Finite Group Databasebeta

← #25146315

Subgroups — #25146315

Order 11008.

856 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583115C211yesmaximal, characteristic
2#19140083C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic, complemented
4#19135975C211yesmaximal, characteristic, complemented
5#19135968C211yesmaximal, characteristic, complemented
6#19135913C211yesmaximal, characteristic, complemented
7#19135906C211yesmaximal, characteristic
8#19135471C211yesmaximal, characteristic
9#19135449C211yesmaximal, characteristic, complemented
10#19135411C211yesmaximal, characteristic, complemented
11#19135359C211yesmaximal, characteristic, complemented
12#19135285C211yesmaximal, characteristic, complemented
13#19135278C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C2×C43×#446C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063301—21no—
20C2×C4×D172C2211yescharacteristic
21#14583115—24no—
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32#14582825—21no—
33#14582821—21no—
34#14582821—21no—
35#14582810—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582789—21no—
45#14582789—21no—
46#14582769C2211yescharacteristic
47#14582756—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#446—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873—41no—
68C2×D344—22no—
69C2×D344—22no—
70C2×D344—41no—
71#13063313—22no—
72#13063313—22no—
73#13063301—44no—
74C4×D172—22no—
75C4×D172—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97#13063257—41no—
98#13063257—41no—
99#13063250—22no—
100#13063250—22no—
101#13063250—41no—
102#13063247—22no—
103#13063247—22no—
104#13063247—22no—
105#13063247—22no—
106#13063247—41no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×Q8×C43D411yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C4×Q8×C43—22no—
120C4×Q8×C43—22no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128C4⋊C8×C43—22no—
129C4⋊C8×C43D414yes—
130#97×C43—22no—
131#97×C43—22no—
132C4×C8×C43—22no—
133C23×D43—21no—
134C23×D43—21no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—41no—
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—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172#4112yes—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
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×C43C2×D412yes—
182C2×C8×C43C2×D412yes—
183C2×C8×C43#4112yes—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C2×D412yes—
192C42×C43#4112yes—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202(C2×D43)⋊C4—81no—
203(C2×D43)⋊C4—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—42no—
215C4⋊Dic43—81no—
216Dic43⋊C4—42no—
217Dic43⋊C4—42no—
218C4×Dic43—81no—
219D344—44no—
220#10621873—44no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—44no—
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×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43#12112yes—
253C2×C4×C43#12112yes—
254C2×C4×C43AGL(1,ℤ/8)12yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
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—41no—
278C2×Dic43—41no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285D172—41no—
286D172—41no—
287C4×D43—84no—
288Dic86—41no—
289Dic86—41no—
290Dic86—41no—
291Dic86—41no—
292C8×C43—22no—
293C8×C43—22no—
294C8×C43—22no—
295C8×C43—41no—
296#25309—431nomaximal, Sylow
297C22×C43C2×#12111yescharacteristic
298C22×C43#54811yescharacteristic
299C22×C43#55011yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43#57511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—22no—
319C4×C43—22no—
320C4×C43—22no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43#52911yescharacteristic
325C4×C43#54211yescharacteristic
326C4×C43#54611yescharacteristic
327C4×C43#54811yescharacteristic
328Dic43—81no—
329Dic43—81no—
330Dic43—81no—
331Dic43—81no—
332Dic43—81no—
333Dic43—81no—
334C2×#463—431no—
335C2×#446D4311yescharacteristic, complemented
336#2592—431no—
337#2538—431no—
338#2066—431no—
339#2065—431no—
340#2055—431no—
341#2054—431no—
342#1972—431no—
343#1968—431no—
344#1959—431no—
345#1948—431no—
346#1935—431no—
347#1934—431no—
348#1762—431no—
349C2×C43#242611yescharacteristic
350C2×C43#305511yescharacteristic
351C2×C43#306011yescharacteristic
352C2×C43#337311yescharacteristic
353C2×C43#337611yescharacteristic
354C2×C43#339711yescharacteristic
355C2×C43#340111yescharacteristic
356D43—82no—
357D43—161no—
358C22×SD16—431no—
359C22×D8—431no—
360C2×#124—431no—
361C2×C22⋊Q8—861no—
362C2×C4×Q8C2×D4311yescharacteristic
363C2×C4×D4—431no—
364#463—864no—
365#446—24no—
366C2×#106—431no—
367C2×#106—431no—
368C2×C4⋊C8C2×D4311yescharacteristic
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×C4⋊C8C2×D4311yescharacteristic
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#97C2×D4311yescharacteristic
380C2×#97C2×D4311yescharacteristic
381C2×C4×C8C2×D4311yescharacteristic
382#397—861no—
383#396—861no—
384#396—861no—
385#393—861no—
386#391—431no—
387#391—431no—
388#390—431no—
389#390—431no—
390#390—431no—
391#390—431no—
392#389—431no—
393#389—431no—
394#388—861no—
395#388—861no—
396#384—431no—
397#380—861no—
398C4×C4⋊C4—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403C43#2530911yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×Q8D17211yescharacteristic
406C22×D4—431no—
407C22×D4—431no—
408C23×C4—861no—
409C2×SD16—862no—
410C2×SD16—862no—
411C2×SD16—1721no—
412C2×D8—862no—
413C2×D8—862no—
414C2×D8—1721no—
415C22×C8C22×D4311yescharacteristic
416C22×C8C22×D4311yescharacteristic
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419#124—862no—
420#124—862no—
421C22⋊Q8—1724no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—862no—
425C4×D4—862no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4D17211yescharacteristic
436C2×C4⋊C4D17211yescharacteristic
437C2×C4⋊C4D17211yescharacteristic
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451C2×C42C22×D4311yescharacteristic
452C2×C42C22×D4311yescharacteristic
453#106—1721no—
454#106—1721no—
455C4⋊C8—22no—
456C4⋊C8—22no—
457C4⋊C8C22⋊D4314yes—
458#103—862no—
459#103—862no—
460#103—1721no—
461#102—862no—
462#102—862no—
463#102—862no—
464#102—862no—
465#102—1721no—
466#97—22no—
467#97—22no—
468C4×C8—22no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476C24—861no—
477C24—861no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—41no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×D4—432no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×D17211yescharacteristic
510C22×C4C2×D17211yescharacteristic
511C22×C4C2×D17211yescharacteristic
512C22×C4C2×D17211yescharacteristic
513C22×C4C2×D17211yescharacteristic
514C22×C4C23×D4311yescharacteristic
515SD16—1724no—
516D8—1724no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8#1062190212yes—
527C2×C8C2×C22⋊D4312yes—
528C2×C8C2×C22⋊D4312yes—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—3441no—
543C4⋊C4—1722no—
544C4⋊C4—1722no—
545C4⋊C4—1722no—
546C22⋊C4—3441no—
547C22⋊C4—3441no—
548C22⋊C4—3441no—
549C22⋊C4—3441no—
550C22⋊C4—1722no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—3441no—
562C42#1062189812yes—
563C42C2×C22⋊D4312yes—
564C23—862no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23C22×D17211yescharacteristic
579Q8—44no—
580Q8—1721no—
581Q8—1721no—
582Q8—1721no—
583Q8—1721no—
584D4—862no—
585D4—862no—
586D4—1721no—
587D4—1721no—
588D4—1721no—
589D4—1721no—
590D4—1721no—
591D4—1721no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—3444no—
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×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4#1306329912yes—
627C2×C4#1306329912yes—
628C2×C4#1306335312yes—
629C2×C4C22×C22⋊D4311yescharacteristic
630C2×C4#41×D4311yescharacteristic
631C2×C4C2×#1062189811yescharacteristic
632C2×C4C2×#1062190211yescharacteristic
633C2×C4#1306337111yescharacteristic
634C2×C4#1306337311yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8—41no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22C2×#1306329911yescharacteristic
654C22#1458356111yescharacteristic
655C22#1458357111yescharacteristic
656C22C2×#1306335311yescharacteristic
657C22#1458369911yescharacteristic
658C22#1458371111yescharacteristic
659C22#1458371111yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—3441no—
667C4—3441no—
668C4—3441no—
669C4—3441no—
670C4—3441no—
671C4—3441no—
672C4#1458343611yescharacteristic
673C4#1458352111yescharacteristic
674C4#1458353711yescharacteristic
675C4#1458356011yescharacteristic
676C2—3442no—
677C2—6881no—
678C2#1913815511yescharacteristic
679C2#1914421411yescharacteristic
680C2#1914425711yescharacteristic
681C2#1914738911yescharacteristic
682C2#1914742411yescharacteristic
683C2#1914761711yescharacteristic
684C2#1914766311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenterC2×#446D43
hypocenterC43#25309
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #19140083C2semidirect
3. #19139513C2semidirect
4. #19135975C2semidirect
5. #19135968C2semidirect
6. #19135913C2semidirect
9. #19135449C2semidirect
10. #19135411C2semidirect
11. #19135359C2semidirect
12. #19135285C2semidirect
13. #19135278C2semidirect
14. #19134421C2semidirect
15. C2×C43×#446C2semidirect
335. C2×#446D43semidirect
403. C43#25309semidirect

Maximal subgroups

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

subgroupindex
C2×#145831152
#191400832
#191395132
#191359752
#191359682
#191359132
#191359062
#191354712
#191354492
#191354112
#191353592
#191352852
#191352782
#191344212
C2×C43×#4462
#2530943