Finite Group Databasebeta

← #25148658

Subgroups — #25148658

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583200C211yesmaximal, characteristic
2#19139983C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic
4#19136093C211yesmaximal, characteristic, complemented
5#19136083C211yesmaximal, characteristic, complemented
6#19135968C211yesmaximal, characteristic
7#19135968C211yesmaximal, characteristic
8#19135564C211yesmaximal, characteristic, complemented
9#19135359C211yesmaximal, characteristic, complemented
10#19135338C211yesmaximal, characteristic, complemented
11#19135323C211yesmaximal, characteristic, complemented
12#19135292C211yesmaximal, characteristic
13#19135278C211yesmaximal, characteristic
14#19134421C211yesmaximal, characteristic
15C2×C43×#446C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063301—21no—
18C2×C4×D172C2211yescharacteristic
19#14583200—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582830—21no—
29#14582821—21no—
30#14582821—21no—
31#14582818—21no—
32#14582801C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582794—21no—
41#14582794—21no—
42#14582769C2211yescharacteristic
43#14582756—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#446—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63#13063317—22no—
64#13063317—22no—
65#13063301—44no—
66C4×D172—22no—
67C4×D172—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×C4×Dic43—21no—
91#13063259—22no—
92#13063257—22no—
93#13063257—22no—
94#13063257—22no—
95#13063247—22no—
96#13063247—22no—
97#13063247—22no—
98#13063247Q814yescomplemented
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43D411yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C4×Q8×C43—22no—
112C4×Q8×C43—22no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—22no—
120C4⋊C8×C43—22no—
121C4⋊C8×C43D414yes—
122#97×C43—22no—
123#97×C43—22no—
124C4×C8×C43—22no—
125C23×D43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C2×Q812yes—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D412yes—
162C2×C8×C43C2×D412yes—
163C2×C8×C43C2×Q812yes—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43C2×D412yes—
172C42×C43#4112yes—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—42no—
191C4⋊Dic43—81no—
192C4⋊Dic43C2×Q812yes—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201Dic43⋊C4—81no—
202C4×Dic43—81no—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211Q8×C43—44no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
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#12112yes—
228C2×C4×C43#12112yes—
229C2×C4×C43AGL(1,ℤ/8)12yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×Q811yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
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—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—84no—
262C8×C43—22no—
263C8×C43—22no—
264C8×C43—22no—
265C8×C43—41no—
266#25486—431nomaximal, Sylow
267C22×C43C2×#12111yescharacteristic
268C22×C43#54811yescharacteristic
269C22×C43D4×Q811yescharacteristic
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43#57511yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43#53311yescharacteristic
288C4×C43#54111yescharacteristic
289C4×C43#54711yescharacteristic
290C4×C43D4×Q811yescharacteristic
291Dic43—42no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#478—431no—
299C2×#446D4311yescharacteristic, complemented
300#2584—431no—
301#2538—431no—
302#2088—431no—
303#2086—431no—
304#2065—431no—
305#2065—431no—
306#1992—431no—
307#1948—431no—
308#1944—431no—
309#1941—431no—
310#1936—431no—
311#1934—431no—
312#1762—431no—
313C2×C43#242911yescharacteristic
314C2×C43#305511yescharacteristic
315C2×C43#306011yescharacteristic
316C2×C43#336811yescharacteristic
317C2×C43#337611yescharacteristic
318C2×C43#338411yescharacteristic
319C2×C43#338811yescharacteristic
320D43—82no—
321C2×#125—431no—
322C2×C22⋊Q8—861no—
323C2×C4×Q8C2×D4311yescharacteristic
324C2×C4×D4—431no—
325#478—864no—
326#446—24no—
327C2×#107—431no—
328C2×#106—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×C4⋊C8C2×D4311yescharacteristic
332C2×C4⋊C8C2×D4311yescharacteristic
333C2×C4⋊C8C2×D4311yescharacteristic
334C2×#102—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#97C2×D4311yescharacteristic
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8C2×D4311yescharacteristic
341#398—861no—
342#396—861no—
343#396—861no—
344#395—861no—
345#390—431no—
346#390—431no—
347#389—431no—
348#389—431no—
349#389—431no—
350#389—431no—
351#389—431no—
352#389—431no—
353#389—861no—
354#389—861no—
355#384—431no—
356#380—861no—
357C4×C4⋊C4—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366C43#2548611yescharacteristic, complemented, Sylow
367C22×Q8D17211yescharacteristic
368C22×D4—431no—
369C23×C4—861no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374#125—862no—
375#125—862no—
376C22⋊Q8—1724no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—862no—
380C4×D4—862no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4D17211yescharacteristic
399C2×C4⋊C4D17211yescharacteristic
400C2×C4⋊C4D17211yescharacteristic
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#106—862no—
412#106—862no—
413#106—862no—
414C4⋊C8—22no—
415C4⋊C8—22no—
416C4⋊C8C22⋊D4314yes—
417#102—434no—
418#102—862no—
419#102—862no—
420#102—862no—
421#97—22no—
422#97—22no—
423C4×C8—22no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431C24—861no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—41no—
435C2×D4—432no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4C2×D17211yescharacteristic
455C22×C4C2×D17211yescharacteristic
456C22×C4C2×D17211yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8Q8×D4312yes—
468C2×C8C2×C22⋊D4312yes—
469C2×C8C2×C22⋊D4312yes—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C22⋊C4—3441no—
498C22⋊C4—3441no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—3441no—
507C42#1062189812yes—
508C42C2×C22⋊D4312yes—
509C23—862no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23C22×D17211yescharacteristic
517Q8—44no—
518D4—862no—
519D4—862no—
520D4—1721no—
521D4—1721no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—3444no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306329912yes—
560C2×C4#1306329912yes—
561C2×C4#1306335312yes—
562C2×C4C22×C22⋊D4311yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C2×C4#1306337211yescharacteristic
567C2×C4#1306337311yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22C2×#1306329911yescharacteristic
580C22#1458356111yescharacteristic
581C22Q8×D17211yescharacteristic
582C22C2×#1306335311yescharacteristic
583C22#1458369911yescharacteristic
584C22#1458371111yescharacteristic
585C22#1458371111yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—3441no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4—1722no—
598C4—1722no—
599C4#1458345311yescharacteristic
600C4#1458350711yescharacteristic
601C4#1458354811yescharacteristic
602C4Q8×C22⋊D4311yescharacteristic
603C2—3442no—
604C2#1913818811yescharacteristic
605C2#1914421411yescharacteristic
606C2#1914425711yescharacteristic
607C2#1914732611yescharacteristic
608C2#1914742411yescharacteristic
609C2#1914749611yescharacteristic
610C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#446D43
hypocenterC43#25486
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #19139983C2semidirect
4. #19136093C2semidirect
5. #19136083C2semidirect
8. #19135564C2semidirect
9. #19135359C2semidirect
10. #19135338C2semidirect
11. #19135323C2semidirect
15. C2×C43×#446C2semidirect
98. #13063247Q8semidirect
299. C2×#446D43semidirect
366. C43#25486semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
#191399832
#191395132
#191360932
#191360832
#191359682
#191355642
#191353592
#191353382
#191353232
#191352922
#191352782
#191344212
C2×C43×#4462
#2548643