Finite Group Databasebeta

← #25148484

Subgroups — #25148484

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583202C211yesmaximal, characteristic
2C2×C8×Dic86C211yesmaximal, characteristic, complemented
3#19139982C211yesmaximal, characteristic, complemented
4#19139955C211yesmaximal, characteristic
5#19136097C211yesmaximal, characteristic, complemented
6#19136089C211yesmaximal, characteristic, complemented
7#19135978C211yesmaximal, characteristic
8#19135966C211yesmaximal, characteristic
9#19135558C211yesmaximal, characteristic, complemented
10#19135360C211yesmaximal, characteristic, complemented
11#19135322C211yesmaximal, characteristic, complemented
12#19135278C211yesmaximal, characteristic
13#19135276C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1942C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14583202—24no—
20C8×Dic86—24no—
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582834—21no—
33#14582832—21no—
34#14582820—21no—
35#14582812—21no—
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582795—21no—
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582773—21no—
45#14582770—21no—
46#14582764C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063316—22no—
67#13063316—22no—
68C4×Dic86—22no—
69C4×Dic86—22no—
70#13063287—22no—
71#13063287—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43D411yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×Dic43⋊C4D411yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92#13063256—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95Dic43⋊C8—22no—
96Dic43⋊C8D414yes—
97#13063247—22no—
98#13063247Q814yescomplemented
99#13063245—22no—
100#13063245—22no—
101C8×Dic43—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#107×C43—22no—
120#107×C43—22no—
121C4×C8×C43—22no—
122#95×C43—21no—
123#95×C43—21no—
124C23×D43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C2×Q812yes—
145C2×C4×D43—42no—
146C2×C4×D43—81no—
147C2×C4×D43—81no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×Q812yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43—81no—
166C4⋊C4×C43#4112yes—
167C42×C43—21no—
168C42×C43—21no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—81no—
173(C2×D43)⋊C4—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—22no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—42no—
181C4⋊Dic43—42no—
182C4⋊Dic43C2×Q812yes—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—81no—
192C4×Dic43C2×D412yes—
193C4×Dic43#4112yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D412yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
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×C43#13512yes—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×Q811yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
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—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43#12112yes—
251C2×Dic43#12112yes—
252C2×Dic43#13512yes—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—84no—
258Dic86—28no—
259C8×C43—22no—
260C8×C43—22no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263#25473—431nomaximal, Sylow
264C22×C43C2×#12111yescharacteristic
265C22×C43#54811yescharacteristic
266C22×C43D4×Q811yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—22no—
279C4×C43—42no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43#53311yescharacteristic
285C4×C43#54111yescharacteristic
286C4×C43#54711yescharacteristic
287C4×C43D4×Q811yescharacteristic
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—42no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295C2×#478—431no—
296C2×C8×Q8—431no—
297#2584—431no—
298#2580—431no—
299#2088—431no—
300#2087—431no—
301#2067—431no—
302#2065—431no—
303#1991—431no—
304#1949—431no—
305#1942D4311yescharacteristic, complemented
306#1941—431no—
307#1934—431no—
308#1934—431no—
309C4×#102—431no—
310C2×C43#242911yescharacteristic
311C2×C43#305011yescharacteristic
312C2×C43#306211yescharacteristic
313C2×C43#336111yescharacteristic
314C2×C43#336511yescharacteristic
315C2×C43#338011yescharacteristic
316C2×C43#338111yescharacteristic
317D43—82no—
318C2×#125—431no—
319C2×C4×Q8—431no—
320C2×C4×D4—431no—
321#478—864no—
322C8×Q8—864no—
323C2×#107C2×D4311yescharacteristic
324C2×#107C2×D4311yescharacteristic
325C2×#106—431no—
326C2×#106—431no—
327C2×C4⋊C8—431no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×C4×C8—431no—
335C2×C4×C8—431no—
336C2×C4×C8C2×D4311yescharacteristic
337#399—861no—
338#398—861no—
339#395—861no—
340#393—861no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—861no—
348#389—861no—
349#389C2×D4311yescharacteristic
350#389C2×D4311yescharacteristic
351#385—861no—
352#385—861no—
353#382—431no—
354C4×C4⋊C4—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363C43#2547311yescharacteristic, complemented, Sylow
364C22×Q8—431no—
365C22×D4—431no—
366C23×C4—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#125—862no—
372#125—862no—
373C4×Q8—862no—
374C4×Q8—862no—
375C4×D4—862no—
376C4×D4—862no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—861no—
403C2×C42C22×D4311yescharacteristic
404#107—22no—
405#107—22no—
406#106—862no—
407#106—862no—
408C4⋊C8—434no—
409C4⋊C8—862no—
410C4⋊C8—862no—
411#102—434no—
412#102—862no—
413#102—862no—
414#102—862no—
415C4×C8—22no—
416C4×C8—862no—
417C4×C8—862no—
418#95—21no—
419#95—21no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—861no—
428C2×Q8—862no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×D4—432no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—3441no—
449C22×C4—3441no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—432no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8D4×D4312yes—
465C2×C8Q8×D4312yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—432no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—3441no—
485C4⋊C4—3441no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4—1722no—
490C4⋊C4#1062189812yes—
491C22⋊C4—3441no—
492C22⋊C4—3441no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C22⋊C4—1722no—
496C42—21no—
497C42—21no—
498C42—432no—
499C42—432no—
500C42—861no—
501C42—861no—
502C42—3441no—
503C23—862no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23C2×D4×D4311yescharacteristic
511Q8—868no—
512D4—862no—
513D4—862no—
514D4—1721no—
515D4—1721no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3444no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4#1306334812yes—
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337211yescharacteristic
561C2×C4#1306337311yescharacteristic
562C8—22no—
563C8—22no—
564C8—862no—
565C8—1721no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22#121×D4311yescharacteristic
574C22#1458355811yescharacteristic
575C22#1458356411yescharacteristic
576C22#135×D4311yescharacteristic
577C22C2×#1306334811yescharacteristic
578C22#1458370011yescharacteristic
579C22#1458370611yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—862no—
587C4—862no—
588C4—862no—
589C4—3441no—
590C4—3441no—
591C4—1721no—
592C4—1722no—
593C4#1458345311yescharacteristic
594C4#1458350811yescharacteristic
595C4#1458355011yescharacteristic
596C4#1458356211yescharacteristic
597C2—3442no—
598C2#1913819311yescharacteristic
599C2#1914417811yescharacteristic
600C2#1914427411yescharacteristic
601C2#1914725611yescharacteristic
602C2#1914728911yescharacteristic
603C2#1914746411yescharacteristic
604C2#1914746711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1942C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1942D43
hypocenterC43#25473
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic86C2semidirect
3. #19139982C2semidirect
5. #19136097C2semidirect
6. #19136089C2semidirect
9. #19135558C2semidirect
10. #19135360C2semidirect
11. #19135322C2semidirect
15. C43×#1942C2semidirect
98. #13063247Q8semidirect
305. #1942D43semidirect
363. C43#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#145832022
C2×C8×Dic862
#191399822
#191399552
#191360972
#191360892
#191359782
#191359662
#191355582
#191353602
#191353222
#191352782
#191352762
#191344092
C43×#19422
#2547343