Finite Group Databasebeta

← #25156699

Subgroups — #25156699

Order 11008.

904 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583105C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138371C211yesmaximal, characteristic, complemented
4C4⋊C4×D172C211yesmaximal, characteristic
5#19136137C211yesmaximal, characteristic, complemented
6#19136093C211yesmaximal, characteristic, complemented
7#19136005C211yesmaximal, characteristic, complemented
8#19135842C211yesmaximal, characteristic, complemented
9#19135271C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134928C211yesmaximal, characteristic
13#19134866C211yesmaximal, characteristic, complemented
14#19134859C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4⋊C4×D43—21no—
24#14583105—24no—
25C4×#10621873—24no—
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582841—21no—
37#14582832—21no—
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582786—21no—
45#14582785—21no—
46#14582773—21no—
47#14582773—21no—
48#14582769C2211yescharacteristic
49#14582756—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873—22no—
72C2×#10621873D414yes—
73#13063325—22no—
74#13063325—41no—
75C4×Dic86—22no—
76C4×Dic86—41no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—22no—
80C4×D172—22no—
81C4×D172—41no—
82C4×D172—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C4⋊C4×D43—44no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101#13063257—22no—
102#13063257—41no—
103#13063250—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—41no—
109#13063247—22no—
110#13063247—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130C4×C8×C43—22no—
131#95×C43D411yescharacteristic
132#95×C43D411yescharacteristic
133C23×D43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C2×D412yes—
152C2×D172#4112yes—
153C2×D172#4112yes—
154C2×C4×D43—24no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C2×D412yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D412yes—
187C4⋊C4×C43—41no—
188C4⋊C4×C43SD1614yescomplemented
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195(C2×D43)⋊C4—24no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—42no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43—81no—
211C4⋊Dic43#4112yes—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—42no—
215Dic43⋊C4—42no—
216C4×Dic43—42no—
217#10621873—28no—
218#10621873—44no—
219C23×C43C22×D411yescharacteristic
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43C2×SD1612yes—
243C2×C4×C43C2×SD1612yes—
244C2×C4×C43C2×SD1612yes—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272D172—22no—
273D172—22no—
274D172—22no—
275D172#12314yes—
276C4×D43—48no—
277C4×D43—84no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283Dic86—41no—
284Dic86—41no—
285Dic86—41no—
286Dic86—41no—
287C8×C43—22no—
288C8×C43—41no—
289C8×C43—41no—
290C8×C43—41no—
291#26166—431nomaximal, Sylow
292C22×C43#52511yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C22×SD1611yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—24no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C2×#12311yescharacteristic
313C4×C43#53911yescharacteristic
314C4×C43#54711yescharacteristic
315C4×C43#55311yescharacteristic
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322Dic43—81no—
323C2×#461—431no—
324C2×C4×SD16—431no—
325#2446—431no—
326D4×C4⋊C4—431no—
327#2096—431no—
328#2088—431no—
329#2072—431no—
330#2043—431no—
331#1933—431no—
332#1916D4311yescharacteristic, complemented
333#1877—431no—
334#1877—431no—
335#1877—431no—
336#1865—431no—
337#1864—431no—
338C2×C43#244311yescharacteristic
339C2×C43#310111yescharacteristic
340C2×C43#312011yescharacteristic
341C2×C43#326911yescharacteristic
342C2×C43D4×SD1611yescharacteristic
343C2×C43#335911yescharacteristic
344C2×C43#337611yescharacteristic
345D43—44no—
346C22×SD16—431no—
347C22×SD16—431no—
348C2×C4⋊Q8—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—431no—
351C2×C4×D4—431no—
352C2×C4×D4—431no—
353C22×C4⋊C4—861no—
354#461—864no—
355C4×SD16—864no—
356C2×#106—431no—
357C2×#106—431no—
358C2×C4⋊C8C2×D4311yescharacteristic
359C2×#103—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×C4×C8C2×D4311yescharacteristic
368#400—861no—
369#398—861no—
370#391—431no—
371#391—431no—
372#391—431no—
373#389—431no—
374#389—431no—
375#389—431no—
376#387—861no—
377#387—861no—
378#385—861no—
379#385—861no—
380#384—431no—
381#380—861no—
382C4×C4⋊C4C2×D4311yescharacteristic
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#336C2×D4311yescharacteristic
388#336C2×D4311yescharacteristic
389#336C2×D4311yescharacteristic
390#336C2×D4311yescharacteristic
391C43#2616611yescharacteristic, complemented, Sylow
392C22×Q8—431no—
393C22×Q8—431no—
394C22×D4—431no—
395C23×C4—861no—
396C23×C4—861no—
397C23×C4—861no—
398C2×SD16—434no—
399C2×SD16—862no—
400C2×SD16—862no—
401C2×SD16—862no—
402C2×SD16—862no—
403C2×SD16—862no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C4⋊Q8—862no—
409C4⋊Q8—1721no—
410C4×Q8—862no—
411C4×Q8—1721no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—1721no—
417C4×D4—1721no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—1724no—
432C2×C4⋊C4D17211yescharacteristic
433C2×C4⋊C4D17211yescharacteristic
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439C2×C42C22×D4311yescharacteristic
440C2×C42C22×D4311yescharacteristic
441#106—862no—
442#106—1721no—
443C4⋊C8—22no—
444#103—862no—
445#103—862no—
446#103—862no—
447#103—862no—
448#103—862no—
449#103—1721no—
450#102—862no—
451#102—862no—
452C4×C8—22no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95D17211yescharacteristic
463#95D17211yescharacteristic
464C24—861no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—432no—
478C2×D4—432no—
479C2×D4—432no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C22×C4—864no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4C2×D17211yescharacteristic
500C22×C4C2×D17211yescharacteristic
501C22×C4C2×D17211yescharacteristic
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4C2×D17211yescharacteristic
505C22×C4C23×D4311yescharacteristic
506SD16—868no—
507SD16—1724no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8D4×D4312yes—
520C4⋊C4—41no—
521C4⋊C4—432no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—3441no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4#1062187314yescomplemented
540C22⋊C4—864no—
541C22⋊C4—1722no—
542C22⋊C4—1722no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—1722no—
550C23—862no—
551C23—862no—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23C22×D17211yescharacteristic
558Q8—862no—
559Q8—862no—
560Q8—1721no—
561Q8—1721no—
562Q8—1721no—
563Q8—1721no—
564Q8—1721no—
565Q8—1721no—
566D4—434no—
567D4—862no—
568D4—862no—
569D4—862no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—3444no—
588C2×C4—3444no—
589C2×C4—1728no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4C2×#1062187312yes—
610C2×C4C2×#1062187312yes—
611C2×C4C2×#1062187312yes—
612C2×C4C2×D4×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4#41×D4311yescharacteristic
616C2×C4#1306337111yescharacteristic
617C2×C4#1306337311yescharacteristic
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C22—864no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22#1458341111yescharacteristic
630C22D4×D17211yescharacteristic
631C22#1458356111yescharacteristic
632C22C22×#1062187311yescharacteristic
633C22#1458369911yescharacteristic
634C22#1458371111yescharacteristic
635C22#1458371611yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—3441no—
643C4—3441no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4—1722no—
649C4#123×D4311yescharacteristic
650C4#1458349711yescharacteristic
651C4#1458355111yescharacteristic
652C4#1458360011yescharacteristic
653C2—1724no—
654C2#1913833511yescharacteristic
655C2#1914460411yescharacteristic
656C2#1914481111yescharacteristic
657C2#1914615511yescharacteristic
658C2D4×#1062187311yescharacteristic
659C2#1914723811yescharacteristic
660C2#1914742411yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26166
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
3. #19138371C2semidirect
5. #19136137C2semidirect
6. #19136093C2semidirect
7. #19136005C2semidirect
8. #19135842C2semidirect
9. #19135271C2semidirect
13. #19134866C2semidirect
15. C43×#1916C2semidirect
188. C4⋊C4×C43SD16semidirect
332. #1916D43semidirect
391. C43#26166semidirect
539. C4⋊C4#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145831052
C2×C4×#106218732
#191383712
C4⋊C4×D1722
#191361372
#191360932
#191360052
#191358422
#191352712
#191349282
#191348662
#191348592
C43×#19162
#2616643