Finite Group Databasebeta

← #25169192

Subgroups — #25169192

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138445C211yesmaximal, characteristic
2#19137689C211yesmaximal, characteristic, complemented
3#19135968C211yesmaximal, characteristic
4#19135934C211yesmaximal, characteristic, complemented
5#19135929C211yesmaximal, characteristic, complemented
6#19135742C211yesmaximal, characteristic
7#19135546C211yesmaximal, characteristic, complemented
8#19135333C211yesmaximal, characteristic, complemented
9#19135223C211yesmaximal, characteristic
10#19135216C211yesmaximal, characteristic
11#19135181C211yesmaximal, characteristic, complemented
12#19135181C211yesmaximal, characteristic, complemented
13#19134859C211yesmaximal, characteristic
14#19134421C211yesmaximal, characteristic
15C43×#1917C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063303—21no—
19C2×C4×D172C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582821—21no—
29#14582812—21no—
30#14582801C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582794—21no—
37#14582781—21no—
38#14582780—21no—
39#14582773—21no—
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582750—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62#13063325—22no—
63#13063325—41no—
64#13063317—22no—
65#13063317—22no—
66#13063303—44no—
67C4×D172—22no—
68C4×D172—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91#13063259—22no—
92#13063257—22no—
93#13063257—22no—
94#13063257—41no—
95#13063247—22no—
96#13063247—22no—
97#13063247—41no—
98#13063247Q814yescomplemented
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C4⋊C8×C43—41no—
116#97×C43—41no—
117#95×C43D411yescharacteristic
118#95×C43D411yescharacteristic
119C23×D43—21no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172C2×Q812yes—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×C4×D43—81no—
143C2×Dic86—42no—
144C2×Dic86—42no—
145C2×Dic86—81no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C2×Q812yes—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—41no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—21no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43C2×Q812yes—
183C4⋊Dic43#4112yes—
184C4⋊Dic43#4112yes—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—81no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C4×Dic43—81no—
195C23×C43C22×D411yescharacteristic
196C22×D43—22no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
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×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43AGL(1,ℤ/8)12yes—
221C2×C4×C43C22×Q811yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—84no—
253Dic86—84no—
254C8×C43—22no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258#27026—431nomaximal, Sylow
259C22×C43#52511yescharacteristic
260C22×C43#54611yescharacteristic
261C22×C43D4×Q811yescharacteristic
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57711yescharacteristic
265C22×C43#57711yescharacteristic
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—22no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43#53311yescharacteristic
280C4×C43#54211yescharacteristic
281C4×C43#55411yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290#2452—431no—
291#2370—431no—
292#2065—431no—
293#2059—431no—
294#2058—431no—
295#2025—431no—
296#1988—431no—
297#1943—431no—
298#1926—431no—
299#1925—431no—
300#1920—431no—
301#1920—431no—
302#1917D4311yescharacteristic, complemented
303#1864—431no—
304#1762—431no—
305C2×C43#246511yescharacteristic
306C2×C43#311511yescharacteristic
307C2×C43#312511yescharacteristic
308C2×C43#331011yescharacteristic
309C2×C43#332611yescharacteristic
310C2×C43#338411yescharacteristic
311C2×C43#338811yescharacteristic
312D43—82no—
313C2×C4⋊Q8—431no—
314C2×#125—431no—
315C2×C22⋊Q8—861no—
316C2×C4×D4—431no—
317C2×#107—431no—
318C2×#106—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×C4⋊C8C2×D4311yescharacteristic
322C2×#102—431no—
323C2×#102—431no—
324C2×#102—431no—
325C2×#102—431no—
326C2×#97C2×D4311yescharacteristic
327#396—861no—
328#393—861no—
329#390—431no—
330#390—431no—
331#389—431no—
332#389—431no—
333#389—431no—
334#389—431no—
335#389—861no—
336#387—861no—
337#387—861no—
338#385—861no—
339C4×C4⋊C4—431no—
340C4×C4⋊C4—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—861no—
343C4×C4⋊C4C2×D4311yescharacteristic
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#336C2×D4311yescharacteristic
353#336C2×D4311yescharacteristic
354#336C2×D4311yescharacteristic
355#336C2×D4311yescharacteristic
356C43#2702611yescharacteristic, complemented, Sylow
357C22×Q8—861no—
358C22×D4—431no—
359C23×C4—861no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364C4⋊Q8—862no—
365C4⋊Q8—1721no—
366#125—862no—
367#125—862no—
368C22⋊Q8—1724no—
369C4×D4—862no—
370C4×D4—1721no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
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⋊C4D17211yescharacteristic
386C2×C4⋊C4D17211yescharacteristic
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398#107—862no—
399#106—862no—
400#106—862no—
401#106—1721no—
402C4⋊C8—41no—
403#102—434no—
404#102—862no—
405#102—862no—
406#102—1721no—
407#97—41no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95D17211yescharacteristic
416#95D17211yescharacteristic
417C24—861no—
418C2×Q8—3441no—
419C2×Q8—1722no—
420C2×Q8—1722no—
421C2×D4—432no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—3441no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4C2×D17211yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4C2×D17211yescharacteristic
440C22×C4C2×D17211yescharacteristic
441C22×C4C2×D17211yescharacteristic
442C22×C4C2×D17211yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8Q8×D4312yes—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—432no—
461C4⋊C4—432no—
462C4⋊C4—864no—
463C4⋊C4—864no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—3441no—
475C4⋊C4—1722no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C22⋊C4—3441no—
480C22⋊C4—1722no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—3441no—
491C42—3441no—
492C42—1722no—
493C23—862no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23C22×D17211yescharacteristic
501Q8—3444no—
502D4—862no—
503D4—862no—
504D4—1721no—
505D4—1721no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—3444no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4#1306335312yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C2×C4#41×D4311yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—22no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1722no—
561C22—1722no—
562C22—1722no—
563C22#1458341111yescharacteristic
564C22#1458354411yescharacteristic
565C22Q8×D17211yescharacteristic
566C22C2×#1306335311yescharacteristic
567C22#1458369911yescharacteristic
568C22#1458371111yescharacteristic
569C22#1458371111yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4—1722no—
580C4—1722no—
581C4—1722no—
582C4—1722no—
583C4#1458345511yescharacteristic
584C4#1458351711yescharacteristic
585C4#1458360311yescharacteristic
586C4#1458361611yescharacteristic
587C2—3442no—
588C2#1913861411yescharacteristic
589C2#1914474711yescharacteristic
590C2#1914487411yescharacteristic
591C2#1914661811yescharacteristic
592C2#1914685011yescharacteristic
593C2#1914749611yescharacteristic
594C2#1914754211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1917C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1917D43
hypocenterC43#27026
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #19137689C2semidirect
4. #19135934C2semidirect
5. #19135929C2semidirect
7. #19135546C2semidirect
8. #19135333C2semidirect
11. #19135181C2semidirect
12. #19135181C2semidirect
15. C43×#1917C2semidirect
98. #13063247Q8semidirect
302. #1917D43semidirect
356. C43#27026semidirect

Maximal subgroups

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

subgroupindex
#191384452
#191376892
#191359682
#191359342
#191359292
#191357422
#191355462
#191353332
#191352232
#191352162
#191351812
#191348592
#191344212
C43×#19172
#2702643