Finite Group Databasebeta

← #25159628

Subgroups — #25159628

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583185C211yesmaximal, characteristic, complemented
2C2×C4×#10621873C211yesmaximal, characteristic
3#19138445C211yesmaximal, characteristic
4C4⋊C4×Dic86C211yesmaximal, characteristic, complemented
5#19136127C211yesmaximal, characteristic
6#19136073C211yesmaximal, characteristic, complemented
7#19135968C211yesmaximal, characteristic
8#19135929C211yesmaximal, characteristic, complemented
9#19135323C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic
11#19134949C211yesmaximal, characteristic
12#19134866C211yesmaximal, characteristic, complemented
13#19134866C211yesmaximal, characteristic, complemented
14#19134859C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18C2×#13063303—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583185—24no—
24C4×#10621873—24no—
25C2×#13063257C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063257C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582821—21no—
37#14582812—21no—
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582797C2211yescharacteristic
42#14582797C2211yescharacteristic
43#14582797C2211yescharacteristic
44#14582796—21no—
45#14582796—21no—
46#14582773—21no—
47#14582769C2211yescharacteristic
48#14582768—21no—
49C4⋊C4×Dic43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621873—22no—
66C2×#10621873—22no—
67C2×#10621873Q814yescomplemented
68#13063325—22no—
69#13063325—41no—
70#13063303—44no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×Dic86—22no—
75C4×Dic86—41no—
76C4×Dic86—41no—
77C4×D172—22no—
78C4×D172—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
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⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063257—22no—
104#13063257—22no—
105#13063257—22no—
106#13063257—22no—
107#13063257—41no—
108#13063250—22no—
109#13063250—22no—
110#13063250D414yes—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128C4×C8×C43—22no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C23×D43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C2×Q812yes—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—81no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—42no—
159C2×Dic86—42no—
160C2×Dic86—81no—
161C2×Dic86C2×D412yes—
162C2×Dic86C2×Q812yes—
163C2×Dic86#4112yes—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
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×C43C2×D412yes—
175C2×C8×C43C2×Q812yes—
176C4⋊C4×C43—41no—
177C4⋊C4×C43SD1614yescomplemented
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188(C2×D43)⋊C4—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43—42no—
201C4⋊Dic43—81no—
202C4⋊Dic43C2×D412yes—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—24no—
205Dic43⋊C4—42no—
206Dic43⋊C4—42no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C4×Dic43—24no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214#10621873—28no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
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×C43C2×SD1612yes—
239C2×C4×C43C2×SD1612yes—
240C2×C4×C43C2×SD1612yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
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×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—84no—
273Dic86—22no—
274Dic86—22no—
275Dic86—22no—
276Dic86—84no—
277Dic86C22⋊Q814yescomplemented
278C8×C43—22no—
279C8×C43—22no—
280C8×C43—41no—
281C8×C43—41no—
282#26373—431nomaximal, Sylow
283C22×C43#52511yescharacteristic
284C22×C43D4211yescharacteristic
285C22×C43D4×Q811yescharacteristic
286C22×C43C22×SD1611yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C4×C43—22no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43C2×C22⋊Q811yescharacteristic
304C4×C43#53911yescharacteristic
305C4×C43#54711yescharacteristic
306C4×C43#55411yescharacteristic
307Dic43—24no—
308Dic43—42no—
309Dic43—42no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314C2×#475—431no—
315C2×C4×SD16—431no—
316#2452—431no—
317Q8×C4⋊C4—431no—
318#2094—431no—
319#2084—431no—
320#2065—431no—
321#2058—431no—
322#1941—431no—
323#1916D4311yescharacteristic, complemented
324#1880—431no—
325#1880—431no—
326#1865—431no—
327#1865—431no—
328#1864—431no—
329C2×C43#244911yescharacteristic
330C2×C43#310311yescharacteristic
331C2×C43#312511yescharacteristic
332C2×C43#327111yescharacteristic
333C2×C43D4×SD1611yescharacteristic
334C2×C43Q8×SD1611yescharacteristic
335C2×C43#338811yescharacteristic
336D43—82no—
337C22×SD16—431no—
338C2×C4⋊Q8—431no—
339C2×C22⋊Q8—861no—
340C2×C4×Q8—431no—
341C2×C4×Q8—431no—
342C2×C4×Q8—431no—
343C2×C4×D4—431no—
344#475—864no—
345C4×SD16—864no—
346C2×#106—431no—
347C2×#106—431no—
348C2×#106—431no—
349C2×#106—431no—
350C2×#106—431no—
351C2×C4⋊C8C2×D4311yescharacteristic
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×C4×C8C2×D4311yescharacteristic
359#396—861no—
360#393—861no—
361#390—431no—
362#390—431no—
363#389—431no—
364#389—431no—
365#389—431no—
366#389—431no—
367#389—861no—
368#389—861no—
369#385—861no—
370#384—431no—
371#384—861no—
372C4×C4⋊C4—861no—
373C4×C4⋊C4C2×D4311yescharacteristic
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#336C2×D4311yescharacteristic
379#336C2×D4311yescharacteristic
380#336C2×D4311yescharacteristic
381#336C2×D4311yescharacteristic
382C43#2637311yescharacteristic, complemented, Sylow
383C22×Q8—431no—
384C22×Q8—861no—
385C22×D4—431no—
386C23×C4—861no—
387C2×SD16—434no—
388C2×SD16—862no—
389C2×SD16—862no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394C4⋊Q8—862no—
395C4⋊Q8—1721no—
396C22⋊Q8—1724no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—1721no—
402C4×Q8—1721no—
403C4×D4—862no—
404C4×D4—1721no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
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⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4D17211yescharacteristic
422C2×C4⋊C4D17211yescharacteristic
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42C22×D4311yescharacteristic
432C2×C42C22×D4311yescharacteristic
433C2×C42C22×D4311yescharacteristic
434#106—862no—
435#106—862no—
436#106—862no—
437#106—862no—
438#106—1721no—
439C4⋊C8—22no—
440#103—434no—
441#103—862no—
442#103—862no—
443#102—862no—
444#102—862no—
445#102—1721no—
446C4×C8—22no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95D17211yescharacteristic
452#95D17211yescharacteristic
453C24—861no—
454C2×Q8—432no—
455C2×Q8—432no—
456C2×Q8—432no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—3441no—
461C2×Q8—1722no—
462C2×Q8—1722no—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3441no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4C23×D4311yescharacteristic
486SD16—868no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8D4×D4312yes—
498C2×C8Q8×D4312yes—
499C4⋊C4—41no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—864no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—3441no—
514C4⋊C4—3441no—
515C4⋊C4—3441no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4#1062187314yescomplemented
523C22⋊C4—3441no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—864no—
535C42—1722no—
536C42—1722no—
537C23—862no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23C22×D17211yescharacteristic
545Q8—434no—
546Q8—862no—
547Q8—862no—
548Q8—862no—
549Q8—3444no—
550D4—862no—
551D4—862no—
552D4—1721no—
553D4—1721no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—3444no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C2×#1062187312yes—
592C2×C4C2×#1062187312yes—
593C2×C4C2×#1062187312yes—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C2×Q8×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#1306337111yescharacteristic
599C2×C4#1306337211yescharacteristic
600C8—22no—
601C8—22no—
602C8—41no—
603C8—41no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22#1458341111yescharacteristic
612C22D4×D17211yescharacteristic
613C22Q8×D17211yescharacteristic
614C22C22×#1062187311yescharacteristic
615C22#1458369911yescharacteristic
616C22#1458371111yescharacteristic
617C22#1458371111yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—864no—
625C4—3441no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—1722no—
630C4—1722no—
631C4C22⋊Q8×D4311yescharacteristic
632C4#1458349011yescharacteristic
633C4#1458354711yescharacteristic
634C4#1458360511yescharacteristic
635C2—3442no—
636C2#1913840911yescharacteristic
637C2#1914462711yescharacteristic
638C2#1914487411yescharacteristic
639C2#1914618511yescharacteristic
640C2D4×#1062187311yescharacteristic
641C2Q8×#1062187311yescharacteristic
642C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26373
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#14583185C2semidirect
4. C4⋊C4×Dic86C2semidirect
6. #19136073C2semidirect
8. #19135929C2semidirect
9. #19135323C2semidirect
12. #19134866C2semidirect
13. #19134866C2semidirect
15. C43×#1916C2semidirect
67. C2×#10621873Q8semidirect
177. C4⋊C4×C43SD16semidirect
277. Dic86C22⋊Q8semidirect
323. #1916D43semidirect
382. C43#26373semidirect
522. C4⋊C4#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145831852
C2×C4×#106218732
#191384452
C4⋊C4×Dic862
#191361272
#191360732
#191359682
#191359292
#191353232
#191349492
#191348662
#191348592
C43×#19162
#2637343