Finite Group Databasebeta

← #25260074

Subgroups — #25260074

Order 11008.

2286 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C211yesmaximal, characteristic
2#19137774C212yesmaximal, complemented
3#19137738C212yesmaximal, complemented
4#19137728C212yesmaximal, complemented
5#19137683C212yesmaximal, complemented
6#19137622C212yesmaximal, complemented
7#19137600C212yesmaximal, complemented
8#19137490C212yesmaximal, complemented
9#19137427C212yesmaximal, complemented
10#19137404C214yesmaximal, complemented
11#19137382C214yesmaximal, complemented
12#19137273C212yesmaximal, complemented
13#19137123C212yesmaximal, complemented
14#19137086C211yesmaximal, characteristic
15C43×#2311C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17#14583470C4116yescomplemented
18C2×#13063323C2212yes—
19C2×#13063312C2212yes—
20C2×#13063306C2212yes—
21C2×#13063306C2212yes—
22C2×#13063304C2212yes—
23C2×#13063304C2212yes—
24C2×#13063290C2212yes—
25C2×#13063290C2212yes—
26C2×#13063284C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29#14582806C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582804C2212yes—
32#14582804C2212yes—
33#14582803C2214yes—
34#14582803C2214yes—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582796C2214yes—
38#14582795C2212yes—
39#14582795C2212yes—
40#14582794C2214yes—
41#14582793C2214yes—
42#14582793C2214yes—
43#14582787C2214yes—
44#14582787C2214yes—
45#14582787C2214yes—
46#14582787C2214yes—
47#14582786C2214yes—
48#14582783C2214yes—
49#14582781C2214yes—
50#14582780C2214yes—
51#14582779C2212yes—
52#14582779C2212yes—
53#14582772C2214yes—
54#14582771C2214yes—
55#14582766C2214yes—
56#14582757C2214yes—
57C4⋊C4×Dic43C2212yes—
58C4⋊C4×Dic43C2212yes—
59C4×Dic43⋊C4C2214yes—
60#14582750C2214yes—
61#14582750C2214yes—
62C22⋊C4×Dic43C2214yes—
63C22⋊C4×Dic43C2214yes—
64C4×C22⋊Dic43C2212yes—
65C4×C22⋊Dic43C2212yes—
66C4×C22⋊Dic43C2214yes—
67C22×#41×C43C2211yescharacteristic
68C2×#117×C43C2211yescharacteristic
69C22×C4⋊C4×C43C2211yescharacteristic
70C43×#391C2212yes—
71C43×#390C2212yes—
72C43×#386C2212yes—
73C43×#386C2212yes—
74C43×#380C2212yes—
75C43×#380C2212yes—
76C22×Dic86—42no—
77C22×Dic86—42no—
78C22×Dic86C2×C418yescomplemented
79C22×Dic86C2312yes—
80C22×Dic86C2312yes—
81C23×Dic43C2312yes—
82C23×Dic43C2312yes—
83#13063323C2×C4116yescomplemented
84#13063312C2×C4116yes—
85#13063306C2×C4116yescomplemented
86#13063306C2×C4116yescomplemented
87#13063304C2×C4116yescomplemented
88#13063304C2×C4116yescomplemented
89#13063290—44no—
90#13063290—44no—
91#13063284—42no—
92#13063284C2×C418yescomplemented
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2312yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×C22⋊Dic43C2312yes—
103C2×C22⋊Dic43C2312yes—
104C2×C22⋊Dic43C2312yes—
105C2×C22⋊Dic43C2312yes—
106C2×C22⋊Dic43C2312yes—
107C2×C22⋊Dic43C2312yes—
108C2×C22⋊Dic43C2314yes—
109C2×C22⋊Dic43C2314yes—
110C2×C4×Dic43—42no—
111C2×C4×Dic43C2312yes—
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119C2×C4×Dic43C2312yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2312yes—
127C43⋊#95C2314yes—
128C43⋊#95C2312yes—
129C43⋊#95C2312yes—
130C43⋊#95C2314yes—
131C43⋊#95C2312yes—
132C2×#41×C43—42no—
133C2×#41×C43—42no—
134C2×#41×C43C2×C418yes—
135C22×Q8×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C22×D4×C43C2311yescharacteristic
138C22×D4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2312yes—
143#117×C43—42no—
144C2×C4⋊C4×C43—42no—
145C2×C4⋊C4×C43C2312yes—
146C2×C4⋊C4×C43C2312yes—
147C2×C4⋊C4×C43C2312yes—
148C2×C22⋊C4×C43C2312yes—
149C2×C22⋊C4×C43C2314yes—
150C2×C22⋊C4×C43C2314yes—
151C2×C42×C43C2312yes—
152#95×C43C2314yes—
153#95×C43C2314yes—
154C24×C43C2411yescharacteristic
155C24×C43C2411yescharacteristic
156C24×C43C2411yescharacteristic
157#41×C43—416no—
158C2×Q8×C43—41no—
159C2×Q8×C43—41no—
160C2×Q8×C43C22×C414yes—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43C22×C414yes—
168C2×D4×C43C22×C414yes—
169C2×D4×C43C22×C414yes—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—42no—
177C22×C4×C43—44no—
178C22×C4×C43C22×C414yes—
179C22×C4×C43C22×C414yes—
180C22×C4×C43C22×C414yes—
181C22×C4×C43C2414yes—
182C22×C4×C43C2414yes—
183C22×C4×C43C2411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C22×Dic43—24no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43C22×C418yes—
193C22×Dic43C2412yes—
194C22×Dic43C2412yes—
195C22×Dic43C2412yes—
196C22×Dic43C2414yes—
197C22×Dic43C2414yes—
198C22×Dic43C2412yes—
199C2×Dic86—24no—
200C2×Dic86—24no—
201C2×Dic86—416no—
202C2×Dic86—42no—
203C2×Dic86—42no—
204C2×Dic86C22×C418yes—
205C2×Dic86C22×C418yes—
206C4⋊C4×C43—24no—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—42no—
209C22⋊C4×C43—44no—
210C22⋊C4×C43—44no—
211C22⋊C4×C43—42no—
212C42×C43—42no—
213C22⋊Dic43—24no—
214C22⋊Dic43—24no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43C22×C418yes—
219C22⋊Dic43C22×C4116yes—
220C22⋊Dic43C22×C4116yes—
221C4⋊Dic43—41no—
222C4⋊Dic43—41no—
223C4⋊Dic43C22×C418yes—
224Dic43⋊C4—28no—
225Dic43⋊C4—44no—
226Dic43⋊C4—44no—
227Dic43⋊C4—44no—
228Dic43⋊C4C22×C4116yes—
229Dic43⋊C4C22×C4116yes—
230C4×Dic43—24no—
231C4×Dic43—24no—
232C4×Dic43—41no—
233C4×Dic43—41no—
234C4×Dic43—44no—
235C4×Dic43—44no—
236C4×Dic43—44no—
237C4×Dic43—44no—
238C4×Dic43C22×C418yes—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43C23×C412yes—
252C23×C43C23×C412yes—
253C23×C43C23×C412yes—
254C23×C43C2511yescharacteristic
255Q8×C43—44no—
256D4×C43—44no—
257D4×C43—44no—
258D4×C43—44no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—28no—
266C2×C4×C43—28no—
267C2×C4×C43—28no—
268C2×C4×C43—24no—
269C2×C4×C43—24no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—84no—
275C2×C4×C43C23×C412yes—
276C2×C4×C43C23×C412yes—
277C2×C4×C43C23×C412yes—
278C2×C4×C43C23×C412yes—
279C2×C4×C43H(5,𝔽2)12yes—
280C2×C4×C43H(5,𝔽2)12yes—
281C2×Dic43—22no—
282C2×Dic43—24no—
283C2×Dic43—24no—
284C2×Dic43—24no—
285C2×Dic43—24no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—48no—
297C2×Dic43—48no—
298C2×Dic43C23×C418yes—
299C2×Dic43C23×C418yes—
300C2×Dic432−1+414yes—
301Dic86—216no—
302Dic86—48no—
303#34413—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—24no—
308C22×C43—24no—
309C22×C43—24no—
310C22×C43—42no—
311C22×C43—42no—
312C22×C43—42no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C24×C411yescharacteristic
320C22×C43C2×H(5,𝔽2)11yescharacteristic
321C22×C43C2×H(5,𝔽2)11yescharacteristic
322C22×C43C2×2−1+412yes—
323C22×C43#58512yes—
324C4×C43—22no—
325C4×C43—22no—
326C4×C43—22no—
327C4×C43—44no—
328C4×C43—44no—
329C4×C43#51814yes—
330Dic43—28no—
331Dic43—28no—
332Dic43—24no—
333Dic43—42no—
334Dic43—42no—
335Dic43—42no—
336C2×#536—431no—
337#2381—432no—
338#2376—432no—
339#2374—432no—
340#2369—432no—
341#2362—432no—
342#2360—432no—
343#2347—432no—
344Q8×C22⋊C4—432no—
345#2337—434no—
346#2335—434no—
347#2323—432no—
348#2311D4311yescharacteristic
349C4×C22⋊Q8—432no—
350#2297—431no—
351C2×C43—42no—
352C2×C43—42no—
353C2×C43—42no—
354C2×C43C2×#51811yescharacteristic
355C2×C43C4×2−1+412yes—
356C2×C43#354112yes—
357C2×C43#355011yescharacteristic
358C2×C43#355111yescharacteristic
359C22×#41C2×D4311yescharacteristic
360C23×Q8—431no—
361#536—4316no—
362C2×C4⋊Q8—432no—
363C2×#124—432no—
364C2×#123—432no—
365C2×#123—432no—
366C2×C22⋊Q8—432no—
367C2×C22⋊Q8—432no—
368C2×C4×Q8—432no—
369C2×C4×Q8—432no—
370C2×#117—431no—
371C2×#117—431no—
372C2×#117C2×D4311yescharacteristic
373C22×C4⋊C4C2×D4311yescharacteristic
374C22×C42—431no—
375#391—431no—
376#391—431no—
377#391—432no—
378#391—432no—
379#391—434no—
380#391—434no—
381#391C2×D4312yes—
382#390—431no—
383#390—431no—
384#390C2×D4312yes—
385#389—434no—
386#389—432no—
387#389—432no—
388#389—434no—
389#388—434no—
390#388—434no—
391#388—434no—
392#388—434no—
393#388—434no—
394#388—434no—
395#387—434no—
396#387—434no—
397#387—434no—
398#387—434no—
399#386—432no—
400#386—432no—
401#386C2×D4312yes—
402#386C2×D4312yes—
403#385—434no—
404#385—434no—
405#383—434no—
406#380—434no—
407#380C2×D4312yes—
408#380C2×D4312yes—
409C4×C4⋊C4—432no—
410C4×C4⋊C4—432no—
411C4×C4⋊C4—434no—
412C4×C4⋊C4—434no—
413C4×C4⋊C4—434no—
414C4×C22⋊C4—434no—
415C4×C22⋊C4—432no—
416C4×C22⋊C4—432no—
417C4×C22⋊C4—434no—
418C4×C22⋊C4—434no—
419C43#3441311yescharacteristic, complemented, Sylow
420C2×#41—42no—
421C2×#41—42no—
422C2×#41C4×D4318yes—
423C22×Q8—438no—
424C22×Q8—432no—
425C22×Q8—432no—
426C22×Q8—1722no—
427C22×Q8—1722no—
428C22×Q8C22×D4311yescharacteristic
429C22×D4C22×D4311yescharacteristic
430C22×D4C22×D4311yescharacteristic
431C22×D4C22×D4311yescharacteristic
432C23×C4—432no—
433C23×C4—432no—
434C23×C4C22×D4311yescharacteristic
435C23×C4C22×D4311yescharacteristic
436C23×C4C22×D4311yescharacteristic
437C23×C4C22×D4312yes—
438C4⋊Q8—4316no—
439#124—4316no—
440#123—4316no—
441#123—4316no—
442C22⋊Q8—4316no—
443C22⋊Q8—4316no—
444C4×Q8—1724no—
445C4×Q8—1724no—
446#117—42no—
447#117—438no—
448#117—1722no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—432no—
451C2×C4⋊C4—434no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—434no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—434no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4C22×D4312yes—
460C2×C4⋊C4C22×D4312yes—
461C2×C4⋊C4C22×D4312yes—
462C2×C22⋊C4—432no—
463C2×C22⋊C4—434no—
464C2×C22⋊C4—434no—
465C2×C22⋊C4—432no—
466C2×C22⋊C4—432no—
467C2×C22⋊C4—432no—
468C2×C22⋊C4—432no—
469C2×C22⋊C4—432no—
470C2×C22⋊C4C22×D4312yes—
471C2×C22⋊C4C22×D4314yes—
472C2×C22⋊C4C22×D4314yes—
473C2×C42—432no—
474C2×C42—432no—
475C2×C42—432no—
476C2×C42—434no—
477C2×C42—434no—
478C2×C42—434no—
479C2×C42—431no—
480C2×C42—434no—
481C2×C42—431no—
482C2×C42—1722no—
483C2×C42C22×D4312yes—
484#95—434no—
485#95—432no—
486#95—432no—
487#95—434no—
488#95—432no—
489#95—434no—
490#95—434no—
491#95—432no—
492#95—434no—
493#95—434no—
494#95—434no—
495#95—434no—
496#95C22×D4314yes—
497#95C22×D4314yes—
498C24C23×D4311yescharacteristic
499C24C23×D4311yescharacteristic
500C24C23×D4311yescharacteristic
501#41—416no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—438no—
505C2×Q8—438no—
506C2×Q8—864no—
507C2×Q8—864no—
508C2×Q8—1722no—
509C2×Q8—1722no—
510C2×Q8—17216no—
511C2×Q8C2×C4×D4314yes—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4C2×C4×D4314yes—
519C2×D4C2×C4×D4314yes—
520C2×D4C2×C4×D4314yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—42no—
528C22×C4—44no—
529C22×C4—432no—
530C22×C4—434no—
531C22×C4—434no—
532C22×C4—438no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—864no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4—1722no—
540C22×C4—1722no—
541C22×C4C2×C4×D4314yes—
542C22×C4C2×C4×D4314yes—
543C22×C4C2×C4×D4314yes—
544C22×C4C23×D4314yes—
545C22×C4C23×D4314yes—
546C22×C4C23×D4311yescharacteristic
547C22×C4C23×D4311yescharacteristic
548C22×C4C23×D4311yescharacteristic
549C22×C4C23×D4311yescharacteristic
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—42no—
553C4⋊C4—438no—
554C4⋊C4—4316no—
555C4⋊C4—4316no—
556C4⋊C4—868no—
557C4⋊C4—1721no—
558C4⋊C4—1721no—
559C4⋊C4—1724no—
560C4⋊C4—1724no—
561C4⋊C4—1724no—
562C22⋊C4—42no—
563C22⋊C4—44no—
564C22⋊C4—44no—
565C22⋊C4—438no—
566C22⋊C4—4316no—
567C22⋊C4—4316no—
568C22⋊C4—864no—
569C22⋊C4—864no—
570C22⋊C4—1722no—
571C22⋊C4—1722no—
572C22⋊C4—1722no—
573C42—42no—
574C42—438no—
575C42—864no—
576C42—864no—
577C42—1721no—
578C42—1721no—
579C42—1724no—
580C42—1724no—
581C42—1724no—
582C42—1724no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23C22×C4×D4312yes—
596C23C22×C4×D4312yes—
597C23C22×C4×D4312yes—
598C23C24×D4311yescharacteristic
599Q8—44no—
600Q8—8616no—
601Q8—1728no—
602D4—44no—
603D4—44no—
604D4—44no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—28no—
612C2×C4—28no—
613C2×C4—28no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—84no—
621C2×C4—438no—
622C2×C4—438no—
623C2×C4—434no—
624C2×C4—862no—
625C2×C4—864no—
626C2×C4—864no—
627C2×C4—864no—
628C2×C4—864no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—1728no—
640C2×C4—1728no—
641C2×C4C22×C4×D4312yes—
642C2×C4C22×C4×D4312yes—
643C2×C4C22×C4×D4312yes—
644C2×C4C22×C4×D4312yes—
645C2×C4#1306337012yes—
646C2×C4#1306337012yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22C23×C4×D4311yescharacteristic
663C22C2×#1306337011yescharacteristic
664C22C2×#1306337011yescharacteristic
665C222−1+4×D4312yes—
666C22#1458373412yes—
667C4—22no—
668C4—22no—
669C4—22no—
670C4—44no—
671C4—44no—
672C4—868no—
673C4—868no—
674C4—864no—
675C4—1722no—
676C4—1722no—
677C4—1722no—
678C4#1458337214yes—
679C2—42no—
680C2—42no—
681C2—42no—
682C2C2×#1458337211yescharacteristic
683C2#1914780612yes—
684C2#1914887612yes—
685C2#1914900411yescharacteristic
686C2#1914901911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2311C2
socle, cosocleC23×C43C25
prime radicalC22×#41×C43C22
hypercenter#2311D43
hypocenterC43#34413
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #19137774C2semidirect
3. #19137738C2semidirect
4. #19137728C2semidirect
5. #19137683C2semidirect
6. #19137622C2semidirect
7. #19137600C2semidirect
8. #19137490C2semidirect
9. #19137427C2semidirect
10. #19137404C2semidirect
11. #19137382C2semidirect
12. #19137273C2semidirect
13. #19137123C2semidirect
17. #14583470C4semidirect
78. C22×Dic86C2×C4semidirect
83. #13063323C2×C4semidirect
85. #13063306C2×C4semidirect
86. #13063306C2×C4semidirect
87. #13063304C2×C4semidirect
88. #13063304C2×C4semidirect
92. #13063284C2×C4semidirect
419. C43#34413semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
#191377742
#191377382
#191377282
#191376832
#191376222
#191376002
#191374902
#191374272
#191374042
#191373822
#191372732
#191371232
#191370862
C43×#23112
#3441343