Finite Group Databasebeta

← C2×#23764580 #34315715

Subgroups — C2×#23764580 #34315715

Order 20224.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579132C211yesmaximal, characteristic
2C22×#14579094C211yesmaximal, characteristic, complemented
3C22×#14579082C211yesmaximal, characteristic, complemented
4C22×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
5C2×#19098420C211yesmaximal, characteristic, complemented
6#23764580C218yesmaximal, direct product factor
7C2×#19098326C211yesmaximal, characteristic, complemented
8C22×#102×C79C211yesmaximal, characteristic, complemented
9C23×C22⋊D79—21no—
10C23×C4×D79C2211yescharacteristic
11C23×C79⋊C8C2211yescharacteristic
12C2×#14579132—22no—
13C2×#14579132—24no—
14C2×#14579132—24no—
15C2×#14579132C2214yes—
16C22×C4⋊Dic79C2211yescharacteristic
17C22×C4⋊Dic79C2211yescharacteristic
18C22×C22⋊Dic79—21no—
19C22×(C2×D79)⋊C4—21no—
20C2×#14579094—24no—
21C2×#14579094C2214yescomplemented
22C2×#14579082—24no—
23C2×#14579082C2214yescomplemented
24C2×(C2×D79)⋊C8—24no—
25C2×(C2×D79)⋊C8C2214yescomplemented
26#19098420—22no—
27#19098420C2214yescomplemented
28C2×C79⋊#95—21no—
29#19098326C2214yescomplemented
30C23×D4×C79C2211yescharacteristic
31C23×C8×C79C2211yescharacteristic
32C22×C4⋊C4×C79C2211yescharacteristic
33C2×#102×C79—24no—
34C2×#102×C79C2214yescomplemented
35C24×D79D411yescharacteristic
36C22×C22⋊D79—28no—
37C22×C22⋊D79—24no—
38C22×C22⋊D79—44no—
39C22×C22⋊D79—44no—
40C23×Dic79—21no—
41C23×Dic79—21no—
42C23×Dic79D411yescharacteristic
43C22×C4×D79—22no—
44C22×C4×D79—22no—
45C22×C4×D79—22no—
46C22×C4×D79—22no—
47C22×C4×D79—22no—
48C22×C4×D79—22no—
49C22×C4×D79D412yes—
50C22×C4×D79C2312yes—
51C22×C79⋊C8—22no—
52C22×C79⋊C8—22no—
53C22×C79⋊C8D414yescomplemented
54C22×C79⋊C8C2312yes—
55#14579132—216no—
56#14579132—28no—
57#14579132—28no—
58C2×C4⋊Dic79—21no—
59C2×C4⋊Dic79—22no—
60C2×C4⋊Dic79—22no—
61C2×C4⋊Dic79—22no—
62C2×C4⋊Dic79—21no—
63C2×C4⋊Dic79D414yes—
64C2×C4⋊Dic79C2312yes—
65C2×C4⋊Dic79C2312yes—
66C2×C22⋊Dic79—28no—
67C2×C22⋊Dic79—24no—
68C2×(C2×D79)⋊C4—24no—
69C2×(C2×D79)⋊C4—44no—
70#14579094—28no—
71#14579082—28no—
72(C2×D79)⋊C8—28no—
73C79⋊#95—24no—
74C25×C79—21no—
75C22×D4×C79—22no—
76C22×D4×C79—21no—
77C22×D4×C79—22no—
78C22×D4×C79—22no—
79C22×D4×C79—22no—
80C22×D4×C79—22no—
81C22×D4×C79D414yes—
82C22×D4×C79C2312yes—
83C23×C4×C79—21no—
84C23×C4×C79C2311yescharacteristic
85C22×C8×C79—22no—
86C22×C8×C79—22no—
87C22×C8×C79—22no—
88C22×C8×C79C2312yes—
89C2×C4⋊C4×C79—22no—
90C2×C4⋊C4×C79—22no—
91C2×C4⋊C4×C79—21no—
92C2×C4⋊C4×C79C2312yes—
93#102×C79—28no—
94C23×D79—22no—
95C23×D79—22no—
96C23×D79—22no—
97C23×D79—22no—
98C23×D79—22no—
99C23×D79—22no—
100C23×D79D814yes—
101C23×D79C2×D412yes—
102C2×C22⋊D79—216no—
103C2×C22⋊D79—48no—
104C2×C22⋊D79—432no—
105C2×C22⋊D79—48no—
106C22×Dic79—22no—
107C22×Dic79—24no—
108C22×Dic79—22no—
109C22×Dic79—22no—
110C22×Dic79—22no—
111C22×Dic79—22no—
112C22×Dic79—42no—
113C22×Dic79—42no—
114C22×Dic79—42no—
115C22×Dic79—42no—
116C22×Dic79—42no—
117C22×Dic79C2×D412yes—
118C2×C4×D79—24no—
119C2×C4×D79—24no—
120C2×C4×D79—24no—
121C2×C4×D79—22no—
122C2×C4×D79—22no—
123C2×C4×D79—22no—
124C2×C4×D79—22no—
125C2×C4×D79—22no—
126C2×C4×D79—22no—
127C2×C4×D79—44no—
128C2×C4×D79—44no—
129C2×C4×D79—44no—
130C2×C4×D79—44no—
131C2×C79⋊C8—28no—
132C2×C79⋊C8—22no—
133C2×C79⋊C8—22no—
134C2×C79⋊C8C2×D414yescomplemented
135C4⋊Dic79—24no—
136C4⋊Dic79—22no—
137C4⋊Dic79—22no—
138C4⋊Dic79—22no—
139C4⋊Dic79—42no—
140C4⋊Dic79C2×D414yes—
141C22⋊Dic79—216no—
142(C2×D79)⋊C4—48no—
143C24×C79—24no—
144C24×C79—22no—
145C24×C79—42no—
146C24×C79—42no—
147C24×C79—42no—
148C24×C79—42no—
149C24×C79—42no—
150C24×C79—42no—
151C24×C79C2×D411yescharacteristic
152C2×D4×C79—24no—
153C2×D4×C79—28no—
154C2×D4×C79—28no—
155C2×D4×C79—22no—
156C2×D4×C79—22no—
157C2×D4×C79—22no—
158C2×D4×C79—22no—
159C2×D4×C79—22no—
160C2×D4×C79—44no—
161C2×D4×C79—42no—
162C2×D4×C79—42no—
163C2×D4×C79—44no—
164C2×D4×C79C2×D414yes—
165C22×C4×C79—22no—
166C22×C4×C79—42no—
167C22×C4×C79—42no—
168C22×C4×C79—42no—
169C22×C4×C79C2×D411yescharacteristic
170C22×C4×C79C2×D412yes—
171C22×C4×C79C2×D412yes—
172C22×C4×C79C2×D412yes—
173C22×C4×C79#4112yes—
174C22×C4×C79#4112yes—
175C22×C4×C79#4112yes—
176C22×C4×C79C2411yescharacteristic
177C2×C8×C79—22no—
178C2×C8×C79—22no—
179C2×C8×C79—22no—
180C2×C8×C79—44no—
181C4⋊C4×C79—22no—
182C4⋊C4×C79—22no—
183C4⋊C4×C79—42no—
184C23×C79—24no—
185C23×C79—42no—
186C23×C79—42no—
187C23×C79—42no—
188C23×C79—42no—
189C23×C79—42no—
190C23×C79—42no—
191C23×C79—48no—
192C23×C79—48no—
193C23×C79—48no—
194C23×C79—84no—
195C23×C79—84no—
196C23×C79—84no—
197C23×C79—84no—
198C23×C79#12012yes—
199C23×C79#12112yes—
200C23×C79#12312yes—
201C23×C79C2×D812yes—
202C23×C79#13512yes—
203C23×C79AGL(1,ℤ/8)12yes—
204C23×C79#13712yes—
205C23×C79C22×D411yescharacteristic
206C22×D79—22no—
207C22×D79—22no—
208C22×D79—22no—
209C22×D79—22no—
210C22×D79—22no—
211C22×D79—22no—
212C22×D79—28no—
213C22×D79—28no—
214C22×D79—28no—
215C22×D79—44no—
216C22×D79—44no—
217C22×D79—44no—
218C22×D79—44no—
219C22×D79C2×D814yes—
220D4×C79—24no—
221D4×C79—24no—
222D4×C79—42no—
223D4×C79—42no—
224D4×C79—48no—
225C2×C4×C79—42no—
226C2×C4×C79—42no—
227C2×C4×C79—42no—
228C2×C4×C79—84no—
229C2×C4×C79#12012yes—
230C2×C4×C79#12114yes—
231C2×C4×C79#12114yes—
232C2×C4×C79#12112yes—
233C2×C4×C79#12312yes—
234C2×C4×C79#12314yes—
235C2×C4×C79#12414yes—
236C2×C4×C79C22×D411yescharacteristic
237C2×C4×C79C22×D411yescharacteristic
238C2×C4×C79C22×D411yescharacteristic
239C2×C4×C79C2×#4111yescharacteristic
240C2×C4×C79C2×#4111yescharacteristic
241C2×C4×C79C2×#4111yescharacteristic
242C22⋊D79—432no—
243C2×Dic79—22no—
244C2×Dic79—24no—
245C2×Dic79—22no—
246C2×Dic79—22no—
247C2×Dic79—42no—
248C2×Dic79—42no—
249C2×Dic79—44no—
250C2×Dic79—48no—
251C2×Dic79—42no—
252C2×Dic79—42no—
253C2×Dic79—42no—
254C2×Dic79—84no—
255C4×D79—42no—
256C4×D79—42no—
257C4×D79—42no—
258C4×D79—42no—
259C4×D79—48no—
260C8×C79—42no—
261C79⋊C8—24no—
262C22×C79—44no—
263C22×C79—44no—
264C22×C79—44no—
265C22×C79—82no—
266C22×C79—82no—
267C22×C79—82no—
268C22×C79—82no—
269C22×C79—816no—
270C22×C79#39414yes—
271C22×C79#44714yes—
272C22×C79#45214yes—
273C22×C79#46614yes—
274C22×C79#46814yes—
275C22×C79#48014yes—
276C22×C79#48214yes—
277C22×C79C2×#12011yescharacteristic
278C22×C79C2×#12111yescharacteristic
279C22×C79C2×#12311yescharacteristic
280C22×C79C22×D811yescharacteristic
281C22×C79C2×#13511yescharacteristic
282C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C79C2×#13711yescharacteristic
284C2×D79—24no—
285C2×D79—24no—
286C2×D79—24no—
287C2×D79—42no—
288C2×D79—42no—
289C2×D79—42no—
290C2×D79—42no—
291C2×D79—416no—
292C4×C79—82no—
293C4×C79#39414yes—
294C4×C79C2×#12111yescharacteristic
295C4×C79C2×#12111yescharacteristic
296C4×C79C2×#12311yescharacteristic
297C4×C79C2×#12411yescharacteristic
298Dic79—42no—
299Dic79—44no—
300Dic79—82no—
301C2×#2033—791nomaximal, Sylow
302C2×C79—84no—
303C2×C79#203318yescomplemented
304C2×C79C2×#39411yescharacteristic
305C2×C79C2×#44711yescharacteristic
306C2×C79C2×#45211yescharacteristic
307C2×C79C2×#46611yescharacteristic
308C2×C79C2×#46811yescharacteristic
309C2×C79C2×#48011yescharacteristic
310C2×C79C2×#48211yescharacteristic
311D79—44no—
312C22×#121—791no—
313C22×#107—791no—
314C22×#102—791no—
315C22×#102D7911yescharacteristic, complemented
316C22×C22⋊C8—791no—
317C2×#380—791no—
318#2033—798no—
319C2×#340—791no—
320C79C2×#203311yescharacteristic, complemented, Sylow
321C23×D4—1581no—
322C23×D4C2×D7911yescharacteristic
323C24×C4—791no—
324C23×C8—791no—
325C23×C8C2×D7911yescharacteristic
326C2×#121—794no—
327C2×#121—1584no—
328C2×#121—1582no—
329C2×#121—1584no—
330C22×C4⋊C4—791no—
331C22×C4⋊C4—791no—
332C22×C4⋊C4C2×D7911yescharacteristic
333C22×C22⋊C4—1581no—
334C22×C22⋊C4—1581no—
335C2×#107—794no—
336C2×#107—1584no—
337C2×#102—24no—
338C2×#102—794no—
339C2×#102—1584no—
340C2×#102C2×D7914yescomplemented
341C2×C22⋊C8—794no—
342C2×C22⋊C8—1584no—
343#380—794no—
344#380—1582no—
345C2×#95—1581no—
346#340—794no—
347C25—21no—
348C25—791no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—3164no—
356C22×D4—3164no—
357C22×D4—1584no—
358C22×D4—1588no—
359C22×D4C22⋊D7914yes—
360C22×D4C22×D7912yes—
361C23×C4—21no—
362C23×C4—791no—
363C23×C4—792no—
364C23×C4—792no—
365C23×C4—1581no—
366C23×C4—1581no—
367C23×C4—1582no—
368C23×C4—1582no—
369C23×C4—1582no—
370C23×C4—1582no—
371C23×C4—1582no—
372C23×C4—1582no—
373C23×C4C22×D7911yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—794no—
378C22×C8—792no—
379C22×C8—1582no—
380C22×C8—1582no—
381C22×C8C22×D7912yes—
382#121—1588no—
383#121—15816no—
384#121—1588no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—794no—
389C2×C4⋊C4—792no—
390C2×C4⋊C4—792no—
391C2×C4⋊C4—1581no—
392C2×C4⋊C4—1582no—
393C2×C4⋊C4—1582no—
394C2×C4⋊C4—1581no—
395C2×C4⋊C4—1582no—
396C2×C4⋊C4C22×D7912yes—
397C2×C22⋊C4—3164no—
398C2×C22⋊C4—1584no—
399C2×C22⋊C4—1584no—
400C2×C22⋊C4—1588no—
401#107—1588no—
402#102—28no—
403#102—1588no—
404C22⋊C8—1588no—
405#95—1584no—
406C24—24no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—794no—
415C24—792no—
416C24—1582no—
417C24—1582no—
418C24—1582no—
419C24—1582no—
420C24—1582no—
421C24—1582no—
422C24D4×D7911yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—3168no—
436C2×D4—31632no—
437C2×D4—3168no—
438C2×D4—15816no—
439C2×D4C2×C22⋊D7914yes—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—3162no—
445C22×C4—3162no—
446C22×C4—3164no—
447C22×C4—3164no—
448C22×C4—3164no—
449C22×C4—3164no—
450C22×C4—3162no—
451C22×C4—3162no—
452C22×C4—3162no—
453C22×C4—792no—
454C22×C4—1582no—
455C22×C4—1582no—
456C22×C4—1584no—
457C22×C4—1582no—
458C22×C4—1582no—
459C22×C4—1582no—
460C22×C4—1582no—
461C22×C4—1582no—
462C22×C4—1582no—
463C22×C4—1584no—
464C22×C4—1584no—
465C22×C4—1584no—
466C22×C4—1582no—
467C22×C4—1582no—
468C22×C4—1582no—
469C22×C4D4×D7911yescharacteristic
470C22×C4D4×D7912yes—
471C22×C4D4×D7912yes—
472C22×C4C2×C22⋊D7912yes—
473C22×C4#1192962312yes—
474C22×C4#1192962412yes—
475C22×C4#1192962412yes—
476C22×C4C23×D7911yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—794no—
482C2×C8—1582no—
483C2×C8—1588no—
484C2×C8—1582no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—3162no—
489C4⋊C4—794no—
490C4⋊C4—1582no—
491C4⋊C4—1582no—
492C4⋊C4—1584no—
493C4⋊C4—1582no—
494C22⋊C4—3168no—
495C22⋊C4—15816no—
496C23—24no—
497C23—48no—
498C23—48no—
499C23—48no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—3164no—
511C23—3164no—
512C23—3164no—
513C23—3164no—
514C23—794no—
515C23—1588no—
516C23—1582no—
517C23—1588no—
518C23—1582no—
519C23—1582no—
520C23—1582no—
521C23—1582no—
522C23—1582no—
523C23—1588no—
524C23#1457912912yes—
525C23#1457913412yes—
526C23#1457914312yes—
527C23D8×D7912yes—
528C23#1457918212yes—
529C23#1457918512yes—
530C23#1457919012yes—
531C23C2×D4×D7911yescharacteristic
532D4—24no—
533D4—24no—
534D4—48no—
535D4—42no—
536D4—42no—
537D4—31632no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—3168no—
543C2×C4—3164no—
544C2×C4—3162no—
545C2×C4—3162no—
546C2×C4—3168no—
547C2×C4—3162no—
548C2×C4—3162no—
549C2×C4—3162no—
550C2×C4—3162no—
551C2×C4—3162no—
552C2×C4—3162no—
553C2×C4—3162no—
554C2×C4—6324no—
555C2×C4—1582no—
556C2×C4—1584no—
557C2×C4—1582no—
558C2×C4—1582no—
559C2×C4#1457912912yes—
560C2×C4#1457913314yes—
561C2×C4#1457913412yes—
562C2×C4#1457913414yes—
563C2×C4#1457914312yes—
564C2×C4#1457914414yes—
565C2×C4#1457914714yes—
566C2×C4C2×D4×D7911yescharacteristic
567C2×C4C2×D4×D7911yescharacteristic
568C2×C4C22×C22⋊D7911yescharacteristic
569C2×C4C2×#1192962311yescharacteristic
570C2×C4C2×#1192962411yescharacteristic
571C2×C4C2×#1192962411yescharacteristic
572C8—42no—
573C8—1584no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—816no—
582C22—3162no—
583C22—3162no—
584C22—3162no—
585C22—31616no—
586C22—3162no—
587C22—1584no—
588C22—1584no—
589C22—1584no—
590C22#1909847814yes—
591C22#1909869514yes—
592C22#1909872214yes—
593C22#1909879814yes—
594C22#1909880814yes—
595C22#1909887514yes—
596C22#1909888614yes—
597C22C2×#1457912911yescharacteristic
598C22C2×#1457913411yescharacteristic
599C22C2×#1457914311yescharacteristic
600C22C2×D8×D7911yescharacteristic
601C22C2×#1457918211yescharacteristic
602C22C2×#1457918511yescharacteristic
603C22C2×#1457919011yescharacteristic
604C4—82no—
605C4—3162no—
606C4—3164no—
607C4—6322no—
608C4#1909847814yes—
609C4C2×#1457913311yescharacteristic
610C4C2×#1457913411yescharacteristic
611C4C2×#1457914411yescharacteristic
612C4C2×#1457914711yescharacteristic
613C2—84no—
614C2—3164no—
615C2#2376458018yesdirect product factor
616C2C2×#1909847811yescharacteristic
617C2C2×#1909869511yescharacteristic
618C2C2×#1909872211yescharacteristic
619C2C2×#1909879811yescharacteristic
620C2C2×#1909880811yescharacteristic
621C2C2×#1909887511yescharacteristic
622C2C2×#1909888611yescharacteristic
subgroupG/H
centerC24D4×D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC22×#102×C79C2
socleC24×C79C2×D4
prime radicalC22×#14579132C2
hypercenterC22×#102D79
hypocenterC79C2×#2033
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14579094C2semidirect
3. C22×#14579082C2semidirect
4. C22×(C2×D79)⋊C8C2semidirect
5. C2×#19098420C2semidirect
6. #23764580C2direct (N × H)
7. C2×#19098326C2semidirect
8. C22×#102×C79C2semidirect
21. C2×#14579094C22semidirect
23. C2×#14579082C22semidirect
25. C2×(C2×D79)⋊C8C22semidirect
27. #19098420C22semidirect
29. #19098326C22semidirect
34. C2×#102×C79C22semidirect
53. C22×C79⋊C8D4semidirect
134. C2×C79⋊C8C2×D4semidirect
303. C2×C79#2033semidirect
315. C22×#102D79semidirect
320. C79C2×#2033semidirect
340. C2×#102C2×D79semidirect
615. C2#23764580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791322
C22×#145790942
C22×#145790822
C22×(C2×D79)⋊C82
C2×#190984202
#237645802
C2×#190983262
C22×#102×C792
C2×#203379