Finite Group Databasebeta

← C4×#19099304 #34450959

Subgroups — C4×#19099304 #34450959

Order 20224.

2568 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099304C211yesmaximal, characteristic
2#23766592C211yesmaximal, characteristic, complemented
3#23766589C211yesmaximal, characteristic, complemented
4#23766576C211yesmaximal, characteristic, complemented
5#23766555C213yesmaximal, complemented
6#23766553C213yesmaximal, complemented
7#23766547C213yesmaximal, complemented
8#23766540C213yesmaximal, complemented
9C4×#14579158C211yesmaximal, characteristic, complemented
10C4×#14579155C211yesmaximal, characteristic, complemented
11C4×#14579146C213yesmaximal, complemented
12C4×#14579136C213yesmaximal, complemented
13C4×#14579134C213yesmaximal, complemented
14C4×#14579131C213yesmaximal, complemented
15C4×#126×C79C211yesmaximal, characteristic, complemented
16C23×C4×D79C2211yescharacteristic
17#19099304C4116yesdirect product factor
18C2×#14579158C2211yescharacteristic
19C2×#14579155C2211yescharacteristic
20C2×#14579146C2213yes—
21C2×#14579136C2213yes—
22C2×#14579134C2213yes—
23C2×#14579131C2213yes—
24C2×C4×D316C2213yes—
25C2×C4×D316C2213yes—
26C2×C4×D316C2213yescomplemented
27C2×C4×C22⋊D79C2213yes—
28C2×C42×D79C2213yescomplemented
29#19098465C2213yes—
30#19098465C2213yescomplemented
31#19098464C2213yes—
32#19098463C2213yes—
33#19098462C2213yescomplemented
34#19098460C2213yescomplemented
35#19098456C2213yes—
36#19098455C2213yes—
37#19098455C2213yescomplemented
38#19098454C2213yes—
39#19098453C2213yes—
40#19098452C2213yes—
41#19098452C2213yescomplemented
42#19098450C2213yescomplemented
43#19098449C2213yescomplemented
44#19098447C2213yescomplemented
45#19098441C2213yes—
46#19098441C2213yes—
47#19098441C2213yes—
48#19098441C2213yes—
49#19098441C2213yescomplemented
50#19098441C2213yescomplemented
51#19098440C2213yes—
52#19098439C2213yes—
53#19098438C2213yes—
54#19098437C2213yes—
55#19098437C2213yes—
56#19098434C2213yescomplemented
57#19098433C2211yescharacteristic, complemented
58#19098431C2211yescharacteristic, complemented
59#19098425C2213yescomplemented
60#19098422C2213yescomplemented
61#19098420C2213yescomplemented
62#19098418C2213yes—
63C4×Dic79⋊C4C2213yescomplemented
64C4×(C2×D79)⋊C4C2213yes—
65C4×(C2×D79)⋊C4C2213yes—
66C4×(C2×D79)⋊C4C2213yescomplemented
67C2×#126×C79C2211yescharacteristic
68#388×C79C2213yes—
69#387×C79C2213yescomplemented
70#383×C79C2211yescharacteristic, complemented
71C4×C4⋊C4×C79C2213yescomplemented
72C4×C22⋊C4×C79C2213yes—
73C43×C79C2211yescharacteristic, complemented
74C24×D79C2311yescharacteristic
75C22×D316C2313yes—
76C22×D316C2313yes—
77C22×D316C2313yes—
78C22×C22⋊D79C2313yes—
79C23×Dic79C2311yescharacteristic
80C22×C4×D79—46no—
81C22×C4×D79C2311yescharacteristic
82C22×C4×D79C2311yescharacteristic
83C22×C4×D79C2313yes—
84C22×C4×D79C2313yes—
85C22×C4×D79C2311yescharacteristic
86C22×C4×D79C2311yescharacteristic
87C22×C4×D79C2313yes—
88#14579158C2×C418yescomplemented
89#14579155C2×C418yescomplemented
90#14579146C2×C4124yescomplemented
91#14579136C2×C4124yescomplemented
92#14579134C2×C4124yescomplemented
93#14579131C2×C4124yescomplemented
94C4×D316—46no—
95C4×D316—46no—
96C4×D316—46no—
97C4×C22⋊D79—46no—
98C2×C4⋊Dic79C2313yes—
99C2×C4⋊Dic79C2313yes—
100C2×C4⋊Dic79C2313yes—
101C2×Dic79⋊C4C2313yes—
102C2×Dic79⋊C4C2313yes—
103C2×Dic79⋊C4C2313yes—
104C2×C22⋊Dic79C2313yes—
105C2×(C2×D79)⋊C4C2313yes—
106C2×(C2×D79)⋊C4C2313yes—
107C2×(C2×D79)⋊C4C2313yes—
108C2×(C2×D79)⋊C4C2313yes—
109C2×(C2×D79)⋊C4C2313yes—
110C2×(C2×D79)⋊C4C2313yes—
111C2×(C2×D79)⋊C4C2313yes—
112C2×(C2×D79)⋊C4C2313yes—
113C2×(C2×D79)⋊C4C2313yes—
114C2×(C2×D79)⋊C4C2313yes—
115C2×(C2×D79)⋊C4C2313yes—
116C2×(C2×D79)⋊C4C2313yes—
117C2×(C2×D79)⋊C4C2313yes—
118C2×C4×Dic79C2313yes—
119C2×C4×Dic79C2313yes—
120C2×C4×Dic79C2313yes—
121C42×D79—46no—
122C79⋊#95C2313yes—
123C79⋊#95C2313yes—
124C79⋊#95C2313yes—
125C79⋊#95C2313yes—
126C79⋊#95C2313yes—
127C79⋊#95C2313yes—
128C79⋊#95C2313yes—
129C79⋊#95C2313yes—
130C23×C4×C79C2311yescharacteristic
131#126×C79C2×C418yescomplemented
132C2×C4⋊C4×C79C2313yes—
133C2×C4⋊C4×C79C2313yes—
134C2×C22⋊C4×C79C2313yes—
135C2×C22⋊C4×C79C2313yes—
136C2×C42×C79C2313yes—
137C2×C42×C79C2313yes—
138C2×C42×C79C2313yes—
139C2×C42×C79C2311yescharacteristic
140#95×C79C2313yes—
141#95×C79C2313yes—
142#95×C79C2313yes—
143#95×C79C2313yes—
144C23×D79—43no—
145C23×D79—43no—
146C23×D79C22×C414yes—
147C23×D79C2411yescharacteristic
148C23×D79C2411yescharacteristic
149C23×D79C2413yes—
150C2×D316—43no—
151C2×D316—43no—
152C2×D316—43no—
153C2×D316—43no—
154C2×D316—43no—
155C2×D316—43no—
156C2×D316C22×C4112yes—
157C2×D316C22×C4112yes—
158C2×D316C22×C4112yescomplemented
159C2×C22⋊D79—43no—
160C2×C22⋊D79—43no—
161C2×C22⋊D79C22×C4112yes—
162C22×Dic79—43no—
163C22×Dic79C2413yes—
164C22×Dic79C2411yescharacteristic
165C22×Dic79C2411yescharacteristic
166C22×Dic79C2413yes—
167C22×Dic79C2413yes—
168C2×C4×D79—26no—
169C2×C4×D79—26no—
170C2×C4×D79—26no—
171C2×C4×D79—26no—
172C2×C4×D79—26no—
173C2×C4×D79—43no—
174C2×C4×D79—43no—
175C2×C4×D79—43no—
176C2×C4×D79—43no—
177C2×C4×D79—43no—
178C2×C4×D79—43no—
179C2×C4×D79—43no—
180C2×C4×D79—416no—
181C2×C4×D79C22×C4112yescomplemented
182C4⋊Dic79—43no—
183C4⋊Dic79—43no—
184C4⋊Dic79—43no—
185Dic79⋊C4—43no—
186Dic79⋊C4—43no—
187Dic79⋊C4C22×C4112yescomplemented
188C22⋊Dic79—43no—
189(C2×D79)⋊C4—43no—
190(C2×D79)⋊C4—43no—
191(C2×D79)⋊C4—43no—
192(C2×D79)⋊C4—43no—
193(C2×D79)⋊C4—43no—
194(C2×D79)⋊C4—43no—
195(C2×D79)⋊C4—43no—
196(C2×D79)⋊C4—43no—
197(C2×D79)⋊C4—43no—
198(C2×D79)⋊C4—43no—
199(C2×D79)⋊C4C22×C4112yes—
200(C2×D79)⋊C4C22×C4112yes—
201(C2×D79)⋊C4C22×C4112yescomplemented
202C4×Dic79—26no—
203C4×Dic79—43no—
204C4×Dic79—43no—
205C24×C79C2411yescharacteristic
206C22×C4×C79—26no—
207C22×C4×C79C2411yescharacteristic
208C22×C4×C79C2413yes—
209C22×C4×C79C2413yes—
210C22×C4×C79C2413yes—
211C22×C4×C79C2413yes—
212C22×C4×C79C2411yescharacteristic
213C4⋊C4×C79—43no—
214C4⋊C4×C79C22×C4112yescomplemented
215C22⋊C4×C79—43no—
216C22⋊C4×C79C22×C4112yes—
217C42×C79—26no—
218C42×C79—26no—
219C42×C79—43no—
220C42×C79C22×C414yescomplemented
221C23×C79—23no—
222C23×C79—23no—
223C23×C79C23×C412yes—
224C23×C79C2511yescharacteristic
225C22×D79—23no—
226C22×D79—23no—
227C22×D79—23no—
228C22×D79—23no—
229C22×D79—23no—
230C22×D79—23no—
231C22×D79—23no—
232C22×D79—23no—
233C22×D79—23no—
234C22×D79—23no—
235C22×D79—412no—
236C22×D79—44no—
237C22×D79—412no—
238C22×D79C23×C412yes—
239C22×D79C23×C412yes—
240C22×D79C23×C416yes—
241C2×C4×C79—23no—
242C2×C4×C79—23no—
243C2×C4×C79—23no—
244C2×C4×C79—23no—
245C2×C4×C79—23no—
246C2×C4×C79—23no—
247C2×C4×C79—23no—
248C2×C4×C79—23no—
249C2×C4×C79—23no—
250C2×C4×C79—23no—
251C2×C4×C79—23no—
252C2×C4×C79—44no—
253C2×C4×C79C23×C416yes—
254C2×C4×C79C23×C416yes—
255C2×C4×C79H(5,𝔽2)16yes—
256C22⋊D79—412no—
257C2×Dic79—23no—
258C2×Dic79—23no—
259C2×Dic79—23no—
260C2×Dic79—23no—
261C2×Dic79—23no—
262C2×Dic79—23no—
263C2×Dic79—23no—
264C2×Dic79—23no—
265C2×Dic79—23no—
266C2×Dic79—23no—
267C2×Dic79—44no—
268C2×Dic79C23×C416yes—
269D316—412no—
270D316—412no—
271D316—412no—
272C4×D79—412no—
273C4×D79—412no—
274C4×D79—44no—
275C4×D79—44no—
276C4×D79—412no—
277C4×D79—44no—
278C4×D79—44no—
279C22×C79—26no—
280C22×C79—41no—
281C22×C79—43no—
282C22×C79C24×C411yescharacteristic
283C22×C79C2×H(5,𝔽2)13yes—
284C22×C79#58513yes—
285C2×D79—26no—
286C2×D79—26no—
287C2×D79—26no—
288C2×D79—26no—
289C2×D79—26no—
290C2×D79—416no—
291C2×D79—41no—
292C2×D79—41no—
293C2×D79—43no—
294C2×D79—43no—
295C2×D79—43no—
296C2×D79—43no—
297C2×D79—43no—
298C2×D79—43no—
299C4×C79—26no—
300C4×C79—26no—
301C4×C79—41no—
302C4×C79—43no—
303C4×C79—43no—
304C4×C79#56014yescomplemented
305Dic79—26no—
306Dic79—41no—
307Dic79—41no—
308Dic79—43no—
309Dic79—43no—
310C4×#560—791nomaximal, Sylow
311C2×C79—42no—
312C2×C79C4×H(5,𝔽2)13yes—
313C2×C79C2×#56011yescharacteristic
314C2×C79#352913yes—
315D79—46no—
316D79—42no—
317D79—42no—
318C2×#560—791no—
319#2383—791no—
320#2383—791no—
321#2380—791no—
322#2377—793no—
323#2377—793no—
324#2376—793no—
325#2375—793no—
326C4×#127—791no—
327C4×#126—791no—
328C4×#126D7911yescharacteristic, complemented
329C4×#123—793no—
330C4×#121—793no—
331C4×#121—793no—
332C4×#120—793no—
333C79C4×#56011yescharacteristic, complemented, Sylow
334C24×C4—791no—
335#560—7916no—
336C2×#127—791no—
337C2×#126—791no—
338C2×#126C2×D7911yescharacteristic
339C2×#123—793no—
340C2×#121—793no—
341C2×#121—793no—
342C2×#120—793no—
343C2×C4×D4—793no—
344C2×C4×D4—793no—
345C2×C4×D4—793no—
346C2×C4×D4—793no—
347C22×C42—793no—
348#390—793no—
349#390—793no—
350#390—793no—
351#390—793no—
352#389—793no—
353#389—793no—
354#388—793no—
355#388—793no—
356#388—793no—
357#388—793no—
358#388—793no—
359#388—793no—
360#388—793no—
361#388C2×D7913yes—
362#387—793no—
363#387—793no—
364#387—793no—
365#387C2×D7913yescomplemented
366#386—793no—
367#386—793no—
368#386—793no—
369#386—793no—
370#386—793no—
371#386—793no—
372#386—793no—
373#386—793no—
374#385—793no—
375#385—793no—
376#385—793no—
377#385—793no—
378#384—791no—
379#383—791no—
380#383C2×D7911yescharacteristic, complemented
381#381—793no—
382#380—793no—
383#380—793no—
384#379—793no—
385C4×C4⋊C4—793no—
386C4×C4⋊C4C2×D7913yescomplemented
387C4×C22⋊C4—793no—
388C4×C22⋊C4—793no—
389C4×C22⋊C4—793no—
390C4×C22⋊C4C2×D7913yes—
391C43C2×D7911yescharacteristic, complemented
392C25—791no—
393C22×D4—793no—
394C22×D4—793no—
395C22×D4—793no—
396C22×D4—793no—
397C23×C4—3166no—
398C23×C4—791no—
399C23×C4—791no—
400C23×C4—791no—
401C23×C4—793no—
402C23×C4—793no—
403C23×C4—793no—
404C23×C4—791no—
405C23×C4—791no—
406C23×C4C22×D7911yescharacteristic
407#127—798no—
408#126—798no—
409#126C4×D7918yescomplemented
410#123—7924no—
411#121—7924no—
412#121—7924no—
413#120—7924no—
414C4×D4—3166no—
415C4×D4—3166no—
416C4×D4—3166no—
417C4×D4—3166no—
418C2×C4⋊C4—793no—
419C2×C4⋊C4—793no—
420C2×C4⋊C4—793no—
421C2×C4⋊C4—793no—
422C2×C4⋊C4—793no—
423C2×C4⋊C4—793no—
424C2×C4⋊C4C22×D7913yes—
425C2×C4⋊C4C22×D7913yes—
426C2×C22⋊C4—793no—
427C2×C22⋊C4—793no—
428C2×C22⋊C4—793no—
429C2×C22⋊C4—793no—
430C2×C22⋊C4—793no—
431C2×C22⋊C4—793no—
432C2×C22⋊C4—793no—
433C2×C22⋊C4—793no—
434C2×C22⋊C4—793no—
435C2×C22⋊C4—793no—
436C2×C22⋊C4—793no—
437C2×C22⋊C4—793no—
438C2×C22⋊C4—793no—
439C2×C22⋊C4—793no—
440C2×C22⋊C4C22×D7913yes—
441C2×C22⋊C4C22×D7913yes—
442C2×C42—3166no—
443C2×C42—793no—
444C2×C42—793no—
445C2×C42—793no—
446C2×C42C22×D7913yes—
447C2×C42C22×D7913yes—
448C2×C42C22×D7913yes—
449C2×C42C22×D7911yescharacteristic
450#95—793no—
451#95—793no—
452#95—793no—
453#95—793no—
454#95—793no—
455#95—793no—
456#95—793no—
457#95—793no—
458#95C22×D7913yes—
459#95C22×D7913yes—
460#95C22×D7913yes—
461#95C22×D7913yes—
462C24—3163no—
463C24—3163no—
464C24—794no—
465C24—791no—
466C24—791no—
467C24—793no—
468C24C23×D7911yescharacteristic
469C2×D4—3163no—
470C2×D4—3163no—
471C2×D4—3163no—
472C2×D4—3163no—
473C2×D4—3163no—
474C2×D4—3163no—
475C2×D4—3163no—
476C2×D4—3163no—
477C2×D4—7912no—
478C2×D4—7912no—
479C2×D4—7912no—
480C2×D4—7912no—
481C22×C4—26no—
482C22×C4—3163no—
483C22×C4—3163no—
484C22×C4—3163no—
485C22×C4—3163no—
486C22×C4—3163no—
487C22×C4—3163no—
488C22×C4—3163no—
489C22×C4—31616no—
490C22×C4—3163no—
491C22×C4—7912no—
492C22×C4—793no—
493C22×C4—793no—
494C22×C4—791no—
495C22×C4—791no—
496C22×C4—793no—
497C22×C4—1586no—
498C22×C4—1586no—
499C22×C4—1586no—
500C22×C4—1586no—
501C22×C4—1586no—
502C22×C4C23×D7913yes—
503C22×C4C23×D7913yes—
504C22×C4C23×D7911yescharacteristic
505C22×C4C23×D7913yes—
506C22×C4C23×D7913yes—
507C22×C4C23×D7911yescharacteristic
508C4⋊C4—43no—
509C4⋊C4—3163no—
510C4⋊C4—3163no—
511C4⋊C4—3163no—
512C4⋊C4—3163no—
513C4⋊C4—3163no—
514C4⋊C4—7912no—
515C4⋊C4C2×C4×D79112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—3163no—
518C22⋊C4—3163no—
519C22⋊C4—3163no—
520C22⋊C4—3163no—
521C22⋊C4—3163no—
522C22⋊C4—3163no—
523C22⋊C4—3163no—
524C22⋊C4—3163no—
525C22⋊C4—3163no—
526C22⋊C4—3163no—
527C22⋊C4—3163no—
528C22⋊C4—7912no—
529C22⋊C4—7912no—
530C22⋊C4—7912no—
531C22⋊C4C2×C4×D79112yes—
532C42—26no—
533C42—26no—
534C42—43no—
535C42—3163no—
536C42—3163no—
537C42—1586no—
538C42C2×C4×D7914yescomplemented
539C23—23no—
540C23—23no—
541C23—31612no—
542C23—3164no—
543C23—31612no—
544C23—792no—
545C23—792no—
546C23—796no—
547C23—1583no—
548C23—1583no—
549C23—1583no—
550C23—1583no—
551C23—1583no—
552C23—1583no—
553C23—1583no—
554C23—1583no—
555C23—1583no—
556C23—1583no—
557C23C22×C4×D7912yes—
558C23C24×D7911yescharacteristic
559D4—31612no—
560D4—31612no—
561D4—31612no—
562D4—31612no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—44no—
575C2×C4—31612no—
576C2×C4—3164no—
577C2×C4—3164no—
578C2×C4—31612no—
579C2×C4—3164no—
580C2×C4—3164no—
581C2×C4—3164no—
582C2×C4—31612no—
583C2×C4—796no—
584C2×C4—1583no—
585C2×C4—1583no—
586C2×C4—1583no—
587C2×C4—1583no—
588C2×C4—1583no—
589C2×C4—1583no—
590C2×C4—1583no—
591C2×C4—1583no—
592C2×C4—1583no—
593C2×C4—1583no—
594C2×C4C22×C4×D7916yes—
595C2×C4C22×C4×D7916yes—
596C2×C4#1457920716yes—
597C22—26no—
598C22—43no—
599C22—41no—
600C22—31616no—
601C22—3163no—
602C22—3163no—
603C22—3163no—
604C22—3163no—
605C22—3163no—
606C22—3161no—
607C22—3161no—
608C22—3163no—
609C22—1586no—
610C22—1586no—
611C22—1586no—
612C22—1586no—
613C22—1586no—
614C22C23×C4×D7911yescharacteristic
615C22C2×#1457920713yes—
616C22#1909939913yes—
617C4—26no—
618C4—26no—
619C4—43no—
620C4—43no—
621C4—41no—
622C4—3163no—
623C4—3161no—
624C4—3161no—
625C4—3163no—
626C4—1586no—
627C4#1909930414yesdirect product factor
628C2—42no—
629C2—3162no—
630C2—3162no—
631C2—3166no—
632C2C4×#1457920713yes—
633C2C2×#1909930411yescharacteristic
634C2#2377753913yes—
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC4×#126×C79C2
socle, cosocleC23×C79C25
prime radicalC2×#19099304C2
hypercenterC4×#126D79
hypocenterC79C4×#560
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #23766592C2semidirect
3. #23766589C2semidirect
4. #23766576C2semidirect
5. #23766555C2semidirect
6. #23766553C2semidirect
7. #23766547C2semidirect
8. #23766540C2semidirect
9. C4×#14579158C2semidirect
10. C4×#14579155C2semidirect
11. C4×#14579146C2semidirect
12. C4×#14579136C2semidirect
13. C4×#14579134C2semidirect
14. C4×#14579131C2semidirect
15. C4×#126×C79C2semidirect
17. #19099304C4direct (N × H)
26. C2×C4×D316C22semidirect
28. C2×C42×D79C22semidirect
30. #19098465C22semidirect
33. #19098462C22semidirect
34. #19098460C22semidirect
37. #19098455C22semidirect
41. #19098452C22semidirect
42. #19098450C22semidirect
43. #19098449C22semidirect
44. #19098447C22semidirect
49. #19098441C22semidirect
50. #19098441C22semidirect
56. #19098434C22semidirect
57. #19098433C22semidirect
58. #19098431C22semidirect
59. #19098425C22semidirect
60. #19098422C22semidirect
61. #19098420C22semidirect
63. C4×Dic79⋊C4C22semidirect
66. C4×(C2×D79)⋊C4C22semidirect
69. #387×C79C22semidirect
70. #383×C79C22semidirect
71. C4×C4⋊C4×C79C22semidirect
73. C43×C79C22semidirect
88. #14579158C2×C4semidirect
89. #14579155C2×C4semidirect
90. #14579146C2×C4semidirect
91. #14579136C2×C4semidirect
92. #14579134C2×C4semidirect
93. #14579131C2×C4semidirect
131. #126×C79C2×C4semidirect
158. C2×D316C22×C4semidirect
181. C2×C4×D79C22×C4semidirect
187. Dic79⋊C4C22×C4semidirect
201. (C2×D79)⋊C4C22×C4semidirect
214. C4⋊C4×C79C22×C4semidirect
220. C42×C79C22×C4semidirect
304. C4×C79#560semidirect
328. C4×#126D79semidirect
333. C79C4×#560semidirect
365. #387C2×D79semidirect
380. #383C2×D79semidirect
386. C4×C4⋊C4C2×D79semidirect
391. C43C2×D79semidirect
409. #126C4×D79semidirect
515. C4⋊C4C2×C4×D79semidirect
538. C42C2×C4×D79semidirect
627. C4#19099304direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190993042
#237665922
#237665892
#237665762
#237665552
#237665532
#237665472
#237665402
C4×#145791582
C4×#145791552
C4×#145791462
C4×#145791362
C4×#145791342
C4×#145791312
C4×#126×C792
C4×#56079