Finite Group Databasebeta

← #25159643

Subgroups — #25159643

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138456C211yesmaximal, characteristic, complemented
4C4⋊C4×D172C211yesmaximal, characteristic
5#19136132C211yesmaximal, characteristic, complemented
6#19136073C211yesmaximal, characteristic, complemented
7#19135989C211yesmaximal, characteristic, complemented
8#19135934C211yesmaximal, characteristic, complemented
9#19135328C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134866C211yesmaximal, characteristic, complemented
13#19134845C211yesmaximal, characteristic
14#19134845C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14583200—24no—
24C4×#10621873—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063259C2211yescharacteristic
27C2×#13063259C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582840—21no—
37#14582830—21no—
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582794—21no—
45#14582781—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×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873Q814yes—
69#13063317—22no—
70#13063317—41no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172—22no—
77C4×D172—41no—
78C4×D172—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—44no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99#13063259—22no—
100#13063259—22no—
101#13063259—41no—
102#13063257—22no—
103#13063257—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250—41no—
107#13063247—22no—
108#13063247—22no—
109#13063247D414yes—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128C4×C8×C43—22no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C23×D43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172C2×D412yes—
150C2×D172C2×Q812yes—
151C2×D172#4112yes—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C2×Q812yes—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
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×C43C2×D412yes—
178C2×C8×C43C2×Q812yes—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—42no—
201C4⋊Dic43—81no—
202C4⋊Dic43C2×D412yes—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211C4×Dic43—42no—
212#10621873—28no—
213C23×C43C22×D411yescharacteristic
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
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#13512yes—
238C2×C4×C43AGL(1,ℤ/8)12yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×Q811yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
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—
266D172—22no—
267D172—22no—
268D172—22no—
269D172C22⋊Q814yes—
270C4×D43—48no—
271C4×D43—84no—
272C4×D43—84no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277C8×C43—22no—
278C8×C43—22no—
279C8×C43—41no—
280C8×C43—41no—
281#26374—431nomaximal, Sylow
282C22×C43#52511yescharacteristic
283C22×C43D4211yescharacteristic
284C22×C43D4×Q811yescharacteristic
285C22×C43C2×#13511yescharacteristic
286C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C43#57711yescharacteristic
288C22×C43#57811yescharacteristic
289C2×D43—24no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C4×C43—22no—
297C4×C43—22no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43C2×C22⋊Q811yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#54711yescharacteristic
305C4×C43#55411yescharacteristic
306Dic43—42no—
307Dic43—42no—
308Dic43—42no—
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313C2×#478—431no—
314C2×C4×SD16—431no—
315#2453—431no—
316D4×C4⋊C4—431no—
317#2095—431no—
318#2084—431no—
319#2068—431no—
320#2059—431no—
321#1942—431no—
322#1916D4311yescharacteristic, complemented
323#1877—431no—
324#1877—431no—
325#1865—431no—
326#1862—431no—
327#1862—431no—
328C2×C43#244911yescharacteristic
329C2×C43#310511yescharacteristic
330C2×C43#312011yescharacteristic
331C2×C43#326511yescharacteristic
332C2×C43#328311yescharacteristic
333C2×C43#338111yescharacteristic
334C2×C43#338611yescharacteristic
335D43—44no—
336C22×SD16—431no—
337C2×#125—431no—
338C2×C4×Q8—431no—
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C2×C4×D4—431no—
342C22×C4⋊C4—861no—
343#478—864no—
344C4×SD16—864no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#107—431no—
348C2×#106—431no—
349C2×#106—431no—
350C2×C4⋊C8C2×D4311yescharacteristic
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×C4×C8C2×D4311yescharacteristic
358#400—861no—
359#398—861no—
360#391—431no—
361#391—431no—
362#389—431no—
363#389—431no—
364#389—431no—
365#389—431no—
366#389—861no—
367#387—861no—
368#385—861no—
369#385—861no—
370#384—431no—
371#380—861no—
372C4×C4⋊C4C2×D4311yescharacteristic
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#336C2×D4311yescharacteristic
378#336C2×D4311yescharacteristic
379#336C2×D4311yescharacteristic
380#336C2×D4311yescharacteristic
381C43#2637411yescharacteristic, complemented, Sylow
382C22×Q8—431no—
383C22×D4—431no—
384C23×C4—861no—
385C23×C4—861no—
386C23×C4—861no—
387C2×SD16—434no—
388C2×SD16—862no—
389C2×SD16—862no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394#125—862no—
395#125—1721no—
396C4×Q8—862no—
397C4×Q8—1721no—
398C4×D4—862no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—862no—
402C4×D4—1721no—
403C4×D4—1721no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—1724no—
420C2×C4⋊C4D17211yescharacteristic
421C2×C4⋊C4D17211yescharacteristic
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429#107—862no—
430#107—862no—
431#107—1721no—
432#106—862no—
433#106—862no—
434C4⋊C8—22no—
435#103—862no—
436#103—862no—
437#103—1721no—
438#102—434no—
439#102—862no—
440#102—862no—
441C4×C8—22no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95D17211yescharacteristic
451#95D17211yescharacteristic
452C24—861no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×D4—432no—
460C2×D4—432no—
461C2×D4—432no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C22×C4—864no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—3441no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4C2×D17211yescharacteristic
486C22×C4C2×D17211yescharacteristic
487C22×C4C23×D4311yescharacteristic
488SD16—868no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8D4×D4312yes—
500C2×C8Q8×D4312yes—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—432no—
504C4⋊C4—432no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4—1722no—
524C22⋊C4—864no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—1722no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C22×D17211yescharacteristic
542Q8—862no—
543Q8—862no—
544Q8—1721no—
545Q8—1721no—
546D4—434no—
547D4—862no—
548D4—862no—
549D4—862no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—3444no—
570C2×C4—3444no—
571C2×C4—1728no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4#1306334712yes—
591C2×C4#1306335312yes—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C2×Q8×D4311yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#1306337111yescharacteristic
597C2×C4#1306337211yescharacteristic
598C8—22no—
599C8—22no—
600C8—41no—
601C8—41no—
602C22—864no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458341111yescharacteristic
610C22D4×D17211yescharacteristic
611C22Q8×D17211yescharacteristic
612C22C2×#1306334711yescharacteristic
613C22C2×#1306335311yescharacteristic
614C22#1458371111yescharacteristic
615C22#1458371611yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—3441no—
623C4—3441no—
624C4—3441no—
625C4—3441no—
626C4—1722no—
627C4—1722no—
628C4—1722no—
629C4C22⋊Q8×D4311yescharacteristic
630C4#1458349011yescharacteristic
631C4#1458354711yescharacteristic
632C4#1458360511yescharacteristic
633C2—1724no—
634C2#1913840911yescharacteristic
635C2#1914464411yescharacteristic
636C2#1914481111yescharacteristic
637C2#1914609511yescharacteristic
638C2#1914631711yescharacteristic
639C2#1914747211yescharacteristic
640C2#1914751811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26374
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. #19138456C2semidirect
5. #19136132C2semidirect
6. #19136073C2semidirect
7. #19135989C2semidirect
8. #19135934C2semidirect
9. #19135328C2semidirect
12. #19134866C2semidirect
15. C43×#1916C2semidirect
322. #1916D43semidirect
381. C43#26374semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
C2×C4×#106218732
#191384562
C4⋊C4×D1722
#191361322
#191360732
#191359892
#191359342
#191353282
#191349282
#191348662
#191348452
C43×#19162
#2637443