Finite Group Databasebeta

← #25113219

Subgroups — #25113219

Order 11008.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583605C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19137507C211yesmaximal, characteristic, complemented
4#19135562C211yesmaximal, characteristic, complemented
5#19135554C211yesmaximal, characteristic, complemented
6#19135553C211yesmaximal, characteristic, complemented
7#19135549C211yesmaximal, characteristic, complemented
8#19135541C211yesmaximal, characteristic, complemented
9#19134594C211yesmaximal, characteristic
10#19134594C211yesmaximal, characteristic
11#19134592C211yesmaximal, characteristic
12#19134421C211yesmaximal, characteristic
13#19134419C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1992C211yesmaximal, characteristic, complemented
16#14583605—24no—
17#14583605C418yescomplemented
18C2×#13063324C2211yescharacteristic
19C2×#13063316C2211yescharacteristic
20C2×#13063305—21no—
21C2×#13063303—21no—
22C2×#13063303—21no—
23C2×C4×Dic86C2211yescharacteristic
24C2×#13063290—21no—
25C2×C4×D172C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×C4⋊C4×D43—21no—
29#14583027—24no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582795—21no—
40#14582794—21no—
41#14582794—21no—
42#14582768C2211yescharacteristic
43#14582768C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86D411yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324C2×C414yes—
72#13063316—22no—
73#13063316C2×C414yes—
74#13063305—28no—
75#13063303—28no—
76#13063303—28no—
77C4×Dic86C2×C414yes—
78C4×Dic86D414yes—
79#13063290—44no—
80C4×D172—22no—
81C4×D172C2×C414yes—
82#13063287—22no—
83#13063287—22no—
84#13063287C2×C414yes—
85#13063287C2×C414yes—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C4⋊C4×D43—28no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C4⋊(C43⋊C8)—22no—
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111#13063247—22no—
112#13063247Q814yescomplemented
113#13063245—22no—
114#13063245—22no—
115#13063235—22no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#125×C43—22no—
123#125×C43C2×C414yes—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#97×C43—22no—
134C23×D43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172C22×C412yes—
153C2×D172C2×Q812yes—
154C2×D172#4112yes—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×Dic86—22no—
165C2×Dic86—22no—
166C2×Dic86—24no—
167C2×Dic86—81no—
168C2×Dic86—81no—
169C2×Dic86C22⋊C414yes—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×Q812yes—
176C4⋊C4×C43—24no—
177C4⋊C4×C43—24no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—81no—
186C4⋊C4×C43C22×C412yes—
187C4⋊C4×C43C22×C412yes—
188C42×C43C22×C412yes—
189C42×C43C2×D412yes—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—24no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C22⋊C414yes—
199C4⋊Dic43C22×C412yes—
200C4⋊Dic43C2×Q812yes—
201Dic43⋊C4—24no—
202Dic43⋊C4—24no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—81no—
206Dic43⋊C4—81no—
207Dic43⋊C4C22⋊C414yes—
208Dic43⋊C4C22⋊C414yes—
209C4×Dic43—42no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43C22×C412yes—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C23×C43C22×D411yescharacteristic
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
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×C43C2×C22⋊C412yes—
247C2×C4×C43C2×C22⋊C412yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×Q811yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C432−1+411yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43C2×C22⋊C412yes—
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43C2×C22⋊C412yes—
272C2×Dic43C2×C22⋊C412yes—
273C2×Dic43AGL(1,ℤ/8)12yes—
274C2×Dic43#13712yes—
275D172—22no—
276D172—22no—
277D172—22no—
278D172C4×Q814yescomplemented
279C4×D43—48no—
280C4×D43—84no—
281C4×D43—84no—
282Dic86—28no—
283Dic86—84no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288#22522—431nomaximal, Sylow
289C22×C43C22×C22⋊C411yescharacteristic
290C22×C43#54811yescharacteristic
291C22×C43D4×Q811yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57711yescharacteristic
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×C4×Q811yescharacteristic
310C4×C43#51911yescharacteristic
311C4×C43#54811yescharacteristic
312C4×C43D4×Q811yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319Dic43#41714yes—
320C2×#554—431no—
321C2×#446—431no—
322Q8×C4⋊C4—431no—
323#1992—431no—
324#1992D4311yescharacteristic, complemented
325#1990—431no—
326#1989—431no—
327#1989—431no—
328#1987—431no—
329#1802—431no—
330#1802—431no—
331#1802—431no—
332#1762—431no—
333#1762—431no—
334C4×#102—431no—
335C2×C43Q8×C22⋊C411yescharacteristic
336C2×C43C2×#41711yescharacteristic
337C2×C43#289711yescharacteristic
338C2×C43#336611yescharacteristic
339C2×C43#337211yescharacteristic
340C2×C43#338411yescharacteristic
341C2×C43#338511yescharacteristic
342D43—44no—
343#554—438no—
344#554—864no—
345C2×C4⋊Q8—431no—
346C2×#125—431no—
347C2×#125C2×D4311yescharacteristic
348C2×C22⋊Q8—861no—
349C2×C22⋊Q8—861no—
350C2×C22⋊Q8—861no—
351C2×C4×Q8—431no—
352C2×C4×Q8—861no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356C22×C4⋊C4—861no—
357#446—864no—
358C2×C4⋊C8—431no—
359C2×C4⋊C8—431no—
360C2×C4⋊C8—431no—
361C2×#102—431no—
362C2×#102—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#97—431no—
366C2×#97C2×D4311yescharacteristic
367C2×C4×C8—431no—
368#389—861no—
369#389—861no—
370#389—861no—
371#384—431no—
372#384—431no—
373#384C2×D4311yescharacteristic
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340C2×D4311yescharacteristic
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388#340C2×D4311yescharacteristic
389C43#2252211yescharacteristic, complemented, Sylow
390C22×Q8—431no—
391C22×Q8—861no—
392C22×D4—431no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4—861no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C4⋊Q8—434no—
401C4⋊Q8—862no—
402#125—22no—
403#125—434no—
404#125—862no—
405#125C4×D4314yes—
406C22⋊Q8—868no—
407C22⋊Q8—868no—
408C22⋊Q8—868no—
409C4×Q8—434no—
410C4×Q8—434no—
411C4×Q8—1724no—
412C4×D4—434no—
413C4×D4—434no—
414C4×D4—434no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
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—868no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452#102—434no—
453#102—862no—
454#102—862no—
455#102—862no—
456#97—22no—
457#97—862no—
458C4×C8—862no—
459#95—861no—
460#95—861no—
461#95—861no—
462C24—861no—
463C2×Q8—434no—
464C2×Q8—862no—
465C2×Q8—862no—
466C2×Q8—864no—
467C2×Q8—3441no—
468C2×Q8—3441no—
469C2×D4—432no—
470C2×D4—432no—
471C2×D4—432no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—864no—
484C22×C4—864no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—864no—
488C22×C4—861no—
489C22×C4—3441no—
490C22×C4—3441no—
491C22×C4—3441no—
492C22×C4—3441no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4C23×D4311yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8Q8×D4312yes—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4—434no—
521C4⋊C4—434no—
522C4⋊C4—434no—
523C4⋊C4—432no—
524C4⋊C4—432no—
525C4⋊C4—864no—
526C4⋊C4—864no—
527C4⋊C4—864no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—3441no—
533C4⋊C4—3441no—
534C4⋊C4—1722no—
535C4⋊C4—1722no—
536C4⋊C4C2×C4×D4312yes—
537C4⋊C4C2×C4×D4312yes—
538C22⋊C4—864no—
539C22⋊C4—864no—
540C22⋊C4—864no—
541C42—432no—
542C42—432no—
543C42—432no—
544C42—432no—
545C42—1722no—
546C42—1722no—
547C42—1722no—
548C42C2×C4×D4312yes—
549C42D4×D4312yes—
550C23—862no—
551C23—862no—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23C2×D4×D4311yescharacteristic
558Q8—868no—
559Q8—3444no—
560D4—434no—
561D4—862no—
562D4—862no—
563D4—862no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—3444no—
595C2×C4—3444no—
596C2×C4—1728no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C22⋊C4×D4312yes—
605C2×C4C22⋊C4×D4312yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C2×C4C2×Q8×D4311yescharacteristic
609C2×C4#41×D4311yescharacteristic
610C2×C4#1306337211yescharacteristic
611C2×C4#1306337311yescharacteristic
612C8—22no—
613C8—41no—
614C8—1721no—
615C8—1721no—
616C22—864no—
617C22—1722no—
618C22—1722no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22—1722no—
623C22C2×C22⋊C4×D4311yescharacteristic
624C22#1458355711yescharacteristic
625C22#1458356411yescharacteristic
626C22AGL(1,ℤ/8)×D4311yescharacteristic
627C22#137×D4311yescharacteristic
628C22#1458370311yescharacteristic
629C22#1458370811yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—434no—
637C4—862no—
638C4—862no—
639C4—862no—
640C4—3441no—
641C4—1722no—
642C4—1722no—
643C4C4×Q8×D4311yescharacteristic
644C4#1458337511yescharacteristic
645C4#1458355911yescharacteristic
646C4#1458356211yescharacteristic
647C2—1724no—
648C2#1913742911yescharacteristic
649C2#417×D4311yescharacteristic
650C2#1914311911yescharacteristic
651C2#1914729911yescharacteristic
652C2#1914737311yescharacteristic
653C2#1914749111yescharacteristic
654C2#1914750211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#22522
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
3. #19137507C2semidirect
4. #19135562C2semidirect
5. #19135554C2semidirect
6. #19135553C2semidirect
7. #19135549C2semidirect
8. #19135541C2semidirect
15. C43×#1992C2semidirect
17. #14583605C4semidirect
112. #13063247Q8semidirect
278. D172C4×Q8semidirect
324. #1992D43semidirect
389. C43#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
C2×#145830272
#191375072
#191355622
#191355542
#191355532
#191355492
#191355412
#191345942
#191345922
#191344212
#191344192
#191344092
C43×#19922
#2252243