Finite Group Databasebeta

← #25126611

Subgroups — #25126611

Order 11008.

796 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063301C211yesmaximal, characteristic
2#19136999C211yesmaximal, characteristic
3#19136155C211yesmaximal, characteristic, complemented
4#19136136C211yesmaximal, characteristic, complemented
5#19136075C211yesmaximal, characteristic, complemented
6#19136033C211yesmaximal, characteristic
7#19136030C211yesmaximal, characteristic
8#19136006C211yesmaximal, characteristic, complemented
9#19135790C211yesmaximal, characteristic
10#19135789C211yesmaximal, characteristic
11C4×#13063256C211yesmaximal, characteristic, complemented
12C4×#13063257C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063282—21no—
18C2×C42×D43C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582806C2211yescharacteristic
29#14582795C2211yescharacteristic
30#14582780—21no—
31#14582770—21no—
32#14582768C2211yescharacteristic
33#14582768C2211yescharacteristic
34#14582763—21no—
35#14582758—21no—
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4×Dic43⋊C4—21no—
40C4×Dic43⋊C4—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063301—22no—
65#13063301—22no—
66#13063282—44no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43—22no—
87C42×D43—22no—
88#13063257—22no—
89#13063257—22no—
90#13063256—22no—
91#13063256—22no—
92#13063249—22no—
93#13063249—22no—
94(C2×D43)⋊C8—22no—
95(C2×D43)⋊C8—22no—
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×Q8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×Q8×C43—22no—
109C4×Q8×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#103×C43—22no—
118#103×C43—22no—
119C4×C8×C43—22no—
120#95×C43—21no—
121C23×D43C2×D411yescharacteristic
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—22no—
152C2×C4×D43—41no—
153C2×C4×D43SD1614yes—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C42×C43—42no—
168C42×C43—42no—
169C42×C43#4112yes—
170C42×C43#4112yes—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43#4112yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43C2×SD1612yes—
209Q8×C43—22no—
210Q8×C43—22no—
211Q8×C43—41no—
212Q8×C43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
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×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43#12312yes—
228C2×C4×C43#12312yes—
229C2×C4×C43C2×SD1612yes—
230C2×C4×C43#13712yes—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
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×Dic43C2×SD1612yes—
257C2×Dic43#13512yes—
258C4×D43—28no—
259C4×D43—44no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268#23756—431nomaximal, Sylow
269C22×C43C2×#12311yescharacteristic
270C22×C43#52511yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43C22×SD1611yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43C2×#13711yescharacteristic
275C22×C43#57511yescharacteristic
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#48314yes—
289C4×C43#52911yescharacteristic
290C4×C43#52911yescharacteristic
291C4×C43#52911yescharacteristic
292C4×C43#52911yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—42no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300C4×C22⋊Q8—431no—
301#2285—431no—
302#2099—431no—
303#2096—431no—
304#2084—431no—
305#2077—431no—
306#2077—431no—
307#2072—431no—
308#2035—431no—
309#2035—431no—
310C4×#106—431no—
311C4×#106—431no—
312C4×#103—431no—
313C4×#103D4311yescharacteristic, complemented
314C4×C22⋊C8—431no—
315C2×C43#239511yescharacteristic
316C2×C43C2×#48311yescharacteristic
317C2×C43#309111yescharacteristic
318C2×C43#310311yescharacteristic
319C2×C43#310711yescharacteristic
320C2×C43#316711yescharacteristic
321C2×C43#317211yescharacteristic
322D43—42no—
323C2×C22⋊Q8—431no—
324C2×C4×Q8C2×D4311yescharacteristic
325C2×#117—861no—
326C22×C42—431no—
327C2×#106—431no—
328C2×#106—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×#103—431no—
332C2×#103—431no—
333C2×#103C2×D4311yescharacteristic
334C2×#103C2×D4311yescharacteristic
335C2×C22⋊C8—431no—
336C2×C22⋊C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8C2×D4311yescharacteristic
339#391—431no—
340#389—431no—
341#387—861no—
342#385—861no—
343#384—431no—
344#384—431no—
345#382—861no—
346#380—431no—
347#380—431no—
348#380—431no—
349#380—861no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—861no—
353C4×C4⋊C4—861no—
354C4×C4⋊C4C2×D4311yescharacteristic
355C4×C22⋊C4—861no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364#336—431no—
365#336—431no—
366C43#2375611yescharacteristic, complemented, Sylow
367C22×Q8C22×D4311yescharacteristic
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—431no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C22⋊Q8—862no—
376C22⋊Q8—862no—
377C4×Q8—22no—
378C4×Q8—22no—
379#117—1724no—
380C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—862no—
404C2×C42—862no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#106—862no—
409#106—862no—
410#106—862no—
411#106—862no—
412#103—22no—
413#103—22no—
414#103—862no—
415#103—862no—
416C22⋊C8—862no—
417C22⋊C8—862no—
418C4×C8—22no—
419C4×C8—862no—
420#95—21no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429C24—431no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8#1062189812yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—434no—
443C22×C4—431no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—861no—
448C22×C4—862no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—432no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8#1062189812yes—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C22⋊C4—864no—
496C22⋊C4—1722no—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C42—42no—
500C42—42no—
501C42—862no—
502C42—862no—
503C42—861no—
504C42—861no—
505C42—1722no—
506C42—1722no—
507C42#1062189812yes—
508C42#1062190012yes—
509C23—432no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—41no—
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—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—868no—
542C2×C4—861no—
543C2×C4—862no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1724no—
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—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306330712yes—
563C2×C4#1306330712yes—
564C2×C4SD16×D4312yes—
565C2×C4#1306335712yes—
566C2×C4#41×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4C2×#1062190011yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4C2×#1062189811yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C8—22no—
573C8—41no—
574C8—862no—
575C8—1721no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22C2×#1306330711yescharacteristic
584C22#1458340811yescharacteristic
585C22#1458344611yescharacteristic
586C22C2×SD16×D4311yescharacteristic
587C22#135×D4311yescharacteristic
588C22C2×#1306335711yescharacteristic
589C22#1458369611yescharacteristic
590C4—22no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—862no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4—1722no—
602C4#1458322814yes—
603C4#1458342711yescharacteristic
604C4#1458342911yescharacteristic
605C4#1458342911yescharacteristic
606C4#1458343311yescharacteristic
607C2—1722no—
608C2#1913785611yescharacteristic
609C2C2×#1458322811yescharacteristic
610C2#1914450611yescharacteristic
611C2#1914462411yescharacteristic
612C2#1914466411yescharacteristic
613C2#1914515111yescharacteristic
614C2#1914519911yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC4×#103D43
hypocenterC43#23756
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. #19136155C2semidirect
4. #19136136C2semidirect
5. #19136075C2semidirect
8. #19136006C2semidirect
11. C4×#13063256C2semidirect
12. C4×#13063257C2semidirect
13. C4×#13063249C2semidirect
15. C4×#103×C43C2semidirect
313. C4×#103D43semidirect
366. C43#23756semidirect

Maximal subgroups

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

subgroupindex
C4×#130633012
#191369992
#191361552
#191361362
#191360752
#191360332
#191360302
#191360062
#191357902
#191357892
C4×#130632562
C4×#130632572
C4×#130632492
C4×(C2×D43)⋊C82
C4×#103×C432
#2375643