Finite Group Databasebeta

← #25146761

Subgroups — #25146761

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×#14583207C211yesmaximal, characteristic, complemented
2#19139761C211yesmaximal, characteristic
3#19139504C211yesmaximal, characteristic
4#19136028C211yesmaximal, characteristic, complemented
5#19136018C211yesmaximal, characteristic, complemented
6#19135799C211yesmaximal, characteristic, complemented
7#19135792C211yesmaximal, characteristic, complemented
8#19135560C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135018C211yesmaximal, characteristic, complemented
11#19135018C211yesmaximal, characteristic, complemented
12#19134624C211yesmaximal, characteristic, complemented
13#19134620C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C2×C8×D4×C43C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583207—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29#14582837—21no—
30#14582830—21no—
31#14582813—21no—
32#14582813—21no—
33#14582793—21no—
34#14582793—21no—
35#14582787—21no—
36#14582787—21no—
37#14582765C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C23×C8×C43C2211yescharacteristic
54C23×C8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C8×D4×C43—24no—
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62#13063317—22no—
63#13063317—22no—
64#13063304—22no—
65#13063304—22no—
66#13063304—41no—
67#13063304—41no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92#13063259—22no—
93#13063259—41no—
94#13063257—22no—
95#13063257—41no—
96#13063250—22no—
97#13063250—22no—
98#13063250—22no—
99#13063250—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43D411yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43—22no—
113C22×C8×C43—22no—
114C22×C8×C43—22no—
115C22×C8×C43—22no—
116C22×C8×C43—41no—
117C22×C8×C43—41no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43D414yes—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131C4×C8×C43—22no—
132C24×C43C2×D411yescharacteristic
133C24×C43C2×D411yescharacteristic
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
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×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—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—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—44no—
178C2×C8×C43—44no—
179C2×C8×C43C2×D412yes—
180C2×C8×C43C2×D412yes—
181C2×C8×C43#4112yes—
182C4⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C42×C43C2×D412yes—
186C42×C43#4112yes—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C22⋊Dic43—81no—
194C22⋊Dic43—81no—
195C4⋊Dic43—21no—
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—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209Dic43⋊C4—42no—
210Dic43⋊C4—42no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214C4×Dic43—42no—
215C4×Dic43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43#13512yes—
229C23×C43#13512yes—
230C23×C43C22×D411yescharacteristic
231D4×C43—28no—
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—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×C43#12112yes—
251C2×C4×C43#12112yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
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—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282Dic86—22no—
283Dic86—22no—
284Dic86—41no—
285Dic86—41no—
286C8×C43—22no—
287C8×C43—22no—
288C8×C43—22no—
289C8×C43—41no—
290#25343—431nomaximal, Sylow
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43C2×#12111yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43#54711yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C22×C43#57711yescharacteristic
311C22×C43#57811yescharacteristic
312C4×C43—22no—
313C4×C43—22no—
314C4×C43—41no—
315C4×C43—41no—
316C4×C43#52911yescharacteristic
317C4×C43#54211yescharacteristic
318C4×C43#54611yescharacteristic
319C4×C43#54811yescharacteristic
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323Dic43—81no—
324Dic43—81no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328C2×#479—431no—
329C2×C8×D4D4311yescharacteristic
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#1808—431no—
341#1807—431no—
342C4×#103—431no—
343C2×C43—42no—
344C2×C43—42no—
345C2×C43#242711yescharacteristic
346C2×C43#305011yescharacteristic
347C2×C43#306311yescharacteristic
348C2×C43#330011yescharacteristic
349C2×C43#330111yescharacteristic
350C2×C43#333611yescharacteristic
351C2×C43#333711yescharacteristic
352C23×C8C2×D4311yescharacteristic
353C23×C8C2×D4311yescharacteristic
354C2×#125—431no—
355C2×C22⋊Q8—431no—
356C2×C22⋊Q8—431no—
357C2×C4×Q8—431no—
358C2×C4×D4C2×D4311yescharacteristic
359#479—864no—
360C8×D4—24no—
361C2×#107—431no—
362C2×#107—431no—
363C2×#106—431no—
364C2×#106—431no—
365C2×C4⋊C8C2×D4311yescharacteristic
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×C22⋊C8C2×D4311yescharacteristic
371C2×C22⋊C8C2×D4311yescharacteristic
372C2×C4×C8C2×D4311yescharacteristic
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#380—431no—
387#380—431no—
388C4×C4⋊C4—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340—431no—
393#340—431no—
394#340—431no—
395#340—431no—
396#340—431no—
397C43#2534311yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×D4D17211yescharacteristic
400C23×C4C22×D4311yescharacteristic
401C23×C4C22×D4311yescharacteristic
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—41no—
407C22×C8—41no—
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
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—22no—
421C4×D4—22no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4D17211yescharacteristic
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C22⋊C4—861no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4D17211yescharacteristic
444C2×C22⋊C4D17211yescharacteristic
445C2×C42—861no—
446C2×C42—861no—
447C2×C42C22×D4311yescharacteristic
448#107—862no—
449#107—1721no—
450#106—862no—
451#106—1721no—
452C4⋊C8C22⋊D4314yes—
453#103—862no—
454#103—862no—
455#103—862no—
456#103—862no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C4×C8—22no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469C24C2×D17211yescharacteristic
470C24C2×D17211yescharacteristic
471C2×Q8—432no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
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—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—861no—
500C22×C4C2×D17211yescharacteristic
501C22×C4C2×D17211yescharacteristic
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4C23×D4311yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—44no—
515C2×C8—44no—
516C2×C8#1062190012yes—
517C2×C8C2×C22⋊D4312yes—
518C2×C8C2×C22⋊D4312yes—
519C4⋊C4—22no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
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—861no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—3441no—
542C22⋊C4—3441no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1722no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C42—3441no—
550C42—1722no—
551C42#1062189812yes—
552C42C2×C22⋊D4312yes—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#1306334712yes—
566C23#1306334712yes—
567C23C22×D17211yescharacteristic
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
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—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
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×C4—1721no—
614C2×C4—1721no—
615C2×C4#1306329912yes—
616C2×C4#1306329912yes—
617C2×C4C22×C22⋊D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4#1306337011yescharacteristic
622C2×C4#1306337211yescharacteristic
623C8—22no—
624C8—22no—
625C8—22no—
626C8—41no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#1306329911yescharacteristic
642C22#1458354411yescharacteristic
643C22#1458355311yescharacteristic
644C22C2×#1306334711yescharacteristic
645C22C2×#1306334711yescharacteristic
646C22#1458371111yescharacteristic
647C22#1458371611yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—3441no—
653C4—3441no—
654C4—3441no—
655C4—3441no—
656C4—3441no—
657C4—3441no—
658C4—3441no—
659C4—1722no—
660C4#1458343111yescharacteristic
661C4#1458351411yescharacteristic
662C4#1458354311yescharacteristic
663C4#1458355611yescharacteristic
664C2—42no—
665C2—42no—
666C2#1913816611yescharacteristic
667C2#1914417611yescharacteristic
668C2#1914428611yescharacteristic
669C2#1914648411yescharacteristic
670C2#1914649911yescharacteristic
671C2#1914696411yescharacteristic
672C2#1914697611yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C8×D4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×C8×D4D43
hypocenterC43#25343
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14583207C2semidirect
4. #19136028C2semidirect
5. #19136018C2semidirect
6. #19135799C2semidirect
7. #19135792C2semidirect
8. #19135560C2semidirect
9. #19135365C2semidirect
10. #19135018C2semidirect
11. #19135018C2semidirect
12. #19134624C2semidirect
13. #19134620C2semidirect
14. C4×#13063250C2semidirect
397. C43#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#145832072
#191397612
#191395042
#191360282
#191360182
#191357992
#191357922
#191355602
#191353652
#191350182
#191346242
#191346202
C4×#130632502
C2×C8×D4×C432
#2534343