Finite Group Databasebeta

← #25146766

Subgroups — #25146766

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583205C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D43C211yesmaximal, characteristic
3#19139758C211yesmaximal, characteristic
4#19139506C211yesmaximal, characteristic
5#19136031C211yesmaximal, characteristic, complemented
6#19136019C211yesmaximal, characteristic, complemented
7#19135800C211yesmaximal, characteristic, complemented
8#19135791C211yesmaximal, characteristic, complemented
9#19135558C211yesmaximal, characteristic, complemented
10#19135360C211yesmaximal, characteristic, complemented
11#19135018C211yesmaximal, characteristic, complemented
12#19135017C211yesmaximal, characteristic, complemented
13#19134619C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1808C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22#14583205—24no—
23C8×C22⋊D43—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582840—21no—
35#14582833—21no—
36#14582814—21no—
37#14582814—21no—
38#14582792—21no—
39#14582792—21no—
40#14582791—21no—
41#14582788—21no—
42#14582764C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C22⋊D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69#13063316—22no—
70#13063316—22no—
71#13063305—22no—
72#13063305—41no—
73#13063304—22no—
74#13063304—41no—
75#13063290—22no—
76#13063290—22no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4D411yescharacteristic
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063256—22no—
100#13063256—41no—
101Dic43⋊C8D414yes—
102#13063250—22no—
103#13063250—22no—
104#13063248—22no—
105#13063248—22no—
106C22⋊(C43⋊C8)—22no—
107(C2×D43)⋊C8—22no—
108C8×Dic43—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C23×C4×C43C2311yescharacteristic
117C22×C8×C43—22no—
118C22×C8×C43—22no—
119C22×C8×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128#107×C43—22no—
129#107×C43—41no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43C2×D411yescharacteristic
133C23×D43C2×D411yescharacteristic
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—22no—
147C2×C22⋊D43—22no—
148C2×C22⋊D43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—44no—
173C2×C8×C43C2×D412yes—
174C2×C8×C43#4112yes—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—42no—
185C22⋊Dic43—22no—
186C22⋊Dic43—42no—
187C22⋊Dic43—81no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191(C2×D43)⋊C4—42no—
192(C2×D43)⋊C4—81no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201Dic43⋊C4—22no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205C4×Dic43—42no—
206C4×Dic43—81no—
207C4×Dic43C2×D412yes—
208C4×Dic43#4112yes—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8C2×D412yes—
215C8×D43—44no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43#13512yes—
223C23×C43C22×D411yescharacteristic
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—21no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43#13512yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C22⋊D43—28no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
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#12112yes—
277C2×Dic43#12112yes—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286C8×C43—22no—
287C8×C43—22no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290#25343—431nomaximal, Sylow
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43C2×#12111yescharacteristic
299C22×C43#54611yescharacteristic
300C22×C43#54711yescharacteristic
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57811yescharacteristic
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—22no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—41no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43—81no—
317C4×C43#52911yescharacteristic
318C4×C43#54211yescharacteristic
319C4×C43#54611yescharacteristic
320C4×C43#54811yescharacteristic
321Dic43—22no—
322Dic43—22no—
323Dic43—42no—
324Dic43—41no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328C2×#479—431no—
329C2×C8×D4—431no—
330#2562—431no—
331#2536—431no—
332#2077—431no—
333#2075—431no—
334#2036—431no—
335#2035—431no—
336#1991—431no—
337#1949—431no—
338#1892—431no—
339#1892—431no—
340#1808D4311yescharacteristic, complemented
341#1807—431no—
342C4×#103—431no—
343C2×C43—42no—
344C2×C43#242711yescharacteristic
345C2×C43#305011yescharacteristic
346C2×C43#306311yescharacteristic
347C2×C43#330011yescharacteristic
348C2×C43#330111yescharacteristic
349C2×C43#333611yescharacteristic
350C2×C43#333711yescharacteristic
351D43—42no—
352C23×C8—431no—
353C23×C8C2×D4311yescharacteristic
354C2×#125—431no—
355C2×C22⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×C4×Q8—431no—
358C2×C4×D4—431no—
359#479—864no—
360C8×D4—864no—
361C2×#107C2×D4311yescharacteristic
362C2×#107C2×D4311yescharacteristic
363C2×#106—431no—
364C2×#106—431no—
365C2×C4⋊C8—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×C22⋊C8—431no—
371C2×C22⋊C8—431no—
372C2×C4×C8—431no—
373#400—861no—
374#398—861no—
375#394—861no—
376#394—861no—
377#388—861no—
378#388—861no—
379#388—861no—
380#388—861no—
381#382—431no—
382#380—431no—
383#380—431no—
384#380—431no—
385#380—431no—
386#380C2×D4311yescharacteristic
387#380C2×D4311yescharacteristic
388C4×C4⋊C4—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340C2×D4311yescharacteristic
396#340C2×D4311yescharacteristic
397C43#2534311yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×D4—431no—
400C23×C4—431no—
401C23×C4C22×D4311yescharacteristic
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—41no—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8—862no—
408C22×C8—862no—
409C22×C8—1721no—
410C22×C8C22×D4311yescharacteristic
411C22×C8C22×D4311yescharacteristic
412#125—862no—
413#125—862no—
414C22⋊Q8—862no—
415C22⋊Q8—862no—
416C22⋊Q8—1721no—
417C22⋊Q8—1721no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×D4—862no—
421C4×D4—862no—
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⋊C4C22×D4311yescharacteristic
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
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×C42—431no—
446C2×C42—861no—
447C2×C42—861no—
448#107—22no—
449#107—41no—
450#106—862no—
451#106—1721no—
452C4⋊C8—434no—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—862no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C4×C8—862no—
460#95—21no—
461#95—21no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469C24—431no—
470C24D4×D4311yescharacteristic
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4—862no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4D4×D4311yescharacteristic
504C22×C4C23×D4311yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—44no—
510C2×C8—432no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—1724no—
517C2×C8#1062189812yes—
518C2×C8D4×D4312yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—862no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—3441no—
544C22⋊C4—3441no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—432no—
550C42—432no—
551C42—3441no—
552C42—1722no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—432no—
560C23—861no—
561C23—861no—
562C23—861no—
563C23—861no—
564C23—861no—
565C23—861no—
566C23#1306334412yes—
567C23C2×D4×D4311yescharacteristic
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572D4—868no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—862no—
600C2×C4—861no—
601C2×C4—861no—
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×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4#1306337011yescharacteristic
622C2×C4#1306337311yescharacteristic
623C8—22no—
624C8—22no—
625C8—862no—
626C8—1721no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—1721no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22#121×D4311yescharacteristic
642C22#1458353811yescharacteristic
643C22#1458355011yescharacteristic
644C22#135×D4311yescharacteristic
645C22C2×#1306334411yescharacteristic
646C22#1458370611yescharacteristic
647C22#1458371211yescharacteristic
648C4—41no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—862no—
654C4—862no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—1721no—
659C4—1722no—
660C4#1458342711yescharacteristic
661C4#1458351911yescharacteristic
662C4#1458353911yescharacteristic
663C4#1458355911yescharacteristic
664C2—42no—
665C2—1722no—
666C2#1913817111yescharacteristic
667C2#1914417411yescharacteristic
668C2#1914428511yescharacteristic
669C2#1914647711yescharacteristic
670C2#1914650311yescharacteristic
671C2#1914695911yescharacteristic
672C2#1914697511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1808C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1808D43
hypocenterC43#25343
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
1. C2×#14583205C2semidirect
5. #19136031C2semidirect
6. #19136019C2semidirect
7. #19135800C2semidirect
8. #19135791C2semidirect
9. #19135558C2semidirect
10. #19135360C2semidirect
11. #19135018C2semidirect
12. #19135017C2semidirect
13. #19134619C2semidirect
14. #19134414C2semidirect
15. C43×#1808C2semidirect
340. #1808D43semidirect
397. C43#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#145832052
C2×C8×C22⋊D432
#191397582
#191395062
#191360312
#191360192
#191358002
#191357912
#191355582
#191353602
#191350182
#191350172
#191346192
#191344142
C43×#18082
#2534343