Finite Group Databasebeta

← #25257543

Subgroups — #25257543

Order 11008.

3106 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583381C211yesmaximal, characteristic
2C2×#14583381C211yesmaximal, characteristic
3C2×C4×#10621902C211yesmaximal, characteristic
4#19137513C211yesmaximal, characteristic, complemented
5Q8×C4⋊Dic43C211yesmaximal, characteristic, complemented
6Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
7#19137504C213yesmaximal, complemented
8#19137503C213yesmaximal, complemented
9C4⋊C4×D172C213yesmaximal, complemented
10#19137496C213yesmaximal, complemented
11#19137220C213yesmaximal, complemented
12#19137210C213yesmaximal, complemented
13#19137075C213yesmaximal, complemented
14#389×D43C213yesmaximal, complemented
15C43×#2351C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17#14583381—28no—
18#14583381C4116yescomplemented
19C4×#10621902—28no—
20C2×Q8×Dic43C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×C4×D172C2213yes—
24C2×C4×D172C2213yes—
25C2×C4×D172C2213yes—
26C2×#13063287C2213yes—
27C2×#13063287C2213yes—
28C2×#13063287C2213yes—
29C2×#13063283C2213yes—
30C2×#13063282C2213yes—
31C2×#13063282C2213yes—
32C2×C4⋊C4×D43C2213yes—
33C2×C4⋊C4×D43C2216yes—
34C2×C4⋊C4×D43C2213yes—
35C2×C42×D43C2213yes—
36#14582798C2213yes—
37#14582798C2213yes—
38#14582797C2213yes—
39#14582797C2213yes—
40#14582796C2216yes—
41#14582796C2211yescharacteristic
42#14582796C2213yes—
43#14582795C2213yes—
44#14582795C2213yes—
45#14582794C2213yes—
46#14582794C2213yes—
47#14582773C2213yes—
48#14582773C2213yes—
49#14582773C2216yes—
50#14582773C2216yes—
51#14582770C2213yes—
52#14582770C2213yes—
53#14582769C2213yes—
54#14582768C2213yes—
55#14582764C2213yes—
56#14582758C2216yes—
57#14582756C2216yes—
58C4×Dic43⋊C4C2213yes—
59C4×Dic43⋊C4C2213yes—
60C4×C4⋊Dic43C2213yes—
61#95×D43C2216yes—
62C2×C4×Q8×C43C2211yescharacteristic
63C2×C4×Q8×C43C2211yescharacteristic
64C2×C4×Q8×C43C2211yescharacteristic
65C43×#389C2213yes—
66C43×#389C2213yes—
67C43×#382C2213yes—
68C4×C4⋊C4×C43C2213yes—
69C2×#10621902C2×C418yes—
70C2×#10621902D418yes—
71C2×#10621902Q818yes—
72C22×D172C2313yes—
73C22×C4×D43C2313yes—
74C22×C4×D43C2313yes—
75C22×C4×D43C2316yes—
76C22×C4×D43C2316yes—
77C22×C4×D43C2313yes—
78Q8×Dic43—24no—
79Q8×Dic43—24no—
80Q8×Dic43C2×C418yescomplemented
81C4×D172—212no—
82C4×D172—212no—
83C4×D172C2×C4124yescomplemented
84#13063287—212no—
85#13063287—212no—
86#13063287C2×C4124yescomplemented
87#13063283—212no—
88#13063282—212no—
89#13063282C2×C4124yescomplemented
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2313yes—
92C2×C4⋊Dic43C2313yes—
93C2×C4⋊Dic43C2316yes—
94C2×C4⋊Dic43C2313yes—
95C2×C4⋊Dic43C2313yes—
96C2×Dic43⋊C4C2311yescharacteristic
97C2×Dic43⋊C4C2313yes—
98C2×Dic43⋊C4C2313yes—
99C2×Dic43⋊C4C2311yescharacteristic
100C2×Dic43⋊C4C2313yes—
101C2×Dic43⋊C4C2316yes—
102C2×Dic43⋊C4C2313yes—
103C2×Dic43⋊C4C2313yes—
104C2×Dic43⋊C4C2311yescharacteristic
105C4⋊C4×D43—212no—
106C4⋊C4×D43—412no—
107C4⋊C4×D43C2×C4124yescomplemented
108C2×(C2×D43)⋊C4C2313yes—
109C2×(C2×D43)⋊C4C2313yes—
110C2×(C2×D43)⋊C4C2316yes—
111C2×(C2×D43)⋊C4C2313yes—
112C2×(C2×D43)⋊C4C2313yes—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2313yes—
115C2×C4×Dic43C2313yes—
116C2×C4×Dic43C2313yes—
117C2×C4×Dic43C2313yes—
118C42×D43—212no—
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2316yes—
124C43⋊#95C2311yescharacteristic
125C43⋊#95C2313yes—
126C22×Q8×C43C2311yescharacteristic
127C4×Q8×C43—24no—
128C4×Q8×C43—24no—
129C4×Q8×C43C2×C418yescomplemented
130C2×C4⋊C4×C43C2313yes—
131C2×C4⋊C4×C43C2313yes—
132C2×C4⋊C4×C43C2313yes—
133C2×C4⋊C4×C43C2313yes—
134C2×C4⋊C4×C43C2313yes—
135C2×C42×C43C2313yes—
136C2×C42×C43C2313yes—
137C2×C42×C43C2313yes—
138#95×C43C2311yescharacteristic
139#95×C43C2313yes—
140#95×C43C2316yes—
141C23×D43C2413yes—
142C2×Q8×C43C22×C414yes—
143C2×Q8×C43C2×D414yes—
144C2×Q8×C43C2×Q814yes—
145C22×C4×C43C2413yes—
146C22×C4×C43C2413yes—
147C22×C4×C43C2411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×C4×C43C2413yes—
150C22×C4×C43C2411yescharacteristic
151C22×C4×C43C2413yes—
152C22×Dic43C2411yescharacteristic
153C22×Dic43C2413yes—
154C22×Dic43C2413yes—
155C22×Dic43C2411yescharacteristic
156C22×Dic43C2413yes—
157C22×Dic43C2411yescharacteristic
158C22×Dic43C2411yescharacteristic
159#10621902C4⋊C4164yescomplemented
160C2×D172C22×C4112yes—
161C2×D172C2×D4112yes—
162C2×D172C2×Q8112yes—
163C2×C4×D43—26no—
164C2×C4×D43—26no—
165C2×C4×D43—26no—
166C2×C4×D43—26no—
167C2×C4×D43—212no—
168C2×C4×D43—46no—
169C2×C4×D43—46no—
170C2×C4×D43—43no—
171C2×C4×D43—43no—
172C2×C4×D43—46no—
173C2×C4×D43—46no—
174C2×C4×D43C22×C4124yes—
175C2×C4×D43C22×C4112yes—
176C2×C4×D43C2×D4112yes—
177C2×C4×D43C2×Q8112yes—
178C4⋊C4×C43—26no—
179C4⋊C4×C43—26no—
180C4⋊C4×C43—26no—
181C4⋊C4×C43—43no—
182C4⋊C4×C43C22×C4112yes—
183C42×C43—26no—
184C42×C43—26no—
185C42×C43C22×C4112yes—
186(C2×D43)⋊C4—26no—
187(C2×D43)⋊C4—26no—
188(C2×D43)⋊C4—212no—
189(C2×D43)⋊C4C22×C4112yes—
190(C2×D43)⋊C4C22×C4112yes—
191C4⋊Dic43—26no—
192C4⋊Dic43—26no—
193C4⋊Dic43—22no—
194C4⋊Dic43—46no—
195C4⋊Dic43—43no—
196C4⋊Dic43C22×C4112yes—
197Dic43⋊C4—26no—
198Dic43⋊C4—26no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—46no—
202Dic43⋊C4—43no—
203Dic43⋊C4—43no—
204Dic43⋊C4C22×C4112yes—
205Dic43⋊C4C22×C414yes—
206C4×Dic43—26no—
207C4×Dic43—26no—
208C4×Dic43—22no—
209C4×Dic43—26no—
210C4×Dic43C22×C4112yes—
211C23×C43C2511yescharacteristic
212C22×D43—23no—
213C22×D43—23no—
214C22×D43—23no—
215C22×D43—23no—
216C22×D43C23×C416yes—
217C22×D43C22×D416yes—
218C22×D43C22×Q816yes—
219Q8×C43C2×C4⋊C4116yescomplemented
220C2×C4×C43—21no—
221C2×C4×C43—23no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—23no—
225C2×C4×C43—21no—
226C2×C4×C43—23no—
227C2×C4×C43—21no—
228C2×C4×C43—23no—
229C2×C4×C43—23no—
230C2×C4×C43—21no—
231C2×C4×C43—23no—
232C2×C4×C43—23no—
233C2×C4×C43—23no—
234C2×C4×C43—21no—
235C2×C4×C43C23×C412yes—
236C2×C4×C43C23×C416yes—
237C2×C4×C43C23×C416yes—
238C2×C4×C43C22×D416yes—
239C2×C4×C43C22×Q816yes—
240C2×C4×C43H(5,𝔽2)12yes—
241C2×Dic43—21no—
242C2×Dic43—23no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—23no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—23no—
249C2×Dic43—23no—
250C2×Dic43—23no—
251C2×Dic43—23no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—23no—
255C2×Dic43—23no—
256C2×Dic43C23×C412yes—
257C2×Dic43C23×C416yes—
258C2×Dic43C23×C412yes—
259C2×Dic43C22×D412yes—
260C2×Dic43C22×Q812yes—
261C2×Dic432−1+412yes—
262D172C2×C4⋊C4148yescomplemented
263C4×D43—424no—
264C4×D43—412no—
265C4×D43—412no—
266C4×D43—812no—
267C4×D43C2×C4⋊C4148yescomplemented
268#34250—431nomaximal, Sylow
269C22×C43C24×C411yescharacteristic
270C22×C43C23×D411yescharacteristic
271C22×C43C23×Q811yescharacteristic
272C22×C43C2×H(5,𝔽2)11yescharacteristic
273C22×C43C2×2−1+411yescharacteristic
274C22×C43#58511yescharacteristic
275C22×C43#58511yescharacteristic
276C2×D43—26no—
277C2×D43—26no—
278C2×D43—26no—
279C2×D43—26no—
280C2×D43—26no—
281C2×D43—26no—
282C2×D43C22×C4⋊C4112yes—
283C4×C43—26no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—43no—
287C4×C43—43no—
288C4×C43—41no—
289C4×C43C22×C4⋊C4112yes—
290Dic43—26no—
291Dic43—22no—
292Dic43—22no—
293Dic43—43no—
294Dic43—43no—
295Dic43—41no—
296Dic43C22×C4⋊C414yes—
297C2×#520—431no—
298C2×#520—431no—
299C2×C4×#41—431no—
300#2351—431no—
301#2351D4311yescharacteristic, complemented
302Q8×C4⋊C4—431no—
303Q8×C4⋊C4—431no—
304#2349—433no—
305#2349—433no—
306D4×C4⋊C4—433no—
307D4×C4⋊C4—433no—
308#2317—433no—
309#2316—433no—
310#2296—433no—
311C2×#389—433no—
312C2×C43C23×C4⋊C411yescharacteristic
313C2×C43C4×H(5,𝔽2)11yescharacteristic
314C2×C43C4×2−1+411yescharacteristic
315C2×C43#348811yescharacteristic
316C2×C43#348911yescharacteristic
317C2×C43#350311yescharacteristic
318C2×C43#350411yescharacteristic
319D43—212no—
320C22×#41—431no—
321#520—4316no—
322#520—868no—
323C4×#41—868no—
324C2×C4×Q8—431no—
325C2×C4×Q8—431no—
326C2×C4×Q8—431no—
327C2×C4×Q8C2×D4311yescharacteristic
328C2×C4×Q8C2×D4311yescharacteristic
329C2×C4×Q8C2×D4311yescharacteristic
330C2×C4×D4—433no—
331C2×C4×D4—433no—
332C2×C4×D4—433no—
333C2×C4×D4—433no—
334C2×C4×D4—433no—
335C2×C4×D4—433no—
336C2×#117—433no—
337C2×#117—433no—
338C2×#117—433no—
339C22×C4⋊C4—433no—
340C22×C4⋊C4—433no—
341C22×C4⋊C4—436no—
342C22×C42—433no—
343#389—433no—
344#389—433no—
345#389—433no—
346#389—433no—
347#389—433no—
348#389—433no—
349#389—433no—
350#389—433no—
351#389—436no—
352#389—433no—
353#389—431no—
354#389C2×D4313yes—
355#389C2×D4313yes—
356#385—433no—
357#385—433no—
358#385—436no—
359#385—436no—
360#385—433no—
361#385—433no—
362#384—433no—
363#384—433no—
364#382—433no—
365#382C2×D4313yes—
366#380—436no—
367#380—436no—
368C4×C4⋊C4—433no—
369C4×C4⋊C4—433no—
370C4×C4⋊C4—433no—
371C4×C4⋊C4C2×D4313yes—
372C2×#95—436no—
373C43#3425011yescharacteristic, complemented, Sylow
374C2×#41—438no—
375C2×#41—438no—
376C2×#41—438no—
377C22×Q8C22×D4311yescharacteristic
378C22×D4—433no—
379C23×C4—433no—
380C23×C4—436no—
381C23×C4—433no—
382C23×C4—433no—
383C23×C4—436no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—438no—
387C4×Q8—864no—
388C4×Q8—864no—
389C4×Q8C4×D4318yescomplemented
390C4×D4—4324no—
391C4×D4—4324no—
392C4×D4—8612no—
393C4×D4—8612no—
394C4×D4—8612no—
395C4×D4—8612no—
396#117—4324no—
397#117—8612no—
398#117—8612no—
399C2×C4⋊C4—433no—
400C2×C4⋊C4—433no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—4324no—
403C2×C4⋊C4—433no—
404C2×C4⋊C4—433no—
405C2×C4⋊C4—433no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—433no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—436no—
411C2×C4⋊C4—436no—
412C2×C4⋊C4—433no—
413C2×C4⋊C4—433no—
414C2×C4⋊C4—433no—
415C2×C4⋊C4—8612no—
416C2×C4⋊C4—17212no—
417C2×C4⋊C4C22×D4313yes—
418C2×C4⋊C4C22×D4313yes—
419C2×C4⋊C4C22×D4313yes—
420C2×C4⋊C4C22×D4313yes—
421C2×C4⋊C4C22×D4313yes—
422C2×C22⋊C4—433no—
423C2×C22⋊C4—433no—
424C2×C22⋊C4—433no—
425C2×C22⋊C4—433no—
426C2×C22⋊C4—436no—
427C2×C42—433no—
428C2×C42—433no—
429C2×C42—433no—
430C2×C42—433no—
431C2×C42—431no—
432C2×C42—8612no—
433C2×C42C22×D4313yes—
434C2×C42C22×D4313yes—
435C2×C42C22×D4313yes—
436#95—433no—
437#95—433no—
438#95—436no—
439#95—431no—
440#95—433no—
441#95—433no—
442#95—433no—
443#95C22×D4316yes—
444#95C22×D4311yescharacteristic
445#95C22×D4313yes—
446C24—433no—
447#41—4364no—
448C2×Q8C2×C4×D4314yes—
449C2×Q8D4×D4314yes—
450C2×Q8Q8×D4314yes—
451C2×D4—4312no—
452C2×D4—4312no—
453C2×D4—4312no—
454C22×C4—431no—
455C22×C4—4312no—
456C22×C4—4312no—
457C22×C4—4312no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—433no—
461C22×C4—4324no—
462C22×C4—431no—
463C22×C4—433no—
464C22×C4—433no—
465C22×C4—866no—
466C22×C4—8612no—
467C22×C4—866no—
468C22×C4—866no—
469C22×C4—866no—
470C22×C4—1726no—
471C22×C4—1726no—
472C22×C4—1726no—
473C22×C4—1726no—
474C22×C4—1723no—
475C22×C4—1723no—
476C22×C4C23×D4313yes—
477C22×C4C23×D4311yescharacteristic
478C22×C4C23×D4313yes—
479C22×C4C23×D4313yes—
480C22×C4C23×D4311yescharacteristic
481C22×C4C23×D4311yescharacteristic
482C22×C4C23×D4313yes—
483C4⋊C4—26no—
484C4⋊C4—26no—
485C4⋊C4—26no—
486C4⋊C4—43no—
487C4⋊C4—4312no—
488C4⋊C4—4312no—
489C4⋊C4—434no—
490C4⋊C4—866no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—866no—
495C4⋊C4—866no—
496C4⋊C4—866no—
497C4⋊C4—1726no—
498C4⋊C4—1726no—
499C4⋊C4—1723no—
500C4⋊C4—1723no—
501C4⋊C4—1723no—
502C4⋊C4C2×C4×D43112yes—
503C22⋊C4—4312no—
504C22⋊C4—4312no—
505C22⋊C4—866no—
506C22⋊C4—8612no—
507C22⋊C4—866no—
508C42—26no—
509C42—26no—
510C42—4312no—
511C42—862no—
512C42—866no—
513C42—866no—
514C42—866no—
515C42C2×C4×D43112yes—
516C23—436no—
517C23—436no—
518C23—436no—
519C23—863no—
520C23—863no—
521C23—863no—
522C23—863no—
523C23C24×D4311yescharacteristic
524Q8C4⋊C4×D43116yescomplemented
525D4—4348no—
526C2×C4—21no—
527C2×C4—23no—
528C2×C4—21no—
529C2×C4—23no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—23no—
534C2×C4—23no—
535C2×C4—23no—
536C2×C4—21no—
537C2×C4—23no—
538C2×C4—21no—
539C2×C4—23no—
540C2×C4—23no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—4348no—
545C2×C4—432no—
546C2×C4—436no—
547C2×C4—432no—
548C2×C4—861no—
549C2×C4—863no—
550C2×C4—861no—
551C2×C4—863no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—863no—
556C2×C4—863no—
557C2×C4—863no—
558C2×C4—863no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—863no—
562C2×C4—863no—
563C2×C4—34412no—
564C2×C4—17224no—
565C2×C4—17212no—
566C2×C4—17212no—
567C2×C4C22×C4×D4312yes—
568C2×C4C22×C4×D4316yes—
569C2×C4C22×C4×D4316yes—
570C2×C4C2×D4×D4316yes—
571C2×C4C2×Q8×D4316yes—
572C2×C4#1306337112yes—
573C22—4312no—
574C22—866no—
575C22—866no—
576C22—866no—
577C22—866no—
578C22—866no—
579C22—866no—
580C22C23×C4×D4311yescharacteristic
581C22C22×D4×D4311yescharacteristic
582C22C22×Q8×D4311yescharacteristic
583C22C2×#1306337111yescharacteristic
584C222−1+4×D4311yescharacteristic
585C22#1458373511yescharacteristic
586C22#1458373611yescharacteristic
587C4—26no—
588C4—22no—
589C4—22no—
590C4—43no—
591C4—43no—
592C4—41no—
593C4—434no—
594C4—866no—
595C4—862no—
596C4—862no—
597C4—1723no—
598C4—1723no—
599C4—1721no—
600C4C2×C4⋊C4×D43112yes—
601C2—8612no—
602C2C22×C4⋊C4×D4311yescharacteristic
603C2C4×#1306337111yescharacteristic
604C2#1914780411yescharacteristic
605C2#1914826111yescharacteristic
606C2#1914827411yescharacteristic
607C2#1914841211yescharacteristic
608C2#1914842011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2351C2
socle, cosocleC23×C43C25
prime radicalC22×#10621902C22
hypercenter#2351D43
hypocenterC43#34250
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
4. #19137513C2semidirect
5. Q8×C4⋊Dic43C2semidirect
6. Q8×Dic43⋊C4C2semidirect
7. #19137504C2semidirect
8. #19137503C2semidirect
9. C4⋊C4×D172C2semidirect
10. #19137496C2semidirect
11. #19137220C2semidirect
12. #19137210C2semidirect
13. #19137075C2semidirect
14. #389×D43C2semidirect
15. C43×#2351C2semidirect
18. #14583381C4semidirect
80. Q8×Dic43C2×C4semidirect
83. C4×D172C2×C4semidirect
86. #13063287C2×C4semidirect
89. #13063282C2×C4semidirect
107. C4⋊C4×D43C2×C4semidirect
129. C4×Q8×C43C2×C4semidirect
159. #10621902C4⋊C4semidirect
219. Q8×C43C2×C4⋊C4semidirect
262. D172C2×C4⋊C4semidirect
267. C4×D43C2×C4⋊C4semidirect
301. #2351D43semidirect
373. C43#34250semidirect
389. C4×Q8C4×D43semidirect
524. Q8C4⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833812
C2×C4×#106219022
#191375132
Q8×C4⋊Dic432
Q8×Dic43⋊C42
#191375042
#191375032
C4⋊C4×D1722
#191374962
#191372202
#191372102
#191370752
#389×D432
C43×#23512
#3425043