Finite Group Databasebeta

← #25199730

Subgroups — #25199730

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140555C211yesmaximal, characteristic, complemented
2#19137239C211yesmaximal, characteristic, complemented
3#19136088C211yesmaximal, characteristic, complemented
4#19135982C211yesmaximal, characteristic, complemented
5#19135982C211yesmaximal, characteristic, complemented
6#19135906C211yesmaximal, characteristic
7#19135461C211yesmaximal, characteristic
8#19135328C211yesmaximal, characteristic, complemented
9#19135292C211yesmaximal, characteristic, complemented
10#19135292C211yesmaximal, characteristic, complemented
11#19135216C211yesmaximal, characteristic, complemented
12#19135188C211yesmaximal, characteristic, complemented
13#19134942C211yesmaximal, characteristic
14#19134845C211yesmaximal, characteristic, complemented
15C43×#1768C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582828—21no—
28#14582828—21no—
29#14582828—21no—
30#14582823—21no—
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582788—21no—
42#14582788—21no—
43#14582761—21no—
44#14582758—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#376C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×D344—22no—
63C2×D344—22no—
64C2×D344—41no—
65C4×D172—22no—
66C4×D172—22no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊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×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90#13063259—22no—
91#13063259—22no—
92#13063259—41no—
93#13063247—22no—
94#13063247—22no—
95#13063247—22no—
96#13063247—22no—
97#13063247—41no—
98#13063247—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113C4⋊C8×C43—22no—
114#97×C43—41no—
115C4×C8×C43—41no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C23×D43—21no—
121C23×D43—21no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172#4112yes—
147C2×C4×D43—24no—
148C2×C4×D43—81no—
149C2×C4×D43—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—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43#4112yes—
161C2×C8×C43#4112yes—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—81no—
170(C2×D43)⋊C4—81no—
171(C2×D43)⋊C4—81no—
172(C2×D43)⋊C4—81no—
173(C2×D43)⋊C4—81no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178(C2×D43)⋊C4—81no—
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#4112yes—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194Dic43⋊C4—81no—
195Dic43⋊C4—81no—
196C4×Dic43—81no—
197D344—44no—
198C23×C43C22×D411yescharacteristic
199C22×D43—22no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
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—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C432−1+411yescharacteristic
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—
255D172—22no—
256D172—22no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—41no—
262D172—41no—
263C4×D43—84no—
264C8×C43—22no—
265C8×C43—22no—
266C8×C43—41no—
267C8×C43—41no—
268#29436—431nomaximal, Sylow
269C22×C43#52511yescharacteristic
270C22×C43#53211yescharacteristic
271C22×C43#53711yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57611yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43#55111yescharacteristic
297C4×C43#55211yescharacteristic
298C4×C43#55311yescharacteristic
299C4×C43#55611yescharacteristic
300Dic43—42no—
301Dic43—81no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305Dic43—81no—
306#2644—431no—
307#2319—431no—
308#2087—431no—
309#2067—431no—
310#2067—431no—
311#2054—431no—
312#1970—431no—
313#1942—431no—
314#1936—431no—
315#1936—431no—
316#1925—431no—
317#1921—431no—
318#1879—431no—
319#1862—431no—
320#1768D4311yescharacteristic, complemented
321C2×C43#260111yescharacteristic
322C2×C43#312211yescharacteristic
323C2×C43#312411yescharacteristic
324C2×C43#317511yescharacteristic
325C2×C43#317611yescharacteristic
326C2×C43#325911yescharacteristic
327C2×C43#326211yescharacteristic
328D43—82no—
329D43—161no—
330C22×D8—431no—
331C2×C4×D4—431no—
332C2×#107—431no—
333C2×#107—431no—
334C2×#107—431no—
335C2×C4⋊C8C2×D4311yescharacteristic
336C2×C4⋊C8C2×D4311yescharacteristic
337C2×#102—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#97C2×D4311yescharacteristic
344C2×C4×C8C2×D4311yescharacteristic
345#397—861no—
346#397—861no—
347#397—861no—
348#396—861no—
349#390—431no—
350#390—431no—
351#390—431no—
352#390—431no—
353#390—431no—
354#389—431no—
355#389—431no—
356#389—431no—
357#389—431no—
358#389—431no—
359#388—861no—
360#388—861no—
361#381—861no—
362#380—861no—
363C4×C4⋊C4—431no—
364#376C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#336C2×D4311yescharacteristic
372#336C2×D4311yescharacteristic
373C43#2943611yescharacteristic, complemented, Sylow
374C22×D4—431no—
375C22×D4—431no—
376C23×C4—861no—
377C2×D8—862no—
378C2×D8—862no—
379C2×D8—1721no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C4×D4—862no—
385C4×D4—862no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—861no—
409C2×C42C22×D4311yescharacteristic
410C2×C42C22×D4311yescharacteristic
411C2×C42C22×D4311yescharacteristic
412#107—862no—
413#107—862no—
414#107—1721no—
415C4⋊C8—22no—
416C4⋊C8—22no—
417#102—862no—
418#102—862no—
419#102—862no—
420#102—862no—
421#102—1721no—
422#102—1721no—
423#97—41no—
424C4×C8—41no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95D17211yescharacteristic
432#95D17211yescharacteristic
433#95D17211yescharacteristic
434#95D17211yescharacteristic
435C24—861no—
436C24—861no—
437C2×D4—432no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C22×C4—864no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—3441no—
457C22×C4—3441no—
458C22×C4C2×D17211yescharacteristic
459C22×C4C2×D17211yescharacteristic
460C22×C4C2×D17211yescharacteristic
461C22×C4C2×D17211yescharacteristic
462C22×C4C2×D17211yescharacteristic
463C22×C4C2×D17211yescharacteristic
464C22×C4C23×D4311yescharacteristic
465D8—1724no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8#1062189812yes—
477C2×C8#1062189812yes—
478C4⋊C4—432no—
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—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C22⋊C4—864no—
496C22⋊C4—3441no—
497C22⋊C4—3441no—
498C22⋊C4—3441no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—3441no—
503C22⋊C4—3441no—
504C22⋊C4—3441no—
505C22⋊C4—3441no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—3441no—
513C23—862no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23C22×D17211yescharacteristic
528D4—862no—
529D4—862no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533D4—1721no—
534D4—1721no—
535D4—1721no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—862no—
555C2×C4—3444no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4C2×#1062189811yescharacteristic
577C2×C4#1306337011yescharacteristic
578C2×C4#1306337311yescharacteristic
579C8—22no—
580C8—22no—
581C8—41no—
582C8—41no—
583C22—3441no—
584C22—3441no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—3441no—
593C22—3441no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22#1458341111yescharacteristic
598C22#1458344911yescharacteristic
599C22#1458348011yescharacteristic
600C22#1458370411yescharacteristic
601C22#1458370411yescharacteristic
602C22#1458370411yescharacteristic
603C22#1458371611yescharacteristic
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—3441no—
611C4—3441no—
612C4—3441no—
613C4—3441no—
614C4—3441no—
615C4—1722no—
616C4#1458357811yescharacteristic
617C4#1458359011yescharacteristic
618C4#1458359811yescharacteristic
619C4#1458362111yescharacteristic
620C2—3442no—
621C2—6881no—
622C2#1914018611yescharacteristic
623C2#1914483911yescharacteristic
624C2#1914485911yescharacteristic
625C2#1914523411yescharacteristic
626C2#1914524511yescharacteristic
627C2#1914603411yescharacteristic
628C2#1914605611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1768C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenter#1768D43
hypocenterC43#29436
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
1. #19140555C2semidirect
2. #19137239C2semidirect
3. #19136088C2semidirect
4. #19135982C2semidirect
5. #19135982C2semidirect
8. #19135328C2semidirect
9. #19135292C2semidirect
10. #19135292C2semidirect
11. #19135216C2semidirect
12. #19135188C2semidirect
14. #19134845C2semidirect
15. C43×#1768C2semidirect
320. #1768D43semidirect
373. C43#29436semidirect

Maximal subgroups

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

subgroupindex
#191405552
#191372392
#191360882
#191359822
#191359062
#191354612
#191353282
#191352922
#191352162
#191351882
#191349422
#191348452
C43×#17682
#2943643