D412yes—
103C22×Dic79—24no—
104C22×Dic79—22no—
105C22×Dic79—22no—
106C22×Dic79—22no—
107C22×Dic79—22no—
108C22×Dic79—42no—
109C22×Dic79—42no—
110C22×Dic79—42no—
111C22×Dic79—42no—
112C22×Dic79—42no—
113C22×Dic79C22⋊C414yes—
114C22×Dic79C2×D412yes—
115C2×C4×D79—28no—
116C2×C4×D79—28no—
117C2×C4×D79—28no—
118C2×C4×D79—24no—
119C2×C4×D79—24no—
120C2×C4×D79—28no—
121C2×C4×D79—22no—
122C2×C4×D79—22no—
123C2×C4×D79—22no—
124C2×C4×D79—22no—
125C2×C4×D79C22⋊C418yes—
126C2×C4×D79C22×C414yes—
127C2×C4×D79C2×D414yes—
128C2×C79⋊C8—28no—
129C2×C79⋊C8—22no—
130C2×C79⋊C8—22no—
131C2×C79⋊C8C2×D414yes—
132C8×D79—232no—
133C4⋊Dic79—24no—
134C4⋊Dic79—22no—
135C4⋊Dic79—22no—
136C4⋊Dic79—22no—
137C4⋊Dic79—42no—
138C4⋊Dic79C22×C414yes—
139Dic79⋊C4—216no—
140(C2×D79)⋊C4—216no—
141(C2×D79)⋊C4—48no—
142C24×C79C2×D411yescharacteristic
143C2×Q8×C79—24no—
144C2×Q8×C79—22no—
145C2×Q8×C79—28no—
146C2×Q8×C79—28no—
147C2×Q8×C79—22no—
148C2×Q8×C79—22no—
149C2×Q8×C79—22no—
150C2×Q8×C79—22no—
151C2×Q8×C79—44no—
152C2×Q8×C79—42no—
153C2×Q8×C79—42no—
154C2×Q8×C79—44no—
155C2×Q8×C79C22×C414yes—
156C22×C4×C79—24no—
157C22×C4×C79—22no—
158C22×C4×C79—22no—
159C22×C4×C79—42no—
160C22×C4×C79—42no—
161C22×C4×C79—42no—
162C22×C4×C79—42no—
163C22×C4×C79—42no—
164C22×C4×C79C22×C412yes—
165C22×C4×C79C2×D411yescharacteristic
166C22×C4×C79C2×D412yes—
167C22×C4×C79C2×D412yes—
168C22×C4×C79C2×D412yes—
169C22×C4×C79#4112yes—
170C22×C4×C79#4112yes—
171C22×C4×C79C2411yescharacteristic
172C2×C8×C79—28no—
173C2×C8×C79—22no—
174C2×C8×C79—22no—
175C2×C8×C79C2×D414yes—
176C4⋊C4×C79—22no—
177C4⋊C4×C79—22no—
178C4⋊C4×C79—42no—
179C23×C79C2×C22⋊C412yes—
180C23×C79#12112yes—
181C23×C79#12112yes—
182C23×C79C2×SD1612yes—
183C23×C79C2×Q1612yes—
184C23×C79#13512yes—
185C23×C79#13512yes—
186C23×C79C22×D411yescharacteristic
187C22×D79—22no—
188C22×D79—22no—
189C22×D79—22no—
190C22×D79—22no—
191C22×D79—28no—
192C22×D79—28no—
193C22×D79—28no—
194C22×D79—28no—
195C22×D79—28no—
196C22×D79—28no—
197C22×D79#103116yescomplemented
198C22×D79C2×C22⋊C414yes—
199C22×D79C2×SD1614yes—
200C22×D79C2×Q1614yes—
201Q8×C79—24no—
202Q8×C79—24no—
203Q8×C79—42no—
204Q8×C79—42no—
205Q8×C79—48no—
206C2×C4×C79—24no—
207C2×C4×C79—42no—
208C2×C4×C79—42no—
209C2×C4×C79—48no—
210C2×C4×C79—42no—
211C2×C4×C79—42no—
212C2×C4×C79—42no—
213C2×C4×C79—84no—
214C2×C4×C79C2×C22⋊C412yes—
215C2×C4×C79C4×D414yes—
216C2×C4×C79C4×D414yes—
217C2×C4×C79#12014yes—
218C2×C4×C79#12112yes—
219C2×C4×C79#12112yes—
220C2×C4×C79#12314yes—
221C2×C4×C79C23×C411yescharacteristic
222C2×C4×C79C22×D411yescharacteristic
223C2×C4×C79C22×D411yescharacteristic
224C2×C4×C79C22×D411yescharacteristic
225C2×C4×C79C2×#4111yescharacteristic
226C2×C4×C79C2×#4111yescharacteristic
227C2×Dic79—22no—
228C2×Dic79—22no—
229C2×Dic79—28no—
230C2×Dic79—24no—
231C2×Dic79—42no—
232C2×Dic79—42no—
233C2×Dic79—48no—
234C2×Dic79—42no—
235C2×Dic79—42no—
236C2×Dic79—42no—
237C2×Dic79—84no—
238C2×Dic79C2×C22⋊C414yes—
239C4×D79—24no—
240C4×D79—24no—
241C4×D79—24no—
242C4×D79—24no—
243C4×D79—216no—
244C8×C79—24no—
245C79⋊C8—24no—
246C22×C79#38614yes—
247C22×C79C2×#10314yes—
248C22×C79#41614yes—
249C22×C79#46514yes—
250C22×C79#46514yes—
251C22×C79#46714yes—
252C22×C79#46714yes—
253C22×C79C22×C22⋊C411yescharacteristic
254C22×C79C2×#12111yescharacteristic
255C22×C79C2×#12111yescharacteristic
256C22×C79C22×SD1611yescharacteristic
257C22×C79C22×Q1611yescharacteristic
258C22×C79C2×#13511yescharacteristic
259C22×C79C2×#13511yescharacteristic
260C2×D79—24no—
261C2×D79—232no—
262C2×D79—24no—
263C2×D79—24no—
264C2×D79—24no—
265C2×D79—24no—
266C2×D79—24no—
267C2×D79C2×#10318yescomplemented
268C4×C79—44no—
269C4×C79—82no—
270C4×C79#38614yes—
271C4×C79C2×C4×D411yescharacteristic
272C4×C79C2×C4×D411yescharacteristic
273C4×C79C2×#12011yescharacteristic
274C4×C79C2×#12311yescharacteristic
275Dic79—24no—
276Dic79—44no—
277Dic79—82no—
278C2×#1892—791nomaximal, Sylow
279C2×C79#189218yescomplemented
280C2×C79C2×#38611yescharacteristic
281C2×C79C22×#10311yescharacteristic
282C2×C79C2×#41611yescharacteristic
283C2×C79C2×#46511yescharacteristic
284C2×C79C2×#46511yescharacteristic
285C2×C79C2×#46711yescharacteristic
286C2×C79C2×#46711yescharacteristic
287D79—28no—
288C24×C8—791no—
289C22×C22⋊Q8—791no—
290C22×#103—791no—
291C22×#103D7911yescharacteristic, complemented
292C2×#380—791no—
293#1892—798no—
294C2×#340—791no—
295C2×#340—791no—
296C79C2×#189211yescharacteristic, complemented, Sylow
297C23×Q8C2×D7911yescharacteristic
298C24×C4—791no—
299C23×C8—791no—
300C23×C8—794no—
301C23×C8—1584no—
302C23×C8—1584no—
303C23×C8—1584no—
304C23×C8C2×D7911yescharacteristic
305C2×C22⋊Q8—794no—
306C2×C22⋊Q8—798no—
307C2×C22⋊Q8—1584no—
308C2×C22⋊Q8—1582no—
309C22×C4⋊C4—791no—
310C22×C4⋊C4—791no—
311C22×C4⋊C4—1581no—
312C22×C4⋊C4C2×D7911yescharacteristic
313C22×C22⋊C4—1581no—
314C22×C22⋊C4—1581no—
315C2×#103—24no—
316C2×#103—794no—
317C2×#103—1584no—
318C2×#103C2×D7914yescomplemented
319#380—794no—
320#380—1582no—
321C2×#95—1581no—
322#340—794no—
323#340—794no—
324C25—791no—
325C22×Q8—22no—
326C22×Q8—21no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8C4×D7914yes—
332C22×Q8C22×D7912yes—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—791no—
336C23×C4—794no—
337C23×C4—794no—
338C23×C4—792no—
339C23×C4—792no—
340C23×C4—1581no—
341C23×C4—1581no—
342C23×C4—1582no—
343C23×C4—1582no—
344C23×C4—1582no—
345C23×C4—1582no—
346C23×C4C22×D7911yescharacteristic
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—794no—
350C22×C8—792no—
351C22×C8—1588no—
352C22×C8—1588no—
353C22×C8—15832no—
354C22×C8—1582no—
355C22×C8—1582no—
356C22×C8—1588no—
357C22×C8C22⋊D7914yes—
358C22×C8C22×D7912yes—
359C22⋊Q8—7916no—
360C22⋊Q8—15816no—
361C22⋊Q8—1588no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—794no—
366C2×C4⋊C4—792no—
367C2×C4⋊C4—792no—
368C2×C4⋊C4—1581no—
369C2×C4⋊C4—1582no—
370C2×C4⋊C4—1582no—
371C2×C4⋊C4—1588no—
372C2×C4⋊C4—1584no—
373C2×C4⋊C4—1581no—
374C2×C4⋊C4—1582no—
375C2×C4⋊C4C22×D7912yes—
376C2×C22⋊C4—3164no—
377C2×C22⋊C4—1584no—
378C2×C22⋊C4—1588no—
379C2×C22⋊C4—1584no—
380#103—28no—
381#103—1588no—
382#95—1584no—
383C24—794no—
384C24—794no—
385C24—794no—
386C24—792no—
387C24—1582no—
388C24—1582no—
389C24—1582no—
390C24—1582no—
391C24D4×D7911yescharacteristic
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—44no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—44no—
404C2×Q8C2×C4×D7914yes—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—3162no—
414C22×C4—3162no—
415C22×C4—3162no—
416C22×C4—3162no—
417C22×C4—3162no—
418C22×C4—794no—
419C22×C4—792no—
420C22×C4—798no—
421C22×C4—794no—
422C22×C4—794no—
423C22×C4—1582no—
424C22×C4—1584no—
425C22×C4—1582no—
426C22×C4—1582no—
427C22×C4—1582no—
428C22×C4—1582no—
429C22×C4—1582no—
430C22×C4—1588no—
431C22×C4—1588no—
432C22×C4—1588no—
433C22×C4—1584no—
434C22×C4—1584no—
435C22×C4—1588no—
436C22×C4—1582no—
437C22×C4—1582no—
438C22×C4C2×C4×D7912yes—
439C22×C4D4×D7911yescharacteristic
440C22×C4D4×D7912yes—
441C22×C4D4×D7912yes—
442C22×C4C2×C22⋊D7912yes—
443C22×C4#1192962312yes—
444C22×C4#1192962412yes—
445C22×C4C23×D7911yescharacteristic
446C2×C8—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—794no—
450C2×C8—15832no—
451C2×C8—1588no—
452C2×C8—1582no—
453C2×C8—1582no—
454C2×C8C2×C22⋊D7914yes—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—3162no—
459C4⋊C4—794no—
460C4⋊C4—15816no—
461C4⋊C4—1582no—
462C4⋊C4—1582no—
463C4⋊C4—1584no—
464C4⋊C4—1582no—
465C22⋊C4—3168no—
466C22⋊C4—15816no—
467C23—794no—
468C23—7916no—
469C23—794no—
470C23—794no—
471C23—1588no—
472C23—1588no—
473C23—1588no—
474C23—1582no—
475C23—1582no—
476C23—1588no—
477C23—1588no—
478C23—1588no—
479C23—1582no—
480C23—1582no—
481C23C22⋊C4×D7912yes—
482C23#1457913212yes—
483C23#1457913412yes—
484C23SD16×D7912yes—
485C23Q16×D7912yes—
486C23#1457918212yes—
487C23#1457918412yes—
488C23C2×D4×D7911yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—48no—
492Q8—42no—
493Q8—42no—
494C2×C4—24no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4—3168no—
503C2×C4—3162no—
504C2×C4—3162no—
505C2×C4—3162no—
506C2×C4—3162no—
507C2×C4—3162no—
508C2×C4—794no—
509C2×C4—6324no—
510C2×C4—1584no—
511C2×C4—1588no—
512C2×C4—1582no—
513C2×C4—1582no—
514C2×C4—15816no—
515C2×C4—1584no—
516C2×C4—1584no—
517C2×C4—1584no—
518C2×C4—1584no—
519C2×C4C22⋊C4×D7912yes—
520C2×C4(C22⋊D79)⋊C414yes—
521C2×C4C4×C22⋊D7914yes—
522C2×C4#1457912914yes—
523C2×C4#1457913212yes—
524C2×C4#1457913412yes—
525C2×C4#1457914314yes—
526C2×C4C22×C4×D7911yescharacteristic
527C2×C4C2×D4×D7911yescharacteristic
528C2×C4C2×D4×D7911yescharacteristic
529C2×C4C22×C22⋊D7911yescharacteristic
530C2×C4C2×#1192962311yescharacteristic
531C2×C4C2×#1192962411yescharacteristic
532C8—24no—
533C8—1584no—
534C22—798no—
535C22—1584no—
536C22—1584no—
537C22—1584no—
538C22—1584no—
539C22—1584no—
540C22—15832no—
541C22—1584no—
542C22#1909843914yes—
543C22#103×D7914yes—
544C22#1909855814yes—
545C22#1909878914yes—
546C22#1909879514yes—
547C22#1909880114yes—
548C22#1909880314yes—
549C22C2×C22⋊C4×D7911yescharacteristic
550C22C2×#1457913211yescharacteristic
551C22C2×#1457913411yescharacteristic
552C22C2×SD16×D7911yescharacteristic
553C22C2×Q16×D7911yescharacteristic
554C22C2×#1457918211yescharacteristic
555C22C2×#1457918411yescharacteristic
556C4—44no—
557C4—82no—
558C4—3164no—
559C4—6322no—
560C4—1584no—
561C4#1909843914yes—
562C4C2×(C22⋊D79)⋊C411yescharacteristic
563C4C2×C4×C22⋊D7911yescharacteristic
564C4C2×#1457912911yescharacteristic
565C4C2×#1457914311yescharacteristic
566C2—1588no—
567C2#2376382018yesdirect product factor
568C2C2×#1909843911yescharacteristic
569C2C2×#103×D7911yescharacteristic
570C2C2×#1909855811yescharacteristic
571C2C2×#1909878911yescharacteristic
572C2C2×#1909879511yescharacteristic
573C2C2×#1909880111yescharacteristic
574C2C2×#1909880311yescharacteristic
subgroupG/H
centerC24D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×#103×C79C2
socleC24×C79C2×D4
prime radicalC24×D79D4
cosocleC22×C4×C79C24
hypercenterC22×#103D79
hypocenterC79C2×#1892
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C22×#14579085C2semidirect
5. #23763820C2direct (N × H)
6. C2×#19098326C2semidirect
7. C2×#19098325C2semidirect
8. C22×#103×C79C2semidirect
17. C2×#14579137C4semidirect
25. C2×#14579085C22semidirect
29. #19098326C22semidirect
30. #19098325C22semidirect
35. C2×#103×C79C22semidirect
58. #14579137C2×C4semidirect
197. C22×D79#103semidirect
267. C2×D79C2×#103semidirect
279. C2×C79#1892semidirect
291. C22×#103D79semidirect
296. C79C2×#1892semidirect
318. C2×#103C2×D79semidirect
567. C2#23763820direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D792
C22×#145791372
C22×#145790852
C2×#190984202
#237638202
C2×#190983262
C2×#190983252
C22×#103×C792
C2×#189279