Finite Group Databasebeta

← #19140921

Subgroups — #19140921

Order 5504.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063308C211yesmaximal, characteristic, complemented
2C2×#13063299C211yesmaximal, characteristic, complemented
3C2×#13063295C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5#14582828C211yesmaximal, characteristic, complemented
6#14582822C211yesmaximal, characteristic, complemented
7#14582817C211yesmaximal, characteristic, complemented
8#14582817C211yesmaximal, characteristic, complemented
9#14582808C211yesmaximal, characteristic, complemented
10#14582807C211yesmaximal, characteristic, complemented
11#14582799C211yesmaximal, characteristic, complemented
12#14582799C211yesmaximal, characteristic, complemented
13#14582791C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#386C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23#13063308—24no—
24#13063299—24no—
25#13063295—24no—
26#13063293—24no—
27C2×C4⋊Dic43C2211yescharacteristic, complemented
28C2×Dic43⋊C4C2211yescharacteristic, complemented
29C2×Dic43⋊C4C2211yescharacteristic, complemented
30C2×Dic43⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic, complemented
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic43C2211yescharacteristic, complemented
46C43⋊#95C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C22×D4×C43C2211yescharacteristic
49C23×C4×C43C2211yescharacteristic, complemented
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic, complemented
53#95×C43C2211yescharacteristic, complemented
54#95×C43C2211yescharacteristic, complemented
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43—22no—
58C23×D43—22no—
59C23×D43—22no—
60C23×D43—41no—
61C23×D43—41no—
62C23×D43—41no—
63C23×D43—41no—
64C23×D43C2311yescharacteristic
65C23×D43C2311yescharacteristic
66C23×D43C2311yescharacteristic
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C22×C4×C43—22no—
71C22×C4×C43—22no—
72C22×C4×C43—41no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C22×C4×C43C2311yescharacteristic
78C2×C22⋊D43—22no—
79C2×C22⋊D43—22no—
80C2×C22⋊D43—22no—
81C2×C22⋊D43—22no—
82C2×C22⋊D43—22no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43D414yescomplemented
90C22×Dic43C2311yescharacteristic
91C22×Dic43C2311yescharacteristic
92C22×Dic43C2311yescharacteristic
93C22×Dic43C2311yescharacteristic
94C22×Dic43C2311yescharacteristic
95C2×D172—22no—
96C2×D172—22no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊Dic43—22no—
105C22⋊Dic43—22no—
106C22⋊Dic43—41no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—41no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4D414yescomplemented
118C4⋊Dic43—22no—
119Dic43⋊C4—22no—
120Dic43⋊C4—22no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43C2×D412yes—
136C23×C43#4112yes—
137C23×C43C2411yescharacteristic
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—44no—
158C22×D43—44no—
159C22×D43—44no—
160C22×D43—44no—
161C22×D43—44no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43C2×D412yes—
165C22×D43C2×D412yes—
166D4×C43—44no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—44no—
182C2×C4×C43C2×D412yes—
183C22⋊D43—44no—
184C22⋊D43—44no—
185C22⋊D43—44no—
186C22⋊D43—44no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43C2×D412yes—
201C2×Dic43C2×D412yes—
202D172—44no—
203D172—44no—
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—22no—
208C22×C43—22no—
209C22×C43—22no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43C22×D411yescharacteristic
219C22×C43C22×D411yescharacteristic
220C22×C43C2×#4111yescharacteristic
221C22×C43H(5,𝔽2)11yescharacteristic
222C22×C43H(5,𝔽2)11yescharacteristic
223C22×C43H(5,𝔽2)11yescharacteristic
224C22×C43H(5,𝔽2)11yescharacteristic
225C2×D43—22no—
226C2×D43—22no—
227C2×D43—22no—
228C2×D43—22no—
229C2×D43—22no—
230C2×D43—22no—
231C2×D43—416no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—41no—
246C2×D43—41no—
247C4×C43—22no—
248C4×C43—41no—
249C4×C43—41no—
250C4×C43—41no—
251C4×C43—41no—
252Dic43—22no—
253Dic43—22no—
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257#2678—431nomaximal, Sylow
258C2×C43—42no—
259C2×C43—42no—
260C2×C43#53411yescharacteristic
261C2×C43#53511yescharacteristic
262C2×C43#53811yescharacteristic
263C2×C43D4211yescharacteristic
264C2×C43#54611yescharacteristic
265C2×C43#54611yescharacteristic
266C2×C43#56011yescharacteristic
267D43—42no—
268D43—42no—
269D43—81no—
270C2×#123—431no—
271C2×#121—431no—
272C2×#120—431no—
273C2×#120—431no—
274#397—431no—
275#396—431no—
276#394—431no—
277#394—431no—
278#392—431no—
279#392—431no—
280#390—431no—
281#390—431no—
282#388—431no—
283#386D4311yescharacteristic, complemented
284#379—431no—
285C43#267811yescharacteristic, complemented, Sylow
286C25—431no—
287C22×D4—431no—
288C22×D4—431no—
289C22×D4—431no—
290C22×D4—431no—
291C22×D4—431no—
292C22×D4—431no—
293C22×D4C2×D4311yescharacteristic
294C23×C4C2×D4311yescharacteristic, complemented
295#123—864no—
296#121—864no—
297#120—864no—
298#120—864no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—431no—
302C2×C4⋊C4—431no—
303C2×C22⋊C4—431no—
304C2×C22⋊C4—431no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—431no—
310C2×C22⋊C4—431no—
311C2×C22⋊C4—431no—
312C2×C22⋊C4—431no—
313C2×C22⋊C4—431no—
314C2×C22⋊C4—431no—
315C2×C22⋊C4—431no—
316C2×C22⋊C4—431no—
317C2×C22⋊C4C2×D4311yescharacteristic
318C2×C22⋊C4C2×D4311yescharacteristic
319C2×C22⋊C4C2×D4311yescharacteristic, complemented
320C2×C42—431no—
321#95—431no—
322#95—431no—
323#95C2×D4311yescharacteristic, complemented
324#95C2×D4311yescharacteristic, complemented
325C24—431no—
326C24—431no—
327C24—431no—
328C24—862no—
329C24—862no—
330C24—862no—
331C24—1721no—
332C24—1721no—
333C24—1721no—
334C24—1721no—
335C24C22×D4311yescharacteristic
336C24C22×D4311yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—41no—
340C2×D4—434no—
341C2×D4—862no—
342C2×D4—862no—
343C2×D4—862no—
344C2×D4—862no—
345C2×D4—862no—
346C2×D4—862no—
347C2×D4—862no—
348C2×D4—862no—
349C2×D4—1721no—
350C2×D4—1721no—
351C2×D4—1721no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4—1721no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—431no—
362C22×C4—431no—
363C22×C4—431no—
364C22×C4—431no—
365C22×C4—431no—
366C22×C4C22×D4311yescharacteristic
367C22×C4C22×D4311yescharacteristic
368C22×C4C22×D4311yescharacteristic
369C22×C4C22×D4311yescharacteristic
370C22×C4C22×D4311yescharacteristic
371C4⋊C4—862no—
372C4⋊C4—862no—
373C4⋊C4—862no—
374C4⋊C4—1721no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—434no—
379C22⋊C4—862no—
380C22⋊C4—862no—
381C22⋊C4—862no—
382C22⋊C4—862no—
383C22⋊C4—862no—
384C22⋊C4—862no—
385C22⋊C4—862no—
386C22⋊C4—862no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—1721no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—432no—
406C23—432no—
407C23—861no—
408C23—861no—
409C23—861no—
410C23—861no—
411C23—861no—
412C23—861no—
413C23—861no—
414C23—861no—
415C23—861no—
416C23—861no—
417C23—861no—
418C23—861no—
419C23—861no—
420C23—861no—
421C23—861no—
422C23—861no—
423C23—861no—
424C23—861no—
425C23—861no—
426C23—1724no—
427C23—1724no—
428C23—1724no—
429C23—1724no—
430C23—1724no—
431C23—1724no—
432C23—1724no—
433C23#1062189812yes—
434C23D4×D4312yes—
435C23C23×D4311yescharacteristic
436D4—44no—
437D4—1724no—
438D4—1724no—
439D4—1724no—
440D4—1724no—
441D4—1724no—
442D4—1724no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—44no—
458C2×C4—432no—
459C2×C4—432no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—861no—
464C2×C4—861no—
465C2×C4—861no—
466C2×C4—861no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—861no—
470C2×C4—861no—
471C2×C4—861no—
472C2×C4—861no—
473C2×C4D4×D4312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—862no—
489C22—862no—
490C22—862no—
491C22—862no—
492C22—862no—
493C22—862no—
494C22—17216no—
495C22—1721no—
496C22—1721no—
497C22—1721no—
498C22—1721no—
499C22—1721no—
500C22—1721no—
501C22—1721no—
502C22—1721no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22—1721no—
507C22—1721no—
508C22—1721no—
509C22—1721no—
510C22C2×D4×D4311yescharacteristic
511C22C2×D4×D4311yescharacteristic
512C22C2×#1062189811yescharacteristic
513C22#1306337011yescharacteristic
514C22#1306337011yescharacteristic
515C22#1306337111yescharacteristic
516C22#1306337111yescharacteristic
517C4—22no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—862no—
523C4—862no—
524C4—1721no—
525C4—1721no—
526C4—1721no—
527C2—42no—
528C2—42no—
529C2—3441no—
530C2—1722no—
531C2—1722no—
532C2#1458346011yescharacteristic
533C2#1458346511yescharacteristic
534C2#1458348211yescharacteristic
535C2#1458353111yescharacteristic
536C2#1458353911yescharacteristic
537C2#1458354511yescharacteristic
538C2#1458363711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2678
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13063308C2semidirect
2. C2×#13063299C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063293C2semidirect
5. #14582828C2semidirect
6. #14582822C2semidirect
7. #14582817C2semidirect
8. #14582817C2semidirect
9. #14582808C2semidirect
10. #14582807C2semidirect
11. #14582799C2semidirect
12. #14582799C2semidirect
13. #14582791C2semidirect
14. #14582754C2semidirect
15. C43×#386C2semidirect
22. C22×C22⋊D43C22semidirect
27. C2×C4⋊Dic43C22semidirect
28. C2×Dic43⋊C4C22semidirect
29. C2×Dic43⋊C4C22semidirect
30. C2×Dic43⋊C4C22semidirect
33. C2×C22⋊Dic43C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C2×C4×Dic43C22semidirect
46. C43⋊#95C22semidirect
47. C43⋊#95C22semidirect
49. C23×C4×C43C22semidirect
52. C2×C22⋊C4×C43C22semidirect
53. #95×C43C22semidirect
54. #95×C43C22semidirect
89. C2×C22⋊D43D4semidirect
117. (C2×D43)⋊C4D4semidirect
283. #386D43semidirect
285. C43#2678semidirect
294. C23×C4C2×D43semidirect
319. C2×C22⋊C4C2×D43semidirect
323. #95C2×D43semidirect
324. #95C2×D43semidirect