Finite Group Databasebeta

← #25100973

Subgroups — #25100973

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2#19137247C211yesmaximal, characteristic, complemented
3#19137239C211yesmaximal, characteristic
4#19135476C211yesmaximal, characteristic
5#19135449C211yesmaximal, characteristic
6#19135333C211yesmaximal, characteristic, complemented
7#19135328C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic
9#19135285C211yesmaximal, characteristic, complemented
10#19135278C211yesmaximal, characteristic
11#19135271C211yesmaximal, characteristic, complemented
12#19134492C211yesmaximal, characteristic, complemented
13C4×#13063250C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic
15C43×#1726C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583001C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582788—21no—
38#14582788—21no—
39#14582781—21no—
40#14582781—21no—
41#14582766—21no—
42#14582763—21no—
43#14582761—21no—
44#14582758—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873C2×C414yes—
66C4×Dic86—22no—
67C4×Dic86C2×C414yes—
68C4×D172—22no—
69C4×D172C2×C414yes—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89#13063259—22no—
90#13063259C2×C414yes—
91#13063257—22no—
92#13063250—22no—
93#13063250—22no—
94#13063250C2×C414yes—
95#13063247—22no—
96#13063247—22no—
97#13063247C2×C414yes—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#97×C43—22no—
116#97×C43—22no—
117#97×C43C2×C414yes—
118C4×C8×C43—22no—
119C4×C8×C43—22no—
120C4×C8×C43—22no—
121#95×C43D411yescharacteristic
122#95×C43D411yescharacteristic
123#95×C43D411yescharacteristic
124#95×C43D411yescharacteristic
125C23×D43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C22×C412yes—
146C2×C4×D43—24no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C22×C412yes—
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×C43C22×C412yes—
162C2×C8×C43C22×C412yes—
163C2×C8×C43#4112yes—
164C2×C8×C43#4112yes—
165C2×C8×C43#4112yes—
166C2×C8×C43#4112yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43C22×C412yes—
172C42×C43#4112yes—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
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⋊Dic43C22×C412yes—
189C4⋊Dic43C22×C412yes—
190Dic43⋊C4—24no—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195C4×Dic43—24no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198#10621873—28no—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
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×C43C4×D412yes—
224C2×C4×C43C4×D412yes—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
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—
252D172—22no—
253D172—22no—
254D172—41no—
255D172—41no—
256C4×D43—84no—
257Dic86—22no—
258Dic86—22no—
259Dic86—41no—
260Dic86—41no—
261C8×C43—22no—
262C8×C43—22no—
263C8×C43—22no—
264C8×C43#11714yes—
265#21291—431nomaximal, Sylow
266C22×C43C2×C4×D411yescharacteristic
267C22×C43#53211yescharacteristic
268C22×C43#53211yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57811yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43C2×#11711yescharacteristic
287C4×C43C4×#4111yescharacteristic
288C4×C43#52911yescharacteristic
289C4×C43#52911yescharacteristic
290Dic43—42no—
291Dic43—42no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296Dic43—81no—
297C2×#440—431no—
298#2320—431no—
299#2319—431no—
300#1973—431no—
301#1968—431no—
302#1943—431no—
303#1942—431no—
304#1936—431no—
305#1935—431no—
306#1934—431no—
307#1933—431no—
308#1776—431no—
309C4×#103—431no—
310C4×#102—431no—
311#1726D4311yescharacteristic, complemented
312C2×C43#229311yescharacteristic
313C2×C43#294611yescharacteristic
314C2×C43#294711yescharacteristic
315C2×C43#317411yescharacteristic
316C2×C43#317511yescharacteristic
317C2×C43#317811yescharacteristic
318C2×C43#317911yescharacteristic
319D43—82no—
320C22×SD16—431no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323#440—438no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#106—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#97C2×D4311yescharacteristic
334C2×#97C2×D4311yescharacteristic
335C2×#97C2×D4311yescharacteristic
336C2×C4×C8C2×D4311yescharacteristic
337C2×C4×C8C2×D4311yescharacteristic
338C2×C4×C8C2×D4311yescharacteristic
339#391—431no—
340#391—431no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#388—861no—
348#388—861no—
349#387—861no—
350#387—861no—
351#383—861no—
352#382—861no—
353#381—861no—
354#380—861no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357#376C2×D4311yescharacteristic
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364C43#2129111yescharacteristic, complemented, Sylow
365C22×Q8—431no—
366C22×D4—431no—
367C23×C4—861no—
368C2×SD16—434no—
369C2×SD16—862no—
370C2×SD16—862no—
371C22×C8C22×D4311yescharacteristic
372C22×C8C22×D4311yescharacteristic
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4×Q8—434no—
376C4×Q8—862no—
377C4×D4—434no—
378C4×D4—862no—
379C2×C4⋊C4—431no—
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×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399C2×C42C22×D4311yescharacteristic
400C2×C42C22×D4311yescharacteristic
401#107—434no—
402#107—862no—
403#106—862no—
404#103—434no—
405#103—862no—
406#103—862no—
407#102—434no—
408#102—862no—
409#102—862no—
410#97—22no—
411#97—22no—
412#97C4×D4314yes—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—22no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95D17211yescharacteristic
427#95D17211yescharacteristic
428#95D17211yescharacteristic
429#95D17211yescharacteristic
430C24—861no—
431C2×Q8—432no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×D4—432no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—864no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—3441no—
452C22×C4—3441no—
453C22×C4C2×D17211yescharacteristic
454C22×C4C2×D17211yescharacteristic
455C22×C4C2×D17211yescharacteristic
456C22×C4C2×D17211yescharacteristic
457C22×C4C2×D17211yescharacteristic
458C22×C4C2×D17211yescharacteristic
459C22×C4C23×D4311yescharacteristic
460SD16—868no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×C4×D4312yes—
468C2×C8C2×C4×D4312yes—
469C2×C8#1062189812yes—
470C2×C8#1062189812yes—
471C2×C8#1062189812yes—
472C2×C8#1062189812yes—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—864no—
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—3441no—
487C4⋊C4—3441no—
488C4⋊C4—3441no—
489C4⋊C4—3441no—
490C22⋊C4—864no—
491C22⋊C4—3441no—
492C22⋊C4—3441no—
493C22⋊C4—3441no—
494C22⋊C4—3441no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—864no—
500C42—3441no—
501C42—3441no—
502C42C2×C4×D4312yes—
503C42#1062189812yes—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23C22×D17211yescharacteristic
512Q8—862no—
513Q8—862no—
514Q8—1721no—
515Q8—1721no—
516D4—862no—
517D4—862no—
518D4—1721no—
519D4—1721no—
520C2×C4—21no—
521C2×C4—21no—
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—862no—
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×C4C4×D17212yes—
559C2×C4C4×D17212yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C2×C4C2×#1062189811yescharacteristic
564C2×C4C2×#1062189811yescharacteristic
565C2×C4C2×#1062189811yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#1306328214yes—
570C22—3441no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22—1722no—
576C22—1722no—
577C22C2×C4×D17211yescharacteristic
578C22#1458344911yescharacteristic
579C22#1458344911yescharacteristic
580C22#1458370411yescharacteristic
581C22#1458371111yescharacteristic
582C22#1458371111yescharacteristic
583C22#1458371611yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—3441no—
591C4—3441no—
592C4—3441no—
593C4—3441no—
594C4—1722no—
595C4—1722no—
596C4—1722no—
597C4C2×#1306328211yescharacteristic
598C4C4×#1062189811yescharacteristic
599C4#1458343311yescharacteristic
600C4#1458343311yescharacteristic
601C2—3442no—
602C2#1913705911yescharacteristic
603C2#1914342911yescharacteristic
604C2#1914344011yescharacteristic
605C2#1914522311yescharacteristic
606C2#1914523411yescharacteristic
607C2#1914526311yescharacteristic
608C2#1914527811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1726C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1726D43
hypocenterC43#21291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #19137247C2semidirect
6. #19135333C2semidirect
7. #19135328C2semidirect
9. #19135285C2semidirect
11. #19135271C2semidirect
12. #19134492C2semidirect
13. C4×#13063250C2semidirect
15. C43×#1726C2semidirect
19. #14583001C4semidirect
311. #1726D43semidirect
364. C43#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
#191372472
#191372392
#191354762
#191354492
#191353332
#191353282
#191352922
#191352852
#191352782
#191352712
#191344922
C4×#130632502
C4×#130632472
C43×#17262
#2129143