Finite Group Databasebeta

← #25199336

Subgroups — #25199336

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137336C211yesmaximal, characteristic, complemented
2#19137239C211yesmaximal, characteristic
3#19136073C211yesmaximal, characteristic, complemented
4#19136000C211yesmaximal, characteristic
5#19135934C211yesmaximal, characteristic, complemented
6#19135742C211yesmaximal, characteristic
7#19135223C211yesmaximal, characteristic
8#19135216C211yesmaximal, characteristic
9#19135181C211yesmaximal, characteristic, complemented
10#19135174C211yesmaximal, characteristic, complemented
11#19135174C211yesmaximal, characteristic, complemented
12#19135167C211yesmaximal, characteristic, complemented
13#19134859C211yesmaximal, characteristic
14#19134859C211yesmaximal, characteristic
15C43×#1840C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26#14582801C2211yescharacteristic
27#14582801C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582796—21no—
33#14582796—21no—
34#14582788—21no—
35#14582788—21no—
36#14582786—21no—
37#14582786—21no—
38#14582769C2211yescharacteristic
39#14582761—21no—
40#14582758—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C43×#376C2211yescharacteristic
53C43×#336C2211yescharacteristic
54C43×#336C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61#13063317—22no—
62#13063317—22no—
63C4×D172—22no—
64C4×D172—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88#13063259—22no—
89#13063257—22no—
90#13063257—22no—
91#13063257—22no—
92#13063247—22no—
93#13063247—22no—
94#13063247—22no—
95#13063247—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×C8×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110#95×C43D411yescharacteristic
111#95×C43D411yescharacteristic
112#95×C43D411yescharacteristic
113#95×C43D411yescharacteristic
114C23×D43—21no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172#4112yes—
135C2×C4×D43—24no—
136C2×C4×D43—81no—
137C2×C4×D43—81no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C42×C43—21no—
151C42×C43—21no—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—81no—
158(C2×D43)⋊C4—81no—
159(C2×D43)⋊C4—81no—
160(C2×D43)⋊C4—81no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—81no—
173C4⋊Dic43—81no—
174C4⋊Dic43#4112yes—
175C4⋊Dic43#4112yes—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183C4×Dic43—81no—
184C4×Dic43—81no—
185C4×Dic43—81no—
186C23×C43C22×D411yescharacteristic
187C22×D43—22no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43C2×#4111yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×C4×C432−1+411yescharacteristic
217C2×C4×C432−1+411yescharacteristic
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—22no—
240D172—22no—
241D172—41no—
242D172—41no—
243C4×D43—84no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248#29406—431nomaximal, Sylow
249C22×C43#52511yescharacteristic
250C22×C43#52511yescharacteristic
251C22×C43#53611yescharacteristic
252C22×C43#57611yescharacteristic
253C22×C43#57711yescharacteristic
254C22×C43#57711yescharacteristic
255C22×C43#57711yescharacteristic
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43#55211yescharacteristic
270C4×C43#55211yescharacteristic
271C4×C43#55611yescharacteristic
272C4×C43#55611yescharacteristic
273Dic43—42no—
274Dic43—42no—
275Dic43—42no—
276Dic43—81no—
277Dic43—81no—
278Dic43—81no—
279Dic43—81no—
280#2330—431no—
281#2319—431no—
282#2084—431no—
283#2071—431no—
284#2059—431no—
285#2025—431no—
286#1926—431no—
287#1925—431no—
288#1920—431no—
289#1919—431no—
290#1919—431no—
291#1918—431no—
292#1864—431no—
293#1864—431no—
294#1840D4311yescharacteristic, complemented
295C2×C43#259911yescharacteristic
296C2×C43#311911yescharacteristic
297C2×C43#311911yescharacteristic
298C2×C43#312311yescharacteristic
299C2×C43#312511yescharacteristic
300C2×C43#324111yescharacteristic
301C2×C43#324411yescharacteristic
302D43—82no—
303C2×#125—431no—
304C2×C4×D4—431no—
305C2×#107—431no—
306C2×#106—431no—
307C2×#106—431no—
308C2×#106—431no—
309C2×#102—431no—
310C2×#102—431no—
311C2×#102—431no—
312C2×#102—431no—
313#390—431no—
314#390—431no—
315#389—431no—
316#389—431no—
317#389—431no—
318#389—431no—
319#389—861no—
320#389—861no—
321#388—861no—
322#388—861no—
323#387—861no—
324#387—861no—
325#384—431no—
326#381—861no—
327#380—861no—
328C4×C4⋊C4—431no—
329C4×C4⋊C4—431no—
330C4×C4⋊C4—431no—
331#376C2×D4311yescharacteristic
332#340—431no—
333#340—431no—
334#340—431no—
335#340—431no—
336#340—431no—
337#340—431no—
338#340—431no—
339#340—431no—
340#336C2×D4311yescharacteristic
341#336C2×D4311yescharacteristic
342#336C2×D4311yescharacteristic
343#336C2×D4311yescharacteristic
344#336C2×D4311yescharacteristic
345#336C2×D4311yescharacteristic
346C43#2940611yescharacteristic, complemented, Sylow
347C22×D4—431no—
348C23×C4—861no—
349C22×C8C22×D4311yescharacteristic
350C22×C8C22×D4311yescharacteristic
351C22×C8C22×D4311yescharacteristic
352C22×C8C22×D4311yescharacteristic
353#125—862no—
354#125—862no—
355C4×D4—862no—
356C4×D4—862no—
357C2×C4⋊C4—431no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C42—861no—
378C2×C42—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381C2×C42C22×D4311yescharacteristic
382C2×C42C22×D4311yescharacteristic
383#107—862no—
384#106—862no—
385#106—862no—
386#106—862no—
387#102—862no—
388#102—862no—
389#102—862no—
390#102—862no—
391#95—861no—
392#95—861no—
393#95—861no—
394#95—861no—
395#95—861no—
396#95—861no—
397#95—861no—
398#95D17211yescharacteristic
399#95D17211yescharacteristic
400#95D17211yescharacteristic
401#95D17211yescharacteristic
402C24—861no—
403C2×D4—432no—
404C2×D4—861no—
405C2×D4—861no—
406C2×D4—861no—
407C2×D4—861no—
408C2×D4—861no—
409C22×C4—864no—
410C22×C4—861no—
411C22×C4—861no—
412C22×C4—861no—
413C22×C4—861no—
414C22×C4—861no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—3441no—
418C22×C4—3441no—
419C22×C4C2×D17211yescharacteristic
420C22×C4C2×D17211yescharacteristic
421C22×C4C2×D17211yescharacteristic
422C22×C4C2×D17211yescharacteristic
423C22×C4C2×D17211yescharacteristic
424C22×C4C2×D17211yescharacteristic
425C22×C4C23×D4311yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C4⋊C4—432no—
439C4⋊C4—432no—
440C4⋊C4—432no—
441C4⋊C4—864no—
442C4⋊C4—864no—
443C4⋊C4—861no—
444C4⋊C4—861no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—3441no—
455C4⋊C4—3441no—
456C4⋊C4—3441no—
457C4⋊C4—3441no—
458C4⋊C4—3441no—
459C4⋊C4—3441no—
460C22⋊C4—864no—
461C22⋊C4—3441no—
462C22⋊C4—3441no—
463C22⋊C4—3441no—
464C22⋊C4—3441no—
465C42—21no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—3441no—
472C42—3441no—
473C42—3441no—
474C23—862no—
475C23—1721no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23C22×D17211yescharacteristic
482D4—862no—
483D4—862no—
484D4—1721no—
485D4—1721no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—3444no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4#41×D4311yescharacteristic
527C2×C4#41×D4311yescharacteristic
528C2×C4#41×D4311yescharacteristic
529C2×C4#41×D4311yescharacteristic
530C2×C4#1306337211yescharacteristic
531C2×C4#1306337211yescharacteristic
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—3441no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22#1458341111yescharacteristic
544C22#1458341111yescharacteristic
545C22#1458347511yescharacteristic
546C22#1458370411yescharacteristic
547C22#1458371111yescharacteristic
548C22#1458371111yescharacteristic
549C22#1458371111yescharacteristic
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—3441no—
557C4—3441no—
558C4—3441no—
559C4—3441no—
560C4—1722no—
561C4—1722no—
562C4—1722no—
563C4#1458358511yescharacteristic
564C4#1458358511yescharacteristic
565C4#1458361611yescharacteristic
566C4#1458361611yescharacteristic
567C2—3442no—
568C2#1914017411yescharacteristic
569C2#1914479611yescharacteristic
570C2#1914479611yescharacteristic
571C2#1914484811yescharacteristic
572C2#1914487411yescharacteristic
573C2#1914585011yescharacteristic
574C2#1914589511yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1840C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1840D43
hypocenterC43#29406
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1840

Complements

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

NH ≅ G/Ntype
1. #19137336C2semidirect
3. #19136073C2semidirect
5. #19135934C2semidirect
9. #19135181C2semidirect
10. #19135174C2semidirect
11. #19135174C2semidirect
12. #19135167C2semidirect
15. C43×#1840C2semidirect
294. #1840D43semidirect
346. C43#29406semidirect

Maximal subgroups

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

subgroupindex
#191373362
#191372392
#191360732
#191360002
#191359342
#191357422
#191352232
#191352162
#191351812
#191351742
#191351672
#191348592
C43×#18402
#2940643