Finite Group Databasebeta

← #25125003

Subgroups — #25125003

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583511C211yesmaximal, characteristic
2C2×#14583007C211yesmaximal, characteristic, complemented
3C2×C4×Dic172C211yesmaximal, characteristic, complemented
4#19137277C211yesmaximal, characteristic
5#19135934C211yesmaximal, characteristic, complemented
6#19135842C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic
8#19135792C211yesmaximal, characteristic
9#19135747C211yesmaximal, characteristic, complemented
10#19135697C211yesmaximal, characteristic, complemented
11#19135605C211yesmaximal, characteristic
12#19135605C211yesmaximal, characteristic
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18#14583511—24no—
19#14583511—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063318—21no—
22C2×#13063318—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063315—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30C2×C4×Dic86C2211yescharacteristic
31C2×C4×Dic86C2211yescharacteristic
32#14583007—24no—
33C4×Dic172—24no—
34C2×#13063259C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44#14582805C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582794—21no—
47#14582793—21no—
48#14582787—21no—
49#14582780—21no—
50#14582759C2211yescharacteristic
51C4×C4⋊Dic43C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×Dic172—22no—
69C2×Dic172—22no—
70C2×Dic172—22no—
71C2×Dic172—22no—
72#13063325—22no—
73#13063325—22no—
74#13063318—28no—
75#13063318—28no—
76#13063317—22no—
77#13063317—22no—
78#13063315—28no—
79#13063315—28no—
80#13063304—22no—
81#13063304—22no—
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86D414yes—
91C4×Dic86D414yes—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063259—22no—
117#13063257—22no—
118#13063250—22no—
119#13063250—22no—
120#13063250—22no—
121#13063250—22no—
122#13063250—22no—
123#13063250—22no—
124#13063250—22no—
125#13063250—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C23×C4×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#117×C43—22no—
137#117×C43—22no—
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C4⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C22⋊C8×C43—22no—
145C22⋊C8×C43—22no—
146#97×C43—22no—
147C4×C8×C43—22no—
148C24×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86C2×D412yes—
185C2×Dic86C2×D412yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43#4112yes—
198C2×C8×C43#4112yes—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43C2×D412yes—
206C42×C43C2×D412yes—
207C22⋊Dic43—24no—
208C22⋊Dic43—24no—
209C22⋊Dic43—24no—
210C22⋊Dic43—81no—
211C4⋊Dic43—24no—
212C4⋊Dic43—24no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C2×D412yes—
221C4⋊Dic43C2×D412yes—
222C4⋊Dic43#4112yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230Dic43⋊C4—42no—
231Dic43⋊C4—81no—
232C4×Dic43—24no—
233C4×Dic43—24no—
234C4×Dic43—42no—
235C4×Dic43—81no—
236Dic172—28no—
237Dic172—28no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C22×D411yescharacteristic
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—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43#12012yes—
264C2×C4×C43#12012yes—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86—22no—
299Dic86—22no—
300Dic86—22no—
301Dic86—41no—
302Dic86—41no—
303Dic86—41no—
304Dic86—41no—
305Dic86—41no—
306Dic86—41no—
307C8×C43—22no—
308C8×C43—22no—
309C8×C43—41no—
310C8×C43—41no—
311#23586—431nomaximal, Sylow
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C2×#12011yescharacteristic
320C22×C43#52511yescharacteristic
321C22×C43#53211yescharacteristic
322C22×C43#57711yescharacteristic
323C22×C43#57811yescharacteristic
324C22×C43#57811yescharacteristic
325C22×C43#57811yescharacteristic
326C4×C43—22no—
327C4×C43—22no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43#52511yescharacteristic
332C4×C43#52511yescharacteristic
333C4×C43#53211yescharacteristic
334C4×C43#53211yescharacteristic
335Dic43—42no—
336Dic43—42no—
337Dic43—42no—
338Dic43—42no—
339Dic43—42no—
340Dic43—42no—
341Dic43—81no—
342Dic43—81no—
343C2×#541—431no—
344C2×#441—431no—
345C2×C4×Q16—431no—
346#2323—431no—
347#2059—431no—
348#2043—431no—
349#2036—431no—
350#2035—431no—
351#2026—431no—
352#2016—431no—
353#2001—431no—
354#2001—431no—
355#1763—431no—
356C4×#103—431no—
357#1750D4311yescharacteristic
358C2×C43—81no—
359C2×C43#238811yescharacteristic
360C2×C43#301111yescharacteristic
361C2×C43#301311yescharacteristic
362C2×C43#312011yescharacteristic
363C2×C43#312711yescharacteristic
364C2×C43#317711yescharacteristic
365C2×C43#317811yescharacteristic
366C22×Q16—431no—
367C22×Q16—431no—
368#541—864no—
369#541—864no—
370C2×C4⋊Q8—431no—
371C2×#126—861no—
372C2×#126—861no—
373C2×#125—431no—
374C2×#125—861no—
375C2×#125—861no—
376C2×C22⋊Q8—431no—
377C2×C22⋊Q8—431no—
378C2×C22⋊Q8—431no—
379C2×C4×Q8—431no—
380C2×C4×Q8—431no—
381C2×C4×Q8—431no—
382C2×#117C2×D4311yescharacteristic
383#441—864no—
384C4×Q16—864no—
385C2×#107—431no—
386C2×#106—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×#103—431no—
395C2×C22⋊C8C2×D4311yescharacteristic
396C2×C22⋊C8C2×D4311yescharacteristic
397C2×#97C2×D4311yescharacteristic
398C2×C4×C8C2×D4311yescharacteristic
399#391—431no—
400#389—431no—
401#389—861no—
402#388—861no—
403#388—861no—
404#387—861no—
405#380—431no—
406C4×C4⋊C4—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#336C2×D4311yescharacteristic
412#336C2×D4311yescharacteristic
413C43#2358611yescharacteristic, complemented, Sylow
414C22×Q8—431no—
415C22×Q8—431no—
416C22×Q8—431no—
417C23×C4C22×D4311yescharacteristic
418C2×Q16—862no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—862no—
422C2×Q16—862no—
423C2×Q16—862no—
424C22×C8C22×D4311yescharacteristic
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C4⋊Q8—862no—
429C4⋊Q8—862no—
430#126—868no—
431#126—868no—
432#125—862no—
433#125—862no—
434#125—868no—
435#125—868no—
436C22⋊Q8—862no—
437C22⋊Q8—862no—
438C22⋊Q8—862no—
439C22⋊Q8—862no—
440C22⋊Q8—862no—
441C22⋊Q8—862no—
442C4×Q8—434no—
443C4×Q8—434no—
444C4×Q8—862no—
445C4×Q8—862no—
446C4×Q8—862no—
447C4×Q8—862no—
448#117—22no—
449#117—22no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4D17211yescharacteristic
467C2×C4⋊C4D17211yescharacteristic
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4D17211yescharacteristic
473C2×C22⋊C4D17211yescharacteristic
474C2×C42—861no—
475C2×C42—861no—
476C2×C42—861no—
477C2×C42—861no—
478C2×C42C22×D4311yescharacteristic
479C2×C42C22×D4311yescharacteristic
480#107—862no—
481#106—862no—
482#103—862no—
483#103—862no—
484#103—862no—
485#103—862no—
486#103—862no—
487#103—862no—
488#103—862no—
489#103—862no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#97—22no—
493C4×C8—22no—
494#95—861no—
495#95—861no—
496#95—861no—
497#95—861no—
498#95—861no—
499C24C2×D17211yescharacteristic
500C2×Q8—432no—
501C2×Q8—432no—
502C2×Q8—432no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8—861no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4C2×D17211yescharacteristic
533C22×C4C2×D17211yescharacteristic
534C22×C4C2×D17211yescharacteristic
535C22×C4C2×D17211yescharacteristic
536C22×C4C2×D17211yescharacteristic
537C22×C4C23×D4311yescharacteristic
538Q16—868no—
539Q16—868no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8#1062189812yes—
551C2×C8#1062189812yes—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—432no—
555C4⋊C4—432no—
556C4⋊C4—432no—
557C4⋊C4—864no—
558C4⋊C4—864no—
559C4⋊C4—864no—
560C4⋊C4—864no—
561C4⋊C4—864no—
562C4⋊C4—864no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4—3441no—
574C4⋊C4—1722no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—864no—
578C22⋊C4—864no—
579C22⋊C4—864no—
580C22⋊C4—3441no—
581C42—21no—
582C42—21no—
583C42—864no—
584C42—864no—
585C42—3441no—
586C42—1722no—
587C42D4×D4312yes—
588C42D4×D4312yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C22×D17211yescharacteristic
597Q8—862no—
598Q8—862no—
599Q8—862no—
600Q8—862no—
601Q8—862no—
602Q8—862no—
603Q8—1721no—
604Q8—1721no—
605Q8—1721no—
606Q8—1721no—
607Q8—1721no—
608Q8—1721no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4#1306329512yes—
651C2×C4#1306329512yes—
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4C2×D4×D4311yescharacteristic
654C2×C4#41×D4311yescharacteristic
655C2×C4#41×D4311yescharacteristic
656C2×C4C2×#1062189811yescharacteristic
657C2×C4C2×#1062189811yescharacteristic
658C8—22no—
659C8—22no—
660C8—41no—
661C8—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×#1306329511yescharacteristic
670C22#1458341111yescharacteristic
671C22#1458344911yescharacteristic
672C22#1458371111yescharacteristic
673C22#1458371611yescharacteristic
674C22#1458371611yescharacteristic
675C22#1458371611yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—3441no—
682C4—3441no—
683C4—1722no—
684C4—1722no—
685C4—1722no—
686C4—1722no—
687C4—1722no—
688C4—1722no—
689C4#1458340811yescharacteristic
690C4#1458340811yescharacteristic
691C4#1458344611yescharacteristic
692C4#1458344611yescharacteristic
693C2—81no—
694C2#1913781111yescharacteristic
695C2#1914389211yescharacteristic
696C2#1914391311yescharacteristic
697C2#1914481111yescharacteristic
698C2#1914489611yescharacteristic
699C2#1914525411yescharacteristic
700C2#1914526311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1750D43
hypocenterC43#23586
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#14583007C2semidirect
3. C2×C4×Dic172C2semidirect
5. #19135934C2semidirect
6. #19135842C2semidirect
9. #19135747C2semidirect
10. #19135697C2semidirect
13. #19134426C2semidirect
14. C4×#13063250C2semidirect
413. C43#23586semidirect

Maximal subgroups

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

subgroupindex
C2×#145835112
C2×#145830072
C2×C4×Dic1722
#191372772
#191359342
#191358422
#191357992
#191357922
#191357472
#191356972
#191356052
#191344262
C4×#130632502
C43×#17502
#2358643