Finite Group Databasebeta

← #25114967

Subgroups — #25114967

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2C2×#14583001C211yesmaximal, characteristic
3C2×C4×#10621873C211yesmaximal, characteristic
4C4⋊C4×Dic86C211yesmaximal, characteristic, complemented
5#19137506C211yesmaximal, characteristic
6#19135333C211yesmaximal, characteristic, complemented
7#19135328C211yesmaximal, characteristic, complemented
8#19134866C211yesmaximal, characteristic, complemented
9#19134859C211yesmaximal, characteristic
10#19134852C211yesmaximal, characteristic, complemented
11#19134845C211yesmaximal, characteristic
12#19134763C211yesmaximal, characteristic, complemented
13#19134611C211yesmaximal, characteristic, complemented
14#19134596C211yesmaximal, characteristic
15C43×#1771C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583001—24no—
24#14583001C418yescomplemented
25C4×#10621873—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063259C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063257C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582796—21no—
43#14582770—21no—
44#14582770—21no—
45#14582769C2211yescharacteristic
46#14582768—21no—
47#14582765C2211yescharacteristic
48#14582758—21no—
49C4⋊C4×Dic43—21no—
50#95×D43—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C2×#10621873C2×C414yes—
68C2×#10621873D414yes—
69C2×#10621873Q814yes—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C4×Dic86C2×C414yescomplemented
76C4×D172—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—41no—
80C4×D172—41no—
81C4×D172C2×C414yes—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063259—22no—
104#13063259—41no—
105#13063259C2×C414yescomplemented
106#13063257—22no—
107#13063257—41no—
108#13063250—22no—
109#13063250—22no—
110#13063250C2×C414yescomplemented
111#13063247—22no—
112#13063247—22no—
113#13063247C2×C414yes—
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—
130#97×C43—22no—
131#97×C43C2×C414yescomplemented
132C4×C8×C43—22no—
133#95×C43D411yescharacteristic
134#95×C43D411yescharacteristic
135C23×D43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C22×C412yes—
154C2×D172C2×D412yes—
155C2×D172C2×Q812yes—
156C2×C4×D43—24no—
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×C4×D43—81no—
164C2×C4×D43—81no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86C22×C412yes—
169C2×Dic86C2×D412yes—
170C2×Dic86C2×Q812yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C2×C8×C43C22×C412yes—
181C2×C8×C43C2×D412yes—
182C2×C8×C43C2×Q812yes—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—41no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C22×C412yes—
190C42×C43#4112yes—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—42no—
193(C2×D43)⋊C4—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—42no—
205C4⋊Dic43—81no—
206C4⋊Dic43C22×C412yes—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—24no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—81no—
212Dic43⋊C4—81no—
213Dic43⋊C4—81no—
214Dic43⋊C4—81no—
215C4×Dic43—24no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218#10621873C4⋊C4116yescomplemented
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×C43C4×D412yes—
243C2×C4×C43C4×D412yes—
244C2×C4×C43#13712yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
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—
275D172C2×C4⋊C414yes—
276C4×D43—84no—
277C4×D43—84no—
278C4×D43—84no—
279Dic86—22no—
280Dic86—22no—
281Dic86—22no—
282Dic86C2×C4⋊C414yes—
283C8×C43—22no—
284C8×C43—41no—
285C8×C43—41no—
286C8×C43C2×C4⋊C414yes—
287#22678—431nomaximal, Sylow
288C22×C43C2×C4×D411yescharacteristic
289C22×C43D4211yescharacteristic
290C22×C43D4×Q811yescharacteristic
291C22×C43C2×#13711yescharacteristic
292C22×C43#57511yescharacteristic
293C22×C43#57611yescharacteristic
294C22×C43#57711yescharacteristic
295C2×D43—24no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43C22×C4⋊C411yescharacteristic
309C4×C43#52011yescharacteristic
310C4×C43#54711yescharacteristic
311C4×C43#55411yescharacteristic
312Dic43—24no—
313Dic43—42no—
314Dic43—42no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318Dic43—81no—
319C2×#440—431no—
320C2×#440—431no—
321C2×C4×SD16—431no—
322Q8×C4⋊C4—431no—
323#2349—431no—
324#1943—431no—
325#1942—431no—
326#1865—431no—
327#1864—431no—
328#1863—431no—
329#1862—431no—
330#1847—431no—
331#1805—431no—
332#1802—431no—
333#1771D4311yescharacteristic, complemented
334C2×C43D4×C4⋊C411yescharacteristic
335C2×C43C4×#13711yescharacteristic
336C2×C43#294611yescharacteristic
337C2×C43#326611yescharacteristic
338C2×C43#326811yescharacteristic
339C2×C43#338511yescharacteristic
340C2×C43#338811yescharacteristic
341D43—44no—
342C22×SD16—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349#440—438no—
350#440—864no—
351C4×SD16—864no—
352C2×#107—431no—
353C2×#107—431no—
354C2×#107—431no—
355C2×#106—431no—
356C2×#106—431no—
357C2×C4⋊C8C2×D4311yescharacteristic
358C2×#103—431no—
359C2×#103—431no—
360C2×#103—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#97C2×D4311yescharacteristic
365C2×#97C2×D4311yescharacteristic
366C2×C4×C8C2×D4311yescharacteristic
367#389—431no—
368#389—431no—
369#389—431no—
370#389—431no—
371#389—861no—
372#389—861no—
373#385—861no—
374#385—861no—
375#384—431no—
376#384—861no—
377#382—431no—
378#380—861no—
379C4×C4⋊C4—861no—
380C4×C4⋊C4C2×D4311yescharacteristic
381C2×#95—861no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#336C2×D4311yescharacteristic
387#336C2×D4311yescharacteristic
388C43#2267811yescharacteristic, complemented, Sylow
389C22×Q8—431no—
390C22×D4—431no—
391C23×C4—861no—
392C23×C4—861no—
393C23×C4—861no—
394C2×SD16—434no—
395C2×SD16—434no—
396C2×SD16—434no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C4×Q8—434no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C4×D4—434no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—1721no—
412C4×D4—1721no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4D17211yescharacteristic
429C2×C4⋊C4D17211yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42—861no—
436C2×C42C22×D4311yescharacteristic
437C2×C42C22×D4311yescharacteristic
438C2×C42C22×D4311yescharacteristic
439#107—434no—
440#107—862no—
441#107—1721no—
442#106—862no—
443#106—1721no—
444C4⋊C8—22no—
445#103—434no—
446#103—862no—
447#103—862no—
448#102—434no—
449#102—862no—
450#102—862no—
451#97—22no—
452#97C4×D4314yescomplemented
453C4×C8—22no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95D17211yescharacteristic
461#95D17211yescharacteristic
462C24—861no—
463C2×Q8—432no—
464C2×Q8—432no—
465C2×Q8—432no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×D4—432no—
470C2×D4—432no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—864no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4C2×D17211yescharacteristic
492C22×C4C2×D17211yescharacteristic
493C22×C4C2×D17211yescharacteristic
494C22×C4C2×D17211yescharacteristic
495C22×C4C2×D17211yescharacteristic
496C22×C4C2×D17211yescharacteristic
497C22×C4C23×D4311yescharacteristic
498SD16—4316no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C2×C4×D4312yes—
508C2×C8C2×C4×D4312yes—
509C2×C8D4×D4312yes—
510C2×C8Q8×D4312yes—
511C4⋊C4—22no—
512C4⋊C4—41no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—864no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—3441no—
527C4⋊C4—3441no—
528C4⋊C4—3441no—
529C4⋊C4—3441no—
530C4⋊C4—3441no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C22⋊C4—864no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—864no—
542C42—1722no—
543C42—1722no—
544C42C2×C4×D4312yes—
545C42#1062189812yes—
546C23—862no—
547C23—862no—
548C23—862no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23C22×D17211yescharacteristic
554Q8—434no—
555Q8—862no—
556Q8—862no—
557Q8—862no—
558D4—434no—
559D4—862no—
560D4—862no—
561D4—862no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—3444no—
584C2×C4—3444no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
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×C4C4×D17212yes—
602C2×C4C4×D17212yes—
603C2×C4#1306335812yes—
604C2×C4C22×C4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C2×C4C2×Q8×D4311yescharacteristic
607C2×C4C2×#1062189811yescharacteristic
608C2×C4#1306337111yescharacteristic
609C2×C4#1306337211yescharacteristic
610C8—22no—
611C8—41no—
612C8—41no—
613C8C4⋊C4×D4314yes—
614C22—864no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22C2×C4×D17211yescharacteristic
622C22D4×D17211yescharacteristic
623C22Q8×D17211yescharacteristic
624C22C2×#1306335811yescharacteristic
625C22#1458369911yescharacteristic
626C22#1458370411yescharacteristic
627C22#1458371111yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—864no—
635C4—3441no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—1722no—
640C4—1722no—
641C4C2×C4⋊C4×D4311yescharacteristic
642C4#1458337911yescharacteristic
643C4#1458355411yescharacteristic
644C4#1458360911yescharacteristic
645C2—1724no—
646C2C4⋊C4×D17211yescharacteristic
647C2C4×#1306335811yescharacteristic
648C2#1914342911yescharacteristic
649C2#1914611011yescharacteristic
650C2#1914614011yescharacteristic
651C2#1914750711yescharacteristic
652C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1771C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1771D43
hypocenterC43#22678
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic86C2semidirect
6. #19135333C2semidirect
7. #19135328C2semidirect
8. #19134866C2semidirect
10. #19134852C2semidirect
12. #19134763C2semidirect
13. #19134611C2semidirect
15. C43×#1771C2semidirect
24. #14583001C4semidirect
75. C4×Dic86C2×C4semidirect
105. #13063259C2×C4semidirect
110. #13063250C2×C4semidirect
131. #97×C43C2×C4semidirect
218. #10621873C4⋊C4semidirect
333. #1771D43semidirect
388. C43#22678semidirect
452. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
C2×C4×#106218732
C4⋊C4×Dic862
#191375062
#191353332
#191353282
#191348662
#191348592
#191348522
#191348452
#191347632
#191346112
#191345962
C43×#17712
#2267843