Finite Group Databasebeta

← #25108633

Subgroups — #25108633

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583177C211yesmaximal, characteristic
2C4×#13063324C211yesmaximal, characteristic, complemented
3#19137057C211yesmaximal, characteristic
4#19135545C211yesmaximal, characteristic, complemented
5#19135350C211yesmaximal, characteristic, complemented
6#19135327C211yesmaximal, characteristic, complemented
7#19135326C211yesmaximal, characteristic, complemented
8#19135280C211yesmaximal, characteristic
9#19135275C211yesmaximal, characteristic
10#19135212C211yesmaximal, characteristic
11#19135167C211yesmaximal, characteristic, complemented
12#19135166C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#19134443C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×C4×Dic86—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063281—21no—
20#14583177C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582803—21no—
31#14582802C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582796—21no—
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582793—21no—
38#14582787—21no—
39#14582768C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4—21no—
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063324—22no—
65#13063324C2×C414yes—
66C4×Dic86—44no—
67D4×Dic43—22no—
68D4×Dic43C2×C414yes—
69#13063281—44no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063259C2×C414yes—
93#13063258—41no—
94#13063258C2×C414yes—
95Dic43⋊C8—22no—
96Dic43⋊C8C2×C414yes—
97#13063246—41no—
98#13063246C2×C414yes—
99C8×Dic43—41no—
100C8×Dic43—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×D4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#102×C43—41no—
119#102×C43C2×C414yes—
120#95×C43—21no—
121C24×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43C22×C412yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—24no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—42no—
140C22×Dic43—42no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×Dic86—24no—
146C2×Dic86—42no—
147C2×Dic86—42no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43C22×C412yes—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43C22×C412yes—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—42no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—42no—
165C22⋊Dic43—24no—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—42no—
175C4⋊Dic43C22×C412yes—
176C4⋊Dic43C22×C412yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—41no—
188C4×Dic43—42no—
189C4×Dic43—42no—
190C4×Dic43D814yes—
191C4×Dic43C22×C412yes—
192C4×Dic43#4112yes—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—41no—
210D4×C43—41no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C2×D812yes—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—48no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43C4×D412yes—
252C2×Dic43C4×D412yes—
253C2×Dic43C2×D812yes—
254C2×Dic43C2×D812yes—
255C2×Dic43#13512yes—
256C2×Dic43#13712yes—
257Dic86—48no—
258C8×C43—22no—
259C8×C43—41no—
260C43⋊C8—22no—
261C43⋊C8—41no—
262#22110—431nomaximal, Sylow
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×C4×D411yescharacteristic
271C22×C43#53611yescharacteristic
272C22×C43#53711yescharacteristic
273C22×C43C22×D811yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C4×C43—22no—
278C4×C43—42no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#51911yescharacteristic
283C4×C43#52011yescharacteristic
284C4×C43#54111yescharacteristic
285C4×C43#54211yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290Dic43—42no—
291Dic43—81no—
292Dic43—81no—
293Dic43C4×D814yes—
294C2×#474—431no—
295C4×C4⋊Q8—431no—
296#2293—431no—
297#1988—431no—
298#1947—431no—
299#1942—431no—
300#1942—431no—
301#1934—431no—
302#1934—431no—
303#1925—431no—
304#1925D4311yescharacteristic
305#1918—431no—
306#1918—431no—
307#1802—431no—
308C4×C4⋊C8—431no—
309C2×C43—82no—
310C2×C43#232311yescharacteristic
311C2×C43C2×C4×D811yescharacteristic
312C2×C43C4×#13711yescharacteristic
313C2×C43#322611yescharacteristic
314C2×C43#323311yescharacteristic
315C2×C43#324511yescharacteristic
316C2×C43#324811yescharacteristic
317C2×C4⋊Q8—431no—
318C2×C4×Q8—861no—
319C2×C4×D4—431no—
320C2×#117—861no—
321#474—438no—
322C2×#107—431no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×C4⋊C8—431no—
327C2×C4⋊C8—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×#102C2×D4311yescharacteristic
331C2×#102C2×D4311yescharacteristic
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334#391—861no—
335#390—431no—
336#390C2×D4311yescharacteristic
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389—861no—
342#388—861no—
343#388—861no—
344#384—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—861no—
348C4×C4⋊C4C2×D4311yescharacteristic
349C4×C22⋊C4—861no—
350C43—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#336—431no—
360#336C2×D4311yescharacteristic
361C43#2211011yescharacteristic, complemented, Sylow
362C22×Q8—861no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—861no—
365C22×C8—431no—
366C22×C8—431no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369C4⋊Q8—434no—
370C4⋊Q8—862no—
371C4×Q8—1724no—
372C4×D4—434no—
373C4×D4—862no—
374#117—1724no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C42—21no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42C22×D4311yescharacteristic
404#107—41no—
405#107—434no—
406#107—434no—
407#107—1721no—
408C4⋊C8—434no—
409C4⋊C8—862no—
410#102—41no—
411#102—434no—
412#102—1721no—
413#102C4×D4314yes—
414C4×C8—1721no—
415C4×C8—1721no—
416#95—21no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423C24—21no—
424C2×Q8—864no—
425C2×Q8—1722no—
426C2×Q8—1722no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×C4×D4312yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—864no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—432no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8C2×C4×D4312yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—432no—
468C4⋊C4—432no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4C2×C4×D4312yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—864no—
486C22⋊C4—1722no—
487C22⋊C4—1722no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—434no—
492C42—432no—
493C42—432no—
494C42—862no—
495C42—862no—
496C42—861no—
497C42—861no—
498C42—1721no—
499C42—1722no—
500C42—1722no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D4311yescharacteristic
509Q8—1728no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—1728no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4D8×D4312yes—
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337211yescharacteristic
558C2×C4#1306337211yescharacteristic
559C2×C4#1306337211yescharacteristic
560C8—22no—
561C8—41no—
562C8—862no—
563C8—1721no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C4×D4×D4311yescharacteristic
572C22#1458347111yescharacteristic
573C22#1458347811yescharacteristic
574C22C2×D8×D4311yescharacteristic
575C22#135×D4311yescharacteristic
576C22#137×D4311yescharacteristic
577C22#1458369511yescharacteristic
578C4—22no—
579C4—41no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—434no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—1722no—
590C4—1722no—
591C4#1458337611yescharacteristic
592C4#1458337811yescharacteristic
593C4#1458350611yescharacteristic
594C4#1458351311yescharacteristic
595C2—82no—
596C2#1913727411yescharacteristic
597C2C4×D8×D4311yescharacteristic
598C2#1914341711yescharacteristic
599C2#1914571411yescharacteristic
600C2#1914577111yescharacteristic
601C2#1914590311yescharacteristic
602C2#1914592911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#22110
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C4×#13063324C2semidirect
4. #19135545C2semidirect
5. #19135350C2semidirect
6. #19135327C2semidirect
7. #19135326C2semidirect
11. #19135167C2semidirect
12. #19135166C2semidirect
14. #19134443C2semidirect
20. #14583177C4semidirect
361. C43#22110semidirect

Maximal subgroups

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

subgroupindex
C2×#145831772
C4×#130633242
#191370572
#191355452
#191353502
#191353272
#191353262
#191352802
#191352752
#191352122
#191351672
#191351662
#191345932
#191344432
C43×#19252
#2211043