Finite Group Databasebeta

← #25146056

Subgroups — #25146056

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583266C211yesmaximal, characteristic, complemented
2C2×#14583202C211yesmaximal, characteristic
3#19139592C211yesmaximal, characteristic
4#19137690C211yesmaximal, characteristic, complemented
5#19135977C211yesmaximal, characteristic, complemented
6#19135836C211yesmaximal, characteristic
7#19135832C211yesmaximal, characteristic
8#19135525C211yesmaximal, characteristic
9#19135524C211yesmaximal, characteristic
10#19135516C211yesmaximal, characteristic, complemented
11#19135315C211yesmaximal, characteristic, complemented
12#19135235C211yesmaximal, characteristic, complemented
13#19135226C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic
15C43×#2068C211yesmaximal, characteristic, complemented
16C2×#13063323C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19C2×#13063313C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21#14583266—24no—
22#14583202—24no—
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582828—21no—
38#14582828—21no—
39#14582804C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582794—21no—
42#14582784—21no—
43#14582781—21no—
44#14582758—21no—
45#14582758—21no—
46C4⋊C4×Dic43—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49C4×Dic43⋊C4C2211yescharacteristic
50C4×C4⋊Dic43C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063323—22no—
67#13063323—22no—
68#13063316—22no—
69#13063316D414yes—
70#13063314—22no—
71#13063314—41no—
72#13063313—22no—
73#13063313—41no—
74#13063287—22no—
75#13063287—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
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×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063256—22no—
96Dic43⋊C8—22no—
97Dic43⋊C8—41no—
98#13063250—22no—
99#13063250—22no—
100#13063249—22no—
101#13063249—22no—
102#13063248—22no—
103#13063248—41no—
104#13063247—22no—
105#13063247—22no—
106#13063245—22no—
107#13063245—22no—
108#13063235—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#107×C43—22no—
126C4⋊C8×C43—41no—
127#103×C43—22no—
128#103×C43—41no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C23×D43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172#4112yes—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43C2×D412yes—
181C42×C43—21no—
182C42×C43—21no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—24no—
191C4⋊Dic43C2×D412yes—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—24no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—81no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—42no—
202C4×Dic43—81no—
203C4×Dic43—81no—
204C4×Dic43C2×D412yes—
205C4×Dic43#4112yes—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43C22×D411yescharacteristic
213C22×D43—22no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224C2×C4×C43—22no—
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×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43#12112yes—
268C2×Dic43#12112yes—
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273C4×D43—84no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—41no—
279C8×C43—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#25289—431nomaximal, Sylow
283C22×C43C2×#12111yescharacteristic
284C22×C43#54611yescharacteristic
285C22×C43#54811yescharacteristic
286C22×C43#57511yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57811yescharacteristic
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43#52911yescharacteristic
304C4×C43#54211yescharacteristic
305C4×C43#54811yescharacteristic
306C4×C43#55011yescharacteristic
307Dic43—22no—
308Dic43—22no—
309Dic43—42no—
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313Dic43—81no—
314C2×#491—431no—
315C2×#478—431no—
316#2547—431no—
317#2370—431no—
318#2068D4311yescharacteristic, complemented
319#2066—431no—
320#2042—431no—
321#2042—431no—
322#1983—431no—
323#1983—431no—
324#1981—431no—
325#1940—431no—
326#1928—431no—
327#1927—431no—
328#1762—431no—
329C2×C43#242611yescharacteristic
330C2×C43#304011yescharacteristic
331C2×C43#304611yescharacteristic
332C2×C43#330711yescharacteristic
333C2×C43#331511yescharacteristic
334C2×C43#337611yescharacteristic
335C2×C43#337711yescharacteristic
336D43—82no—
337C2×C4⋊Q8—431no—
338C2×#125—431no—
339C2×#124—431no—
340C2×#124—431no—
341C2×C4×D4—431no—
342#491—864no—
343#478—864no—
344C2×#107C2×D4311yescharacteristic
345C2×#106—431no—
346C2×C4⋊C8—431no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8C2×D4311yescharacteristic
349C2×#103—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103C2×D4311yescharacteristic
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#97—431no—
362#397—861no—
363#397—861no—
364#391—431no—
365#391C2×D4311yescharacteristic
366#389—431no—
367#389—861no—
368#389C2×D4311yescharacteristic
369#387—861no—
370#387—861no—
371#380—861no—
372#380—861no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4—861no—
378#340—431no—
379#340C2×D4311yescharacteristic
380#336—431no—
381#336—431no—
382C43#2528911yescharacteristic, complemented, Sylow
383C22×Q8—431no—
384C22×Q8C22×D4311yescharacteristic
385C22×D4—431no—
386C23×C4—861no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391C4⋊Q8—862no—
392C4⋊Q8—862no—
393#125—434no—
394#125—862no—
395#124—862no—
396#124—862no—
397#124—1721no—
398#124—1721no—
399C4×D4—862no—
400C4×D4—862no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42—861no—
424C2×C42C22×D4311yescharacteristic
425#107—22no—
426#106—862no—
427C4⋊C8—41no—
428C4⋊C8—862no—
429C4⋊C8—1721no—
430#103—22no—
431#103—41no—
432#103—862no—
433#103—862no—
434#103—862no—
435#103—862no—
436#103—862no—
437#103—1721no—
438#102—862no—
439#102—862no—
440#102—862no—
441#102—862no—
442#97—862no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—861no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—432no—
509C4⋊C4—432no—
510C4⋊C4—864no—
511C4⋊C4—864no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—3441no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4D4×D4312yes—
520C22⋊C4—1722no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C42—21no—
526C42—21no—
527C42—432no—
528C42—432no—
529C42—861no—
530C42—861no—
531C42—3441no—
532C42—3441no—
533C42—1722no—
534C23—862no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C2×D4×D4311yescharacteristic
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—1721no—
547Q8—1721no—
548Q8—1721no—
549Q8—1721no—
550D4—862no—
551D4—862no—
552D4—1721no—
553D4—1721no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3444no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#1306337011yescharacteristic
599C2×C4#1306337311yescharacteristic
600C8—41no—
601C8—41no—
602C8—1721no—
603C8—1721no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22#121×D4311yescharacteristic
612C22#1458353811yescharacteristic
613C22#1458355911yescharacteristic
614C22#1458369511yescharacteristic
615C22#1458369611yescharacteristic
616C22#1458370811yescharacteristic
617C22#1458371211yescharacteristic
618C4—41no—
619C4—42no—
620C4—41no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—862no—
625C4—862no—
626C4—3441no—
627C4—1721no—
628C4—1722no—
629C4—1721no—
630C4—1722no—
631C4#1458343211yescharacteristic
632C4#1458351911yescharacteristic
633C4#1458355911yescharacteristic
634C4#1458356711yescharacteristic
635C2—3442no—
636C2#1913815611yescharacteristic
637C2#1914408411yescharacteristic
638C2#1914414211yescharacteristic
639C2#1914656611yescharacteristic
640C2#1914669711yescharacteristic
641C2#1914742011yescharacteristic
642C2#1914744411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2068C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2068D43
hypocenterC43#25289
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2068

Complements

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

NH ≅ G/Ntype
1. C2×#14583266C2semidirect
4. #19137690C2semidirect
5. #19135977C2semidirect
10. #19135516C2semidirect
11. #19135315C2semidirect
12. #19135235C2semidirect
13. #19135226C2semidirect
15. C43×#2068C2semidirect
318. #2068D43semidirect
382. C43#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#145832662
C2×#145832022
#191395922
#191376902
#191359772
#191358362
#191358322
#191355252
#191355242
#191355162
#191353152
#191352352
#191352262
#191344192
C43×#20682
#2528943