Finite Group Databasebeta

← #25113470

Subgroups — #25113470

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583622C211yesmaximal, characteristic
2#19137552C211yesmaximal, characteristic, complemented
3#19135525C211yesmaximal, characteristic
4#19135525C211yesmaximal, characteristic
5#19135517C211yesmaximal, characteristic, complemented
6#19135415C211yesmaximal, characteristic, complemented
7#19135411C211yesmaximal, characteristic
8#19135406C211yesmaximal, characteristic
9#19134611C211yesmaximal, characteristic, complemented
10#19134606C211yesmaximal, characteristic
11#19134601C211yesmaximal, characteristic, complemented
12#19134426C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic
14C4×#13063250C211yesmaximal, characteristic, complemented
15C2×C43×#446C211yesmaximal, characteristic, complemented
16#14583622—24no—
17#14583622C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063320—21no—
21C2×#13063313C2211yescharacteristic
22C2×#13063313C2211yescharacteristic
23C2×#13063301—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×#13063283—21no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40#14582806—21no—
41#14582785—21no—
42#14582785—21no—
43#14582769C2211yescharacteristic
44#14582765C2211yescharacteristic
45#14582765C2211yescharacteristic
46C4⋊C4×Dic43—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#446—24no—
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C2×C4×C8×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66#13063325—22no—
67#13063325C2×C414yes—
68#13063320—28no—
69#13063320—28no—
70#13063313—22no—
71#13063313—22no—
72#13063313C2×C414yes—
73#13063313C2×C414yes—
74#13063301—28no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C4×Dic86C2×C414yes—
78C4×Dic86C2×C414yes—
79C4×D172—22no—
80C4×D172C2×C414yes—
81#13063283—28no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063250—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—41no—
108#13063250—41no—
109#13063250—41no—
110#13063250—41no—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114#13063247—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C22×Q8×C43D411yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C4×Q8×C43C2×C414yes—
128C4×Q8×C43D414yes—
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136C4⋊C8×C43—22no—
137C4⋊C8×C43—22no—
138#97×C43—22no—
139#97×C43—22no—
140C4×C8×C43—22no—
141C23×D43—21no—
142C2×Q8×C43—41no—
143C2×Q8×C43—41no—
144C2×Q8×C43C22⋊C414yes—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172C22×C412yes—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×Dic86—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×Dic86C22×C412yes—
179C2×Dic86C22×C412yes—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43#4112yes—
192C4⋊C4×C43C22⋊C414yes—
193C4⋊C4×C43C22⋊C414yes—
194C4⋊C4×C43C22⋊C414yes—
195C42×C43C22×C412yes—
196C42×C43C22×C412yes—
197C42×C43C22×C412yes—
198C42×C43C2×D412yes—
199C42×C43C2×D412yes—
200C42×C43C2×D412yes—
201(C2×D43)⋊C4—24no—
202(C2×D43)⋊C4—24no—
203(C2×D43)⋊C4—24no—
204(C2×D43)⋊C4—24no—
205(C2×D43)⋊C4—24no—
206C4⋊Dic43—24no—
207C4⋊Dic43—24no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—42no—
217C4⋊Dic43—81no—
218C4⋊Dic43C22×C412yes—
219C4⋊Dic43#4112yes—
220Dic43⋊C4—24no—
221Dic43⋊C4—24no—
222C4×Dic43—24no—
223C4×Dic43—24no—
224C4×Dic43—42no—
225C4×Dic43—81no—
226C4×Dic43—81no—
227C23×C43C22×D411yescharacteristic
228C22×D43—22no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235Q8×C43—44no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C2×C22⋊C412yes—
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281D172—22no—
282D172—22no—
283D172—41no—
284D172—41no—
285C4×D43—48no—
286Dic86—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—22no—
290Dic86—41no—
291Dic86—41no—
292Dic86—41no—
293Dic86—41no—
294C8×C43—22no—
295C8×C43—41no—
296C8×C43—41no—
297C8×C43—41no—
298#22548—431nomaximal, Sylow
299C22×C43C22×C22⋊C411yescharacteristic
300C22×C43#54811yescharacteristic
301C22×C43#55011yescharacteristic
302C22×C43#57511yescharacteristic
303C22×C43#57511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C4×C43—22no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43C4×#4111yescharacteristic
320C4×C43#52011yescharacteristic
321C4×C43#54811yescharacteristic
322C4×C43#55011yescharacteristic
323Dic43—42no—
324Dic43—42no—
325Dic43—42no—
326Dic43—42no—
327Dic43—81no—
328Dic43—81no—
329Dic43—81no—
330C2×#556—431no—
331C2×#446D4311yescharacteristic, complemented
332#2355—431no—
333#1983—431no—
334#1983—431no—
335#1981—431no—
336#1960—431no—
337#1959—431no—
338#1958—431no—
339#1805—431no—
340#1804—431no—
341#1803—431no—
342#1763—431no—
343#1762—431no—
344C4×#103—431no—
345C2×C43#234111yescharacteristic
346C2×C43#289611yescharacteristic
347C2×C43#289811yescharacteristic
348C2×C43#337611yescharacteristic
349C2×C43#337711yescharacteristic
350C2×C43#340111yescharacteristic
351C2×C43#340211yescharacteristic
352D43—82no—
353#556—438no—
354#556—864no—
355C2×C4⋊Q8—431no—
356C2×#126—861no—
357C2×#126—861no—
358C2×#124—431no—
359C2×#124—431no—
360C2×C22⋊Q8—861no—
361C2×C4×Q8—431no—
362C2×C4×Q8—431no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×C4×D4—431no—
365C2×#117—861no—
366#446—24no—
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×C4⋊C8C2×D4311yescharacteristic
369C2×C4⋊C8C2×D4311yescharacteristic
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#97C2×D4311yescharacteristic
383C2×#97C2×D4311yescharacteristic
384C2×C4×C8C2×D4311yescharacteristic
385#391—861no—
386#387—861no—
387#387—861no—
388#384—431no—
389#382—431no—
390#382—431no—
391C4×C4⋊C4—431no—
392C4×C4⋊C4—431no—
393C4×C4⋊C4—431no—
394C4×C4⋊C4—861no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399C43#2254811yescharacteristic, complemented, Sylow
400C22×Q8—431no—
401C22×Q8—431no—
402C22×Q8D17211yescharacteristic
403C22×D4—431no—
404C23×C4—861no—
405C22×C8C22×D4311yescharacteristic
406C22×C8C22×D4311yescharacteristic
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409C4⋊Q8—434no—
410C4⋊Q8—862no—
411#126—868no—
412#126—868no—
413#124—434no—
414#124—434no—
415#124—862no—
416#124—862no—
417C22⋊Q8—868no—
418C4×Q8—434no—
419C4×Q8—434no—
420C4×Q8—862no—
421C4×Q8—862no—
422C4×Q8C4×D4314yes—
423C4×Q8C22⋊D4314yes—
424C4×D4—434no—
425C4×D4—862no—
426#117—868no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4D17211yescharacteristic
439C2×C4⋊C4D17211yescharacteristic
440C2×C4⋊C4D17211yescharacteristic
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42—861no—
451C2×C42C22×D4311yescharacteristic
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454C4⋊C8—22no—
455C4⋊C8—22no—
456C4⋊C8—22no—
457#103—862no—
458#103—862no—
459#103—862no—
460#103—862no—
461#103—1721no—
462#103—1721no—
463#103—1721no—
464#103—1721no—
465#102—862no—
466#102—862no—
467#102—1721no—
468#102—1721no—
469#97—22no—
470#97—22no—
471C4×C8—22no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—861no—
480C2×Q8—41no—
481C2×Q8—41no—
482C2×Q8—432no—
483C2×Q8—432no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8(C2×D43)⋊C414yes—
495C2×D4—432no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—864no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—1722no—
510C22×C4—1722no—
511C22×C4C2×D17211yescharacteristic
512C22×C4C2×D17211yescharacteristic
513C22×C4C2×D17211yescharacteristic
514C22×C4C2×D17211yescharacteristic
515C22×C4C2×D17211yescharacteristic
516C22×C4C2×D17211yescharacteristic
517C22×C4C23×D4311yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8#1062190212yes—
530C4⋊C4—432no—
531C4⋊C4—432no—
532C4⋊C4—864no—
533C4⋊C4—864no—
534C4⋊C4—864no—
535C4⋊C4—864no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—1722no—
546C4⋊C4(C2×D43)⋊C414yes—
547C4⋊C4(C2×D43)⋊C414yes—
548C4⋊C4(C2×D43)⋊C414yes—
549C22⋊C4—864no—
550C22⋊C4—864no—
551C22⋊C4—864no—
552C22⋊C4—864no—
553C22⋊C4—864no—
554C42—864no—
555C42—864no—
556C42—3441no—
557C42—3441no—
558C42—1722no—
559C42C2×C4×D4312yes—
560C42C2×C4×D4312yes—
561C42C2×C4×D4312yes—
562C42C2×C22⋊D4312yes—
563C42C2×C22⋊D4312yes—
564C42C2×C22⋊D4312yes—
565C23—862no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23C22×D17211yescharacteristic
573Q8—44no—
574Q8—862no—
575Q8—862no—
576Q8—862no—
577Q8—862no—
578Q8—1721no—
579Q8—1721no—
580Q8—1721no—
581Q8—1721no—
582D4—862no—
583D4—862no—
584D4—1721no—
585D4—1721no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—1728no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4C2×(C2×D43)⋊C412yes—
621C2×C4C2×(C2×D43)⋊C412yes—
622C2×C4C2×(C2×D43)⋊C412yes—
623C2×C4C2×(C2×D43)⋊C412yes—
624C2×C4C2×(C2×D43)⋊C412yes—
625C2×C4C2×(C2×D43)⋊C412yes—
626C2×C4C22×C4×D4311yescharacteristic
627C2×C4C22×C22⋊D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C2×C4C2×#1062190211yescharacteristic
630C2×C4#1306337111yescharacteristic
631C2×C4#1306337311yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—3441no—
637C22—3441no—
638C22—3441no—
639C22—3441no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22C22×(C2×D43)⋊C411yescharacteristic
644C22#1458356111yescharacteristic
645C22#1458357111yescharacteristic
646C22#1458369911yescharacteristic
647C22#1458369911yescharacteristic
648C22#1458371111yescharacteristic
649C22#1458371611yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—3441no—
657C4—3441no—
658C4—3441no—
659C4—1722no—
660C4—1722no—
661C4—1722no—
662C4—1722no—
663C4C4×#1062190211yescharacteristic
664C4#1458338111yescharacteristic
665C4#1458356011yescharacteristic
666C4#1458356811yescharacteristic
667C2—3442no—
668C2#1913743311yescharacteristic
669C2#1914311511yescharacteristic
670C2#1914312911yescharacteristic
671C2#1914742411yescharacteristic
672C2#1914743911yescharacteristic
673C2#1914766311yescharacteristic
674C2#1914767611yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC2×#446D43
hypocenterC43#22548
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #19137552C2semidirect
5. #19135517C2semidirect
6. #19135415C2semidirect
9. #19134611C2semidirect
11. #19134601C2semidirect
12. #19134426C2semidirect
14. C4×#13063250C2semidirect
15. C2×C43×#446C2semidirect
17. #14583622C4semidirect
331. C2×#446D43semidirect
399. C43#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#145836222
#191375522
#191355252
#191355172
#191354152
#191354112
#191354062
#191346112
#191346062
#191346012
#191344262
#191344212
C4×#130632502
C2×C43×#4462
#2254843