Finite Group Databasebeta

← C2×#23763634 #34289132

Subgroups — C2×#23763634 #34289132

Order 20224.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099043C211yesmaximal, characteristic
2C2×#19098606C211yesmaximal, characteristic, complemented
3C22×#14579089C211yesmaximal, characteristic
4C2×#19098565C211yesmaximal, characteristic
5C2×#19098429C211yesmaximal, characteristic, complemented
6#23763634C218yesmaximal, direct product factor
7C2×#19098331C211yesmaximal, characteristic, complemented
8C2×#339×C79C211yesmaximal, characteristic, complemented
9C22×#11929624C2211yescharacteristic
10C22×#11929608C2211yescharacteristic
11#19099043—22no—
12#19099043—22no—
13#19099043—22no—
14#19099043C2214yes—
15C2×C4×Dic158—21no—
16C2×C4×D316—21no—
17C2×(C22⋊D79)⋊C4—22no—
18C2×#14579119—21no—
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊C4×D79—21no—
22#19098606—22no—
23#19098606C2214yescomplemented
24C2×#14579094—21no—
25C2×#14579092—21no—
26C2×#14579089C418yescomplemented
27C2×#14579089C2214yes—
28#19098565—22no—
29#19098565C2214yes—
30C2×#14579086—21no—
31C2×#14579083—21no—
32#19098429—22no—
33#19098429C2214yescomplemented
34C2×C79⋊#95—22no—
35#19098331C2214yescomplemented
36C22×M16×C79C2211yescharacteristic
37C2×#117×C79C2211yescharacteristic
38C22×C42×C79C2211yescharacteristic
39#339×C79C2214yescomplemented
40C2×#11929624—21no—
41C2×#11929624—21no—
42C2×#11929624—22no—
43C2×#11929624—22no—
44C2×#11929624C2×C414yes—
45C2×#11929624D412yes—
46C2×#11929624Q814yes—
47C2×#11929624C2312yes—
48C22×Dic158D411yescharacteristic
49C22×D316D411yescharacteristic
50C22×C22⋊D79—21no—
51C23×Dic79—21no—
52C23×Dic79D412yes—
53C22×C4×D79—21no—
54C22×C4×D79—22no—
55C2×#11929608—21no—
56C2×#11929608—22no—
57C2×#11929608C2×C414yescomplemented
58C2×#11929608C2312yes—
59C22×C79⋊C8—21no—
60C4×Dic158—24no—
61C4×Dic158—24no—
62C4×D316—24no—
63C4×D316—24no—
64(C22⋊D79)⋊C4—28no—
65(C22⋊D79)⋊C4—28no—
66#14579119—24no—
67#14579119—24no—
68C2×C4⋊Dic79—21no—
69C2×C4⋊Dic79—21no—
70C2×C4⋊Dic79—21no—
71C2×C4⋊Dic79—21no—
72C2×C4⋊Dic79—21no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79D412yes—
78C2×C4⋊Dic79C2312yes—
79C2×C4⋊Dic79C2312yes—
80C2×Dic79⋊C4—22no—
81C4⋊C4×D79—24no—
82C4⋊C4×D79—24no—
83C2×(C2×D79)⋊C4—22no—
84C2×C4×Dic79—22no—
85#14579094—24no—
86#14579092—24no—
87#14579089C2×C4116yescomplemented
88#14579086—24no—
89#14579083—24no—
90C79⋊#95—28no—
91C23×C4×C79—21no—
92C23×C4×C79C2311yescharacteristic
93C2×M16×C79—21no—
94C2×M16×C79—22no—
95C2×M16×C79—22no—
96C2×M16×C79C2312yes—
97C22×C8×C79—21no—
98#117×C79—21no—
99#117×C79—21no—
100#117×C79D412yes—
101#117×C79C2312yes—
102C2×C4⋊C4×C79D411yescharacteristic
103C2×C4⋊C4×C79D411yescharacteristic
104C2×C22⋊C4×C79—21no—
105C2×C42×C79—21no—
106C2×C42×C79—21no—
107C2×C42×C79—22no—
108C2×C42×C79C2×C414yescomplemented
109C2×C42×C79C2312yes—
110C23×D79—21no—
111#11929624—24no—
112#11929624—24no—
113#11929624—24no—
114#11929624—24no—
115#11929624—24no—
116#11929624—22no—
117#11929624—22no—
118#11929624C4⋊C418yes—
119#11929624C22×C414yes—
120#11929624C2×Q814yes—
121C2×Dic158—21no—
122C2×Dic158—22no—
123C2×Dic158C4⋊C414yes—
124C2×Dic158C2×D412yes—
125C2×D316—21no—
126C2×D316—22no—
127C2×D316C4⋊C414yes—
128C2×D316C2×D412yes—
129C2×C22⋊D79—24no—
130C2×C22⋊D79—22no—
131C2×C22⋊D79—24no—
132C2×C22⋊D79—22no—
133C22×Dic79—21no—
134C22×Dic79—22no—
135C22×Dic79—22no—
136C22×Dic79—22no—
137C22×Dic79—44no—
138C22×Dic79—44no—
139C22×Dic79—41no—
140C22×Dic79—41no—
141C22×Dic79C2×D414yes—
142C2×C4×D79—28no—
143C2×C4×D79—24no—
144C2×C4×D79—22no—
145C2×C4×D79—24no—
146C2×C4×D79—22no—
147C2×C4×D79—84no—
148#11929608—24no—
149#11929608—22no—
150#11929608C22×C414yescomplemented
151C2×C79⋊C8—24no—
152C2×C79⋊C8—22no—
153C4⋊Dic79—22no—
154C4⋊Dic79—22no—
155C4⋊Dic79—22no—
156C4⋊Dic79—22no—
157C4⋊Dic79—22no—
158C4⋊Dic79—22no—
159C4⋊Dic79—41no—
160C4⋊Dic79—41no—
161Dic79⋊C4—28no—
162(C2×D79)⋊C4—28no—
163C4×Dic79—28no—
164C24×C79C2×D411yescharacteristic
165C22×C4×C79—24no—
166C22×C4×C79—21no—
167C22×C4×C79—21no—
168C22×C4×C79—22no—
169C22×C4×C79—42no—
170C22×C4×C79—42no—
171C22×C4×C79C22×C412yes—
172C22×C4×C79C2×D411yescharacteristic
173C22×C4×C79C2×D411yescharacteristic
174C22×C4×C79C2×D411yescharacteristic
175C22×C4×C79C2×D411yescharacteristic
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×Q812yes—
178C22×C4×C79#4112yes—
179C22×C4×C79#4112yes—
180C22×C4×C79C2411yescharacteristic
181M16×C79—22no—
182M16×C79—22no—
183M16×C79—42no—
184C2×C8×C79—22no—
185C2×C8×C79—42no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—21no—
188C4⋊C4×C79C2×D412yes—
189C4⋊C4×C79C2×D412yes—
190C22⋊C4×C79—22no—
191C22⋊C4×C79—22no—
192C42×C79—24no—
193C42×C79—22no—
194C42×C79—22no—
195C42×C79—22no—
196C42×C79C22×C414yescomplemented
197C23×C79—22no—
198C23×C79—22no—
199C23×C79C4×D412yes—
200C23×C79#12011yescharacteristic
201C23×C79#12011yescharacteristic
202C23×C79C22⋊Q812yes—
203C23×C79C22×D411yescharacteristic
204C22×D79—22no—
205C22×D79—24no—
206C22×D79—42no—
207C22×D79—42no—
208C2×C4×C79—24no—
209C2×C4×C79—22no—
210C2×C4×C79—22no—
211C2×C4×C79—48no—
212C2×C4×C79—42no—
213C2×C4×C79—42no—
214C2×C4×C79—42no—
215C2×C4×C79—42no—
216C2×C4×C79C2×C4⋊C412yes—
217C2×C4×C79C2×C4⋊C412yes—
218C2×C4×C79C4×D412yes—
219C2×C4×C79C4×D412yes—
220C2×C4×C79C4×D412yes—
221C2×C4×C79#12011yescharacteristic
222C2×C4×C79#12011yescharacteristic
223C2×C4×C79C22⋊Q812yes—
224C2×C4×C79C22⋊Q812yes—
225C2×C4×C79C22⋊Q812yes—
226C2×C4×C79#12312yes—
227C2×C4×C79#12312yes—
228C2×C4×C79C23×C411yescharacteristic
229C2×C4×C79C22×D411yescharacteristic
230C2×C4×C79C22×D411yescharacteristic
231C2×C4×C79C22×Q811yescharacteristic
232C2×C4×C79C2×#4111yescharacteristic
233C2×C4×C79C2×#4111yescharacteristic
234C22⋊D79—24no—
235C22⋊D79—24no—
236C22⋊D79—28no—
237C2×Dic79—22no—
238C2×Dic79—24no—
239C2×Dic79—24no—
240C2×Dic79—44no—
241C2×Dic79—44no—
242C2×Dic79—44no—
243C2×Dic79—42no—
244C2×Dic79—82no—
245C2×Dic79—82no—
246C2×Dic79—82no—
247D316—22no—
248D316—24no—
249D316C2×C4⋊C414yes—
250C4×D79—24no—
251C4×D79—24no—
252C4×D79—28no—
253C4×D79—88no—
254Dic158—22no—
255Dic158—24no—
256Dic158C2×C4⋊C414yes—
257C8×C79—42no—
258C79⋊C8—24no—
259C22×C79—24no—
260C22×C79—24no—
261C22×C79—21no—
262C22×C79—21no—
263C22×C79—21no—
264C22×C79—21no—
265C22×C79#38512yes—
266C22×C79#38512yes—
267C22×C79#45412yes—
268C22×C79#45512yes—
269C22×C79C2×C4×D411yescharacteristic
270C22×C79C2×#12011yescharacteristic
271C22×C79C2×C22⋊Q811yescharacteristic
272C2×D79—24no—
273C2×D79—48no—
274C2×D79—42no—
275C2×D79—42no—
276C4×C79—44no—
277C4×C79—42no—
278C4×C79—42no—
279C4×C79#38512yes—
280C4×C79#38512yes—
281C4×C79C22×C4⋊C411yescharacteristic
282C4×C79C2×C4×D411yescharacteristic
283C4×C79C2×C22⋊Q811yescharacteristic
284C4×C79C2×#12311yescharacteristic
285Dic79—24no—
286Dic79—44no—
287Dic79—82no—
288C2×#1860—791nomaximal, Sylow
289C2×C79—21no—
290C2×C79—21no—
291C2×C79—22no—
292C2×C79#186014yescomplemented
293C2×C79C2×#38511yescharacteristic
294C2×C79C2×#45511yescharacteristic
295C2×C79C2×#45411yescharacteristic
296D79—44no—
297C2×#520—791no—
298C2×#428—791no—
299C22×#104—791no—
300C2×#417—791no—
301C2×#382—791no—
302#1860—798no—
303C2×#343—791no—
304C2×#339D7911yescharacteristic, complemented
305C79C2×#186011yescharacteristic, complemented, Sylow
306C22×#41—791no—
307C22×M16—791no—
308C22×M16C2×D7911yescharacteristic
309#520—794no—
310#520—1582no—
311#520—1582no—
312#520—1582no—
313C2×C4×Q8—1581no—
314C2×C4×D4—1581no—
315C2×C4×D4—1582no—
316C2×#117—1581no—
317C2×#117C2×D7911yescharacteristic
318C22×C4⋊C4—791no—
319C22×C4⋊C4—791no—
320C22×C4⋊C4—1581no—
321C22×C42C2×D7911yescharacteristic
322#428—794no—
323#428—1582no—
324C2×#107—1581no—
325C2×#106—1581no—
326C2×#104—794no—
327C2×#104—798no—
328#417—794no—
329#417—1582no—
330C2×#103—1581no—
331C2×#102—1581no—
332#382—794no—
333#382—1582no—
334C2×#95—1582no—
335#343—794no—
336#339C2×D7914yescomplemented
337C2×#41—794no—
338C2×#41—792no—
339C2×#41—794no—
340C2×#41—792no—
341C2×#41—1581no—
342C2×#41—1581no—
343C2×#41—1582no—
344C2×#41—1582no—
345C22×Q8—791no—
346C22×D4—791no—
347C22×D4—1581no—
348C23×C4—21no—
349C23×C4—792no—
350C23×C4—1582no—
351C23×C4—1581no—
352C23×C4—1581no—
353C23×C4C22×D7911yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—794no—
358C2×M16—792no—
359C2×M16—1581no—
360C2×M16—1582no—
361C2×M16C22×D7912yes—
362C22×C8—21no—
363C22×C8—1581no—
364C4×Q8—1584no—
365C4×Q8—1584no—
366C4×D4—1584no—
367C4×D4—1584no—
368C4×D4—1588no—
369C4×D4—1588no—
370#117—21no—
371#117—21no—
372#117—1584no—
373#117—1584no—
374#117D31612yes—
375#117C22×D7912yes—
376C2×C4⋊C4—792no—
377C2×C4⋊C4—792no—
378C2×C4⋊C4—792no—
379C2×C4⋊C4—1584no—
380C2×C4⋊C4—1581no—
381C2×C4⋊C4—1581no—
382C2×C4⋊C4—1581no—
383C2×C4⋊C4—1581no—
384C2×C4⋊C4—1581no—
385C2×C4⋊C4—1582no—
386C2×C4⋊C4—1581no—
387C2×C4⋊C4—1581no—
388C2×C4⋊C4—1581no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1584no—
391C2×C4⋊C4D31611yescharacteristic
392C2×C4⋊C4D31611yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—1582no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—22no—
398C2×C42—1582no—
399C2×C42C4×D7914yescomplemented
400C2×C42C22×D7912yes—
401#107—1584no—
402#106—1584no—
403#104—7916no—
404#103—1584no—
405#102—1584no—
406#95—1588no—
407C24—1581no—
408C24D4×D7911yescharacteristic
409#41—794no—
410#41—798no—
411#41—794no—
412#41—1582no—
413#41—1582no—
414#41—1584no—
415#41—1584no—
416#41—1584no—
417#41—1584no—
418#41—1584no—
419C2×Q8—794no—
420C2×Q8—792no—
421C2×Q8—1581no—
422C2×Q8—1582no—
423C2×D4—794no—
424C2×D4—792no—
425C2×D4—1584no—
426C2×D4—1582no—
427C2×D4—1584no—
428C2×D4—1582no—
429C2×D4—1581no—
430C2×D4—1582no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—3164no—
438C22×C4—3164no—
439C22×C4—3161no—
440C22×C4—3161no—
441C22×C4—794no—
442C22×C4—6324no—
443C22×C4—1588no—
444C22×C4—1582no—
445C22×C4—1582no—
446C22×C4—1582no—
447C22×C4—1581no—
448C22×C4—1584no—
449C22×C4—1582no—
450C22×C4—1584no—
451C22×C4—1582no—
452C22×C4C2×C4×D7912yes—
453C22×C4D4×D7911yescharacteristic
454C22×C4D4×D7911yescharacteristic
455C22×C4D4×D7911yescharacteristic
456C22×C4C2×D31611yescharacteristic
457C22×C4C2×D31611yescharacteristic
458C22×C4Q8×D7912yes—
459C22×C4#1192962312yes—
460C22×C4#1192962412yes—
461C22×C4C23×D7911yescharacteristic
462M16—22no—
463M16—22no—
464M16—42no—
465M16—794no—
466M16—1582no—
467M16—1584no—
468C2×C8—22no—
469C2×C8—42no—
470C2×C8—1584no—
471C2×C8—1582no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—3161no—
475C4⋊C4—3161no—
476C4⋊C4—1588no—
477C4⋊C4—1582no—
478C4⋊C4—1582no—
479C4⋊C4—1582no—
480C4⋊C4—1582no—
481C4⋊C4—1582no—
482C4⋊C4—1582no—
483C4⋊C4C2×D31612yes—
484C4⋊C4C2×D31612yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—1588no—
488C42—22no—
489C42—24no—
490C42—22no—
491C42—22no—
492C42—1588no—
493C42C2×C4×D7914yescomplemented
494C23—22no—
495C23—22no—
496C23—3162no—
497C23—3162no—
498C23—1584no—
499C23—1582no—
500C23(C22⋊D79)⋊C412yes—
501C23#1457913111yescharacteristic
502C23#1457913111yescharacteristic
503C23#1457913912yes—
504C23C2×D4×D7911yescharacteristic
505Q8—794no—
506Q8—1584no—
507Q8—1582no—
508D4—794no—
509D4—1588no—
510D4—1584no—
511D4—1584no—
512D4—1584no—
513D4—1582no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—48no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—3164no—
523C2×C4—3164no—
524C2×C4—3164no—
525C2×C4—3162no—
526C2×C4—6328no—
527C2×C4—6322no—
528C2×C4—6322no—
529C2×C4—6322no—
530C2×C4—1584no—
531C2×C4—1584no—
532C2×C4—1582no—
533C2×C4—1588no—
534C2×C4—1584no—
535C2×C4—1584no—
536C2×C4C4⋊C4×D7912yes—
537C2×C4C4⋊C4×D7912yes—
538C2×C4(C22⋊D79)⋊C412yes—
539C2×C4C4×D31612yes—
540C2×C4C4×D31612yes—
541C2×C4#1457913111yescharacteristic
542C2×C4#1457913111yescharacteristic
543C2×C4#1457913912yes—
544C2×C4#1457914112yes—
545C2×C4#1457914112yes—
546C2×C4#1457914312yes—
547C2×C4#1457914312yes—
548C2×C4C22×C4×D7911yescharacteristic
549C2×C4C2×D4×D7911yescharacteristic
550C2×C4C22×D31611yescharacteristic
551C2×C4C2×Q8×D7911yescharacteristic
552C2×C4C2×#1192962311yescharacteristic
553C2×C4C2×#1192962411yescharacteristic
554C8—42no—
555C8—1584no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—3162no—
563C22—3162no—
564C22—3168no—
565C22—1584no—
566C22#1909843712yes—
567C22#1909843712yes—
568C22#1909873712yes—
569C22#1909874212yes—
570C22C2×(C22⋊D79)⋊C411yescharacteristic
571C22C2×#1457913111yescharacteristic
572C22C2×#1457913911yescharacteristic
573C4—44no—
574C4—42no—
575C4—42no—
576C4—3164no—
577C4—6322no—
578C4—1584no—
579C4#1909843712yes—
580C4#1909843712yes—
581C4C2×C4⋊C4×D7911yescharacteristic
582C4C2×C4×D31611yescharacteristic
583C4C2×#1457914111yescharacteristic
584C4C2×#1457914311yescharacteristic
585C2—21no—
586C2—22no—
587C2—21no—
588C2—3164no—
589C2#2376363414yesdirect product factor
590C2C2×#1909843711yescharacteristic
591C2C2×#1909874211yescharacteristic
592C2C2×#1909873711yescharacteristic
subgroupG/H
centerC23#14579131
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#339×C79C2
socleC23×C79#120
prime radicalC22×#11929624C22
cosocleC22×C4×C79C24
hypercenterC2×#339D79
hypocenterC79C2×#1860
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. C2×#19098606C2semidirect
5. C2×#19098429C2semidirect
6. #23763634C2direct (N × H)
7. C2×#19098331C2semidirect
8. C2×#339×C79C2semidirect
23. #19098606C22semidirect
26. C2×#14579089C4semidirect
33. #19098429C22semidirect
35. #19098331C22semidirect
39. #339×C79C22semidirect
57. C2×#11929608C2×C4semidirect
87. #14579089C2×C4semidirect
108. C2×C42×C79C2×C4semidirect
150. #11929608C22×C4semidirect
196. C42×C79C22×C4semidirect
292. C2×C79#1860semidirect
304. C2×#339D79semidirect
305. C79C2×#1860semidirect
336. #339C2×D79semidirect
399. C2×C42C4×D79semidirect
493. C42C2×C4×D79semidirect
589. C2#23763634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990432
C2×#190986062
C22×#145790892
C2×#190985652
C2×#190984292
#237636342
C2×#190983312
C2×#339×C792
C2×#186079