Finite Group Databasebeta

← #25119077

Subgroups — #25119077

Order 11008.

954 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583122C211yesmaximal, characteristic
2C2×#14583007C211yesmaximal, characteristic, complemented
3C2×C4×#10621873C211yesmaximal, characteristic
4#19137664C211yesmaximal, characteristic
5C4⋊C4×Dic86C211yesmaximal, characteristic, complemented
6#19135411C211yesmaximal, characteristic
7#19135359C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic
9#19135271C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic
11#19134935C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134859C211yesmaximal, characteristic
14#19134426C211yesmaximal, characteristic, complemented
15C43×#1771C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24#14583122C418yescomplemented
25#14583007—24no—
26C4×#10621873—24no—
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582796—21no—
43#14582789—21no—
44#14582788—21no—
45#14582770—21no—
46#14582769C2211yescharacteristic
47#14582768—21no—
48C4⋊C4×Dic43—21no—
49C4×C4⋊Dic43C2211yescharacteristic
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×Dic172C2×C414yescomplemented
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873C2×C414yes—
72#13063313—22no—
73#13063313C2×C414yes—
74C4×Dic86—22no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C4×Dic86—22no—
78C4×Dic86—41no—
79C4×Dic86—41no—
80C4×Dic86—41no—
81C4×Dic86C2×C414yescomplemented
82C4×D172—22no—
83C4×D172—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107#13063257—22no—
108#13063257—22no—
109#13063250—22no—
110#13063250—22no—
111#13063250—41no—
112#13063250C2×C414yescomplemented
113#13063250D414yes—
114#13063247—22no—
115#13063247—41no—
116#13063247C2×C414yes—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43D411yescharacteristic
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43C2×C414yescomplemented
132#97×C43—22no—
133#97×C43—22no—
134C4×C8×C43—22no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C22×C412yes—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C22×C412yes—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
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×C43C22×C412yes—
183C2×C8×C43C22×C412yes—
184C2×C8×C43C2×D412yes—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—41no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C22×C412yes—
192C42×C43#4112yes—
193(C2×D43)⋊C4—24no—
194(C2×D43)⋊C4—24no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—42no—
207C4⋊Dic43—81no—
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C2×D412yes—
210Dic43⋊C4—24no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4—81no—
215Dic43⋊C4—81no—
216C4×Dic43—24no—
217C4×Dic43—42no—
218C4×Dic43—42no—
219C4×Dic43—42no—
220C4×Dic43—81no—
221Dic172—28no—
222#10621873—28no—
223C23×C43C22×D411yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
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—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43C4×D412yes—
247C2×C4×C43C4×D412yes—
248C2×C4×C43#13712yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
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—
276D172—22no—
277D172—22no—
278D172—41no—
279D172—41no—
280C4×D43—84no—
281Dic86—22no—
282Dic86—22no—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86—41no—
287Dic86—41no—
288Dic86C4×D414yes—
289C8×C43—22no—
290C8×C43—22no—
291C8×C43—22no—
292C8×C43—41no—
293#23013—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43D4211yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57711yescharacteristic
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43#52011yescharacteristic
316C4×C43#54711yescharacteristic
317C4×C43#55311yescharacteristic
318Dic43—24no—
319Dic43—42no—
320Dic43—42no—
321Dic43—42no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325C2×#464—431no—
326C2×#441—431no—
327C2×C4×SD16—431no—
328#2367—431no—
329Q8×C4⋊C4—431no—
330#1959—431no—
331#1948—431no—
332#1936—431no—
333#1933—431no—
334#1880—431no—
335#1878—431no—
336#1865—431no—
337#1864—431no—
338#1771D4311yescharacteristic, complemented
339#1763—431no—
340C2×C43#236111yescharacteristic
341C2×C43C4×#13711yescharacteristic
342C2×C43#295211yescharacteristic
343C2×C43#326611yescharacteristic
344C2×C43#327111yescharacteristic
345C2×C43#336911yescharacteristic
346C2×C43#337111yescharacteristic
347D43—82no—
348C22×Q16—431no—
349C22×SD16—431no—
350C2×#124—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356#464—438no—
357#441—864no—
358C4×SD16—864no—
359C2×#106—431no—
360C2×#106—431no—
361C2×C4⋊C8C2×D4311yescharacteristic
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#102—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#97C2×D4311yescharacteristic
371C2×#97C2×D4311yescharacteristic
372C2×C4×C8C2×D4311yescharacteristic
373#391—431no—
374#390—431no—
375#389—431no—
376#389—431no—
377#389—861no—
378#389—861no—
379#388—861no—
380#388—861no—
381#385—861no—
382#384—431no—
383#384—861no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—861no—
386C4×C4⋊C4C2×D4311yescharacteristic
387C4×C22⋊C4—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336C2×D4311yescharacteristic
393#336C2×D4311yescharacteristic
394C43#2301311yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8—431no—
397C22×D4—431no—
398C23×C4—861no—
399C2×Q16—434no—
400C2×Q16—862no—
401C2×Q16—862no—
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409#124—434no—
410#124—862no—
411C4×Q8—434no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—1721no—
417C4×Q8—1721no—
418C4×Q8—1721no—
419C4×D4—862no—
420C4×D4—1721no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4D17211yescharacteristic
435C2×C4⋊C4D17211yescharacteristic
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42C22×D4311yescharacteristic
447C2×C42C22×D4311yescharacteristic
448C2×C42C22×D4311yescharacteristic
449#106—862no—
450#106—862no—
451C4⋊C8C4×D4314yescomplemented
452#103—434no—
453#103—434no—
454#103—862no—
455#103—862no—
456#103—1721no—
457#102—434no—
458#102—862no—
459#102—1721no—
460#97—22no—
461#97—22no—
462C4×C8—22no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95D17211yescharacteristic
469#95D17211yescharacteristic
470C24—861no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—432no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×D4—432no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—3441no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4C2×D17211yescharacteristic
500C22×C4C2×D17211yescharacteristic
501C22×C4C2×D17211yescharacteristic
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4C2×D17211yescharacteristic
505C22×C4C23×D4311yescharacteristic
506Q16—868no—
507SD16—868no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C2×C4×D4312yes—
518C2×C8C2×C4×D4312yes—
519C2×C8D4×D4312yes—
520C4⋊C4—22no—
521C4⋊C4—41no—
522C4⋊C4—432no—
523C4⋊C4—432no—
524C4⋊C4—864no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—3441no—
534C4⋊C4—3441no—
535C4⋊C4—3441no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—864no—
541C22⋊C4—864no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—864no—
550C42—3441no—
551C42—1722no—
552C42—1722no—
553C42—1722no—
554C42C2×C4×D4312yes—
555C42#1062189812yes—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23C22×D17211yescharacteristic
564Q8—434no—
565Q8—862no—
566Q8—862no—
567Q8—862no—
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572D4—862no—
573D4—862no—
574D4—1721no—
575D4—1721no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
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—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—3444no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
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×C4C4×D17212yes—
614C2×C4C4×D17212yes—
615C2×C4#1306335812yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062189811yescharacteristic
620C2×C4#1306337111yescharacteristic
621C2×C4#1306337311yescharacteristic
622C8—22no—
623C8—22no—
624C8—22no—
625C8—41no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C2×C4×D17211yescharacteristic
634C22D4×D17211yescharacteristic
635C22#1458356111yescharacteristic
636C22C2×#1306335811yescharacteristic
637C22#1458369911yescharacteristic
638C22#1458371111yescharacteristic
639C22#1458371111yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—864no—
647C4—3441no—
648C4—3441no—
649C4—3441no—
650C4—1722no—
651C4—1722no—
652C4—1722no—
653C4C4×D4×D4311yescharacteristic
654C4#1458338111yescharacteristic
655C4#1458355011yescharacteristic
656C4#1458359311yescharacteristic
657C2—3442no—
658C2#1913761311yescharacteristic
659C2C4×#1306335811yescharacteristic
660C2#1914348011yescharacteristic
661C2#1914611011yescharacteristic
662C2#1914618511yescharacteristic
663C2#1914733711yescharacteristic
664C2#1914736511yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1771C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1771D43
hypocenterC43#23013
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. C2×#14583007C2semidirect
5. C4⋊C4×Dic86C2semidirect
7. #19135359C2semidirect
9. #19135271C2semidirect
11. #19134935C2semidirect
12. #19134866C2semidirect
14. #19134426C2semidirect
15. C43×#1771C2semidirect
24. #14583122C4semidirect
68. C2×Dic172C2×C4semidirect
81. C4×Dic86C2×C4semidirect
112. #13063250C2×C4semidirect
131. C4⋊C8×C43C2×C4semidirect
338. #1771D43semidirect
394. C43#23013semidirect
451. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831222
C2×#145830072
C2×C4×#106218732
#191376642
C4⋊C4×Dic862
#191354112
#191353592
#191352922
#191352712
#191349492
#191349352
#191348662
#191348592
#191344262
C43×#17712
#2301343