Finite Group Databasebeta

← #25106153

Subgroups — #25106153

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583529C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic
3#19137200C211yesmaximal, characteristic
4#19135566C211yesmaximal, characteristic, complemented
5#19135562C211yesmaximal, characteristic, complemented
6#19135558C211yesmaximal, characteristic, complemented
7#19135554C211yesmaximal, characteristic, complemented
8#19135553C211yesmaximal, characteristic, complemented
9#19135547C211yesmaximal, characteristic, complemented
10#19135542C211yesmaximal, characteristic, complemented
11#19134689C211yesmaximal, characteristic
12#19134688C211yesmaximal, characteristic
13#19134684C211yesmaximal, characteristic
14#19134680C211yesmaximal, characteristic
15C43×#1989C211yesmaximal, characteristic, complemented
16#14583529—24no—
17#14583529C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063305—21no—
24C2×#13063303—21no—
25C2×#13063283C2211yescharacteristic
26C2×#13063282C2211yescharacteristic
27C2×C4⋊C4×D43C2211yescharacteristic
28#14582959—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582790—21no—
35#14582788—21no—
36#14582783—21no—
37#14582781—21no—
38#14582768C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86—21no—
64C22×C4×D43—21no—
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063325—22no—
69#13063325C2×C414yes—
70#13063324—28no—
71#13063324—22no—
72#13063324C2×C414yes—
73#13063316—22no—
74#13063316C2×C414yes—
75#13063315—28no—
76#13063305—28no—
77#13063303—28no—
78#13063283—22no—
79#13063283C2×C414yes—
80#13063282C2×C414yes—
81#13063282D414yes—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4D411yescharacteristic
94C2×Dic43⋊C4D411yescharacteristic
95C4⋊C4×D43—22no—
96C4⋊C4×D43C2×C414yes—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C4⋊(C43⋊C8)—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8—22no—
108#13063235—22no—
109C8×Dic43—22no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117#125×C43—22no—
118#125×C43C2×C414yes—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128#95×C43—21no—
129C23×D43C2×D411yescharacteristic
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—24no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
151C2×C4×D43C22×C412yes—
152C2×C4×D43C2×D412yes—
153C2×Dic86—24no—
154C2×Dic86—24no—
155C2×Dic86—81no—
156C2×Dic86—81no—
157C2×Dic86—81no—
158C2×Dic86—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C412yes—
174C4⋊C4×C43C22×C412yes—
175C42×C43—81no—
176C42×C43C22×C412yes—
177C42×C43C2×D412yes—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181(C2×D43)⋊C4C22⋊C414yes—
182(C2×D43)⋊C4C22⋊C414yes—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—24no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C412yes—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—24no—
194Dic43⋊C4—24no—
195Dic43⋊C4—24no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198Dic43⋊C4C22⋊C414yes—
199Dic43⋊C4C22⋊C414yes—
200C4×Dic43—24no—
201C4×Dic43—81no—
202C4×Dic43C22×C412yes—
203C4×Dic43C2×D412yes—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43C22×D411yescharacteristic
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C22×D43C2×C22⋊C412yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C2×C22⋊C412yes—
235C2×C4×C43C2×C22⋊C412yes—
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—84no—
268Dic86—84no—
269Dic86—84no—
270C8×C43—41no—
271C8×C43—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274#21843—431nomaximal, Sylow
275C22×C43C22×C22⋊C411yescharacteristic
276C22×C43#53611yescharacteristic
277C22×C43#53611yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57711yescharacteristic
281C22×C43#57811yescharacteristic
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#51911yescharacteristic
296C4×C43#51911yescharacteristic
297C4×C43#53611yescharacteristic
298C4×C43#53611yescharacteristic
299Dic43—22no—
300Dic43—22no—
301Dic43—22no—
302Dic43—42no—
303Dic43—42no—
304Dic43—81no—
305Dic43—81no—
306C2×#544—431no—
307C2×#433—431no—
308#2314—431no—
309#1993—431no—
310#1992—431no—
311#1991—431no—
312#1990—431no—
313#1989—431no—
314#1989D4311yescharacteristic, complemented
315#1988—431no—
316#1987—431no—
317#1825—431no—
318#1825—431no—
319#1824—431no—
320#1823—431no—
321C2×C43#231011yescharacteristic
322C2×C43#289711yescharacteristic
323C2×C43#289811yescharacteristic
324C2×C43#324111yescharacteristic
325C2×C43#324211yescharacteristic
326C2×C43#324311yescharacteristic
327C2×C43#324411yescharacteristic
328D43—42no—
329#544—438no—
330#544—864no—
331C2×C4⋊Q8—431no—
332C2×C4⋊Q8—431no—
333C2×C4⋊Q8—861no—
334C2×#125—431no—
335C2×#125—861no—
336C2×#125C2×D4311yescharacteristic
337C2×C22⋊Q8—861no—
338C2×C22⋊Q8—861no—
339C2×#117—431no—
340C2×#117—431no—
341C22×C4⋊C4—431no—
342#433—864no—
343C2×C4⋊C8—431no—
344C2×C4⋊C8C2×D4311yescharacteristic
345C2×C22⋊C8—431no—
346C2×C22⋊C8—431no—
347C2×#97—431no—
348C2×C4×C8—431no—
349#388—861no—
350#388—861no—
351#387—861no—
352#387—861no—
353#384—431no—
354#382—431no—
355#380—431no—
356#380—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4C2×D4311yescharacteristic
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375C43#2184311yescharacteristic, complemented, Sylow
376C22×Q8—861no—
377C22×Q8—861no—
378C23×C4—431no—
379C23×C4—861no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384C4⋊Q8—434no—
385C4⋊Q8—434no—
386C4⋊Q8—862no—
387C4⋊Q8—868no—
388C4⋊Q8—862no—
389#125—22no—
390#125—434no—
391#125—862no—
392#125—868no—
393#125C4×D4314yes—
394C22⋊Q8—868no—
395C22⋊Q8—868no—
396#117—434no—
397#117—434no—
398#117—434no—
399#117—862no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—434no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—862no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—431no—
422C2×C22⋊C4—431no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—21no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431C4⋊C8—22no—
432C4⋊C8—862no—
433C22⋊C8—862no—
434C22⋊C8—862no—
435#97—862no—
436C4×C8—862no—
437#95—21no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—431no—
444C2×Q8—864no—
445C2×Q8—864no—
446C2×Q8—3441no—
447C2×Q8—3441no—
448C2×Q8—3441no—
449C2×Q8—3441no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—864no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3441no—
469C22×C4—3441no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—434no—
494C4⋊C4—434no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—864no—
498C4⋊C4—864no—
499C4⋊C4—864no—
500C4⋊C4—864no—
501C4⋊C4—864no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—3441no—
509C4⋊C4—3441no—
510C4⋊C4C2×C4×D4312yes—
511C4⋊C4C2×C4×D4312yes—
512C22⋊C4—434no—
513C22⋊C4—434no—
514C22⋊C4—864no—
515C22⋊C4—3441no—
516C22⋊C4—3441no—
517C42—81no—
518C42—432no—
519C42—432no—
520C42—864no—
521C42—3441no—
522C42C2×C4×D4312yes—
523C42D4×D4312yes—
524C23—432no—
525C23—861no—
526C23—861no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23C2×D4×D4311yescharacteristic
532Q8—3444no—
533Q8—3444no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4C22⋊C4×D4312yes—
577C2×C4C22⋊C4×D4312yes—
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4#1306337211yescharacteristic
581C2×C4#1306337211yescharacteristic
582C2×C4#1306337311yescharacteristic
583C2×C4#1306337311yescharacteristic
584C8—41no—
585C8—41no—
586C8—1721no—
587C8—1721no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22—1721no—
592C22—1721no—
593C22—1721no—
594C22—1721no—
595C22C2×C22⋊C4×D4311yescharacteristic
596C22#1458347211yescharacteristic
597C22#1458347211yescharacteristic
598C22#1458370311yescharacteristic
599C22#1458370611yescharacteristic
600C22#1458370811yescharacteristic
601C22#1458371311yescharacteristic
602C4—22no—
603C4—22no—
604C4—42no—
605C4—42no—
606C4—81no—
607C4—81no—
608C4—862no—
609C4—862no—
610C4—862no—
611C4—3441no—
612C4—3441no—
613C4—1722no—
614C4—1722no—
615C4#1458337511yescharacteristic
616C4#1458337511yescharacteristic
617C4#1458346911yescharacteristic
618C4#1458347411yescharacteristic
619C2—1722no—
620C2#1913717811yescharacteristic
621C2#1914311911yescharacteristic
622C2#1914312411yescharacteristic
623C2#1914585311yescharacteristic
624C2#1914586811yescharacteristic
625C2#1914587711yescharacteristic
626C2#1914590011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1989C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1989D43
hypocenterC43#21843
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #19135566C2semidirect
5. #19135562C2semidirect
6. #19135558C2semidirect
7. #19135554C2semidirect
8. #19135553C2semidirect
9. #19135547C2semidirect
10. #19135542C2semidirect
15. C43×#1989C2semidirect
17. #14583529C4semidirect
314. #1989D43semidirect
375. C43#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145829592
#191372002
#191355662
#191355622
#191355582
#191355542
#191355532
#191355472
#191355422
#191346892
#191346882
#191346842
#191346802
C43×#19892
#2184343