Finite Group Databasebeta

← #25154193

Subgroups — #25154193

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138293C211yesmaximal, characteristic
2#19137463C211yesmaximal, characteristic
3#19136156C211yesmaximal, characteristic, complemented
4#19136086C211yesmaximal, characteristic, complemented
5#19136085C211yesmaximal, characteristic, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135350C211yesmaximal, characteristic, complemented
8#19135168C211yesmaximal, characteristic, complemented
9#19135167C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic
11#19134774C211yesmaximal, characteristic
12#19134680C211yesmaximal, characteristic
13#19134621C211yesmaximal, characteristic
14#340×D43C211yesmaximal, characteristic
15C43×#2057C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063301—21no—
18C2×#13063283—21no—
19C2×C4⋊C4×D43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26#14582832—21no—
27#14582818—21no—
28#14582798C2211yescharacteristic
29#14582798C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582786—21no—
32#14582780—21no—
33#14582770—21no—
34#14582768C2211yescharacteristic
35#14582761—21no—
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×(C2×D43)⋊C4C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C2×C8×D43—22no—
65C2×C8×D43—22no—
66C2×C8×D43—41no—
67#13063301—44no—
68#13063283—44no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43—22no—
82C4⋊C4×D43—41no—
83C4⋊C4×D43Q814yescomplemented
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063258—41no—
93C4⋊(C43⋊C8)—41no—
94Dic43⋊C8—22no—
95(C2×D43)⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4⋊Q8×C43—22no—
109C4⋊Q8×C43—41no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#107×C43—22no—
118#107×C43—41no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C2×Q8×C43—42no—
122C2×Q8×C43—42no—
123C2×Q8×C43—81no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—24no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C2×C4×D43—81no—
148C2×C4×D43C2×Q812yes—
149C2×C4×D43#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43#4112yes—
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×C43—42no—
164C4⋊C4×C43C2×Q812yes—
165C4⋊C4×C43#4112yes—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—22no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4D814yes—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—42no—
180C4⋊Dic43—42no—
181C4⋊Dic43C2×Q812yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—81no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C8×D43—44no—
198C23×C43C22×D411yescharacteristic
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43C22⋊Q812yes—
204C22×D43C2×D812yes—
205C22×D43#13712yes—
206Q8×C43—84no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
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×C43C2×D812yes—
225C2×C4×C43C22×Q811yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
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×Dic43C22⋊Q812yes—
251C2×Dic43C2×D812yes—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—48no—
257C4×D43—84no—
258C8×C43—22no—
259C8×C43—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#25988—431nomaximal, Sylow
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#54611yescharacteristic
265C22×C43#54711yescharacteristic
266C22×C43C22×D811yescharacteristic
267C22×C43C2×#13711yescharacteristic
268C22×C43#57711yescharacteristic
269C22×C43#57811yescharacteristic
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43#47414yes—
277C4×C43—22no—
278C4×C43—42no—
279C4×C43—41no—
280C4×C43—42no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#53311yescharacteristic
284C4×C43#54411yescharacteristic
285C4×C43#55111yescharacteristic
286C4×C43#55211yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—41no—
290Dic43—42no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294#2440—431no—
295#2344—431no—
296#2099—431no—
297#2086—431no—
298#2086—431no—
299#2057D4311yescharacteristic, complemented
300#1988—431no—
301#1947—431no—
302#1918—431no—
303#1918—431no—
304#1852—431no—
305#1850—431no—
306#1823—431no—
307#1808—431no—
308C2×#340—431no—
309C2×C43#243811yescharacteristic
310C2×C43C2×#47411yescharacteristic
311C2×C43#308211yescharacteristic
312C2×C43#329411yescharacteristic
313C2×C43#331211yescharacteristic
314C2×C43#333411yescharacteristic
315C2×C43#334411yescharacteristic
316D43—24no—
317C23×C8—431no—
318C2×C4⋊Q8C2×D4311yescharacteristic
319C2×C22⋊Q8—861no—
320C2×#117—861no—
321C22×C4⋊C4—431no—
322C22×C4⋊C4—431no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×#107C2×D4311yescharacteristic
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×C22⋊C8—431no—
330#398—861no—
331#395—861no—
332#389—431no—
333#389—431no—
334#389—431no—
335#389C2×D4311yescharacteristic
336#387—861no—
337#387—861no—
338#385—861no—
339#384—431no—
340#381—861no—
341#380—431no—
342#380—431no—
343C4×C4⋊C4—431no—
344C4×C4⋊C4—431no—
345C4×C22⋊C4—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358#336—431no—
359#336C2×D4311yescharacteristic
360C43#2598811yescharacteristic, complemented, Sylow
361C22×Q8—21no—
362C23×C4—431no—
363C23×C4—861no—
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8—862no—
368C22×C8—862no—
369C22×C8—1721no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374C22⋊Q8—1724no—
375#117—1724no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—434no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—862no—
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⋊C4—1721no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—431no—
398C2×C22⋊C4—431no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—431no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42C22×D4311yescharacteristic
405#107—22no—
406#107—41no—
407#107—862no—
408#107—1721no—
409C4⋊C8—862no—
410C4⋊C8—1721no—
411C22⋊C8—862no—
412#95—21no—
413#95—431no—
414#95—431no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422C24—431no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—432no—
433C22×C4—432no—
434C22×C4—431no—
435C22×C4—864no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—3441no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4—1722no—
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4C23×D4311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1724no—
464C2×C8#1062190212yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—432no—
474C4⋊C4—864no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4#1062190012yes—
489C4⋊C4Q8×D4312yes—
490C22⋊C4—434no—
491C22⋊C4—862no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C42—21no—
495C42—21no—
496C42—861no—
497C42—861no—
498C42—1722no—
499C42—1722no—
500C23—432no—
501C23—432no—
502C23—432no—
503C23—861no—
504C23—861no—
505C23—861no—
506C23—861no—
507C23C2×D4×D4311yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—861no—
537C2×C4—862no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3444no—
541C2×C4—1728no—
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×C4D8×D4312yes—
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4C2×#1062190011yescharacteristic
557C2×C4C2×#1062190211yescharacteristic
558C2×C4#1306337011yescharacteristic
559C2×C4#1306337311yescharacteristic
560C8—22no—
561C8—41no—
562C8—1721no—
563C8—1721no—
564C22—434no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22C22⋊Q8×D4311yescharacteristic
572C22#1458353611yescharacteristic
573C22#1458355211yescharacteristic
574C22C2×D8×D4311yescharacteristic
575C22#137×D4311yescharacteristic
576C22#1458370911yescharacteristic
577C22#1458371211yescharacteristic
578C4—22no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—862no—
585C4—862no—
586C4—3441no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4—1722no—
591C4#1458345411yescharacteristic
592C4#1458352611yescharacteristic
593C4#1458357611yescharacteristic
594C4#1458358311yescharacteristic
595C2—864no—
596C2#1913826411yescharacteristic
597C2#474×D4311yescharacteristic
598C2#1914443211yescharacteristic
599C2#1914640111yescharacteristic
600C2#1914663911yescharacteristic
601C2#1914694211yescharacteristic
602C2#1914704911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2057C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2057D43
hypocenterC43#25988
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
3. #19136156C2semidirect
4. #19136086C2semidirect
5. #19136085C2semidirect
6. #19135548C2semidirect
7. #19135350C2semidirect
8. #19135168C2semidirect
9. #19135167C2semidirect
15. C43×#2057C2semidirect
83. C4⋊C4×D43Q8semidirect
299. #2057D43semidirect
360. C43#25988semidirect

Maximal subgroups

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

subgroupindex
#191382932
#191374632
#191361562
#191360862
#191360852
#191355482
#191353502
#191351682
#191351672
#191347812
#191347742
#191346802
#191346212
#340×D432
C43×#20572
#2598843