Finite Group Databasebeta

← #25164656

Subgroups — #25164656

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138969C211yesmaximal, characteristic, complemented
2#19137609C211yesmaximal, characteristic
3#19135913C211yesmaximal, characteristic, complemented
4#19135785C211yesmaximal, characteristic
5#19135732C211yesmaximal, characteristic, complemented
6#19135600C211yesmaximal, characteristic
7#19135542C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134900C211yesmaximal, characteristic, complemented
13#19134682C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22C22×C4⋊Dic43C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30#14582841—21no—
31#14582811—21no—
32#14582805C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582803—21no—
35#14582801C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582792—21no—
38#14582791—21no—
39#14582776—21no—
40#14582773—21no—
41#14582759C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—41no—
67C2×#10621873—41no—
68#13063325—22no—
69#13063325—41no—
70#13063304—22no—
71#13063304—41no—
72#13063299—22no—
73#13063299—22no—
74C4×D172—22no—
75C4×D172—41no—
76(C22⋊D43)⋊C4—44no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97#13063257—22no—
98#13063250—22no—
99#13063250—22no—
100#13063250—41no—
101#13063247—22no—
102#13063247—22no—
103#13063247—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C4⋊C8×C43—41no—
122C22⋊C8×C43—41no—
123C22⋊C8×C43—41no—
124C4×C8×C43—41no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172#4112yes—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×Dic86—81no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43SD1614yescomplemented
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—42no—
191C22⋊Dic43—81no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206C4⋊Dic43—42no—
207C4⋊Dic43#4112yes—
208C4⋊Dic43#4112yes—
209C4⋊Dic43#4112yes—
210Dic43⋊C4—42no—
211Dic43⋊C4—42no—
212C4×Dic43—42no—
213C4×Dic43—81no—
214#10621873—44no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43C2×SD1612yes—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C2×SD1612yes—
248C2×C4×C43C2×SD1612yes—
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C22⋊D43—48no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—84no—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283Dic86—41no—
284Dic86—41no—
285Dic86—41no—
286Dic86—41no—
287Dic86—84no—
288C8×C43—41no—
289C8×C43—41no—
290C8×C43—41no—
291C8×C43—41no—
292#26722—431nomaximal, Sylow
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43#52511yescharacteristic
301C22×C43#54611yescharacteristic
302C22×C43#54611yescharacteristic
303C22×C43C22×SD1611yescharacteristic
304C22×C43#57511yescharacteristic
305C22×C43#57611yescharacteristic
306C22×C43#57811yescharacteristic
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43#52911yescharacteristic
320C4×C43#53811yescharacteristic
321C4×C43#55511yescharacteristic
322C4×C43#55911yescharacteristic
323Dic43—42no—
324Dic43—42no—
325Dic43—42no—
326Dic43—81no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330#2492—431no—
331#2361—431no—
332#2055—431no—
333#2034—431no—
334#2023—431no—
335#2000—431no—
336#1987—431no—
337#1933—431no—
338#1927—431no—
339#1923D4311yescharacteristic, complemented
340#1919—431no—
341#1877—431no—
342#1872—431no—
343#1823—431no—
344C4×#102—431no—
345C2×C43—42no—
346C2×C43#245911yescharacteristic
347C2×C43#310111yescharacteristic
348C2×C43#312411yescharacteristic
349C2×C43#329511yescharacteristic
350C2×C43#329811yescharacteristic
351C2×C43#331311yescharacteristic
352C2×C43#332211yescharacteristic
353D43—82no—
354C22×SD16—431no—
355C2×C4⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×#121—431no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C22×C4⋊C4—431no—
361C2×#106—431no—
362C2×C4⋊C8C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×C22⋊C8C2×D4311yescharacteristic
370C2×C22⋊C8C2×D4311yescharacteristic
371C2×C4×C8C2×D4311yescharacteristic
372#400—861no—
373#393—861no—
374#391—431no—
375#391—431no—
376#391—861no—
377#390—431no—
378#389—431no—
379#388—861no—
380#388—861no—
381#386—861no—
382#385—861no—
383#380—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C22⋊C4C2×D4311yescharacteristic
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#336C2×D4311yescharacteristic
396#336C2×D4311yescharacteristic
397C43#2672211yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×Q8—861no—
400C22×D4—431no—
401C22×D4—861no—
402C23×C4—861no—
403C23×C4—861no—
404C23×C4C22×D4311yescharacteristic
405C2×SD16—862no—
406C2×SD16—1721no—
407C2×SD16—1721no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412C4⋊Q8—862no—
413C4⋊Q8—1721no—
414C22⋊Q8—862no—
415C22⋊Q8—1721no—
416#121—862no—
417#121—862no—
418C4×D4—862no—
419C4×D4—1721no—
420C4×D4—1724no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—1721no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4D17211yescharacteristic
440C2×C22⋊C4D17211yescharacteristic
441C2×C42—861no—
442C2×C42—861no—
443C2×C42C22×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445#106—862no—
446C4⋊C8—41no—
447#103—862no—
448#103—862no—
449#103—1721no—
450#102—862no—
451#102—862no—
452#102—1721no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455C4×C8—41no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95D17211yescharacteristic
465#95D17211yescharacteristic
466C24—861no—
467C24C2×D17211yescharacteristic
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—3441no—
475C2×Q8—1722no—
476C2×Q8—1722no—
477C2×D4—432no—
478C2×D4—864no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—1722no—
485C2×D4—1722no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—3441no—
500C22×C4—3441no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4C2×D17211yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×D17211yescharacteristic
510C22×C4C23×D4311yescharacteristic
511SD16—1724no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C4⋊C4—432no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—41no—
541C22⋊C4—864no—
542C22⋊C4—3441no—
543C22⋊C4—3441no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4#1062187314yescomplemented
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—3441no—
553C42—1722no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—862no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23C2×#1062187312yes—
568C23C22×D17211yescharacteristic
569Q8—3444no—
570Q8—1721no—
571Q8—1721no—
572Q8—1721no—
573Q8—1721no—
574D4—862no—
575D4—862no—
576D4—1728no—
577D4—1721no—
578D4—1721no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—3444no—
600C2×C4—3444no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4C2×#1062187312yes—
620C2×C4C2×#1062187312yes—
621C2×C4#41×D4311yescharacteristic
622C2×C4#41×D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4#41×D4311yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337011yescharacteristic
627C8—41no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22#1458341111yescharacteristic
646C22#1458354411yescharacteristic
647C22#1458354411yescharacteristic
648C22C22×#1062187311yescharacteristic
649C22#1458369911yescharacteristic
650C22#1458370411yescharacteristic
651C22#1458371611yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—3441no—
658C4—3441no—
659C4—3441no—
660C4—3441no—
661C4—1722no—
662C4—1722no—
663C4—1722no—
664C4#1458343211yescharacteristic
665C4#1458348111yescharacteristic
666C4#1458361111yescharacteristic
667C4#1458363311yescharacteristic
668C2—42no—
669C2—3442no—
670C2#1913853011yescharacteristic
671C2#1914460411yescharacteristic
672C2#1914485911yescharacteristic
673C2#1914642011yescharacteristic
674C2#1914646111yescharacteristic
675C2#1914666311yescharacteristic
676C2#1914679811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1923C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1923D43
hypocenterC43#26722
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #19138969C2semidirect
3. #19135913C2semidirect
5. #19135732C2semidirect
7. #19135542C2semidirect
8. #19135271C2semidirect
9. #19135230C2semidirect
10. #19135174C2semidirect
11. #19134928C2semidirect
12. #19134900C2semidirect
13. #19134682C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1923C2semidirect
185. C22⋊C4×C43SD16semidirect
339. #1923D43semidirect
397. C43#26722semidirect
547. C22⋊C4#10621873semidirect

Maximal subgroups

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

subgroupindex
#191389692
#191376092
#191359132
#191357852
#191357322
#191356002
#191355422
#191352712
#191352302
#191351742
#191349282
#191349002
#191346822
C4×#130632472
C43×#19232
#2672243