Finite Group Databasebeta

← #25154679

Subgroups — #25154679

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139623C211yesmaximal, characteristic, complemented
2#19137540C211yesmaximal, characteristic
3#19135980C211yesmaximal, characteristic
4#19135978C211yesmaximal, characteristic
5#19135732C211yesmaximal, characteristic
6#19135730C211yesmaximal, characteristic
7#19135547C211yesmaximal, characteristic, complemented
8#19135545C211yesmaximal, characteristic, complemented
9#19135350C211yesmaximal, characteristic, complemented
10#19135312C211yesmaximal, characteristic, complemented
11#19135169C211yesmaximal, characteristic, complemented
12#19134721C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1918C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063324—21no—
18C2×#13063324C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063282—21no—
21C2×#13063258C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582820—21no—
31#14582819—21no—
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582796—21no—
36#14582790—21no—
37#14582788—21no—
38#14582768C2211yescharacteristic
39#14582768C2211yescharacteristic
40#14582758—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86—21no—
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063325—22no—
66#13063325—41no—
67#13063324—22no—
68#13063324—41no—
69#13063324—44no—
70#13063287—22no—
71#13063287Q814yescomplemented
72#13063282—44no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
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—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063258—22no—
95C4⋊(C43⋊C8)—41no—
96Dic43⋊C8—22no—
97Dic43⋊C8—41no—
98#13063247—22no—
99#13063247—41no—
100#13063245—22no—
101#13063245—41no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172C2×Q812yes—
141C2×C4×D43—24no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×Dic86—42no—
145C2×Dic86—42no—
146C2×Dic86—42no—
147C2×Dic86—42no—
148C2×Dic86—81no—
149C2×Dic86—81no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43C2×Q812yes—
164C4⋊C4×C43#4112yes—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—42no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—81no—
172(C2×D43)⋊C4—81no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—42no—
179C4⋊Dic43—42no—
180C4⋊Dic43#4112yes—
181Dic43⋊C4—22no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187Dic43⋊C4D814yes—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—42no—
191C4×Dic43—42no—
192C4×Dic43C2×Q812yes—
193C4×Dic43#4112yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×D812yes—
226C2×C4×C43C22×Q811yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
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×Dic43C22⋊Q812yes—
249C2×Dic43C22⋊Q812yes—
250C2×Dic43C2×D812yes—
251C2×Dic43C2×D812yes—
252C2×Dic43#13712yes—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—48no—
258Dic86—84no—
259Dic86—84no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#26020—431nomaximal, Sylow
265C22×C43C2×C22⋊Q811yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54811yescharacteristic
268C22×C43C22×D811yescharacteristic
269C22×C43C2×#13711yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43#53311yescharacteristic
286C4×C43#54411yescharacteristic
287C4×C43#55511yescharacteristic
288C4×C43#55611yescharacteristic
289Dic43—22no—
290Dic43—22no—
291Dic43—41no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43#47414yes—
296#2551—431no—
297#2354—431no—
298#2067—431no—
299#2067—431no—
300#2023—431no—
301#2023—431no—
302#1988—431no—
303#1988—431no—
304#1947—431no—
305#1939—431no—
306#1918—431no—
307#1918D4311yescharacteristic, complemented
308#1834—431no—
309#1802—431no—
310C4×#102—431no—
311C2×C43#243911yescharacteristic
312C2×C43C2×#47411yescharacteristic
313C2×C43#308411yescharacteristic
314C2×C43#329411yescharacteristic
315C2×C43#332911yescharacteristic
316C2×C43#335811yescharacteristic
317C2×C43#336911yescharacteristic
318D43—82no—
319C2×C4⋊Q8—431no—
320C2×C4⋊Q8—431no—
321C2×C4⋊Q8—861no—
322C2×C4×D4—431no—
323C2×#117—861no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×C4⋊C8—431no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×C4×C8—431no—
334#395—861no—
335#395—861no—
336#390—431no—
337#390—431no—
338#389—431no—
339#389—861no—
340#389C2×D4311yescharacteristic
341#388—861no—
342#388—861no—
343#384—431no—
344#384—431no—
345#380—861no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4C2×D4311yescharacteristic
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340C2×D4311yescharacteristic
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#336—431no—
361#336C2×D4311yescharacteristic
362C43#2602011yescharacteristic, complemented, Sylow
363C22×Q8—861no—
364C22×Q8—861no—
365C22×D4—431no—
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371C4⋊Q8—862no—
372C4⋊Q8—862no—
373C4⋊Q8—1721no—
374C4⋊Q8—1721no—
375C4⋊Q8—1724no—
376C4×D4—434no—
377C4×D4—862no—
378#117—1724no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—21no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—861no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407#107—22no—
408#107—862no—
409C4⋊C8—862no—
410C4⋊C8—1721no—
411C4⋊C8—1721no—
412#102—862no—
413#102—862no—
414#102—1721no—
415#102—1721no—
416C4×C8—862no—
417#95—21no—
418#95—21no—
419#95—431no—
420#95—431no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—861no—
425C2×Q8—3441no—
426C2×Q8—3441no—
427C2×Q8—1722no—
428C2×Q8—1722no—
429C2×Q8—1722no—
430C2×Q8—1722no—
431C2×D4—432no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—864no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—434no—
474C4⋊C4—432no—
475C4⋊C4—862no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4#1062189812yes—
489C4⋊C4Q8×D4312yes—
490C22⋊C4—864no—
491C22⋊C4—3441no—
492C22⋊C4—3441no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—432no—
499C42—432no—
500C42—861no—
501C42—861no—
502C42—1722no—
503C42—1722no—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23C2×D4×D4311yescharacteristic
512Q8—3444no—
513Q8—3444no—
514D4—862no—
515D4—862no—
516D4—1721no—
517D4—1721no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—862no—
548C2×C4—1728no—
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×C4D8×D4312yes—
558C2×C4C2×Q8×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4#1306337111yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—41no—
565C8—41no—
566C8—1721no—
567C8—1721no—
568C22—3441no—
569C22—3441no—
570C22—3441no—
571C22—3441no—
572C22—1722no—
573C22—1722no—
574C22—1722no—
575C22C22⋊Q8×D4311yescharacteristic
576C22#1458354111yescharacteristic
577C22#1458355811yescharacteristic
578C22C2×D8×D4311yescharacteristic
579C22#137×D4311yescharacteristic
580C22#1458370611yescharacteristic
581C22#1458370811yescharacteristic
582C4—22no—
583C4—41no—
584C4—42no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—434no—
589C4—862no—
590C4—862no—
591C4—3441no—
592C4—3441no—
593C4—1721no—
594C4—1722no—
595C4#1458345311yescharacteristic
596C4#1458352911yescharacteristic
597C4#1458361211yescharacteristic
598C4#1458361611yescharacteristic
599C2—3442no—
600C2#1913828511yescharacteristic
601C2#474×D4311yescharacteristic
602C2#1914446011yescharacteristic
603C2#1914640611yescharacteristic
604C2#1914688711yescharacteristic
605C2#1914722811yescharacteristic
606C2#1914733611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1918C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1918D43
hypocenterC43#26020
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
1. #19139623C2semidirect
7. #19135547C2semidirect
8. #19135545C2semidirect
9. #19135350C2semidirect
10. #19135312C2semidirect
11. #19135169C2semidirect
12. #19134721C2semidirect
15. C43×#1918C2semidirect
71. #13063287Q8semidirect
307. #1918D43semidirect
362. C43#26020semidirect

Maximal subgroups

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

subgroupindex
#191396232
#191375402
#191359802
#191359782
#191357322
#191357302
#191355472
#191355452
#191353502
#191353122
#191351692
#191347212
#191345942
#191344092
C43×#19182
#2602043