Finite Group Databasebeta

← #25118890

Subgroups — #25118890

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583118C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C2×C4×#10621883C211yesmaximal, characteristic
4#19137515C211yesmaximal, characteristic, complemented
5#19135407C211yesmaximal, characteristic
6#19135363C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic
8#19135274C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic
10#19134939C211yesmaximal, characteristic, complemented
11#19134863C211yesmaximal, characteristic, complemented
12#19134842C211yesmaximal, characteristic
13C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
14C4×#13063248C211yesmaximal, characteristic, complemented
15C43×#2367C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583118C418yescomplemented
22C4×#10621885—24no—
23C4×#10621883—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582794—21no—
41#14582794—21no—
42#14582765C2211yescharacteristic
43#14582763—21no—
44#14582750—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×#124×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#388—21no—
57C43×#388—21no—
58C43×#385—21no—
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43—21no—
62C22×Dic86C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885C2×C414yescomplemented
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883C2×C414yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C4×Dic86—22no—
74C4×Dic86—22no—
75C4×Dic86—22no—
76C4×Dic86—41no—
77C4×Dic86—41no—
78C4×Dic86C2×C414yescomplemented
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063258—22no—
91#13063256—22no—
92C4⋊(C43⋊C8)C2×C414yescomplemented
93#13063249—22no—
94#13063249—41no—
95#13063249C2×C414yescomplemented
96#13063248—22no—
97#13063248D414yes—
98#13063246—22no—
99#13063246—41no—
100#13063246C2×C414yes—
101C4×C43⋊C8—22no—
102C4×C43⋊C8—22no—
103C4×C43⋊C8—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111#124×C43—22no—
112#124×C43C2×C414yes—
113C4×Q8×C43—22no—
114C4×Q8×C43—41no—
115C4×D4×C43—22no—
116C4×D4×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C24×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—81no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C412yes—
171C2×Dic86C2×D412yes—
172C2×Dic86#4112yes—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—42no—
190C42×C43—81no—
191C42×C43C22×C412yes—
192C42×C43#4112yes—
193#10621885—28no—
194#10621883—28no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—24no—
202Dic43⋊C4—42no—
203Dic43⋊C4—42no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206C4×Dic43—24no—
207C4×Dic43—42no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C2×D412yes—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C22×D411yescharacteristic
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—41no—
236D4×C43—41no—
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—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—84no—
261C2×C4×C43C4×D412yes—
262C2×C4×C43C4×D412yes—
263C2×C4×C43#13512yes—
264C2×C4×C43#13512yes—
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283Dic86—22no—
284Dic86—22no—
285Dic86—22no—
286Dic86C4×D414yes—
287C43⋊C8—22no—
288C43⋊C8—22no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#23000—431nomaximal, Sylow
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×C4×D411yescharacteristic
300C22×C43D4211yescharacteristic
301C22×C43#54811yescharacteristic
302C22×C43C2×#13511yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43#57711yescharacteristic
305C22×C43#57811yescharacteristic
306C4×C43—22no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43—41no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43C2×C4×D411yescharacteristic
316C4×C43#52011yescharacteristic
317C4×C43#54711yescharacteristic
318C4×C43#55311yescharacteristic
319Dic43—24no—
320Dic43—42no—
321Dic43—81no—
322Dic43—81no—
323C2×#464—431no—
324C2×C4×Q16—431no—
325C2×C4×SD16—431no—
326#2367D4311yescharacteristic
327#2351—431no—
328#1958—431no—
329#1949—431no—
330#1934—431no—
331#1933—431no—
332#1880—431no—
333#1878—431no—
334#1865—431no—
335#1862—431no—
336C8×C4⋊C4—431no—
337C4×#103—431no—
338C2×C43—82no—
339C2×C43#236111yescharacteristic
340C2×C43C4×#13511yescharacteristic
341C2×C43#294711yescharacteristic
342C2×C43#328211yescharacteristic
343C2×C43#328511yescharacteristic
344C2×C43#336411yescharacteristic
345C2×C43#336511yescharacteristic
346C22×Q16—431no—
347C22×SD16—431no—
348C2×#124C2×D4311yescharacteristic
349C2×C4×Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4C2×D4311yescharacteristic
354#464—438no—
355C4×Q16—864no—
356C4×SD16—864no—
357C2×#107—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371#391C2×D4311yescharacteristic
372#390C2×D4311yescharacteristic
373#389—431no—
374#389—431no—
375#389—861no—
376#389—861no—
377#388—21no—
378#388—21no—
379#385—21no—
380#382—431no—
381#382—861no—
382C4×C4⋊C4—861no—
383C4×C4⋊C4C2×D4311yescharacteristic
384C4×C4⋊C4C2×D4311yescharacteristic
385C4×C22⋊C4—21no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392C43#2300011yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×Q8C22×D4311yescharacteristic
395C22×D4C22×D4311yescharacteristic
396C23×C4—21no—
397C2×Q16—434no—
398C2×Q16—862no—
399C2×Q16—862no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8—431no—
407#124—22no—
408#124C4×D4314yes—
409C4×Q8—22no—
410C4×Q8—41no—
411C4×Q8—434no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—1721no—
416C4×Q8—1721no—
417C4×D4—22no—
418C4×D4—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4C22⋊D4311yescharacteristic
429C2×C4⋊C4C22⋊D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—861no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445#107—862no—
446#106—862no—
447C4⋊C8—434no—
448#103—434no—
449#103—434no—
450#103—862no—
451#103—862no—
452#103—1721no—
453#102—434no—
454#102—862no—
455#102—1721no—
456C4×C8—862no—
457C4×C8—862no—
458C4×C8—862no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95C22⋊D4311yescharacteristic
467#95C22⋊D4311yescharacteristic
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—432no—
475C2×Q8—432no—
476C2×Q8—432no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4312yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C4×D4312yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C2×C22⋊D4311yescharacteristic
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—868no—
505SD16—868no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—432no—
525C4⋊C4—864no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1722no—
534C4⋊C4—1722no—
535C4⋊C4D4×D4312yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—81no—
547C42—864no—
548C42—1722no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062189812yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22×C22⋊D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—434no—
565Q8—862no—
566Q8—862no—
567Q8—862no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4C4×C22⋊D4312yes—
609C2×C4C4×C22⋊D4312yes—
610C2×C4#1306334512yes—
611C2×C4#1306334512yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4#41×D4311yescharacteristic
615C2×C4C2×#1062189811yescharacteristic
616C2×C4#1306337011yescharacteristic
617C2×C4#1306337211yescharacteristic
618C8—862no—
619C8—862no—
620C8—862no—
621C8—1721no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×C4×C22⋊D4311yescharacteristic
630C22D4×C22⋊D4311yescharacteristic
631C22#1458355611yescharacteristic
632C22C2×#1306334511yescharacteristic
633C22C2×#1306334511yescharacteristic
634C22#1458371011yescharacteristic
635C22#1458371411yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—41no—
641C4—42no—
642C4—42no—
643C4—41no—
644C4—81no—
645C4—864no—
646C4—3441no—
647C4—3441no—
648C4—1722no—
649C4C4×D4×D4311yescharacteristic
650C4#1458337811yescharacteristic
651C4#1458355411yescharacteristic
652C4#1458359911yescharacteristic
653C2—82no—
654C2#1913760711yescharacteristic
655C2C4×#1306334511yescharacteristic
656C2#1914343411yescharacteristic
657C2#1914629811yescharacteristic
658C2#1914633211yescharacteristic
659C2#1914727611yescharacteristic
660C2#1914728711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2367C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#2367D43
hypocenterC43#23000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
4. #19137515C2semidirect
6. #19135363C2semidirect
8. #19135274C2semidirect
10. #19134939C2semidirect
11. #19134863C2semidirect
13. C4⋊C4×C43⋊C8C2semidirect
14. C4×#13063248C2semidirect
21. #14583118C4semidirect
65. C2×#10621885C2×C4semidirect
78. C4×Dic86C2×C4semidirect
92. C4⋊(C43⋊C8)C2×C4semidirect
95. #13063249C2×C4semidirect
392. C43#23000semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
C2×C4×#106218852
C2×C4×#106218832
#191375152
#191354072
#191353632
#191352812
#191352742
#191349532
#191349392
#191348632
#191348422
C4⋊C4×C43⋊C82
C4×#130632482
C43×#23672
#2300043