Finite Group Databasebeta

← C4×#19152339 #36717118

Subgroups — C4×#19152339 #36717118

Order 22784.

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×#19152339C211yesmaximal, characteristic
2#26023444C211yesmaximal, characteristic, complemented
3#26023441C211yesmaximal, characteristic, complemented
4#26023428C211yesmaximal, characteristic, complemented
5#26023407C213yesmaximal, complemented
6#26023405C213yesmaximal, complemented
7#26023399C213yesmaximal, complemented
8#26023392C213yesmaximal, complemented
9C4×#15668009C211yesmaximal, characteristic, complemented
10C4×#15668006C211yesmaximal, characteristic, complemented
11C4×#15667997C213yesmaximal, complemented
12C4×#15667987C213yesmaximal, complemented
13C4×#15667985C213yesmaximal, complemented
14C4×#15667982C213yesmaximal, complemented
15C4×#126×C89C211yesmaximal, characteristic, complemented
16C23×C4×D89C2211yescharacteristic
17#19152339C4116yesdirect product factor
18C2×#15668009C2211yescharacteristic
19C2×#15668006C2211yescharacteristic
20C2×#15667997C2213yes—
21C2×#15667987C2213yes—
22C2×#15667985C2213yes—
23C2×#15667982C2213yes—
24C2×C4×D356C2213yes—
25C2×C4×D356C2213yes—
26C2×C4×D356C2213yescomplemented
27C2×C4×C22⋊D89C2213yes—
28C2×C42×D89C2213yescomplemented
29#19151500C2213yes—
30#19151500C2213yescomplemented
31#19151499C2213yes—
32#19151498C2213yes—
33#19151497C2213yescomplemented
34#19151495C2213yescomplemented
35#19151491C2213yes—
36#19151490C2213yes—
37#19151490C2213yescomplemented
38#19151489C2213yes—
39#19151488C2213yes—
40#19151487C2213yes—
41#19151487C2213yescomplemented
42#19151485C2213yescomplemented
43#19151484C2213yescomplemented
44#19151482C2213yescomplemented
45#19151476C2213yes—
46#19151476C2213yes—
47#19151476C2213yes—
48#19151476C2213yes—
49#19151476C2213yescomplemented
50#19151476C2213yescomplemented
51#19151475C2213yes—
52#19151474C2213yes—
53#19151473C2213yes—
54#19151472C2213yes—
55#19151472C2213yes—
56#19151469C2213yescomplemented
57#19151468C2211yescharacteristic, complemented
58#19151466C2211yescharacteristic, complemented
59#19151460C2213yescomplemented
60#19151457C2213yescomplemented
61#19151455C2213yescomplemented
62#19151453C2213yes—
63C4×#13083553C2213yescomplemented
64C4×#13083551C2213yes—
65C4×#13083551C2213yes—
66C4×#13083551C2213yescomplemented
67C2×#126×C89C2211yescharacteristic
68#388×C89C2213yes—
69#387×C89C2213yescomplemented
70#383×C89C2211yescharacteristic, complemented
71C4×C4⋊C4×C89C2213yescomplemented
72C4×C22⋊C4×C89C2213yes—
73C43×C89C2211yescharacteristic, complemented
74C24×D89C2311yescharacteristic
75C22×D356C2313yes—
76C22×D356C2313yes—
77C22×D356C2313yes—
78C22×C22⋊D89C2313yes—
79C23×Dic89C2311yescharacteristic
80C22×C4×D89—46no—
81C22×C4×D89C2311yescharacteristic
82C22×C4×D89C2311yescharacteristic
83C22×C4×D89C2313yes—
84C22×C4×D89C2311yescharacteristic
85C22×C4×D89C2311yescharacteristic
86C22×C4×D89C2313yes—
87C22×C4×D89C2313yes—
88#15668009C2×C418yescomplemented
89#15668006C2×C418yescomplemented
90#15667997C2×C4124yescomplemented
91#15667987C2×C4124yescomplemented
92#15667985C2×C4124yescomplemented
93#15667982C2×C4124yescomplemented
94C4×D356—46no—
95C4×D356—46no—
96C4×D356—46no—
97C4×C22⋊D89—46no—
98C2×C4⋊Dic89C2313yes—
99C2×C4⋊Dic89C2313yes—
100C2×C4⋊Dic89C2313yes—
101C2×#13083553C2313yes—
102C2×#13083553C2313yes—
103C2×#13083553C2313yes—
104C2×C22⋊Dic89C2313yes—
105C2×#13083551C2313yes—
106C2×#13083551C2313yes—
107C2×#13083551C2313yes—
108C2×#13083551C2313yes—
109C2×#13083551C2313yes—
110C2×#13083551C2313yes—
111C2×#13083551C2313yes—
112C2×#13083551C2313yes—
113C2×#13083551C2313yes—
114C2×#13083551C2313yes—
115C2×#13083551C2313yes—
116C2×#13083551C2313yes—
117C2×#13083551C2313yes—
118C2×C4×Dic89C2313yes—
119C2×C4×Dic89C2313yes—
120C2×C4×Dic89C2313yes—
121C42×D89—46no—
122#15667919C2313yes—
123#15667919C2313yes—
124#15667919C2313yes—
125#15667919C2313yes—
126#15667919C2313yes—
127#15667919C2313yes—
128#15667919C2313yes—
129#15667919C2313yes—
130C23×C4×C89C2311yescharacteristic
131#126×C89C2×C418yescomplemented
132C2×C4⋊C4×C89C2313yes—
133C2×C4⋊C4×C89C2313yes—
134C2×C22⋊C4×C89C2313yes—
135C2×C22⋊C4×C89C2313yes—
136C2×C42×C89C2313yes—
137C2×C42×C89C2313yes—
138C2×C42×C89C2313yes—
139C2×C42×C89C2311yescharacteristic
140#95×C89C2313yes—
141#95×C89C2313yes—
142#95×C89C2313yes—
143#95×C89C2313yes—
144C23×D89—43no—
145C23×D89—43no—
146C23×D89C22×C414yes—
147C23×D89C2413yes—
148C23×D89C2411yescharacteristic
149C23×D89C2411yescharacteristic
150C2×D356—43no—
151C2×D356—43no—
152C2×D356—43no—
153C2×D356—43no—
154C2×D356—43no—
155C2×D356—43no—
156C2×D356C22×C4112yes—
157C2×D356C22×C4112yes—
158C2×D356C22×C4112yescomplemented
159C2×C22⋊D89—43no—
160C2×C22⋊D89—43no—
161C2×C22⋊D89C22×C4112yes—
162C22×Dic89—43no—
163C22×Dic89C2411yescharacteristic
164C22×Dic89C2411yescharacteristic
165C22×Dic89C2413yes—
166C22×Dic89C2413yes—
167C22×Dic89C2413yes—
168C2×C4×D89—26no—
169C2×C4×D89—26no—
170C2×C4×D89—26no—
171C2×C4×D89—26no—
172C2×C4×D89—26no—
173C2×C4×D89—43no—
174C2×C4×D89—43no—
175C2×C4×D89—43no—
176C2×C4×D89—43no—
177C2×C4×D89—43no—
178C2×C4×D89—43no—
179C2×C4×D89—43no—
180C2×C4×D89—416no—
181C2×C4×D89C22×C4112yescomplemented
182C4⋊Dic89—43no—
183C4⋊Dic89—43no—
184C4⋊Dic89—43no—
185#13083553—43no—
186#13083553—43no—
187#13083553C22×C4112yescomplemented
188C22⋊Dic89—43no—
189#13083551—43no—
190#13083551—43no—
191#13083551—43no—
192#13083551—43no—
193#13083551—43no—
194#13083551—43no—
195#13083551—43no—
196#13083551—43no—
197#13083551—43no—
198#13083551—43no—
199#13083551C22×C4112yes—
200#13083551C22×C4112yes—
201#13083551C22×C4112yescomplemented
202C4×Dic89—26no—
203C4×Dic89—43no—
204C4×Dic89—43no—
205C24×C89C2411yescharacteristic
206C22×C4×C89—26no—
207C22×C4×C89C2411yescharacteristic
208C22×C4×C89C2413yes—
209C22×C4×C89C2413yes—
210C22×C4×C89C2413yes—
211C22×C4×C89C2413yes—
212C22×C4×C89C2411yescharacteristic
213C4⋊C4×C89—43no—
214C4⋊C4×C89C22×C4112yescomplemented
215C22⋊C4×C89—43no—
216C22⋊C4×C89C22×C4112yes—
217C42×C89—26no—
218C42×C89—26no—
219C42×C89—43no—
220C42×C89C22×C414yescomplemented
221C23×C89—23no—
222C23×C89—23no—
223C23×C89C23×C412yes—
224C23×C89C2511yescharacteristic
225C22×D89—23no—
226C22×D89—23no—
227C22×D89—23no—
228C22×D89—23no—
229C22×D89—23no—
230C22×D89—23no—
231C22×D89—23no—
232C22×D89—23no—
233C22×D89—23no—
234C22×D89—23no—
235C22×D89—412no—
236C22×D89—44no—
237C22×D89—412no—
238C22×D89C23×C412yes—
239C22×D89C23×C412yes—
240C22×D89C23×C416yes—
241C2×C4×C89—23no—
242C2×C4×C89—23no—
243C2×C4×C89—23no—
244C2×C4×C89—23no—
245C2×C4×C89—23no—
246C2×C4×C89—23no—
247C2×C4×C89—23no—
248C2×C4×C89—23no—
249C2×C4×C89—23no—
250C2×C4×C89—23no—
251C2×C4×C89—23no—
252C2×C4×C89—44no—
253C2×C4×C89C23×C416yes—
254C2×C4×C89C23×C416yes—
255C2×C4×C89H(5,𝔽2)16yes—
256C22⋊D89—412no—
257C2×Dic89—23no—
258C2×Dic89—23no—
259C2×Dic89—23no—
260C2×Dic89—23no—
261C2×Dic89—23no—
262C2×Dic89—23no—
263C2×Dic89—23no—
264C2×Dic89—23no—
265C2×Dic89—23no—
266C2×Dic89—23no—
267C2×Dic89—44no—
268C2×Dic89C23×C416yes—
269D356—412no—
270D356—412no—
271D356—412no—
272C4×D89—412no—
273C4×D89—412no—
274C4×D89—44no—
275C4×D89—44no—
276C4×D89—412no—
277C4×D89—44no—
278C4×D89—44no—
279C22×C89—26no—
280C22×C89—41no—
281C22×C89—43no—
282C22×C89C24×C411yescharacteristic
283C22×C89C2×H(5,𝔽2)13yes—
284C22×C89#58513yes—
285C2×D89—26no—
286C2×D89—26no—
287C2×D89—26no—
288C2×D89—26no—
289C2×D89—26no—
290C2×D89—416no—
291C2×D89—41no—
292C2×D89—41no—
293C2×D89—43no—
294C2×D89—43no—
295C2×D89—43no—
296C2×D89—43no—
297C2×D89—43no—
298C2×D89—43no—
299C4×C89—26no—
300C4×C89—26no—
301C4×C89—41no—
302C4×C89—43no—
303C4×C89—43no—
304C4×C89#56014yescomplemented
305Dic89—26no—
306Dic89—41no—
307Dic89—41no—
308Dic89—43no—
309Dic89—43no—
310C4×#560—891nomaximal, Sylow
311C2×C89—42no—
312C2×C89C4×H(5,𝔽2)13yes—
313C2×C89C2×#56011yescharacteristic
314C2×C89#352913yes—
315D89—46no—
316D89—42no—
317D89—42no—
318C2×#560—891no—
319#2383—891no—
320#2383—891no—
321#2380—891no—
322#2377—893no—
323#2377—893no—
324#2376—893no—
325#2375—893no—
326C4×#127—891no—
327C4×#126—891no—
328C4×#126D8911yescharacteristic, complemented
329C4×#123—893no—
330C4×#121—893no—
331C4×#121—893no—
332C4×#120—893no—
333C89C4×#56011yescharacteristic, complemented, Sylow
334C24×C4—891no—
335#560—8916no—
336C2×#127—891no—
337C2×#126—891no—
338C2×#126C2×D8911yescharacteristic
339C2×#123—893no—
340C2×#121—893no—
341C2×#121—893no—
342C2×#120—893no—
343C2×C4×D4—893no—
344C2×C4×D4—893no—
345C2×C4×D4—893no—
346C2×C4×D4—893no—
347C22×C42—893no—
348#390—893no—
349#390—893no—
350#390—893no—
351#390—893no—
352#389—893no—
353#389—893no—
354#388—893no—
355#388—893no—
356#388—893no—
357#388—893no—
358#388—893no—
359#388—893no—
360#388—893no—
361#388C2×D8913yes—
362#387—893no—
363#387—893no—
364#387—893no—
365#387C2×D8913yescomplemented
366#386—893no—
367#386—893no—
368#386—893no—
369#386—893no—
370#386—893no—
371#386—893no—
372#386—893no—
373#386—893no—
374#385—893no—
375#385—893no—
376#385—893no—
377#385—893no—
378#384—891no—
379#383—891no—
380#383C2×D8911yescharacteristic, complemented
381#381—893no—
382#380—893no—
383#380—893no—
384#379—893no—
385C4×C4⋊C4—893no—
386C4×C4⋊C4C2×D8913yescomplemented
387C4×C22⋊C4—893no—
388C4×C22⋊C4—893no—
389C4×C22⋊C4—893no—
390C4×C22⋊C4C2×D8913yes—
391C43C2×D8911yescharacteristic, complemented
392C25—891no—
393C22×D4—893no—
394C22×D4—893no—
395C22×D4—893no—
396C22×D4—893no—
397C23×C4—893no—
398C23×C4—891no—
399C23×C4—891no—
400C23×C4—891no—
401C23×C4—893no—
402C23×C4—893no—
403C23×C4—891no—
404C23×C4—891no—
405C23×C4—3566no—
406C23×C4C22×D8911yescharacteristic
407#127—898no—
408#126—898no—
409#126C4×D8918yescomplemented
410#123—8924no—
411#121—8924no—
412#121—8924no—
413#120—8924no—
414C4×D4—3566no—
415C4×D4—3566no—
416C4×D4—3566no—
417C4×D4—3566no—
418C2×C4⋊C4—893no—
419C2×C4⋊C4—893no—
420C2×C4⋊C4—893no—
421C2×C4⋊C4—893no—
422C2×C4⋊C4—893no—
423C2×C4⋊C4—893no—
424C2×C4⋊C4C22×D8913yes—
425C2×C4⋊C4C22×D8913yes—
426C2×C22⋊C4—893no—
427C2×C22⋊C4—893no—
428C2×C22⋊C4—893no—
429C2×C22⋊C4—893no—
430C2×C22⋊C4—893no—
431C2×C22⋊C4—893no—
432C2×C22⋊C4—893no—
433C2×C22⋊C4—893no—
434C2×C22⋊C4—893no—
435C2×C22⋊C4—893no—
436C2×C22⋊C4—893no—
437C2×C22⋊C4—893no—
438C2×C22⋊C4—893no—
439C2×C22⋊C4—893no—
440C2×C22⋊C4C22×D8913yes—
441C2×C22⋊C4C22×D8913yes—
442C2×C42—893no—
443C2×C42—893no—
444C2×C42—893no—
445C2×C42—3566no—
446C2×C42C22×D8913yes—
447C2×C42C22×D8913yes—
448C2×C42C22×D8913yes—
449C2×C42C22×D8911yescharacteristic
450#95—893no—
451#95—893no—
452#95—893no—
453#95—893no—
454#95—893no—
455#95—893no—
456#95—893no—
457#95—893no—
458#95C22×D8913yes—
459#95C22×D8913yes—
460#95C22×D8913yes—
461#95C22×D8913yes—
462C24—894no—
463C24—891no—
464C24—891no—
465C24—893no—
466C24—3563no—
467C24—3563no—
468C24C23×D8911yescharacteristic
469C2×D4—8912no—
470C2×D4—8912no—
471C2×D4—8912no—
472C2×D4—8912no—
473C2×D4—3563no—
474C2×D4—3563no—
475C2×D4—3563no—
476C2×D4—3563no—
477C2×D4—3563no—
478C2×D4—3563no—
479C2×D4—3563no—
480C2×D4—3563no—
481C22×C4—26no—
482C22×C4—893no—
483C22×C4—8912no—
484C22×C4—893no—
485C22×C4—891no—
486C22×C4—891no—
487C22×C4—893no—
488C22×C4—3563no—
489C22×C4—3563no—
490C22×C4—3563no—
491C22×C4—3563no—
492C22×C4—3563no—
493C22×C4—3563no—
494C22×C4—3563no—
495C22×C4—35616no—
496C22×C4—3563no—
497C22×C4—1786no—
498C22×C4—1786no—
499C22×C4—1786no—
500C22×C4—1786no—
501C22×C4—1786no—
502C22×C4C23×D8913yes—
503C22×C4C23×D8913yes—
504C22×C4C23×D8911yescharacteristic
505C22×C4C23×D8913yes—
506C22×C4C23×D8913yes—
507C22×C4C23×D8911yescharacteristic
508C4⋊C4—43no—
509C4⋊C4—8912no—
510C4⋊C4—3563no—
511C4⋊C4—3563no—
512C4⋊C4—3563no—
513C4⋊C4—3563no—
514C4⋊C4—3563no—
515C4⋊C4C2×C4×D89112yescomplemented
516C22⋊C4—43no—
517C22⋊C4—8912no—
518C22⋊C4—8912no—
519C22⋊C4—8912no—
520C22⋊C4—3563no—
521C22⋊C4—3563no—
522C22⋊C4—3563no—
523C22⋊C4—3563no—
524C22⋊C4—3563no—
525C22⋊C4—3563no—
526C22⋊C4—3563no—
527C22⋊C4—3563no—
528C22⋊C4—3563no—
529C22⋊C4—3563no—
530C22⋊C4—3563no—
531C22⋊C4C2×C4×D89112yes—
532C42—26no—
533C42—26no—
534C42—43no—
535C42—3563no—
536C42—3563no—
537C42—1786no—
538C42C2×C4×D8914yescomplemented
539C23—23no—
540C23—23no—
541C23—892no—
542C23—892no—
543C23—896no—
544C23—35612no—
545C23—3564no—
546C23—35612no—
547C23—1783no—
548C23—1783no—
549C23—1783no—
550C23—1783no—
551C23—1783no—
552C23—1783no—
553C23—1783no—
554C23—1783no—
555C23—1783no—
556C23—1783no—
557C23C22×C4×D8912yes—
558C23C24×D8911yescharacteristic
559D4—35612no—
560D4—35612no—
561D4—35612no—
562D4—35612no—
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—896no—
576C2×C4—35612no—
577C2×C4—35612no—
578C2×C4—3564no—
579C2×C4—3564no—
580C2×C4—3564no—
581C2×C4—3564no—
582C2×C4—3564no—
583C2×C4—35612no—
584C2×C4—1783no—
585C2×C4—1783no—
586C2×C4—1783no—
587C2×C4—1783no—
588C2×C4—1783no—
589C2×C4—1783no—
590C2×C4—1783no—
591C2×C4—1783no—
592C2×C4—1783no—
593C2×C4—1783no—
594C2×C4C22×C4×D8916yes—
595C2×C4C22×C4×D8916yes—
596C2×C4#1566805816yes—
597C22—26no—
598C22—41no—
599C22—43no—
600C22—35616no—
601C22—3561no—
602C22—3561no—
603C22—3563no—
604C22—3563no—
605C22—3563no—
606C22—3563no—
607C22—3563no—
608C22—3563no—
609C22—1786no—
610C22—1786no—
611C22—1786no—
612C22—1786no—
613C22—1786no—
614C22C23×C4×D8911yescharacteristic
615C22C2×#1566805813yes—
616C22#1915243413yes—
617C4—26no—
618C4—26no—
619C4—41no—
620C4—43no—
621C4—43no—
622C4—3561no—
623C4—3561no—
624C4—3563no—
625C4—3563no—
626C4—1786no—
627C4#1915233914yesdirect product factor
628C2—42no—
629C2—3562no—
630C2—3562no—
631C2—3566no—
632C2C4×#1566805813yes—
633C2C2×#1915233911yescharacteristic
634C2#2603439113yes—
subgroupG/H
centerC22×C4C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC4×#126×C89C2
socle, cosocleC23×C89C25
prime radicalC2×#19152339C2
hypercenterC4×#126D89
hypocenterC89C4×#560
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #26023444C2semidirect
3. #26023441C2semidirect
4. #26023428C2semidirect
5. #26023407C2semidirect
6. #26023405C2semidirect
7. #26023399C2semidirect
8. #26023392C2semidirect
9. C4×#15668009C2semidirect
10. C4×#15668006C2semidirect
11. C4×#15667997C2semidirect
12. C4×#15667987C2semidirect
13. C4×#15667985C2semidirect
14. C4×#15667982C2semidirect
15. C4×#126×C89C2semidirect
17. #19152339C4direct (N × H)
26. C2×C4×D356C22semidirect
28. C2×C42×D89C22semidirect
30. #19151500C22semidirect
33. #19151497C22semidirect
34. #19151495C22semidirect
37. #19151490C22semidirect
41. #19151487C22semidirect
42. #19151485C22semidirect
43. #19151484C22semidirect
44. #19151482C22semidirect
49. #19151476C22semidirect
50. #19151476C22semidirect
56. #19151469C22semidirect
57. #19151468C22semidirect
58. #19151466C22semidirect
59. #19151460C22semidirect
60. #19151457C22semidirect
61. #19151455C22semidirect
63. C4×#13083553C22semidirect
66. C4×#13083551C22semidirect
69. #387×C89C22semidirect
70. #383×C89C22semidirect
71. C4×C4⋊C4×C89C22semidirect
73. C43×C89C22semidirect
88. #15668009C2×C4semidirect
89. #15668006C2×C4semidirect
90. #15667997C2×C4semidirect
91. #15667987C2×C4semidirect
92. #15667985C2×C4semidirect
93. #15667982C2×C4semidirect
131. #126×C89C2×C4semidirect
158. C2×D356C22×C4semidirect
181. C2×C4×D89C22×C4semidirect
187. #13083553C22×C4semidirect
201. #13083551C22×C4semidirect
214. C4⋊C4×C89C22×C4semidirect
220. C42×C89C22×C4semidirect
304. C4×C89#560semidirect
328. C4×#126D89semidirect
333. C89C4×#560semidirect
365. #387C2×D89semidirect
380. #383C2×D89semidirect
386. C4×C4⋊C4C2×D89semidirect
391. C43C2×D89semidirect
409. #126C4×D89semidirect
515. C4⋊C4C2×C4×D89semidirect
538. C42C2×C4×D89semidirect
627. C4#19152339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191523392
#260234442
#260234412
#260234282
#260234072
#260234052
#260233992
#260233922
C4×#156680092
C4×#156680062
C4×#156679972
C4×#156679872
C4×#156679852
C4×#156679822
C4×#126×C892
C4×#56089